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Smarandache's Concurrent Lines Theorem

Authors: M. Khoshnevisan
Comments: 2 pages.

In this paper we present the Smarandache's Concurrent Lines Theorem in the geometry of the triangle.

A Group-Permutation Algorithm to Solve the Generalized Sudoku

Authors: Florentin Smarandache
Comments: 3 pages.

Sudoku is a game with numbers, formed by a square with the side of 9, and on each row and column are placed the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, written only one time; the square is subdivided in 9 smaller squares with the side of 3x3, which, also, must satisfy the same condition, i.e. each square to contain all digits from 1 to 9 written only once.

Smarandache's Cevians Theorem (Ii)

Authors: M. Khoshnevisan
Comments: 2 pages.

In this paper we present the Smarandache's Cevians Theorem (II) in the geometry of the triangle.

Smarandache's Cevians Theorem (I)

Authors: M. Khoshnevisan
Comments: 2 pages.

We present the Smarandache's Cevians Theorem in the geometry of the triangle.

Smarandache's Ratio Theorem

Authors: M. Khoshnevisan
Comments: 2 pages.

In this paper we present the Smarandache's Ratio Theorem in the geometry of the triangle.

The Smarandache-Pătraşcu Theorem of Orthohomological Triangles

Authors: Mihai Dicu
Comments: 1 page.

The Smarandache-Pătraşcu Theorem of Orthohomological Triangles is the folllowing:

Smarandache's Orthic Theorem

Authors: Ion Pătraşcu
Comments: 3 pages.

We present the Smarandache's Orthic Theorem in the geometry of the triangle.

Particle Mass Ratios

Authors: D.T. Froedge
Comments: 11 pages 20 equations 240kb

Based on the developments in a previous paper, this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative, the mass ratios calculated for elementary particles are very close the observed mass ratios.

A Multiple Particle System Equation Underlying the Klein-Gordon-Dirac-Schrödinger Equations

Authors: D.T. Froedge
Comments: 16 pages 38 equations 98kb

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are single particle special cases. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an interacting atomic system, eigenvalues represent particle energies in an interacting system of particles. An equation is proposed that has vector solutions defined in Dirac, or Clifford algebra, that treats a collection of particles as a single system..The proposed solution is a descriptor of a symmetric, light speed expanding group of interacting particles having real, as well as the familiar QM constituents.

A Case Against the First Quantization

Authors: Nicolae Mazilu
Comments: 15 pages

The blackbody radiation is an open problem, in the sense that there is no classical counterpart to describe the spectrum in physical terms. The usual derivation of Planck implicitly assumes that the spectral density is a mean for a special kind of exponential distributions. There is however a case where the classical statistics makes sense for the spectrum, if we consider the spectral density as a probability density for the values of the frequency at a certain temperature. We show here this case and illustrate it on contemporary COBE-FIRAS data, pointing out to a special tensor nature of the cosmic background radiation. Some conclusions about the measurement process and about the progress in general are drawn.

New Method of Genenating of Primes and Its Application to the Goldbach's Conjecture

Authors: Kunikazu Tanaka
Comments: 21 pages

Showing how to derive new expressions of generating prime numbers to demonstrate the Goldbach's Conjecture

7.0 Gev Dark Matter Candidate Could be the Missing Particle in Planck Framework

Authors: Bernard Riley
Comments: 6 pages, including 3 figures.

In a recent paper, Hooper et al. have shown that the excess of low energy events observed by the CoGeNT collaboration and the annual modulation observed for some years by the DAMA and DAMA/LIBRA collaborations could be explained by a dark matter particle with a mass of approximately 7.0 GeV. Such a dark matter candidate could be the missing particle within a framework that relates particle masses to the Planck Mass. Massive particles occupy coincident levels and sublevels within three sequences that descend in geometric progression, with common ratios 1/π, 2/π and 1/e, from the Planck Mass. The putative fundamental particles are arranged precisely upon or, in partnership, about mass superlevels and their coincidences within sequences with common ratios (1/π)³, (2/π)³ and (1/e)³. Four close superlevel coincidences, of which three are occupied, occur within the range of mass scales from that of the electron to that of the top quark. The fourth and uniquely precise superlevel coincidence occurs at 7.0 GeV.

Causality is Inconsistent with Quantum Field Theory

Authors: Fred Alan Wolf
Comments: 15 pages

It is shown that the usual quantum field theoretical argument for the vanishing of the commutator (VC) for spacelike separated fields implying causality is not tenable. For VC to be tenable negative energy antiparticles traveling forward in time must exist and negative energy particles traveling backward in time are not allowed. Hence VC denies the existence of positive energy antiparticles.

Supplying Conditions for Having up to 1000 Degress of Freedom in the Onset of Inflation, Instead of 2 to 3 Degrees of Freedom, Today, in Space-Time.

Authors: Andrew Beckwith
Comments: 5 pages, no figures. Specifically written to answer a question about a non standard departure from usual degrees of freedom theory , as reported by Kolb and Turner, with usual peak values of N(T) ~ 10²

The following document attempts to answer the role additional degrees of freedom have as to initial inflationary cosmology. A comparison is made to two representations of a scale evolutionary Friedman equation, with one of the equations based upon LQG, and another involving an initial Hubble expansion parameter with initial temperature T_Planck ~ 10¹⁹ GeV used as an input into T⁴ times N(T). The upshot is that initial assumptions as to the number of degrees of freedom has for T_Planck ~ 10¹⁹ GeV a maximum value of N(T)~ 10³ . Making that upper end approximation for the value of permissible degrees of freedom is dependent upon a minimum grid size length as of about l_Planck ~ 10³³ centimeters. Should the minimum uncertainty and permissible grid size for space time be significantly higher than be much higher than l_Planck ~ 10³³ centimeters, the net effect will be to reduce to top level value of N(T)~ 10³ to something lower. The author submits that such degrees of freedom is important for initial configurations for the initial configuration of the arrow of time , i.e entropy growth for reasons which will be made clear in the manuscript.

A Hypothesis on the Nature of Light

Authors: J. Arnold
Comments: 14 Pages

It is proposed that light is at absolute rest, its apparent motion being the reflection of the motion of mass in time. The hypothesis resolves the paradox of the apparent wave/particle duality of light, accounts for its speed being invariant and a limit, explains numerous other peculiarities of its behavior, and identifies the motion of mass in time as the source of gravitational energy.

Tides ( According to "Hypothesis on MATTER" )

Authors: Nainan K. Varghese
Comments: 24 pages, Originally published in General Science Journal

Present explanations on mechanism of tides are based either on centrifugal action or on gravitational attraction. Centrifugal force (due to motion of a body in circular path), used in analytical solutions, is an imaginary effort. Explanations, based on actions by an imaginary effort, cannot be factually correct. One of the fundamental assumptions used to derive the equation for gravitational attraction is that whole matter content (mass) of each body is concentrated at its centre. This makes it illogical to assume that different parts of same body have different magnitudes of gravitational attraction towards another body. Therefore, explanations on tides, based on differences in gravitational attractions on different parts of bodies, are perversions of present theory on gravitational attraction. Apparent orbital motion of a body about epicentre of a system is also used in some explanations. In nature, no free body can orbit around another moving body [3] in geometrically closed path. Orbital path of earth about the sun (or that of moon about earth) is not circular or elliptical around a central body but it zigzags about sun's (earth's) median path in space. Hence, an explanation based on revolution of earth around an epicentre is pure imagination. According to current rules of dynamics, more than one external linear effort on a rigid body can produce only one resultant linear motion. Yet, earth experiences distinctly separate sets of tides from central forces towards moon and sun. Only logical reason for lunar tides to be greater than solar tides is that the central force between earth and moon is greater than that between earth and sun. This cannot be substantiated by current gravitational laws. This article attempts to give a simple and logical explanation to tidal mechanism, based on a radically different dynamics, put forward in 'Hypothesis on MATTER [1]. Tides are caused by (accelerating) actions of external efforts on a linearly moving spinning-body. Each external effort alters shape of the spinning body, separately, to produce its own set of tides. Change in the shape of a spinning body, rather than displacement of its parts, cause tides. Absolute linear motion of the spinning body shifts zenith points of tides from local meridians facing the sun (or moon) and on opposite side. Orbital motion of a spinning body enhances deflection of tides from local meridian. Displacement of ocean water in the direction of moving tide is superficial and it cannot produce tidal drag on earth's solid core body.

A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy, Neutrosophic Set, Neutrosophic Probability and Statistics

Authors: Florentin Smarandache
Comments: 157 pages

It was a surprise for me when in 1995 I received a manuscript from the mathematician, experimental writer and innovative painter Florentin Smarandache, especially because the treated subject was of philosophy - revealing paradoxes - and logics. He had generalized the fuzzy logic, and introduced two new concepts: a) "neutrosophy" - study of neutralities as an extension of dialectics; b) and its derivative "neutrosophic", such as "neutrosophic logic", "neutrosophic set", "neutrosophic probability", and "neutrosophic statistics" and thus opening new ways of research in four fields: philosophy, logics, set theory, and probability/statistics.

Interval Groupoids

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, Moon Kumar Chetry
Comments: 242 pages

This book introduces several new classes of groupoid, like polynomial groupoids, matrix groupoids, interval groupoids, polynomial interval groupoids, matrix interval groupoids and their neutrosophic analogues.

The New Prime Theorem (441)-(490)

Authors: Chun-Xuan Jiang
Comments: 69 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J₂(ω) we prove that the new prime theorems (441)-(490) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. π_k(N₀,2) ≥ 1. This is the Book theorem.

Goldbach' Conjecture (9): Proved Hardy-Littlewood Conjecture (A)

Authors: Tong Xin Ping
Comments: 4 pages, In Chinese

We have inclusion-exclusion formula of π(N) and inclusion-exclusion formula of r₂(N). Make use of inclusion-exclusion formula, we can obtain Hardy-Littlewood Conjecture (A).

The New Prime Theorem (541)-(590)

Authors: Chun-Xuan Jiang
Comments: 69 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J₂(ω) we prove that the new prime theorems (541)-(590) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. π_k(N₀,2) ≥ 1. This is the Book theorem.

The New Prime Theorem (491)-(540)

Authors: Chun-Xuan Jiang
Comments: 69 pages

Using Jiang function we are able to prove almost all prime problems in prime distribution. This is the Book proof. In this paper using Jiang function J₂(ω) we prove that the new prime theorems (491)-(540) contain infinitely many prime solutions and no prime solutions.From (6) we are able to find the smallest solution. π_k(N₀,2) ≥ 1. This is the Book theorem.

Earth History from the Ancient Texts and It's Relevance to the Science

Authors: Karunakar Marasakatla
Comments: 7 pages

Ancient descriptions of beginning of the Earth and the global deluge are relevant to the Earth history. Beginning of the Earth or beginning of the time appears to be the beginning of the Supercontinent cycle on the surface of the Earth around 2800 million years ago. Since then, six Supercontinent cycles were completed on the surface of the Earth and the present is the seventh cycle. Global deluge appears to be the description of the rise in sea level occurred with the breakup of each Supercontinent. Therefore global deluge occurs in the beginning of every Supercontinent cycle. Descriptions of the Manvantara cycles, seven Earths and seven Karshvars are similar to the Supercontinent cycles.

Cause, Origin and Continuation of Plate Tectonics

Authors: Karunakar Marasakatla
Comments: 12 pages

Cause of the Earth's surface manifestations appears to be external to the Earth. Gravitational attraction of the galactic center causes the tides to form in the mantle of the Earth when the solar system reaches the nearest position to the galactic center. Pair of troughs takes shape in the mantle adjacent to the tides as the low and high tides in the ocean. Upwelling tides or megablobs breaks the continental crust and disperses the plates towards the troughs on the surface. In the subsequent cycle, when the solar system again reaches the nearest position to the galactic center, megablobs interchange with the troughs and reassemble the continental crust. In other words, two galactic cycles of the solar system makes one Supercontinent cycle on the surface of the Earth. It appears that the Supercontinent cycle started on the Earth around 2800 million years ago. Nucleation of the inner core was initiated in this period with the beginning of the Plate tectonics. Supercontinent cycle continues as long as the solar system revolves around the galactic center in the presence of liquid outer core in the interior and water on the surface of the Earth.

Tectonic Pause: Towards the Unification of Earth Sciences

Authors: Karunakar Marasakatla
Comments: 16 pages

Life on Earth reels under the Supercontinent cycles. Every Supercontinent forms with the collision and merger of all the plates causing a "tectonic pause". Reduced seafloor spreading and albedo advances the ice sheets towards the equator. Massive ice sheets cover the ocean and whole or part of the Supercontinent causing a global ice age or snowball Earth event. Base of the continents further sinks into the mantle with the increased weight of the ice sheets. Increased pressure within the mantle forms as a superplume under the Supercontinent and eventually breaks the Supercontinental crust giving the new plates. Superplume with the increased seafloor spreading and the albedo causes a severe global warming and rapidly melts the ice sheets, exiting the global ice age. Rapid melting of the ice sheets floods the lowered continental regions. Isostacy gradually uplifts the submerged continental crust above the sea level. Each break in the crust causes a global warming and merger of plates causes an ice age. Mass extinctions occur in the ice age and global warming periods. Evolution takes place in the post global warming period. Ice ages and global warming forms the distinct boundaries in the sedimentary layers.

A Set of Conjectures on Smarandache Sequences

Authors: Sylvester Smith
Comments: 9 pages

Searching through the Archives of the Arizona State University, I found interesting sequences of numbers and problems related to them. I display some of them, and the readers are welcome to contribute with solutions or ideas.

Smarandache's Minimum Theorem in the Einstein Relativistic Velocity Model of Hyperbolic Geometry

Authors: Catalin Barbu
Comments: 3 pages

In this note, we present a proof to the Smarandache's Minimum Theorem in the Einstein Relativistic Velocity Model of Hyperbolic Geometry.

The New Prime Theorem (391)-(440)

Authors: Chun-Xuan Jiang
Comments: 69 pages

Using Jiang function we prove that the new prime theorems (391)-(440) contain infinitely many prime solutions and no prime solutions.

Entropy Shows that Global Warming Should Cause Increased Variability in the Weather

Authors: John Michael Williams
Comments: 6 pages

Elementary physical reasoning seems to leave it inevitable that global warming would increase the variability of the weather. The first two terms in an approximation to the global entropy may be used to show that global warming has increased the free energy available to drive the weather, and that the variance of the weather is expected to have increased correspondingly.

Approximations of the Fine Structure Constant Reciprocal

Authors: J. S. Markovitch
Comments: 2 Pages

A "brute force" computer search was made for the most accurate approximations of the experimental fine structure constant reciprocal in the form (A^a - D^d)/B^b + C^c - E^e, where A, B, C, D, and E were integers ranging from 0 to 30, while the exponents a, b, and c, were integers ranging from 0 to 3, and d and e were integers ranging from 0 to -3. Within these restrictions, and ignoring all trivial variants, a fit better than or equal to 137.036 was achieved only twice, by (10^3 - 10^-3)/3^3 + 10^2 - 10^-3 = 137.036 and (22^3 - 2^-1)/25^2 + 11^2 - 1^-1 = 137.036, where the search employed a fine structure constant inverse equaling its 2006 CODATA value of 137.035999679. The comparative simplicity of the first of these approximations, its symmetrical reuse of the constant 10, and the small size of its integers, together suggest its origin may be physical, and that the integers 10 and 3 may be important physical constants.

A Note on Astrometric Data and Time Varying Sun-Earth Distance in the Light of Carmeli Metric

Authors: V. Christianto
Comments: 7 Pages

In this note, we describe shortly time varying Sun-Earth distance in the light of Carmeli metric and compare the result with recent astrometric data. The graphical plot suggests that there should be linear-linear correspondence between Sun-planets distances and their time variation.

Why Trimmer et Al. "Did not Detect" Aether Wind in 1973?

Authors: V.V.Demjanov
Comments: 4 Pages

          In 1960s several authors began independently studies of the interferometric detection of "aether wind" using in the device optical media. Shamir&Fox in 1969 made measurements on the plexiglas and declared them "negative" (whereas they registered the shift of the fringe at ~1/3000 of its width, and "determined" a corresponding to it velocity of aether wind ~6.6 km/s). In 1973 Trimmer et al. mounted at the one-armed device the glass optics and registered with a big resolution the shift of the interference fringe (at most ~10^–6 of its width) and determined by it the speed of "aether wind" ~3.8 cm/s. This result enhanced still more the confidence in that the attempts to detect aether are unfavorable. However, my results of the same years being favorable fell out of the common line of "negative" verdicts to aether. I managed to register on gases, liquids and solid optical materials million times greater relative fringe shifts (0.01÷5.0), revealed the horizontal projection of the aether wind velocity hundreds km/s. Since my results "weakened the experimental foundation of special relativity", their publishing is rejected until now.
          In the current report I argue reasonably, relying on my experience, that Trimmer et al. (as well as Shamir &Fox), actually obtained positive results in their measurements of aether wind which amounts to several hundreds km/s, proceeding from the declared by them resolution of their experimental units. I believe their experimental data. But I guess that they were faced with hidden artefacts in the interferometer with solid optic materials and not aware of it. The theory used by them for processing the measurements of the interference fringe shift obtained is not appropriate for interferometers with solid optical materials. I have found the possible reason why Trimmer et al. did not reveal the experimental facts undermining theories repudiating aether.

An Explanation of Redshift in a Static Universe

Authors: Lyndon Ashmore
Comments: 7 Pages

A review of the literature on the Lyman alpha forest gives direct evidence on the dynamics of the universe. In an expanding universe one would expect the average temperature of the universe to fall as it expands - but a review of the Doppler parameters of the Hydrogen clouds in Quasar spectra shows that contrary to this, they are increasing in temperature (or at least, becoming increasingly disturbed) as the universe ages. Addition-ally, in an expanding universe, hydrogen clouds must become further apart with time, so, as redshift increases, the clouds would be closer together. Instead, the evidence is that, on average, they are evenly spaced up to a redshift of one - if not beyond. How can this be so if the universe is expanding? Especially since this range of redshifts includes the supernovae data used to show 'acceleration' and so called 'time dilation.' Taking these results in isolation implies that the universe has been static for at least the last billion years or so and therefore a new model of redshift is needed to explain redshifts in a static universe. The model proposed here is that in a static universe, photons of light from distant galaxies are absorbed and reemitted by electrons in the plasma of intergalactic space and on each interaction the electron recoils. Energy is lost to the recoiling electron (New Tired Light theory) and thus the reemitted photon has less energy, a reduced frequency and therefore an increased wavelength. It has been redshifted. The Hubble relationship be-comes 'photons of light from a galaxy twice as far away, make twice as many interactions with the electrons in the plasma of IG space, lose twice as much energy and undergo twice the redshift.' A relationship between redshift and distance is found and, using published values of collision cross-sections and number density of electrons in IG space, a value for the Hubble constant is derived which is in good agreement with measured values. Assuming that the energy transferred to the recoiling electron is emitted as secondary radiation; the wavelength is calculated and found to be consistent with the wavelengths of the CMB. On the basis that plasma clouds result in periodicity or 'quantised' galaxy redshifts it is shown that the average spacing between hydrogen clouds (z = 0.026) compares favourably with an average spacing between galaxy clusters (z = 0.023). A test of this theory in the laboratory is proposed whereby a high powered laser could be fired through sparse cold plasma and the theories predicted increase in emission of microwave radiation of a particular frequency determined.

A Proposed Recoil Interaction Between Photons and the Electrons in the Plasma of Intergalactic Space Leading to the Hubble Constant and CMB

Authors: Lyndon Ashmore
Comments: 8 Pages

The Hubble diagram for type Ia Supernovae gives the value of the Hubble constant, H as 64±3 km/s Mpc^-1 which, in SI units, is equal to 'hr_e/m_e per unit volume of space' (2.1x10^-18 s^-1). This coincidence could suggest a relationship between H and the electrons in the plasma of intergalactic space that act collectively and oscillate if displaced. The possibility that light from distant galaxies is absorbed and reemitted by the electrons is considered with the electron recoiling on both occasions. A double Mössbauer effect leads to a redshift in the transmitted light. Introduction of the photoabsorption cross section 2r_eλ leads to the relationship H = 2n_ehr_e/m_e giving H = 12 km/s Mpc^-1 when ne has the reported value of n_e ~ 10^-7cm^-3. The small amount of energy transferred to the electron by recoil is radiated as bremstrahlung with a wavelength in the microwave region.

Gravitation, Force and Geometry

Authors: J. Arnold
Comments: 2 Pages

Gravitation is described as a uniquely geometric phenomenon, incompatible with the concepts of force and energy, and only analogically associable with non-geometric mathematical formalizations. In particular, the mathematical derivation of gravitational waves from the field equations is shown to be arbitrary and physically untenable.

Earth's Charge and the Charges of the Van Allen Belts

Authors: Jacob Biemond
Comments: 11 Pages, including 2 figures and 2 tables

In this paper three separate charges are distinguished for the Earth and its magnetosphere. First, it is assumed, that the Earth and its nearest atmosphere bear a net negative charge Q_E. Secondly, a positive charge Q_i and a negative charge Q_o are proposed for the inner and outer Van Allen belt, respectively. Thirdly, a belt with net zero charge (electron slot) will be assumed to be present between both charged belts. According to the three tori model, recently developed for pulsars and black holes, equilibrium may exist between the charges Q_E, Q_i and Q_o. Three expressions for the Coulomb electric field at different distances from Earth's centre are derived from the same model. Using available data, values for the three charges are deduced for the solar minimum and maximum, respectively. An averaged charge Q_E of about −1 C is extracted for the Earth. Some other features of the model are discussed, among them the flow of charge during the change from solar minimum to maximum. Furthermore, it is shown that the magnitude of Earth's magnetic field cannot be explained by the motion of the charges Q_E, Q_i and Q_o. In order to obtain a better explanation, the so-called Wilson-Blackett law is discussed. In addition, a large toroidal electric current in the Earth is proposed

The Creator and the Physicist How not to Talk Physics in the Face of God

Authors: John Michael Williams
Comments: 4 pages

This paper is less about religion than about science. It is meant as advice to physicists, physics teachers, biologists, or others who may find themselves confronted by Creationism when discussion of the theory of evolution, or of other scientific issues, is perceived as bearing on religious writings or dogma.

Wandering in the World of Smarandache Numbers

Authors: A.A.K. Majumdar
Comments: 217 pages

It was in mid-nineties of the last century when I received a letter from Professor Ion Patrascu of the Fratii Buzesti College, Craiova, Romania, with lots of enclosures, introducing me with this new branch of Mathematics. Though my basic undergraduate degree is in Mathematics, my research field at that time was Operations Research and Mathematical Programming.

Vedic Mathematics 'vedic' or 'mathematics': a Fuzzy & Neutrosophic Analysis

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 220 pages

Religious extremism has been the root cause of most of the world problems since time immemorial. It has decided the fates of men and nations. In a vast nation like India, the imposition of religious dogma and discrimination upon the people has taken place after the upsurge of Hindu rightwing forces in the political arena. As a consequence of their political ascendancy in the northern states of India, they started to rewrite school textbooks in an extremely biased manner that was fundamentalist and revivalist. Not only did they meddle with subjects like history (which was their main area of operation), but they also imposed their religious agenda on the science subjects. There was a plan to introduce Vedic Astrology in the school syllabus across the nation, which was dropped after a major hue and cry from secular intellectuals.

Target Type Tracking with a New Probabilistic Belief Transformation

Authors: Jean Dezert, Florentin Smarandache, Albena Tchamova, Pavlina Konstantinova
Comments: 8 pages

Abstract-In this paper we analyze the performances of a new probabilistic belief transformation, denoted DSmP, for the sequential estimation of target ID from classifier outputs in the Target Type Tracking problem (TTT). We complicate here a bit the TTT problem by considering three types of targets (Interceptor, Fighter and Cargo) and show through Monte-Carlo simulations the advantages of DSmP over the classical pignistic transformation which is classically used for decision-making under uncertainty when dealing with belief assignments. Based on our previous works for the justification of rules of combination for TTT problem, only the Proportional Conflict Redistribution rule and the hybrid fusion rules are considered in this work for their ability to deal consistently with high conflicting sources of evidence with three different belief assignment modelings.

Neutrino Oscillations: the Indefinite Mass Defined

Authors: John Michael Williams
Comments: 10 pages

This paper outlines the usual neutrino oscillation theory and points out the analogy between Lyman energy eigenstates and neutrino mass eigenstates. It then suggests several alternative interpretations of the neutrino oscillation theory in regard to determination of the rest mass of the neutrino.

The Theory of Relativity is Wrong

Authors: Emil Gigov
Comments: 18 pages

Very true scientists, such as Rutherford, Soddy, Michelson, Sagnac, Lenard, Larmor, McMillan and others, have claimed, that the Theory of relativity is wrong. Even Poincare and Einstein are hinted something similar. Classical physics is far from simple, already during the XIX century has been spoken about things like gravity waves, nuclear power and variable mass. Theory of relativity as a whole, is based only on the hypothesis, that the speed of light in Euclidean empty space is, invariant universal constant. But in reality this velocity is variable, in Newtonian sense. Newton's emission theory of light, has been proven through many experiments, for example by those of Michelson, Sagnac and Fizeau. Also, the velocity of photons in one ray, is variable with respect to lateral observer, and is consistent with the classical law for velocity addition.

Goldbach' Conjecture (8): Upper Bound Estimation of Number of Goldbach' Primes

Authors: Tong Xin Ping
Comments: 3 pages, In Chinese

This upper bound estimation prevailed over upper bound estimation of Chen Jing Run

Temperature of the Sn1987a Supernova Provides an Estimate of the Electron Neutrino Mass

Authors: John Michael Williams
Comments: 13 pages

Numerous upper bounds on the (anti)neutrino rest mass have been published based on the SN1987A observations. Here, we use a nonkinematic (thermal) time extent to provide a rest-mass estimate of a few eV (as mc2 energy), if not zero. In the solution, we find that a typical upper-bound formula for the mass implies that this thermal extent was attributable to about 10% of the particle energy measured on Earth. The present approach yields an expected value for the mass, given any theoretical or model-dependent estimate of the fraction of the detected neutrino energy attributable to the supernova temperature. This is a reposting of an old paper which describes an analysis protocol which can be applied for any supernova for which a population of neutrinos is observed.

Smarandache Consecutive Prime Sequences (n = 1 to 100)

Authors: Robert G. Wilson V
Comments: 3 pages

"Smarandache consecutive sequences" is the nth member of the consecutive sequence, e. g. Sm(11)=1234567891011, and RSm(11)=1110987654321. Following is the prime version of "Smarandache consecutive sequences"

Some Properties of the Pseudo-Smarandache Function

Authors: Richard Pinch
Comments: 6 pages

Charles Ashbacher [1] has posed a number of questions relating to the pseudo-Smarandache function Z(n). In this note we show that the ratio of consecutive values Z(n + 1)/Z(n) and Z(n - 1)/Z(n) are unbounded; that Z(2n)/Z(n) is unbounded; that n/Z(n) takes every integer value infinitely often; and that the series Σ_n 1/Z(n)^α is convergent for any α > 1.

Gravitons Writ Large; I.e. Stability, Contributions to Early Arrow of Time, and Also Their Possible Role in re Acceleration of the Universe 1 Billion Years Ago?

Authors: Andrew Beckwith
Comments: 17 pages, one figure. A distillation of work done since January 2010: Last 9 months of derivational work done, and condensed on DM, DE, and Arrow of time issues w.r.t. gravitons, coherent states of gravitons <=> GW, and other issues. From conference material from Beyond the Standard Model, 2010, S.A, Dark Side of the Universe in Leon, Mexico, Rudn 10 of Moscow, Fundamental Frontiers of Physics, 11, Paris, Blois, France, 2010. MAIN work is in cross referencing different research and regularizing what was, initially partly contradictory research results. This is the result. Source document for all these discussions condensed to 17 pages. Done to cross reference numerous issues which the author will bring up in DICE itself. Commentary from DICE, will lead to a substantially revised document, i.e. that is to be expected considering the quality of the attendees at DICE, which is very high. First phase of preparation for a 8-10 page conference proceedings entry for DICE 2010

This document is due to a question by Debasish of the Saha institute of India asked in the Dark Side of the Universe conference, 2010, in Leon, Mexico[1], and also is connected with issues as to the initial configuration of the arrow of time brought up in both Rudn 10 [2], in Rencontres de Blois[3], and Fundamental frontiers of physics 11 [4], in Paris, in July 2010. Further reference is made as to how to reconcile early inflation with re acceleration, partly by dimensional analysis and partly due to recounting a suggestion as by Yurov [5] , which the author thinks has merit and which ties into, to a point with using massive gravitons as a re acceleration of the universe a billion years ago enabler, as perhaps a variant of DE.

Tornado Genesis

Authors: Kiyoung Kim
Comments: 37 Pages.

It is inferred from the phenomenological facts of tornado that tornado itself should have a driving force generating the updraft in the vortex of tornado. The driving force is supposed to be originated from the electric interaction between a storm cloud and a crustal conducting body underground. The electric interaction in tornado is considered to be similar to a lightning discharge in respect that the electric potential is reduced between a storm cloud and the ground, but the electric discharging process in tornado should be much slower than the lightning discharge and result in the atmospheric vortex formation of tornado. The mechanism of tornado formation is suggested, in which Townsend avalanche process is assumed inside the tornado vortex with a dangling conducting channel that is embedded in the funnel cloud of tornado. The strong updraft inside the vortex of tornado is produced by momentum diffusion process when the positively ionized air molecules move upward under the influence of electric field inside the vortex. With the mechanism of tornado formation, phenomenological expectations are followed.

The Big Boing Theory (The Exam at the End of All Exams)

Authors: John Michael Williams
Comments: 9 Pages.

Two cosmonauts had been living in an obscure compartment of the Mir Orbiter for seven years, ever since Ground Control inadvertently omitted them from a list of return passengers...

Nonlinear Theory of Elementary Particles 3. the Mass Origin Theory

Authors: A.G. Kyriakos
Comments: 30 Pages.

Two hypotheses of the mass origin are examined: 1) the theory of mass, developed within the framework of electron theory, and 2) Higgs's mechanism of the mass generation of Standard Model. The advantages and disadvantages of each of them are shown. The connections between these two approaches and nonlinear theory of elementary particles are also noted.

Gravity Waves and the Constancy of the Speed of Light

Authors: John R. McWhinnie
Comments: 9 pages.

This paper takes two phenomena in physics, attempts to show that the solutions to them are linked and that these solutions shall require a radical re-think of physics

Configuration of the Arrow of Time, in Initial Start of Inflation?

Authors: Andrew Beckwith
Comments: 2 pages, 1 figure. Actual proceedings submission to the Rencontres De Blois 2010 conference , with an emphasis upon issues brought up earlier, in a less organized fashion un Rudn 10, in Moscow, May 30.

Initial relic entropy growth is presented in the context of a zero valued chemical potential and different formulations of overall energy values, which may be tied into massive gravitons appearing at the onset of inflation This is contrasted with the role of gravitons with non zero rest mass in four dimensions a billion years ago. Questions as to if an interplay between two different regimes for 'heavy' gravity are presented s open research issues.

Goldbach' Conjecture (7): Five Proofs that is Under Five Assumptions Term

Authors: Tong Xin Ping
Comments: 4 pages, In Chinese

According to five assumptions, get five proofs

Gravitons, and the Initial Configuration of Arrow of Time in Inflation?. Part 2, of a Discussion Started at Rudn 10, in Moscow, June 30, 2010

Authors: Andrew Beckwith
Comments: 7 pages, one figure. Significant enhancement of arrow of time issue at the onset of inflation which will be brought up in the DICE meeting , with other topics, in September 13-17, 2010.

This investigation sets forth initial conditions for a start of the arrow of time in cosmology based upon the idea that of having initil degrees of freedom set as g_star ~ 1000 initially , instead of a maximum value of g_star ~ 100 - 120 for the number of degrees of freedom during the electro weak era.

Is Initial Data for Cosmological Arrow of Time Emerging Due to Inflation Start?

Authors: Andrew Beckwith
Comments: 5 pages. One figure. Contribution to the Rudn 10 conference by Andrew Beckwith, in a parallel session in cosmology, May 30, 2010 at Peoples Friendship University, Moscow, Russia as a guest of the Russian Gravitational society.

We ask if setting the vanishing chemical potential limit μ -> 0 with entropy S ∝ T³ [1] for a number of degrees of freedom significantly greater than the standard electroweak value of g_star ~ 100 - 120, do we have a new foundation for the arrow of time in quantum cosmology with inflation?

Covariant Energy-Momentum Conservation in General Relativity with Cosmological Constant

Authors: Philip Gibbs
Comments: 11 pages, this is an updated version of an earlier paper originally archived as arXiv:gr-qc/9701028. The cosmological constant has been added to the analysis, plus other small additions. Submitted to Prespacetime Journal.

A covariant formula for conserved currents of energy, momentum and angular-momentum is derived from a general form of Noether's theorem applied directly to the Einstein-Hilbert action of classical general relativity. Energy conservation in closed and flat big-bang cosmologies including cosmic radiation and dark energy is discussed as special cases. Special care is taken to distinguish between kinematic and dynamic expressions.

Could Gravitons from Prior Universe Survive Quantum Bounce to Reappear in Present Universe

Authors: Andrew Beckwith
Comments: 12 pages, 1 figure. Part of what will be brought up in DICE 2010, as of September 13-17, 2010, in Italy . The other part of the DICE presentation will be finished by the end of next week

We ask the question if an entropy S = E/T with a usual value ascribed of initial entropy S ~ 10⁵ of the onset of inflation can allow an order of magnitude resolution of the question of if there could be a survival of a graviton from a prior to the present universe, using typical Planckian peak temperature values of T ~ 10¹⁹ GeV. We obtain the values consistent with up to 1038 gravitons contributing to an energy value of E ~ 10²⁴ GeV if we assume a relic energy contribution based upon each graviton initially exhibiting a frequency spike of 1010 Hz. The value of E ~ 10²⁴ GeV is picked from looking at the aftermath of what happens if there exists a quantum bounce with a peak density value of ρ_maximum ~ 2.07 ρ_Planck as has been considered recently by P. Malkiewicz and W. Piechocki [15] in the LQG bounce regime radii of the order of magnitude of l ~ 10³⁵ meters. In this paper estimates specifically avoids using S = (E - μN)/T are done, by setting vanishing chemical potential μ = 0 for ultra high temperatures. Finally we compare briefly the obtained results with the ones recently investigated by G. 't Hooft [20] and L.A. Glinka [21, 22].

A Model of the Proton

Authors: R. Wayte
Comments: 27 Pages.

AA geometrical/mechanical model of the proton is developed which satisfies general empirical features. A Yukawa / Paris-type potential due to a mesonic field is incorporated into Einstein's equations of general relativity to predict a hadronic force constant, stronger than the fine structure constant by (137/√3) times Proton mass is expressed in terms of muonic mass building-blocks. Analysis of the magnetic moment allows substructure modelling, incorporating 2 grades of triplets. Creation of these component parts is described in terms of action-integrals. The gluon field energy holding the triplets together is related to total energy. Uniqueness of electromagnetic charge is attributed to a governing action principle. Finally, a neutron model has been proposed, consisting of a proton core orbited by a heavy-electron.

A Model of the Muon

Authors: R. Wayte
Comments: 17 Pages.

A geometrical/mechanical model of the muon has been developed based on a previous detailed model of the electron and the fine structure constant. The anomalous magnetic moment and lifetime have been calculated in terms of muon component parts. Known features of the tauon have also been related to the muon.

A Model of Charmonium

Authors: R. Wayte
Comments: 7 Pages.

A geometrical/mechanical model of charmonium has been developed, based on the logarithmic confinement potential. The quark and antiquark pair orbit around the centre of mass, with their gluon and colour fields contained within a torus structure of characteristic radius.

Doppler Shift Reveals Light Speed Variation

Authors: Stephan J. G. Gift
Comments: 8 pages

Light speed variation relative to a moving observer occurring according to classical velocity composition is demonstrated using Doppler Shift. This directly contradicts the light speed invariance postulate of special relativity and confirms ether drift.

Transition of Expansion Acceleration of the Universe Through Negative Mass

Authors: Hyoyoung Choi
Comments: 5 Pages.

This letter explains that density of positive mass and negative mass is almost uniformly throughout the whole universe, but density of positive mass and negative mass included in a random universe radius R can be different from each other. Like this, positive, zero, negative values of total gravitational potential energy are all possible due to density difference of positive mass and negative mass included in a random universe radius R. This letter is showing possibility in explaining the decelerating expansion and accelerating expansion due to density difference of positive mass and negative mass because negative mass and positive mass conducts different forms of movement depending on the density difference of positive mass and negative mass. As change of total gravitational potential energy sign occurs from UT=0 and total gravitational potential energy oscillates based on 0. This provides valid explanation regarding to the problems of the atness of the universe and fine tuning.

Degrees of Freedom: a Correction to Chi Square for Physical Hypotheses

Authors: John Michael Williams
Comments: 47 Pages.

In common practice, degrees of freedom (df) may be corrected for the number of theoretical free parameters as though parameters were the same as data categories. However, a free physical parameter generally is not equivalent to a data category in terms of goodness of the fit. Here we use synthetic, nonrandom data to show the effect of choice of categorization and df on goodness of fit. We then explain the origin of the df problem and show how to avoid it in a three-step process: First, the theoretical curve is fit to the data to remove its variance, leaving what, under the null hypothesis, should be structureless residuals. Second, the residuals are fit by a set of orthogonal polynomials up to the degree, should it occur, at which significant variance was removed. Third, the number of nonsignificant polynomial terms in the original + orthogonal set become the df in a standard chi square test. This process reduces a general df problem to one of polynomial df and allows goodness of a fit to be determined by data categorization and significance level alone. An example is given of an evaluation of physical data on neutrino oscillation.

Differentiable Structures on Real Grassmannians

Authors: Jeidsan A. C. Pereira
Comments: 10 Pages.

Given a vector space V of dimension n and a natural number k < n, the grassmannian G_k(V) is defined as the set of all subspaces W ⊂ V such that dim(W) = k. In the case of V = Rⁿ, G_k(V) is the set of k-fl ats in Rⁿ and is called real grassmannian [1]. Recently the study of these manifolds has found applicability in several areas of mathematics, especially in Modern Differential Geometry and Algebraic Geometry. This work will build two differential structures on the real grassmannian, one of which is obtained as a quotient space of a Lie group [1], [3], [2], [7]

An Interpretation of the Laws of Gravity and Inertia

Authors: Giuliano Bettini
Comments: 16 Pages. v1 in Italian, v2 in English

Ideas on a source of inertia from fixed stars have crossed Physics least Mach onwards. Equations "Maxwell-like" for gravitation and inertia were obtained by several authors as a subspecies of the simplified theory of General Relativity. A precursor was Dennis Sciama. Introducing a four-potential, I submit here a tentative interpretation of our laws about gravity and inertia, in complete analogy with electromagnetism. In classical mechanics is not introduced, usually, a four potential. The field produced by this four-potential describes both gravitational and inertial forces. Admit the gauge transformation on potential is equivalent to enunciate the equivalence principle, and vice versa. Inertial forces (ex. Coriolis force) are interpreted as a field action. All the inertia is interpreted as a field action. The physical presence of this field seems to be a fact, even more concrete the usual admission of inertial "fictitious forces".

Problemes Avec et Sans... Problemes!

Authors: Florentin Smarandache
Comments: 175 Pages. In French

Problems with and without... problems!

Smarandache Hyper (∩, ∈)-Idealson Smarandache Hyper K-Algebras

Authors: Kyung Ho Kim, Young Bae Jun, Eun Hwan Roh, Habib Harizavi
Comments: 6 Pages.

We introduce the notion of a Smarandache hyper (∩, ∈)-ideal and Ω-reflexive in hyper K-algebra, and some related properties are given.

Divisibility Tests for Smarandache Semigroups

Authors: AKS Chandra Sekhar Rao.
Comments: 12 Pages.

Two Divisibility Tests for Smarandache semigroups are given . Further, the notion of divisibility of elements in a semigroup is applied to characterize the Smarandache semigroups. Examples are provided for justification.

Time Paradox, Zitterbewegung and Noncommutative Geometry

Authors: Lawrence B. Crowell
Comments: 21 Pages.

The zitterbewgung of the electron is associated with an intrinsic time for an electron, or any of the fermionic particles with mass such as quarks and leptons. In this article it is shown that a massless particle coupled to noncommutative coordinate geometry is subjected to a gauge-like force. This force acts to trap the massless particle in an orbit within a region. This bottled massless particle then has an induced mass. This is then argued to be tied to fundamental aspects of physics, such as a dynamical Higgs model, as well as strings and p-brane theory.

A Direct Proof of the Yff's Conjecture

Authors: Marian Dincă
Comments: 2 Pages.

In this paper it is given proof Yff's conjecture using convexity arguments.

On the Distribution of Prime Numbers in the Intervals Defined by the Fibonacci Numbers

Authors: J. S. Markovitch
Comments: 4 pages

The number of primes in the inclusive intervals defined by consecutive Fibonacci numbers exhibits interesting behavior between the Fibonacci numbers 55 and 196418. Specifically, starting with the interval [55, 89] through the interval [121393,196418] the ratio of the number of primes in successive intervals is a value that alternates high, low, high, low, etc.

One-Way Light Speed Determination Using the Range Measurement Equation of the GPS

Authors: Stephan J. G. Gift
Comments: 8 pages

The one-way speed of light is determined using the range measurement equation of the Global Positioning System. This equation has been rigorously and extensively tested and verified in the Earth-Centred Inertial frame, a frame that moves with the Earth as it revolves around the Sun but does not share its rotation. The result is a simple demonstration of one-way light speed anisotropy depending on the direction of propagation relative to the rotating Earth that contradicts the principle of light speed constancy.

Rural Migration a Significant Cause of Urbanization: a District Level Review of Census Data for Rajasthan

Authors: Jayant Singh, Hansraj Yadav, Florentin Smarandache
Comments: 8 pages

Migration plays an important role in urbanization of a state. In general more the migration higher the urbanization rate though it many not necessarily true in all the situations but in general it is witnessed that migration have a fairly large share in urbanization. A district level analysis for Rajasthan state is attempted to comprehend Urbanization due to migration their interlinkages and association.

Urbanization Due to Migration: a District Level Analysis of Migrants from Different Distances for the Rajasthan State

Authors: Jayant Singh, Hansraj Yadav, Florentin Smarandache
Comments: 10 pages

People migrate to different distances and there migration is governed by different reasons. Distance of place of migration plays an important role in the migration process and an analysis based on the remoteness of the origin and destination will reveal the push and pull factors in more explicit way. However, a common phenomenon is that people do migrate to a longer distance with a more focused objective and there propensity to settle in urban areas is always higher than the small distance migration.

A Unit Based Crashing Pert Network for Optimization of Software Project Cost

Authors: Priti Singh, Florentin Smarandache, Dipti Chauhan, Amit Bhaghel
Comments: 10 pages

Crashing is a process of expediting project schedule by compressing the total project duration. It is helpful when managers want to avoid incoming bad weather season. However, the downside is that more resources are needed to speed-up a part of a project, even if resources may be withdrawn from one facet of the project and used to speed-up the section that is lagging behind. Moreover, that may also depend on what slack is available in a non-critical activity, thus resources can be reassigned to critical project activity. Hence, utmost care should be taken to make sure that appropriate activities are being crashed and that diverted resources are not causing needless risk and project scope integrity. In this paper we want to present a technique called "Unit Crashing" to reduce the total cost of project. Unit Crashing means to crash the project duration by one unit (day) instead of crashing it completely. This technique uses an iterative approach to perform unit crashing until all activities along the critical path are crashed by desired amount. The output of this method will reduce the cost of project, and is useful at places where cost is of major consideration. Crashing PERT networks can save a significant amount of money in crashing and overrun costs of a company. Even if there are no direct costs in the form of penalties for late completion of projects, there is likely to be intangible costs because of reputation damage.

Another Proof of a Theorem Relative to the Orthological Triangles

Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 3 pages

In [1] we proved, using barycentric coordinates, the following theorem

Proof Wolstenholme-Lenhard Ciclic Inequality for Real Numbers and L.fejes Tóth Conjecture

Authors: Marian Dincă
Comments: 4 Pages.

In this paper an elementary proof of the Wolstenholme-Lenhard ciclic inequality for real numbers and L.Fejes T&oactute;th conjecture( equivalent by Erdis-Mordell inequality for polygon) is given, using a remarcable identity We give the following:

Planetary Spin ( According to "Hypothesis on MATTER" )

Authors: Nainan K. Varghese
Comments: 17 pages, Originally published in General Science Journal

A part of central force between planetary and central bodies cause their spin motions. All bodies in planetary systems develop mean accelerating spin motion. Depending on their orbital parameters, planets and central bodies may spin in forward direction, rearward direction or, in rare cases, may have no spin motion at all. All bodies in a planetary system tend to spin in their common orbital plane. Angular accelerations of orbiting bodies continue indefinitely until their high spin speeds cause disintegration of planets and planetary system. In a planetary system, consistency of body-matter and radial size of a body determine relative spin speeds at different parts of its body. Equatorial region of all very large bodies spin faster than their polar region or regions towards their spin-axes. Lengthening of (terrestrial) solar days, presently misinterpreted as slowing down of earth's spin motion, is the result of insufficient compensation to earth's apparent spin motion about the sun.

Symmetrically Reproducing Quark and Lepton Mass and Charge

Authors: J. S. Markovitch
Comments: 3 pages

It is shown that a particle set possessing electric charges and masses that coincide with those of the quarks and leptons can be produced with the aid of the symmetry of the cuboctahedron. Specifically, it is shown that small powers of 4.1 are useful in economically reproducing the quark and lepton masses, and that these powers - and thereby the masses they represent - can be joined automatically with their correct values for electric charge with the aid of cuboctahedral symmetry.

Conformal Gauge Relativity on the Geometrical Unification of Gravitation and Gauge Fields

Authors: Juan Andrés Musante Apolo
Comments: 44 pages

A Lagrangian depending on geometric variables (metric, affine connection, gauge group generators) is given which maintains compatibility with General Relativity. It generates the dynamics for Electromagnetism and other Gauge Fields along with Gravitation, at the time it gives a geometric foundation for the stress-energy tensor of continuous matter. The geometric-invariance principle under this integration is exposed and the resulting field equations are obtained. The theory is developed over the tangent space of a four-dimensional real manifold and the generators become those from the Homogenous Lorentz group.

Threat Assessment of a Possible Vehicle-Borne Improvised Explosive Device Using DSmT

Authors: Jean Dezert, Florentin Smarandache
Comments: 24 pages

This paper presents the solution about the threat of a VBIED (Vehicle-Borne Improvised Explosive Device) obtained with the DSmT (Dezert-Smarandache Theory). This problem has been proposed recently to the authors by Simon Maskell and John Lavery as a typical illustrative example to try to compare the different approaches for dealing with uncertainty for decision-making support. The purpose of this paper is to show in details how a solid justified solution can be obtained from DSmT approach and its fusion rules thanks to a proper modeling of the belief functions involved in this problem.

Survey on Singularities and Differential Algebras of Generalized Functions :A Basic Dichotomic Sheaf Theoretic Singularity Test

Authors: Elemér E Rosinger
Comments: 166 pages

It is shown how the infinity of differential algebras of generalized functions is naturally subjected to a basic dichotomic singularity test regarding their significantly different abilities to deal with large classes of singularities. In this respect, a review is presented of the way singularities are dealt with in four of the infinitely many types of differential algebras of generalized functions. These four algebras, in the order they were introduced in the literature are : the nowhere dense, Colombeau, space-time foam, and local ones. And so far, the first three of them turned out to be the ones most frequently used in a variety of applications. The issue of singularities is naturally not a simple one. Consequently, there are different points of view, as well as occasional misunderstandings. In order to set aside, and preferably, avoid such misunderstandings, two fundamentally important issues related to singularities are pursued. Namely, 1) how large are the sets of singularity points of various generalized functions, and 2) how are such generalized functions allowed to behave in the neighbourhood of their point of singularity. Following such a two fold clarification on singularities, it is further pointed out that, once one represents generalized functions - thus as well a large class of usual singular functions - as elements of suitable differential algebras of generalized functions, one of the main advantages is the resulting freedom to perform globally arbitrary algebraic and differential operations on such functions, simply as if they did not have any singularities at all. With the same freedom from singularities, one can perform globally operations such as limits, series, and so on, which involve infinitely many generalized functions. The property of a space of generalized functions of being a flabby sheaf proves to be essential in being able to deal with large classes of singularities. The first and third type of the mentioned differential algebras of generalized functions are flabby sheaves, while the second type fails to be so. The fourth type has not yet been studied in this regard.

Hydrodynamics of the Rotating Spherical Matter Fields and Atomic Structure

Authors: Ibrahim Mutlay
Comments: 6 pages, 1 figure.

Atomic structure model was proposed as a rotating stratified fl uidic matter field with the particles corresponded to solitary waves in the field. Mathematical formulation of the proposed structure was constructed on the model of thermal convection in rotating spherical shells of conducting fluids using magnetohydrodynamic Navier-Stokes Equations. Acceleration term was derived using Coulomb potential. Novel model showed that internal structure of atoms is subjected to complex fluid dynamics.

Lorentz Contraction of Space and the Gravitational Field

Authors: Morgan D. Rosenberg
Comments: 10 pages

By considering the gravitational field as an optical medium with a radially-dependent index of refraction, we are able to show that a physical model of space being radially compressed by mass, rather than curved by mass, as in general relativity, yields the same results predicted by Einstein's theory of general relativity. We are further able to show that this spatial compression is equivalent to the Lorentz contraction of special relativity. The predictions of general relativity are all derived with relatively basic mathematics without reliance on the grossly complex Riemannian geometry needed for Einstein's curved space-time model.

A Short Algebraic Proof of Fermat's Last Theorem

Authors: Morgan D. Rosenberg
Comments: 11 pages

Presented herein is a proof of Fermat's Last Theorem, which is not only short (relative to Wiles' 109 page proof), but is also performed using relatively elementary mathematics. Particularly, the binomial theorem is utilized, which was known in the time of Fermat (as opposed to the elliptic curves of Wiles' proof, which belong to modern mathematics). Using the common integer expression aⁿ + bⁿ = cⁿ for Fermat's Last Theorem, the substitutions c = b+i and b = a+j are made, where i and j are integers. Using a Taylor expansion (i.e., in the form of the binomial theorem), Fermat's Last Theorem reduces to (see paper) and what remains to be proven, from this equation, is that (see paper) only has rational solutions for n=1 and n=2. This proof is presented herein, thus proving that aⁿ + bⁿ = cⁿ only has integer solutions for a, b and c for integer values of the exponent n=1 or n=2.

The Philosophy Error of the "Almost Prime"

Authors: Tong Xin Ping
Comments: 2 pages, In Chinese

Don't confuse quantitative change and qualitative change.

A Family of Estimators for Estimating Population Mean in Stratified Sampling Under Non-Response

Authors: Manoj K. Chaudhary, Rajesh Singh, Rakesh K. Shukla, Mukesh Kumar, Florentin Smarandache
Comments: 8 pages

Khoshnevisan et al. (2007) proposed a general family of estimators for population mean using known value of some population parameters in simple random sampling. The objective of this paper is to propose a family of combined-type estimators in stratified random sampling adapting the family of estimators proposed by Khoshnevisan et al. (2007) under non-response. The properties of proposed family have been discussed. We have also obtained the expressions for optimum sample sizes of the strata in respect to cost of the survey. Results are also supported by numerical analysis.

Russian Alphabet: Message to Slavs

Authors: Valery P. Dmitriyev
Comments: 4 pages

Russian letters have ancient names which add up to a meaningful text following the alphabet acrophony. The second half of this text, known as Message to Slavs, calls for a translation into modern language, and its interpretation is, generally speaking, ambiguous. The recently accepted translation sounds pompous and perhaps somewhat sanctimonious. Below I give an alternative interpretation of the message's second part, that is formed of sensual images, and someone may see it as scabrous. However that may be, I proceed from the assumption that our ancestors were more honest in their emotions than today's coprolalics.

Time Travel: Some Science of Fiction

Authors: John Michael Williams
Comments: 11 pages.

The fiction of time-travel usually makes it paradoxical and therefore impossible beyond physics. A few physical postulates, however, can make time-travel merely impossible physically.

Why We Should Favor Heavier Vehicles for Highway Driving

Authors: John Michael Williams
Comments: 12 pages.

Elementary calculations show that the mass of the passenger's vehicle should have an important influence on risk of injury, greater mass yielding greater protection independent of the other mass(es) in the collision. This holds for collisions treated either as purely elastic, or as quasi-inelastic. Passengers in more massive vehicles thus would seem better off no matter what the size or weight of other vehicle(s) in a collision. The approximations used suggest that highway vehicles should be at least 20 times the mass of the average passenger, or injuries in a collision will be disproportionately grave.

On the Limit for the Periodic Table of the Elements

Authors: Chun-Xuan Jiang
Comments: 7 Pages.

It has been proved that the 5g = 18 is unstable, the heaviest element that occurs naturally is uranium with an atomic number of 92 and the island of stability does not exist using the modified Pauli principle. This is the Book proof.

Arithmetic Information in Particle Mixing

Authors: M. D. Sheppeard
Comments: 5 pages.

The mutually unbiased bases of quantum information theory are used to study the MNS and CKM mixing matrices. The resulting mixing matrix parameterisation requires only three real parameters, and is thus potentially more constraining than those in current use. We also discuss related results from MINOS and Fermilab.

A New Proof Viorel Vîjîitu Inequality

Authors: Marian Dincă
Comments: 2 pages.

In the paper given new proof the inequality using convex function

Generalisation of the Inequalities Proposed I.m.o. Madrid 2008 and India-International Mathematical Olympiad Training Camp2010

Authors: Marian Dincă
Comments: 3 pages.

In the paper given generalisation inequalities using Lagrange identity.

Time Relativity a Model for Relative Time

Authors: Michael Devine
Comments: 15 pages.

We introduce a new relativistic model of the universe in which the time of an observer is precisely defined relative to all other observers. Within this redefinition of time, light is considered to propagate in a single instant, while still appearing to be traveling at an invariable constant speed c to any observer who fails to perceive time across distances. The intuitive correctness of the new model is presented, and it is shown to properly account for historical experiments related to light and measurements of c. Built from the ground up to match the predictions of special relativity, the new model of "Time Relativity" is shown to display the same relativistic effects. We prove this by deriving the Lorentz transformation as a direct consequence of the theory's hypothesis. We discuss the startling possible consequences of accepting the model as an accurate description of our reality. Finally, we present the beginnings of a time-relativistic explanation of quantum mechanical observations of light as seen in the double-slit experiment, suggesting a possible role for Time Relativity in leading to a unified theory.

Reflections on an Asymmetry on the Occasion of Arnold's Passing Away ...

Authors: Elemér E Rosinger
Comments: 4 pages.

Keeping silent by authorities in science about breakthroughs made by less well known scientists creates a massively asymmetric situation which is to the detriment of science.

Planetary Orbits ( According to "Hypothesis on MATTER" )

Authors: Nainan K. Varghese
Comments: 28 pages, Originally published in General Science Journal

In any system of bodies, relativistic considerations can provide only those parameters of the constituent bodies, which are related to their relative positions. Use of a reference frame, related to a static central body, causes a planetary orbit to appear as closed geometrical figure around the central body. As the central body, itself is a moving body, this does not reflect physical reality. Although they help to explain apparent phenomena, all properties attributed to elliptical/circular planetary orbital path are unreal. Real physical actions are restricted to real entities and they have to be understood with reference to an absolute reference. Since, elliptical shape of a planetary orbit is an imaginary aspect; it has its limitations to explain real actions in nature. Due to constant motions of free bodies in space, it is practically impossible for a free body to orbit around another. However, they may orbit about each other and follow a common median path in space. Mechanism of orbit-formation and the limitations of orbiting bodies, described in this article, are based on a radically different dynamics from an alternative concept put forward in 'Hypothesis on MATTER'. A planet's parameters, during initial entry into its datum orbit, determine size and eccentricity of its apparent orbit. Only those bodies, which approach the central body from the rear, on the outer side of its curved path, through a small window in space can form stable orbits. Hence, it is imperative that all bodies of a planetary system orbit in the same sense and are (almost) in the same plane. Perihelion/aphelion of an orbital path could be anywhere in the orbit, but the point at which the orbiting body has its highest/lowest linear speeds are fixed in relation to the central body's path. All natural planets, whose perihelion are in front of their point of entry; arrive from outside the planetary system.

An Expansion Theory of the Universe with no Dark Matter and no Dark Energy

Authors: Chun-Xuan Jiang
Comments: 7 Pages.

In this paper we find a new gravitational formula: F-bar = -mc²/R = and establish an expansion theory of the universe with no dark matter and no dark energy

What Causes the Mass to be Deficit Inside a Nucleus?

Authors: Karunakar Marasakatla
Comments: 4 Pages.

Deficit of mass is a change in the physical characteristics of an object. What corresponding changes, if any, in the nucleus represents the observed deficit in mass?

The Derivation of the Fine Structure Constant

Authors: Richard B. Dowd
Comments: 3 Pages.

A derivation of the fine structure constant by deduction

The Philosophy Error of the Proposition "9+9"~"1+2"

Authors: Tong Xin Ping
Comments: 2 Pages. In Chinese

The method of the quantitative change can not solve the problem of the qualitative change.

The Weight Change of a Body in Connection with the Electrical Tension

Authors: H.-J. Hochecker
Comments: 3 Pages.

I stick metal foil on an a 1 square meter large and 10 kilograms heavy dielectric so that a condenser is build. By putting a tension of 10 kV on the condenser or by short-circuiting it I measure a real reduction of the weight of about 0.1 grams each time. This result confirms my theoretical conclusion which says that the weight of a body is related with the movements of its charges (protons and electrons). Keywords: Gravitation, movement of electrical charges, relativity

Methods in Environmental Biotechnology for Environmentalists

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, S. R. Kannan, S. Ramathilagam
Comments: 144 Pages.

The study of environmental pollution by chemicals used in agriculture as pesticide or as fertilizers or pollution caused by industries and chemical plants which use chemicals have not been analysed systematically. This book has five chapters. First chapter is introductory in nature. Here we just study chemical pollution caused by garment industries in chapter two of this book using fuzzy associative memories.

Why Shamir and Fox Did not Detect "Aether Wind" in 1969?

Authors: V.V. Demjanov
Comments: 5 Pages.

Up to 1960ies the measurement of the aether wind velocity by the technology of Michelson presumed that a medium placed across the path of light rays has no substantial significance (except as being an obstacle) for obtaining the expected shift of the interference fringe from the brought together orthogonal rays on the interference of the turnabout device. In 1960ties several authors began independent research on the Michelson-type interferometers with different optical media used as light carriers. J.Shamir and R.Fox declared "negative" the results of their measurements on the plexiglas (though they registered the fringe shift 1/3000 fraction of the fringe's width and determined the respective velocity of aether wind 6.5 km/s). The authors considered this result as "enhancing the experimental basis of special relativity", and their report has been published. My results of same years appeared to be positive. I managed to register on gaseous, liquid and solid optically transparent bodies hundred times greater relative shifts of the fringe (0.01-5.0) giving for horizontal projection of the aether wind velocity the value hundreds km/s. At different times of day and night at the latitude of Obninsk city I registered the changing of this velocity in the interval 140-480 km/s. Insofar as my results "weaken the experimental basis of special relativity", their publication is still refused. I will show in the present report, basing on my experimental experience, that in reality Shamir and Fox obtained positive results. The historical precedence of misunderstanding the positive measurements of aether wind of the order 200-400 km/s, performed by Michelson and Miller in 1920-1930ies at lengthened to 32 m air light carriers, described by me in arXiv:0910.5658v3, 24 June 2010, repeated in the work by Shamir and Fox. Misunderstood was another artifact, manifesting itself in an interferometer with a solid light carrier. In the current work, I explain the nature of this artifact, hiding from Shamir and Fox their experimental success in detecting the aether wind velocity of hundreds km/s. I discussed also the inadequacy of their own interpretation of the results.

The Emerging Clan Capitalism in the World

Authors: V. Christianto
Comments: 21 Pages.

In the present article a number of critical economics situations are discussed based on clan capitalism as starting point. One can see clearly then, that instead of assuming 'ordinary economy' and clan/crony capitalism is an exception in particular nation because of certain socio-historical context, one should begin with the opposite assumption instead: that can capitalism can be found almost everywhere in this planet.

The Theory About Infinity of Simple Numbers-Twins

Authors: Valery Demidovich
Comments: 15 Pages.

The work maintenance: attempt to solve a problem about definition of set of simple numbers-twins is made. In work absolutely new approach which is based on algorithm of a sieve of Eratosfena is applied.

Determination of Proton and Neutron Radii

Authors: Chun-Xuan Jiang
Comments: 2 Pages.

In note we calculate Proton and Neutron radii

M-Theory (2)

Authors: Min-Young Yun
Comments: 58 Pages.

The problem of summing of like powers is completely solved by J. Bernoulli's polynomials. Apart from pure mathematics, the Bernoulli numbers appear prominently in perturbative quantum field theory. Here I present a way, using elementary Bernoulli numbers and Riemann zeta function and expanding mathematical meaning then, gain of another physical meaning. The behavior of smallest unit that creating from superstring and quark is indeterminate, but can be described as Unification Theory according to macroscopic-rules. So, it is easy to understand in all ages and countries, at any times and places. Newborns speak out the easiest word 'Mom' at the first time they speaking, which decided the title of the theory

The Cyclotron Notebooks

Authors: Philip Gibbs
Comments: 66 Pages, originally published as a website in March 1996.

The cyclotron note books are a collection of essays about fundamental physics and metaphysics. The central essay is about the principle of event-symmetric space-time, a new theory about how to do quantum gravity. The style is more technical in some parts than in others. Each essay can be read independently but if you find that one of them has terms which you don't understand you may find them explained in an earlier one. The later ones may be too difficult for the layman and even I don't understand the last one.

A Model of the Electron

Authors: R. Wayte
Comments: 47 Pages.

A geometrical/mechanical model of the electron has been developed based on the measured fine structure constant, anomalous magnetic moment, and a solution of Einstein's equations of general relativity applied to electromagnetism. Properties such as charge, mass and spin have been explained from a classical viewpoint, and then α and μ calculated in agreement with experiment.

Aether and Gravitational Wave from Electromagnetic-Dynamics Equations

Authors: Yoshiro Nohara
Comments: 6 pages

The generalized Maxwell equations in vacuum are basically the equations for steady states, which satisfy both energy and force conservation laws. However, superpositions of the steady states often break those conservation laws, although the generalized Maxwell equations are kept. To study those cases, we derived electromagnetic-dynamics equations, which include the generalized Maxwell equations, energy and force conservation laws, and dynamics of scalar fields. These equations explain that the scalar fields work as the aether propagating the electromagnetic wave, scalar waves work as the gravitational waves, and how the electromagnetic waves advance along the way in the gravitational waves.

Russian Numerals: a Clue to Aryan Counting

Authors: Valery P. Dmitriyev
Comments: 1 pages

Russian numerals fit into a rhymed mnemonic verse. Almost exact correspondence to names of respective Greek letters and many parallels with Sanscrit, Greek, Latin, English and German numerals occur.

A Mathematical Model of the Quark and Lepton Mixing Angles

Authors: J. S. Markovitch
Comments: 15 pages

A single mathematical model encompassing both quark and lepton mixing is described. This model exploits the fact that when a 3×3 rotation matrix whose elements are squared is subtracted from its transpose, a matrix is produced whose non-diagonal elements have a common absolute value, where this value is an intrinsic property of the rotation matrix. For the traditional CKM quark mixing matrix with its second and third rows interchanged (i.e., c - t interchange), this value equals one-third the corresponding value for the leptonic matrix (roughly, 0.05 versus 0.15). By imposing this and two additional related constraints on mixing, and letting leptonic ϕ₂₃ be maximal, a framework is defined possessing just two free parameters. A mixing model is then specified using values for these two parameters that derive from the solution to a simple equation, where this solution also accurately reproduces the fine structure constant. The resultant model, which is entirely free from parameters adjusted to fit the mixing data, possesses the following angles θ₂₃ = 2.367442^◦, θ₁₃ = 0.190986^◦, θ₁₂ = 12.920966^◦, ϕ₂₃ = maximal, ϕ₁₃ = 0.013665^◦, and ϕ₁₂ = 33.210911^◦, which fit the experimental quark and lepton mixing angles. At the time of its introduction in 2007, this model had a 7.0σ disagreement with the value for |V_ub|, whereas a revised value for |V_ub| from the same source now yields a disagreement of just 1.6σ.

On the Invariance of the Velocity of Light

Authors: Bertrand Wong
Comments: 14 pages

The Special Theory of Relativity postulates that the velocity of light would always be invariant at 186,000 miles per second at all inertial frames. The paper examines this aspect of the Theory.

Thermodynamic Foundations of General Relativity (The Primary Gas Representation of Particle-X)

Authors: V.A.Induchoodan Menon
Comments: 19 pages

The author after introducing the concept of the vean (vacuum energy absorption) process shows that it not only crystallizes the progressive nature of time but also causes gravitation and the red shift of light emitted by far off galaxies [1]. He now shows that the thermodynamics of the primary gas in a gravitational field leads to the principle of equivalence and to its field equations of general relativity. The curvature of the space-time is seen to emerge from the anisotropy of the fluctuations in the Higgs field in the neighborhood of a massive body arising from the vean process. According to him unlike the currently accepted interpretation of general relativity the gravitational field based on the vean process does not exhibit non-linearity.

Goldbach' Conjecture (6): the Chinese Remainder Theorem and Goldbach' Primes

Authors: Tong Xin Ping
Comments: 4 pages. In Chinese

By the Chinese Remainder Theorem, we can obtain Goldbach' Primes

Goldbach' Conjecture (5): When I=1~r, the P and N Are Incongruent Modulo P_i, the P is Goldbach' Primes

Authors: Tong Xin Ping
Comments: 2 pages. In Chinese

When i=1~r, the p and N are incongruent modulo p_i, The p is Goldbach' Primes

Using Gravitation to Emulate Electromagnetism.

Authors: S. Halayka
Comments: 3 Pages.

The possibility of Universe-scale black holes living in closed 3D space of constant positive curvature was briefly considered in previous work. Further consideration of this possibility is given here. A possible link between gravitation and electromagnetism is discussed.

Goldbach' Conjecture (4): the Expression of the Number of Goldbach' Primes

Authors: Tong Xin Ping
Comments: 3 pages. In Chinese

Use the inclusion-exclusion to show that the expression of the number of Goldbach' Primes.

Goldbach' Conjecture (3): Goldbach' Primes and Eratosthenes' Sieve Method

Authors: Tong Xin Ping
Comments: 1 pages. In Chinese

By Eratosthenes' sieve method, we can obtain Goldbach' Primes.

On Using Greenberger-Horne-Zeilinger Three-Particle States for Superluminal Communication

Authors: Raymond W Jensen
Comments: 19 pages, Presented at the SPESIF-2010 Conference at JHU Applied Physics lab in Feb. 2010

Using a three-particle entangled system (triple), it is possible in principle to transmit signals faster than the speed of light from sender to receiver in the following manner: From an emitter, for every triple, particles 1 and 2 are sent to the receiver and 3 to the sender. The sender is given the choice of whether or not to measure polarization of particle 3. Meanwhile the receiver measures particle correlation vs. relative polarization angle for the polarizers of particles 1 and 2. The particle 1 and 2 correlation statistics depend on whether or not particle 3 polarization was measured, instantaneously. This dependence is a basis for faster-than-light communication.

Special Theory of Relativity in Absolute Space and the Symmetric Twin Paradox ( on the Possibility of Absolute Motion )

Authors: Golden Gadzirayi Nyambuya, Mabedle Donald Ngobeni
Comments: 21 pages, 10 figures, 1 table.

Departing from the traditional case where one twin stays put while the other rockets into space, we consider the case of identically accelerated twins. Both twins depart at uniform relativistic speeds in opposite directions for a round trip from the Earth on their 21th birthday destined into space to some distant constellation that is a distance L₀ in the rest frame of the Earth. A "proper" application of the Special Theory of Relativity (STR) tells us that the Earth bound observers will conclude that on the day of reunion, both twins must both have aged the same albeit their clocks (which where initially synchronized with that of the Earth bound observers) will have registered a duration less than that registered by the Earth bound observers. In the traditional twin paradox, it is argued that the stay at home twin will have aged more than the traveling twin and the asymmetry is attributed to the fact that the travelling twin's frame of reference is not an inertial reference frame during the periods of acceleration and deceleration making it illegal for the travelling twin to use the STR in their frame, thus "resolving" the paradox. This same argument does not hold in the case considered here as both twins will undergo identical experiences where each twin sees the other as the one that is in motion. This means, each twin must conclude that the other twin is the one that is younger. They will conclude that their ages must be numerically different, thus disagreeing with the Earth bound observers that their ages are the same. This leads us to a true paradox whose resolution is found in the deduction that motion must be absolute. We provide a thought-experiment on how to measure absolute motion. Through this thought-experiment, we extend the second postulate of the STR to include the direction of propagation of light, namely that not only is the speed of light the same for all observers, but the direction of propagation as-well. Succinctly, the speed of light along its direction of motion in the absolute frame of reference is the same for all observers in the Universe. In an effort to try and resolve the symmetric twin paradox, we set-forth a relativistic aether model, which at best can be described as the Special Theory of Relativity in Absolute Space. By recalibrating several experiments performed by other researchers in the past, we find that the Earth's speed through the aether is in the range 240 ± 80 kms^-1.

Universal Medium ( According to "Hypothesis on MATTER" )

Authors: Nainan K. Varghese
Comments: 17 pages.

Space is a functional entity, presupposed by rational beings, whenever real entities are envisaged. Being a functional entity, space has no structure or form. It can neither physically act nor is able to undergo physical actions. By realising a real entity that fills the entire space as an all-encompassing universal medium, the formless space can be replaced with a structured real entity. This real entity will have positive existence and at the same time, it can have all properties currently assigned to space or to other imaginary entities like; different types of aether, imaginary particles or various types of fields. No actions can be performed at a distance through empty space. An all-encompassing medium is essential to facilitate (apparent) physical actions between matter bodies at a distance. Aether, used in aether-theories is too vague and fails to describe many physical actions of matter bodies, logically. 'Hypothesis on MATTER' envisages an all-encompassing medium, which has only one type of real (postulated) constituent particles and definite properties. Envisaging a universal medium, as described in the concept, helps to logically explain all physical phenomena, related to matter.

Electromagnetic Stealth with Parallel Electric and Magnetic Fields

Authors: T. E. Raptis
Comments: 8 pages.

We analyze a theoretical example of parallel electric and magnetic fields in a hypothetical anisotropic medium with varying susceptibility. We deduce the polarization characteristics and we discuss the conditions under which this could be utilized in electromagnetic invisibility.

Entropy and 'the Arrow of Time', a Love Story

Authors: Constantinos Ragazas
Comments: 3 pages

In this short note we offer a new definition of entropy and derive an interesting relationship between entropy and time. In light of this relationship, we show how The Second Law of Thermodynamics can be interpreted as saying that every physical process requires a lapse of time. In simple language, the Second Law says that 'everything happens over some positive time-interval'. This defines 'the arrow of time'. This understanding of entropy maintains the reciprocal relationship between entropy and temperature, makes entropy 'additive', and preserves the notion that entropy provides a measure of 'available energy' to do work. What does change, however, is the idea that entropy is a measure of disorder, and the Universe is doomed to thermal death.

Can the Edges of a Complete Graph Form a Radially Symmetric Field in Closed Space of Constant Positive Curvature?

Authors: S. Halayka
Comments: 13 Pages.

In earlier work, it was found that the edges of a complete graph can very nearly form a radially symmetric field at long distance in at 2D and 3D space if the number of graph vertices is great enough. In this work, it is confirmed that the edges of a complete graph can also very nearly form a radially symmetric field in closed 2D and 3D space of constant positive curvature if the graph is small compared to the entirety of the space in which it lives and if the number of graph vertices is great enough.

Michelson-Type Interferometer Operating at Effects of First Order with Respect to V/c

Authors: V.V. Demjanov
Comments: 11 pages

          More than hundred years the opinion persists that Michelson interferometer can not detect aether wind by effects of first order with respect to the ratio υ/c. Below there will be shown that the degenerations of the interfer-ometer's sensitivity to effects of first order can be lifted changing the traditional configurations of the device. My experiment demonstrated that a two-media device operating at effects of first order can reliably measure the shift of the interference fringe (and thus the speed of "aether wind"), and much more successfully than by Michelson interferometer operating at effects of second order. Unlike in the traditional approach, in the interferometer of first order light rays (after splitting at semi-transparent plate) propagate in both orthogonal arms to rebounding mirrors in a one optical medium (with the dielectric permittivity ε₁), and return after reflection to a plate re-uniting them for interference via another medium (with the dielectric permittivity ε₂). The shift of interference fringe is reliably registered (in rotation of the interferometer by 90^o) even at gas light carrying pairs with arm's length up to 1 m. With this the fringe shift appears to be proportional to υ/c and difference ε₁–ε₂.
          The experimental findings have been interpreted basing on classical scheme of ray optics by two methods: 1) with the Fresnel model of dragging light by moving optical medium neglecting terms quadratic in υ/c (including the Lorentz contraction of the longitudinal to v arm as quadratic with respect to υ/c), 2) with the classical theory of the frequency dispersion of moving dielectric media, supplemented by the accounting classical and relativistic Doppler effects describing translatory motion (with velocity v) of particles of interferometer light carriers in aether. From observations of the fringe shift on the interferometer of first order with respect to υ/c there was found (at the latitude of Obninsk) the change of the horizontal projection of the Earth's velocity relative to luminiferous aether in the limits 140<υ<480 km/s depending on the local time of the day and night.

Goldbach' Conjecture (2): When the P is Congruent to N Modulo P_i, the P is not Goldbach' Primes

Authors: Tong Xin Ping
Comments: 2 pages.

When the p is congruent to N modulo p_i, the p is not Goldbach' Primes.

Goldbach' Conjecture (1): Goldbach' Primes Are Symmetric Primes

Authors: Tong Xin Ping
Comments: 2 pages.

When n/2 + x and n/2 - x or y and y + (N-y) are primes, they are Goldbach' Primes. Put it another way, The Goldbach' Primes are symmetric primes.

A New Proof of an Inequality of Oppenheim

Authors: Marian Dincă, J. L. Díaz-Barrero
Comments: 4 pages.

In this short note a new proof of a classical inequality involving the areas of a pair of triangles is presented.

On the Gini Mean Difference Arc-Lengths Test for Circular Data

Authors: David D. Tung, S. Rao Jammalamadaka
Comments: 15 pages.

In this paper, we propose a new test of uniformity on the circle based on the Gini mean difference of the sample arc-lengths, i.e. the gaps between successive observations on the circumference of the circle. These sample arc-lengths are analogous to sample spacings, which are the gaps between successive observations on the real line. Such a Gini mean difference test is analogous to Rao's spacings test, which has been used to test the uniformity of circular data. We obtain both the exact and asymptotic distributions of the Gini mean difference arc-lengths test, under the null hypothesis of circular uniformity. We also provide a table of upper percentile values of the exact distribution for small to moderate sample sizes. Some examples of circular data analysis are also considered. It is also seen that the Gini mean difference arc-lengths tests is more asymptotically efficient than Rao's test in the sense of Pitman asymptotic relative efficiency.

Universal Theory of Dimensionless Constants of Nature

Authors: Mark A. Thomas
Comments: 15 pages.

An analytic structural approach to calculating dimensionless constants of Nature is presented which shows a direct relation between physics, and a number theoretic form involving transcendental forms and the Monster group. A development inherent in the consistency of the calculation leads to the deduction of the fine structure constant from pure mathematical structure. The fine structure constant is calculated as pure number in transcendental form 0.00729735256884151851344... This lies within the margin of error of Gabrielse?s 2008 experimentally determined value 0.007297352569(5). An argument is made that the naturalness of the mathematical structure explains away the hierarchical mass scale problem of physics and that the structure could be core to the Standard Model with the inclusion of the gravitational gauge force. The universality of the approach is presented to show its reaching domain. If the forms and calculation are true the fine tuning argument of physics may be overturned.

Because there is Inertial and Gravitational Mass

Authors: Raffaele Cogoni
Comments: 4 pages. Italian and English combined

The matter in the universe, is equipped with inertial and gravitational mass and thus weight, this is due to the fact that interactions between bodies, traveling at a finite speed not exceeding that of light.

A New Generic Class of Beltrami "Force-Free" Fields. Part-i: Theoretical Considerations

Authors: T. E. Raptis
Comments: 13 pages.

We report on a new general class of solutions of the Beltrami equation, with special characteristics. We also provide examples of solutions that also satisfy Maxwell equations. A subset of these solutions can be isolated which corresponds to "gauge" fields. A special projective geometry of vacuum fields is also revealed and discussed.

The Alpha Torque and Quantum Physics

Authors: Zhiliang Cao, Henry Cao
Comments: The paper is from a published book "The Alpha Torque" by Zhiliang Cao and Henry Cao. The title was published by CreateSpace with the following eStore URL: https://www.createspace.com/3458701

In the center of the universe, there isn't a super massive black hole or any specific energy holding the universe together. The source of this supposed energy is in the space itself. The space itself is not a complete void. In fact, space itself has a simple movement. This very movement dominates every aspect of physical existence. Nothing can exist without it. The movement is called the Torque. This theory can make it easier to understand Quantum Physics.

Super Linear Algebra

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 294 pages

In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra.

Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Amal
Comments: 280 pages

The concept of supermatrix for social scientists was first introduced by Paul Horst. The main purpose of his book was to introduce this concept to social scientists, students, teachers and research workers who lacked mathematical training. He wanted them to be equipped in a branch of mathematics that was increasingly valuable for the analysis of scientific data.

Superbimatrices and Their Generalizations

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 410 pages

The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers.

Using Simple Number Theory to Predict Stable Isotopes

Authors: Sean C. Williams
Comments: 15 pages

An abstract method is described for predicting stable isotopes using simple number theory based on a system of predefined combinations, or "Blocks", of protons and neutrons. Each Block is made up of a prime number of protons, and a binary power increase in the number of neutrons. Predictions using the Block system fully includes all the stable isotopes.

The New Prime Theorem (341)-(390)

Authors: Chun-Xuan Jiang
Comments: 61 pages

Using Jiang function we prove that the new prime theorems (341)-(390) contain infinitely many prime solutions and no prime solutions.

Verification of Cepheid Variable Distance Measurements Using Roxy's Ruler

Authors: Bruce Rout
Comments: 12 pages

There has been some controversy over the validation of using the period/luminosity relationship of Cepheid variables to measure the distance to galaxies[2]. We present here a statistical analysis of distance variations for 21 galaxies between Cepheid variables and Roxy's Ruler. The analysis shows there is no systemic error in Measurements to galaxies using Cepheid variables and that such measurements are valid within well defined degrees of error.

Planck Constant Estimation Using Constant Period Relativistic Symmetric Oscillator

Authors: J. Bar-Sagi
Comments: 15 pages

The electromagnetic wave quantum-energy depends only on its frequency, not on the emitting system's radiation power. The proportionality constant between the frequency and the quantumenergy of the electromagnetic wave, the Planck's constant is in the essence of quantum mechanics. This constant is known experimentally but till now there was no clue for calculating its value on a theoretical basis. In the present work a methodology for calculating a lower bound for Planck's constant is presented, based on simple principles. In order to get a reasonable good lower bound it is necessary to have a model of a relativistic oscillator whose period is independent of its energy and which efficiently radiates electromagnetic energy. It is highly desired that the mathematics involved is simple enough to enable good insight into the results. Such a model can also be used for other investigations, and therefore, in this work a potential that conserves the vibration period of symmetric oscillators at relativistic velocities is found and analyzed. The electrically charged system of constant period is used to calculate a lower bound H_m of the Planck's constant h . The value of H_m is smaller than h by a factor very close to √3 . The explanation of this factor also explains the value of Planck's constant. From this value the fine structure constant value is calculated and a new interpretation of this constant obtained.

Inertial Frame Error Discovery Derives Stellar Aberration and Paradox Free Special Relativity Via Huygens Principle.

Authors: P A Jackson, R K Nixey
Comments: 23 pages

We uncover an error of conception, influential on physics at a critical moment. Refraction due to relative motion was observed from the incorrect inertial frame for Stellar Aberration, the path 'dragged' by the new medium. Lodge discussed and showed this[1] in his influential 1893 paper following Michelson & Morley's null result. Jones's 1970 glass disks experiment repeated it.[2] Within the frames of moving media lights paths refract towards the normal, as in more dense media at rest. We show how in the Special Theory of Relativity (SR) using the correct observer frame is essential and how this wrongly affected consideration of Stellar Aberration and Stokes Ether Drag theory. We test subtle variations on Young's experiment, and consider, non-technically, implications on and relationship with SR, the interstellar medium, and EM field potential. Through the Huygens-Fresnel Principle,[3] WFS, interplanetary shocks and FM a possible simple clarification of SR emerges to connect it with a quantum mechanism, apparently requiring no more field than GR. We test it's predictive power and ability to remove perceived paradox and dissent. New perspectives on Snell and Fermat arise from a discrete field model using Einsteins 1952 view that 'space' is actually; "infinitely many spaces in relative motion."

The New Prime Theorem (191)-(240)

Authors: Chun-Xuan Jiang
Comments: 61 pages

Using Jiang function we prove that the new prime theorems (191)-(240) contain infinitely many prime solutions and no prime solutions.

The Formula of the Particle Radii

Authors: Chun-Xuan Jiang
Comments: 1 page

The Formula of the Particle Radii

An Equation that Changed the Universe: F-Bar = Mc²/R

Authors: Chun-Xuan Jiang
Comments: 14 pages

This paper explains the behavior of the entire universe from the smallest to the largest scales,found an equation that changed the universe: F-bar = -mc²/R, established the expansion theory of the universe without dark matter and dark energy, It shows that gravity is action-at-a-distance and that a gravitational wave is unobservable.Thus,a new universe model is suggested that the universe has a centre consisting of the tachyonic matter.

The Single Thread

Authors: Giuliano Bettini
Comments: 9 pages, In Italian

This short paper explores intriguing analogies between helical structures of electron and elementary particles and circular supercoiled DNA. I propose a strong relation between the dispositions Lk=Tw+Wr (Lk=cost., changing Twist and Writhe) and the quark compositions Q=I3+Y/2 (Q=cost., varying Isospin an Hypercharge).

Studies in Statistical Inference, Sampling Techniques and Demography

Authors: Rajesh Singh, Jayant Singh, Florentin Smarandache
Comments: 64 pages

This volume is a collection of five papers. Two chapters deal with problems in statistical inference, two with inferences in finite population, and one deals with demographic problem. The ideas included here will be useful for researchers doing works in these fields.

A Class of Stationary Sequences

Authors: Florentin Smarandache
Comments: 3 pages

We define a class of sequences {a_n} by a₁ = a and a_n+1 = P(a_n), where P is a polynomial with real coefficients. For which a values, and for which polynomials P will these sequences be constant after a certain rank? Then we generalize it from polynomials P to real functions f. In this note, the author answers this question using as reference F. Lazebnik & Y. Pilipenko's E 3036 problem from A. M. M., Vol. 91, No. 2/1984, p. 140. An interesting property of functions admitting fixed points is obtained.

Special Set Linear Algebra and Special Set Fuzzy Linear Algebra

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K Ilanthenral
Comments: 469 pages

This book for the first time introduces the notion of special set linear algebra and special set fuzzy linear algebra. This is an extension of the book set linear algebra and set fuzzy linear algebra. These algebraic structures basically exploit only the set theoretic property, hence in applications one can include a finite number of elements without affecting the systems property. These new structures are not only the most generalized structures but they can perform multi task simultaneously; hence they would be of immense use to computer scientists.

The New Prime Theorem (291)-(340)

Authors: Chun-Xuan Jiang
Comments: 61 pages

Using Jiang function J₂(ω) we prove that the new prime theorems (291)-(340) contain infinitely many prime solutions and no prime solutions.

Surmounting the Cartesian Cut Further: Torsion Fields, the Extended Photon, Quantum Jumps, the Klein-Bottle, Multivalued Logic, the Time Operator Chronomes, Perception, Semiosis, Neurology and Cognition

Authors: Diego L. Rapoport
Comments: 89 page.

We present a conception that surmounts the Cartesian Cut -prevailing in science- based on a representation of the fusion of the physical 'objective' and the 'subjective' realms. We introduce a mathematical-physics and philosophical theory for the physical realm and its mapping to the cognitive and perceptual realms and a philosophical reflection on the bearings of this fusion in cosmology, cognitive sciences, human and natural systems and its relations with a time operator and the existence of time cycles in Nature's and human systems. This conception stems from the self-referential construction of spacetime through torsion fields and its singularities; in particular the photon's self-referential character, basic to the embodiment of cognition ; we shall elaborate this in detail in perception and neurology. We discuss the relations between this embodiment, bio-photons and wave genetics, and the relation with the enactive approach in cognitive sciences due to Varela. We further discuss the relation of the present conception with Penrose's theory of consciousness related to non-computatibility -in the sense of the Goedel-Turing thesis- of quantum processes in the brain.

A New Proof Daniel Pedoe and Oene Bottema Inequalities

Authors: Marian Dincă, Şcoala Generală
Comments: 1 page.

In the paper given a new proof the two inequalities using unitary method.

On the Critical Temperatures of Superconductors: a Quantum Gravity Approach

Authors: Andrea Gregori
Comments: 30 pages.

We consider superconductivity in the light of the quantum gravity theoretical framework introduced in [1]. In this framework, the degree of quantum delocalization depends on the geometry of the energy distribution along space. This results in a dependence of the critical temperature characterizing the transition to the superconducting phase on the complexity of the structure of a superconductor. We consider concrete examples, ranging from low to high temperature superconductors, and discuss how the critical temperature can be predicted once the quantum gravity effects are taken into account.

Neutrosophic Bilinear Algebras and Their Generalizations

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 404 pages.

This book introduces the concept of neutrosophic bilinear algebras and their generalizations to n-linear algebras, n>2.

A "New and Simple Idea", Dark Matter-Energy and the Crisis in Physical Theory

Authors: Frederick E. Alzofon
Comments: 20 Pages.

Correction of an omission in A. Einstein's operational definitions of time and space intervals in the special theory of relativity leads to an improved phenomenological and conceptual foundation for a previously proposed unified field theory. In combination with Einstein's researches on the fluctuation in energy of black body radiation, there results a "new and simple idea" of the kind Professor Richard Feynman felt to be necessary for the solution of the cosmological constant problem. A brief description of the formalism of the theory is presented. The infinite zero-point energy of the vacuum is eliminated. A model for the origin of inertial mass and dark matter-energy is deduced. The resulting relation between observed matter and dark matter-energy leads to a restriction on their magnitudes. The magnitudes of the latter quantities are then estimated from astronomical data. A model is proposed for the origin of the gravitational field in terms of a dynamic process at the basis of the proposed theory. The success of the special theory of relativity in predicting the results of three crucial observations establishing the validity of the general theory of relativity and the elimination of the infinite vacuum energy suggest that the unified field theory can lead to a solution of the cosmological constant problem.

Fiat Lux

Authors: Ron Bourgoin
Comments: 3 Pages.

In the vast reaches of space between galaxies, we find dust. Where did it come from, this dust? We hypothesize it is generated by light escaping from the galaxies. We then make a quantum leap and suggest our Universe began from light escaping from other universes.

Effective Relativistic Quantum Mechanics on a Causal Net

Authors: R.D. Bateson
Comments: 11 pages.

The observation of emergent particles in condensed matter physics such as phonons, holes, and recently magnetic monopoles [1] may lead one to speculate that real particles themselves could exist as emergent properties of a space-time lattice. There are many examples in the literature of the Dirac equation being supported by a lattice structure [2,3,4,5], related, for example, to the physics of ice [6] or of graphene [7]. In particular the case of the Dirac equation on the ice lattice is of potential practical interest as ice models can now be realised in a variety of new experimental systems, including spin ice materials [1] and artificial micromagnetic arrays [8]. We noticed that a Reichenbach causal net [9] has the same topology as an ice lattice and hence, if formulated in space-time, might support a version of relativistic quantum mechanics. In this paper we explore this idea at its simplest level. We propose a causal net for the free motion of a particle based on a relational concept of time as an ordered series of possible events that are linked by a principle of common cause. The causal net is 1+1 dimensional but applies along the direction of motion of the particle in three dimensions. It is reminiscent of the Feynman chequerboard [2] and the ice model [6] but differs from both in important respects. The causal net appears to support the 3+1 dimensional Dirac equation [10] for a free fermion and hence the Schrödinger equation in the low velocity limit. The causal net idea gives an intuitive picture of relativistic quantum mechanical motion and the origin of quantization although it is not a complete re-derivation of conventional quantum mechanics, partly because the space-time is discrete, and partly because it does not automatically imply a principle of superposition. If however we identify a causal net as representing a Dirac state vector then superposition of nets allows a development more consistent with conventional quantum mechanics. We therefore suggest that a more detailed study of effective quantum mechanics on causal nets, based on the transparent underlying concepts of causality and probability, might be a fruitful exercise.

A Conjecture About the Riemann XI-Function ξ(1/2 + Iz) and Functional Determinants

Authors: Jose Javier Garcia Moreta
Comments: 7 pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant det (E - H) for a certain Hamiltonian quantum operator in one dimension ... (see paper for full abstract)

On Smarandache Semigroups

Authors: A.K.S.Chandra Sekhar Rao
Comments: 4 pages.

The notion of completely regular element of a semigroup is applied to characterize Smarandache Semigroups. Examples are provided for justification.

Gravitation as a Thermodynamic Process of the Primary Gas that Represents a Particle-ix

Authors: V.A.Induchoodan Menon
Comments: 19 pages

The author after clarifying the concepts of imaginary time, reversible time showed that the progressive time which is experienced by the macroscopic systems are a direct result of the vean (vacuum energy absorption) process which also leads to the collapse of wave function apart from introducing limits to entanglements [1]. He now shows that the vean process could lead to a gradient in the energy of the vacuum fluctuations background near a massive body which in turn could produce the gravitational field. According to the author, the accumulation of the rest mass by a particle by the vean process would be so small that an electron would have increased its rest mass by only 40% over a period of 10 billion years. It is shown that part of the red shift observed in distant galaxies could be attributed to the reduced mass of electrons in the distant past. He suggests that the observed expansion of universe could be a direct result of the vean process.

The New Prime Theorem (241)-(290)

Authors: Chun-Xuan Jiang
Comments: 61 pages

Using Jiang function J₂(ω) we prove that the new prime theorems (241)-(290) contain infinitely many prime solutions and no prime solutions.

Efecto Doppler, Transformaciones de Lorentz Y Dilatación Del Tiempo

Authors: Xavier Terri Castañé
Comments: 11 pages

It is generally considered that the Doppler effect, predicted by the theory of special relativity of Einstein, is an indirect proof for the correctness of the Lorentz transformations. In this article it appears the formula for the Doppler effect from the new relational transformations. We also study the relationship between the Doppler effect and the time dilation of Einstein's special relativity theory.

Causal Set Theory and the Origin of Mass-Ratio

Authors: Carey R Carlson
Comments: 16 pages.

Quantum theory is reconstructed using standalone causal sets. The frequency ratios inherent in causal sets are used to define energy-ratios, implicating the causal link as the quantum of action. Space-time and its particle-like sequences are then constructed from causal links. A 4-D time-lattice structure is defined and then used to model neutrinos and electron clouds, which together constitute a 4-D manifold. A 6-D time-lattice is used to model the nucleons. The integration of the nucleus with its electron cloud affords calculation of the mass-ratio of the proton (or the neutron) with respect to the electron. Arrow diagrams, along with several ball-and-stick models, are used to streamline the presentation.

An Application of Sondat's Theorem Regarding the Orthohomological Triangles

Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 4 pages.

In this article we prove the Sodat's theorem regarding the orthohomological triangle and then we use this theorem and Smarandache-Patrascu's theorem in order to obtain another theorem regarding the orthohomological triangles.

Central Force (According to "Hypothesis on MATTER")

Authors: Nainan K. Varghese
Comments: 11 pages.

Currently, a central force - an apparent effort between two free bodies along the line joining them - is estimated in relativistic frames of references. Estimation of magnitude and direction of central force on planetary bodies/central body in a planetary system assumes that the centre of planetary system is static in space. While considering a satellite's orbit, centre of corresponding planet is assumed static in space. Although such calculations help to determine relative positions of the bodies, it obscures causes of many other important phenomena related to planetary motion. Determining magnitude and direction of central force with respect to an absolute reference can give us logical explanations to many puzzling phenomena on planetary motions/systems.

The Alpha Torque and the Charged Field

Authors: Zhiliang Cao, Henry Cao
Comments: 8 pages. The paper is from a published book "The Alpha Torque" by Zhiliang Cao and Henry Cao. The title is published by CreateSpace with the following eStore URL: https://www.createspace.com/3458701

The space itself is not a true void. In fact, space has energy in it. The energies and forces have a simple movement. This very movement dominates every aspect of physical existence. Nothing can exist without it. The movement is called the Torque. Torque movements can explain why there are electronic fields and magnetic fields. The torque theory can make it easier to understand why there are charged fields.

Possibility of Gravitational Wave from Generalized Maxwell Equations

Authors: Yoshiro Nohara
Comments: 4 pages

The generalized Maxwell equations in vacuum are basically the same with Dirac's extended Maxwell equations, although intrinsic charges and currents are defined by the time differential and gradation of scalar fields, respectively. Consequently, the electromagnetic stress-energy tensors make important conservation lows. Then, we found scalar fields acting like the gravitational wave interacting with the electromagnetic wave. Interestingly, those gravitational waves due to the scalar fields push out the electromagnetic waves. Moreover, there is a possibility of the existence of the materials, from which we feel no gravitational forces although the electromagnetic waves are kicked out by those gravitational waves. We also discussed about the relation with weight.

Deficit of Mass: an Unfortunate Development in Physics

Authors: Karunakar Marasakatla
Comments: 4 pages

Balance scale based measurement of mass is simply a comparison of gravity. The mass of an object, when measured using the balance scale, will be dependent on the volume of the object along with the amount of matter inside the object. Mass deficit is simply the variation in the mass of the object due to the change in volume of the object.

A Clifford Algebra Realization of Supersymmetry and Its Polyvector Extension in Clifford Spaces

Authors: Carlos Castro
Comments: 15 pages, submitted to Foundations of Physics.

It is shown explicitly how to construct a novel (to our knowledge) realization of the Poincare superalgebra in 2D. These results can be extended to other dimensions and to (extended) superconformal and (anti) de Sitter superalgebras. There is a fundamental difference between the findings of this work with the other approaches to Supersymmetry (over the past four decades) using Grassmannian calculus and which is based on anti-commuting numbers. We provide an algebraic realization of the anticommutators and commutators of the 2D super-Poincare algebra in terms of the generators of the tensor product Cl1,1(R) x A of a two-dim Clifford algebra and an internal algebra A whose generators can be represented in terms of powers of a 3 x 3 matrix Q, such that Q3 = 0. Our realization differs from the standard realization of superalgebras in terms of differential operators in Superspace involving Grassmannian (anticommuting) coordinates θ^α and bosonic coordinates x^μ. We conclude in the final section with an analysis of how to construct Polyvector-valued extensions of supersymmetry in Clifford Spaces involving spinor-tensorial supercharge generators Qμ1μ2.....μn and momentum polyvectors Pμ1μ2....μn. Clifford-Superspace is an extension of Clifford-space and whose symmetry transformations are generalized polyvector-valued supersymmetries.

A More Natural Reference Model Integrating Relativity and Quantum Mechanics

Authors: J Gregory Moxness
Comments: 28 pages, 1 figure, Latex. Original ideas from 1997, latest modifications Nov 22, 2007.

M Theory and/or Loop Quantum Gravity hold the promise of resolving the conflict between general relativity and quantum mechanics but lack experimental connections to predictability in physics. A connection is made to these and other theories vying for the title of a "Theory of Everything" by questioning the value of the traditional Planck unit reference point for the scales at which they operate. It also suggests a cosmological model which has acceleration as being fundamental. It provides for an intuitive understanding of the Standard Model and its relationship to particle masses and the structure of the atom. The prediction of particle mass and lifetimes is a good indicator for its validity.

Super Special Codes Using Super Matrices

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral
Comments: 163 pages

The new classes of super special codes are constructed in this book using the specially constructed super special vector spaces. These codes mainly use the super matrices. These codes can be realized as a special type of concatenated codes.

A Method to Solve the Diophantine Equation a X²-B Y² + C = 0

Authors: Florentin Smarandache
Comments: 10 pages.

We consider the equation ...

Properties of a Hexagon Circumscribed to a Circle

Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 3 pages.

In this paper we analyze and prove two properties of a hexagon circumscribed to a circle

A Multiple Theorem with Isogonal and Concyclic Points

Authors: Florentin Smarandache, Ion Pătraşcu
Comments: 3 pages.

A Multiple Theorem with Isogonal and Concyclic Points

Retrospective Examination of Three Articles Published in the Revue Des Questions Scientifiques in 2005 and 2006.

Authors: François Barriquand
Comments: 20 pages, The present article is going to be submitted to the "Revue des Questions Scientifiques"

Three articles published by the same author in the Revue des Questions Scientifiques in 2005 and 2006 are reexamined with special attention paid to a theorem published by Allahverdyan and Nieuwenhuizen in 2002 concerning Thomson's formulation of the second law, as well as to the results of the so-called "before-before" experiment performed on entangled pairs by Stefanov, Zbinden, Gisin and Suarez. As far as thermodynamics are concerned, it is explained here that a macroscopic observer can generate quasi "cycles", whose cyclical characteristics are in fact only valid from the macroscopic point of view, that can potentially enable her/him to retrieve work from a thermalizer without causing any perpetual motion. Concerning quantum entanglement, it is recognized - in contrast with what the author originally published in 2005 and 2006 - that superluminal transmission of decipherable information cannot be achieved if the Copenhagen interpretation of quantum theory remains universally valid. It is also pointed out that the foundations of general relativity cannot be easily reconciled with the implications of Einstein-Podolsky-Rosen measurements.

Explaining the Arrow of Time and the Collapse of Wave Function Based on the Primary Gas Structure of Particle-Viii

Authors: V.A.Induchoodan Menon
Comments: 14 pages

The author after clarifying the physical implications of the imaginary time approach and the reversible real time approach goes on to explain how they differ from the progressive time which is experienced by all macroscopic systems [1]. He proposes that the progressive nature of time is a direct result of the increase in the entropy at the level of the structure of the elementary particles. According to him just as the vacuum fluctuations confine the photino (single luminal wave) to form a staphon (standing wave) which is the basic structure of a particle, a small part of the energy gets converted into heat which gets expressed in the jiggling motion of the particle. It is proposed that this random motion arising from the absorption of the vacuum energy contributes to infinitesimal increase in the internal heat of the particle which results in the increase in entropy right at the level of the elementary particle. He calls the process by which the particles absorb energy from vacuum "the vean process". He proposes that this increase in entropy at the level of the elementary particles results in time acquiring the progressive nature. With this interpretation of the progressive nature of time, the problem of the collapse of wave function gets resolved without invoking the presence of a conscious observer. Even the process of entanglement appears to have space-time limitations. He suggests that the existence of gravitational field and the expansion of the universe also may be traced to this vean process.

A Note of Widening on the Redshift Mechanism

Authors: José Francisco García Juliá
Comments: 5 Pages.

A single tired light mechanism has been proposed for explaining the cosmological redshift without expansion of the universe and also the intrinsic redshift, that is, the excess of redshift of the radio sources. In this note of widening, we show that the mechanism would be similar to the discharge of an electric capacitor, to the radiation loss by fast electrons and to the radioactive nuclei decay.

Searching for Life on Habitable Planets and Moons

Authors: Ashwini Kumar Lal
Comments: 16 pages, 2 figures, published in 'Journal of Cosmology',2010, vol.5, pp.801-810 ; also archived at ARXIV as arXiv: 0912.1040

Earth is the only known inhabited planet in the universe to date. However, advancements in the fields of astrobiology and observational astronomy, as also discovery of large varieties of extremophiles with extraordinary capability to thrive in harshest environments on Earth, have led to speculation that life may possibly be thriving on many of the extraterrestrial bodies in the universe. Coupled with the growing number of exoplanets detected over the past decade, the search for the possibility of life on other planets and satellites within the solar system and beyond has become a passion as well as a challenge for scientists in a variety of fields. This paper examines such possibility in the light of findings of the numerous space probes and theoretical research undertaken in this field over the past few decades.

The Creative Acts of a Youthful God

Authors: Ron Bourgoin
Comments: 2 Pages.

We can never know a thing completely. The more we think about something, the more about it we find to think about. When one considers the number of things in creation, to have thought about all aspects of an infinite number of things would have taken an eternity. A youthful God would have created with sufficient but incomplete knowledge. The changes we see in nature are evidence of tweaking: a mature God is making adjustments.

Handbook of Functions Errata

Authors: Fredy Zypman
Comments: 2 pages

Formulas connecting toroidal functions and elliptical functions are useful in various areas of physics. In solving a problem in electrostatics we run across an error in the Handbook of mathematical functions of Abramowitz and Stegun. In this paper we report the details.

Massive Gravitons Stability , and a Review of How Many Gravitons Make up a Gravity Wave Detectable / Congruent with B.P. Abbott, Et.al., Nature 460, 991 (2009).

Authors: Andrew Beckwith
Comments: 6 pages, 1 figure. Set of notes being turned into an article as to inter relating a graviton count, versus gravitational waves. Will be part of discussions raised in conferences this summer. coming up with specifics as far as the inter relationship

The following questions are raised. First, can there be a stable (massive) graviton? Secondly, what is the relationship between a Gravity Wave, and Gravitons? The inter relationship between a graviton, and a gravity wave is raised, with an idea of eventually making sense of a numerical count presented by Claus Kieffer, in his book on Quantum gravity, in conjunction with how a gravity wave/ graviton count could have some over lap.

Origin of Life

Authors: Ashwini Kumar Lal
Comments: 44 pages, 7 figures, invited review article, published in 'Astrophysics & Space Science' (2008), 317, 267-278; also archived at ARXIV as arXiv:0907.3552

The evolution of life has been a big enigma despite rapid advancements in the fields of biochemistry, astrobiology, and astrophysics in recent years. The answer to this puzzle has been as mind-boggling as the riddle relating to evolution of Universe itself. Despite the fact that panspermia has gained considerable support as a viable explanation for origin of life on the Earth and elsewhere in the Universe, the issue remains far from a tangible solution. This paper examines the various prevailing hypotheses regarding origin of life like abiogenesis, RNA World, iron-sulphur world, and panspermia; and concludes that delivery of life-bearing organic molecules by the comets in the early epoch of the Earth alone possibly was not responsible for kick-starting the process of evolution of life on our planet.

Did We Get the Fundamentals in Physics Wrong?

Authors: Karunakar Marasakatla
Comments: 4 pages

Definition and measurement of the fundamental units is essential to the principles of physics. Distance has an obvious and simple relationship with the measuring scale. Such a relationship is absent in measuring the mass of an object using the balance scale. This is one of the important factors for the present chaotic scenario in the field of physics.

The New Prime Theorem (101)-(130)

Authors: Chun-Xuan Jiang
Comments: 38 pages

Using Jiang function we prove that the new prime theorems (101)-(130) contain infinitely many prime solutions and no prime solutions.

The New Prime Theorem (71)-(100)

Authors: Chun-Xuan Jiang
Comments: 38 pages

Using Jiang function we prove that the new prime theorems (71)-(100) contain infinitely many prime solutions and no prime solutions.

U-Statistics Based on Spacings

Authors: David D. Tung, S. Rao Jammalamadaka
Comments: 23 pages.

In this paper, we investigate the asymptotic theory for U-statistics based on sample spacings, i.e. the gaps between successive observations. The usual asymptotic theory for U-statistics does not apply here because spacings are dependent variables. However, under the null hypothesis, the uniform spacings can be expressed as conditionally independent Exponential random variables. We exploit this idea to derive the relevant asymptotic theory both under the null hypothesis and under a sequence of close alternatives. The generalized Gini mean difference of the sample spacings is a prime example of a U-statistic of this type. We show that such a Gini spacings test is analogous to Rao's spacings test. We find the asymptotically locally most powerful test in this class, and it has the same efficacy as the Greenwood statistic.

Theoretical Foundation of Gravito-Electromagnetism: the Theory of Informatons

Authors: Antoine Acke
Comments: 37 pages.

The theory of gravitoelectromagnetism (G.E.M.) - that assumes a perfect isomorphism between electromagnetism and gravitation - has been established by Oliver Heaviside (1) and Oleg Jefimenko (2). Within the framework of general relativity, G.E.M. has been discussed by a number of authors (3). It is shown that the gravitational analogs to Maxwell's equations (the G.E.M. equations) can be derived from the Einstein field equation. In this paper we propose an alternative theoretical foundation of G.E.M.: we explain the gravitational interactions, we identify the physical quantities that play a role in that context, and we mathematically derive the laws of gravitoelectromagnetism .

Is Dowsing a Useful Tool for Serious Scientific Research?

Authors: Jeffrey S. Keen
Comments: 22 pages, 10 Figures, 3 Tables.

It is well known that the act of observation can appear to affect the results of certain scientific experiments. However, some research techniques into the causes of this phenomenon have been branded as non-scientific due to the mind producing personal, un-metered, and seemingly inconsistent results. This research into the reasons for this variability has produced two important conclusions. First, a powerful technique for studying the mind has been established, in which confidence exists because measurements using this technique have led to universal constants. Subsequent use of this technique in further research has shown that the mind and the perception of an observer may be significantly affected by the local and non-local environment, and is dependant on the time of the day, month, or year on which those measurements are made. This research has led towards a greater understanding of the structure of the universe and its connection to consciousness and information. It has also demonstrated that it is possible to communicate information faster than the speed of light.

Wave, Formal-Mathematical and Corpuscular Description of the World

Authors: Vladislav Konovalov
Comments: 2 pages.

The contents of the article is mirrored in its title.

The Geometry of CP₂ and Its Relationship to Standard Model

Authors: Matti Pitkänen
Comments: 13 Pages.

This appendix contains basic facts about CP₂ as a symmetric space and Kähler manifold. The coding of the standard model symmetries to the geometry of CP₂, the physical interpretation of the induced spinor connection in terms of electro-weak gauge potentials, and basic facts about induced gauge fields are discussed

Could the Dynamics of Kähler Action Predict the Hierarchy of Planck Constants?

Authors: Matti Pitkänen
Comments: 5 Pages.

The original justification for the hierarchy of Planck constants came from the indications that Planck constant could have large values in both astrophysical systems involving dark matter and also in biology. The realization of the hierarchy in terms of the singular coverings and possibly also factor spaces of CD and CP₂ emerged from consistency conditions. It however seems that TGD actually predicts this hierarchy of covering spaces. The extreme non-linearity of the field equations defined by Kähler action means that the correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates is 1-to-many. This leads naturally to the introduction of the covering space of CD x CP₂, where CD denotes causal diamond defined as intersection of future and past directed light-cones.

Weak Form of Electric-Magnetic Duality, Electroweak Massivation, and Color Confinement

Authors: Matti Pitkänen
Comments: 13 Pages.

The notion of electric magnetic duality emerged already two decades ago in the attempts to formulate the Kähler geometry of the "world of classical worlds". Quite recently a considerable step of progress took place in the understanding of this notion. This concept leads to the identification of the physical particles as string like objects defined by magnetic charged wormhole throats connected by magnetic ux tubes. The second end of the string contains particle having electroweak isospin neutralizing that of elementary fermion and the size scale of the string is electro-weak scale would be in question. Hence the screening of electro-weak force takes place via weak confinement. This picture generalizes to magnetic color confinement. Electric-magnetic duality leads also to a detailed understanding of how TGD reduces to almost topological quantum field theory. A surprising outcome is the necessity to replace CP₂ Kähler form in Kähler action with its sum with S² Kähler form.

How to Define Generalized Feynman Diagrams?

Authors: Matti Pitkänen
Comments: 16 Pages.

Generalized Feynman diagrams have become the central notion of quantum TGD and one might even say that space-time surfaces can be identified as generalized Feynman diagrams. The challenge is to assign a precise mathematical content for this notion, show their mathematical existence, and develop a machinery for calculating them. Zero energy ontology has led to a dramatic progress in the understanding of generalized Feynman diagrams at the level of fermionic degrees of freedom. In particular, manifest finiteness in these degrees of freedom follows trivially from the basic identifications as does also unitarity and non-trivial coupling constant evolution. There are however several formidable looking challenges left.

1. One should perform the functional integral over WCW degrees of freedom for fixed values of on mass shell momenta appearing in the internal lines. After this one must perform integral or summation over loop momenta.
2. One must define the functional integral also in the p-adic context. p-Adic Fourier analysis relying on algebraic continuation raises hopes in this respect. p-Adicity suggests strongly that the loop momenta are discretized and ZEO predicts this kind of discretization naturally.

Physics as Generalized Number Theory: Infinite Primes

Authors: Matti Pitkänen
Comments: 37 Pages.

Physics as a generalized number theory program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields, and infinite primes discussed in this article. The construction of infinite primes is formally analogous to a repeated second quantization of an arithmetic quantum field theory by taking the many particle states of previous level elementary particles at the new level. Besides free many particle states also the analogs of bound states appear. In the representation in terms of polynomials the free states correspond to products of first order polynomials with rational zeros. Bound states correspond to nth order polynomials with non-rational but algebraic zeros. The construction can be generalized to classical number fields and their complexifications obtained by adding a commuting imaginary unit. Special class corresponds to hyper-octonionic primes for which the imaginary part of ordinary octonion is multiplied by the commuting imaginary unit so that one obtains a sub-space M⁸ with Minkowski signature of metric. Also in this case the basic construction reduces to that for rational or complex rational primes and more complex primes are obtained by acting using elements of the octonionic automorphism group which preserve the complex octonionic integer property. Can one map infinite primes/integers/rationals to quantum states? Do they have space-time surfaces as correlates? Quantum classical correspondence realized in terms of modified Dirac operator implies that if infinite rationals can be mapped to quantum states then the mapping of quantum states to space-time surfaces automatically gives the map to space-time surfaces. The question is therefore whether the mapping to quantum states defined by WCW spinor fields is possible. A natural hypothesis is that number theoretic fermions can be mapped to real fermions and number theoretic bosons to WCW ("world of classical worlds") Hamiltonians. The crucial observation is that one can construct infinite hierarchy of hyper-octonionic units by forming ratios of infinite integers such that their ratio equals to one in real sense: the integers have interpretation as positive and negative energy parts of zero energy states. One can construct also sums of these units with complex coefficients using commuting imaginary unit and these sums can be normalized to unity and have interpretation as states in Hilbert space. These units can be assumed to possess well defined standard model quantum numbers. It is possible to map the quantum number combinations of WCW spinor fields to these states. Hence the points of M⁸ can be said to have infinitely complex number theoretic anatomy so that quantum states of the universe can be mapped to this anatomy. One could talk about algebraic holography or number theoretic Brahman=Atman identity. One can also ask how infinite primes relate to the p-adicization program and to the hierarchy of Planck constants. The key observation is that infinite primes are in one-one correspondence with rational numbers at the lower level of hierarchy. At the first level of hierarchy the p-adic norm with respect to p-adic prime for this rational gives power p^-n so that one has two powers of p - pⁿ⁺ and p^n- since two infinite primes corresponding to fermionic vacua X±1, where X is the product of all primes at given level of hierarchy, characterize the partonic 2-surface. The proposal inspired by the p-adicization program is that Δφ = 2π/pⁿ defines angle measurement resolution crucial in the construction of p-adic variants of WCW ("world of classical world") as a union of symmetric coset spaces by starting from discrete variants of the real counterpart of symmetric space having common points with tis p-adic variant. The two measurement resolutions correspond to CD and CP₂ degrees of freedom. The hierarchy of Planck constants generalizes imbedding space to a book like structure with pages identified in terms of singular coverings and factor spaces of CD and CP₂. There are good arguments suggesting that only coverings characterized by integers n_a and n_bare realized. The identifications na = n₊ and nb = n- lead to highly non-trivial physical predictions and allow sharpen the view about the hierarchy of Planck constants. Therefore the notion of finite measurement resolution becomes the common denominator for the three threads of the number theoretic vision and give also a connection with the physics as infinite-dimensional geometry program and with the inclusions of hyper-finite factors defined by WCW spinor fields and proposed to characterize finite measurement resolution at quantum level.

Physics as Generalized Number Theory: Classical Number Fields

Authors: Matti Pitkänen
Comments: 28 Pages.

Physics as a generalized number theory program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields discussed in this article, and infinite primes whose construction is formally analogous to a repeated second quantization of an arithmetic quantum field theory. In this article the connection between standard model symmetries and classical number fields is discussed. The basis vision is that the geometry of the infinite-dimensional WCW ("world of classical worlds") is unique from its mere existence. This leads to its identification as union of symmetric spaces whose Kähler geometries are fixed by generalized conformal symmetries. This fixes space-time dimension and the decomposition M⁴ x S and the idea is that the symmetries of the Kähler manifold S make it somehow unique. The motivating observations are that the dimensions of classical number fields are the dimensions of partonic 2-surfaces, space-time surfaces, and imbedding space and M⁸ can be identified as hyper-octonions- a sub-space of complexified octonions obtained by adding a commuting imaginary unit. This stimulates some questions. Could one understand S = CP₂ number theoretically in the sense that M⁸ and H = M⁴ x CP₂ be in some deep sense equivalent ("number theoretical compactification" or M⁸ - H duality)? Could associativity define the fundamental dynamical principle so that space-time surfaces could be regarded as associative or co-associative (defined properly) sub-manifolds of M⁸ or equivalently of H. One can indeed define the associativite (co-associative) 4-surfaces using octonionic representation of gamma matrices of 8-D spaces as surfaces for which the modified gamma matrices span an associate (co-associative) sub-space at each point of space-time surface. Also M⁸ - H duality holds true if one assumes that this associative sub-space at each point contains preferred plane of M⁸ identifiable as a preferred commutative or co-commutative plane (this condition generalizes to an integral distribution of commutative planes in M⁸). These planes are parametrized by CP₂ and this leads to M⁸ - H duality. WCW itself can be identified as the space of 4-D local sub-algebras of the local Clifford algebra of M⁸ or H which are associative or co-associative. An open conjecture is that this characterization of the space-time surfaces is equivalent with the preferred extremal property of Kähler action with preferred extremal identified as a critical extremal allowing infinite-dimensional algebra of vanishing second variations.

Physics as Generalized Number Theory: P-Adic Physics and Number Theoretic Universality

Authors: Matti Pitkänen
Comments: 51 Pages.

Physics as a generalized number theory program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields (in particular, identifying associativity condition as the basic dynamical principle), and infinite primes whose construction is formally analogous to a repeated second quantization of an arithmetic quantum field theory. In this article p-adic physics and the technical problems relates to the fusion of p-adic physics and real physics to a larger structure are discussed. The basic technical problems relate to the notion of definite integral both at space-time level, imbedding space level and the level of WCW (the "world of classical worlds"). The expressibility of WCW as a union of symmetric spacesleads to a proposal that harmonic analysis of symmetric spaces can be used to define various integrals as sums over Fourier components. This leads to the proposal the p-adic variant of symmetric space is obtained by a algebraic continuation through a common intersection of these spaces, which basically reduces to an algebraic variant of coset space involving algebraic extension of rationals by roots of unity. This brings in the notion of angle measurement resolution coming as Δφ = 2π/pⁿ for given p-adic prime p. Also a proposal how one can complete the discrete version of symmetric space to a continuous p-adic versions emerges and means that each point is effectively replaced with the p-adic variant of the symmetric space identifiable as a p-adic counterpart of the real discretization volume so that a fractal p-adic variant of symmetric space results. If the Kähler geometry of WCW is expressible in terms of rational or algebraic functions, it can in principle be continued the p-adic context. One can however consider the possibility that that the integrals over partonic 2-surfaces defining ux Hamiltonians exist p-adically as Riemann sums. This requires that the geometries of the partonic 2-surfaces effectively reduce to finite sub-manifold geometries in the discretized version of δM₊⁴. If Kähler action is required to exist p-adically same kind of condition applies to the space-time surfaces themselves. These strong conditions might make sense in the intersection of the real and p-adic worlds assumed to characterized living matter.

Construction of Configuration Space Spinor Structure

Authors: Matti Pitkänen
Comments: 34 Pages.

There are three separate approaches to the challenge of constructing WCW Kähler geometry and spinor structure. The first approach relies on a direct guess of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry needed to guarantee the mathematical existence of Riemann connection. The third approach discussed in this article relies on the construction of spinor structure based on the hypothesis that complexified WCW gamma matrices are representable as linear combinations of fermionic oscillator operator for the second quantized free spinor fields at space-time surface and on the geometrization of super-conformal symmetries in terms of spinor structure. This implies a geometrization of fermionic statistics. The basic philosophy is that at fundamental level the construction of WCW geometry reduces to the second quantization of the induced spinor fields using Dirac action. This assumption is parallel with the bosonic emergence stating that all gauge bosons are pairs of fermion and antifermion at opposite throats of wormhole contact. Vacuum function is identified as Dirac determinant and the conjecture is that it reduces to the exponent of Kähler function. In order to achieve internal consistency induced gamma matrices appearing in Dirac operator must be replaced by the modified gamma matrices defined uniquely by Kähler action and one must also assume that extremals of Kähler action are in question so that the classical space-time dynamics reduces to a consistency condition. This implies also super-symmetries and the fermionic oscillator algebra at partonic 2-surfaces has intepretation as N = 1 generalization of space-time supersymmetry algebra different however from standard SUSY algebra in that Majorana spinors are not needed. This algebra serves as a building brick of various super-conformal algebras involved. The requirement that there exist deformations giving rise to conserved Noether charges requires that the preferred extremals are critical in the sense that the second variation of the Kähler action vanishes for these deformations. Thus Bohr orbit property could correspond to criticality or at least involve it. Quantum classical correspondence demands that quantum numbers are coded to the properties of the preferred extremals given by the Dirac determinant and this requires a linear coupling to the conserved quantum charges in Cartan algebra. Effective 2-dimensionality allows a measurement interaction term only in 3-D Chern-Simons Dirac action assignable to the wormhole throats and the ends of the space-time surfaces at the boundaries of CD. This allows also to have physical propagators reducing to Dirac propagator not possible without the measurement interaction term. An essential point is that the measurement interaction corresponds formally to a gauge transformation for the induced Kähler gauge potential. If one accepts the weak form of electric-magnetic duality Kähler function reduces to a generalized Chern-Simons term and the effect of measurement interaction term to Kähler function reduces effectively to the same gauge transformation. The basic vision is that WCW gamma matrices are expressible as super-symplectic charges at the boundaries of CD. The basic building brick of WCW is the product of infinite-D symmetric spaces assignable to the ends of the propagator line of the generalized Feynman diagram. WCW Kähler metric has in this case "kinetic" parts associated with the ends and "interaction" part between the ends. General expressions for the super-counterparts of WCW ux Hamiltoniansand for the matrix elements of WCW metric in terms of their anticommutators are proposed on basis of this picture.

Construction of Configuration Space Geometry from Symmetry Principles

Authors: Matti Pitkänen
Comments: 26 Pages.

There are three separate approaches to the challenge of constructing WCW Kähler geometry and spinor structure. The first one relies on a direct guess of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry needed to guarantee the mathematical existence of Riemann connection. The third approach relies on the construction of spinor structure assuming that complexified WCW gamma matrices are representable as linear combinations of fermionic oscillator operator for the second quantized free spinor fields at space-time surface and on the geometrization of super-conformal symmetries in terms of spinor structure. In this article the construction of Kähler form and metric based on symmetries is discussed. The basic vision is that WCW can be regarded as the space of generalized Feynman diagrams with lines thickned to light-like 3-surfaces and vertices identified as partonic 2-surfaces. In zero energy ontology the strong form of General Coordinate Invariance (GCI) implies effective 2-dimensionality and the basic objects are pairs partonic 2-surfaces X² at opposite light-like boundaries of causal diamonds (CDs). The hypothesis is that WCW can be regarded as a union of infinite-dimensional symmetric spaces G/H labeled by zero modes having an interpretation as classical, non-quantum uctuating variables. A crucial role is played by the metric 2-dimensionality of the light-cone boundary δM₊⁴ + and of light-like 3-surfaces implying a generalization of conformal invariance. The group G acting as isometries of WCW is tentatively identified as the symplectic group of δM₊⁴ x CP₂ localized with respect to X². H is identified as Kac-Moody type group associated with isometries of H = M₊⁴ x CP₂ acting on light-like 3-surfaces and thus on X². An explicit construction for the Hamiltonians of WCW isometry algebra as so called ux Hamiltonians is proposed and also the elements of Kähler form can be constructed in terms of these. Explicit expressions for WCW ux Hamiltonians as functionals of complex coordinates of the Cartesisian product of the infinite-dimensional symmetric spaces having as points the partonic 2-surfaces defining the ends of the the light 3-surface (line of generalized Feynman diagram) are proposed.

Identification of the Configuration Space Kähler Function

Authors: Matti Pitkänen
Comments: 38 Pages.

There are two basic approaches to quantum TGD. The first approach, which is discussed in this article, is a generalization of Einstein's geometrization program of physics to an infinitedimensional context. Second approach is based on the identification of physics as a generalized number theory. The first approach relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of classical worlds" (WCW) identified as the space of 3-surfaces in in certain 8-dimensional space. There are three separate approaches to the challenge of constructing WCW Kähler geometry and spinor structure. The first approach relies on direct guess of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry needed to guarantee the mathematical existence of Riemann connection. The third approach relies on the construction of spinor structure based on the hypothesis that complexified WCW gamma matrices are representable as linear combinations of fermionic oscillator operator for second quantized free spinor fields at space-time surface and on the geometrization of super-conformal symmetries in terms of WCW spinor structure. In this article the proposal for Kähler function based on the requirement of 4-dimensional General Coordinate Invariance implying that its definition must assign to a given 3-surface a unique space-time surface. Quantum classical correspondence requires that this surface is a preferred extremal of some some general coordinate invariant action, and so called Kähler action is a unique candidate in this respect. The preferred extremal has intepretation as an analog of Bohr orbit so that classical physics becomes and exact part of WCW geometry and therefore also quantum physics. The basic challenge is the explicit identification of WCW Kähler function K. Two assumptions lead to the identification of K as a sum of Chern-Simons type terms associated with the ends of causal diamond and with the light-like wormhole throats at which the signature of the induced metric changes. The first assumption is the weak form of electric magnetic duality. Second assumption is that the Kähler current for preferred extremals satisfies the condition jK ^ djK = 0 implying that the ow parameter of the ow lines of jK defines a global space-time coordinate. This would mean that the vision about reduction to almost topological QFT would be realized. Second challenge is the understanding of the space-time correlates of quantum criticality. Electric-magnetic duality helps considerably here. The realization that the hierarchy of Planck constant realized in terms of coverings of the imbedding space follows from basic quantum TGD leads to a further understanding. The extreme non-linearity of canonical momentum densities as functions of time derivatives of the imbedding space coordinates implies that the correspondence between these two variables is not 1-1 so that it is natural to introduce coverings of CD x CP₂. This leads also to a precise geometric characterization of the criticality of the preferred extremals.

Physics as Infinite-Dimensional Geometry and Generalized Number Theory: Basic Visions

Authors: Matti Pitkänen
Comments: 32 Pages.

There are two basic approaches to the construction of quantum TGD. The first approach relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of classical worlds" identified as the space of 3-surfaces in in certain 8-dimensional space. Essentially a generalization of the Einstein's geometrization of physics program is in question. The second vision is the identification of physics as a generalized number theory. This program involves three threads: various p-adic physics and their fusion together with real number based physics to a larger structure, the attempt to understand basic physics in terms of classical number fields (in particular, identifying associativity condition as the basic dynamical principle), and infinite primes whose construction is formally analogous to a repeated second quantization of an arithmetic quantum field theory. In this article brief summaries of physics as infinite-dimensional geometry and generalized number theory are given to be followed by more detailed articles.

The Final Prophesies of Jesus Christ and the Announcement of the End of Days

Authors: Jeremey Razelle
Comments: 5 Pages.

From the dawn of time (nearly 10,000 years ago) The One and Only Lord Jesus Christ has been authoritating a sequence of events directed at the culmination of the fulfillment of human prophesy namely, the final battle for the souls of all humans kind. Much has been written1 already on the End of Days as it is pertinent to the humans kind, and recent events points to the fulfillment of these events in our own time. This paper contains the declaration of End Times and Final Prophesize of Jesus Christ as dictated to his humble and faithful servents who He loves and wants to see saved from the Final Temptation of Science. There is great evil in the current organizations of NSF, DOE, and CERN as they prepare to wage The War of End Times. They refuse to hear the words of God and speak only to the false sciences of their Godless forefathers. As such they will bring about the end of days for their Science Pride. These are the very words of The Lord and Savior Jesus Christ and are to be heeded as the most important of all the words.

A Promise We Make to the Dead: a Comment on Arxiv:1006.2312

Authors: Ron Bourgoin
Comments: 3 Pages.

The authors of Arxiv:1006.2312 study the effect of mentors on their protégés. The study is quantitative, resting its conclusions on measurable outcomes, such as professorships, publications, etc. But what about the mentor who is a paradigm shifter? The paradigm shifter maybe has one protégé, if that. The paradigm shifter does not get published in the mainstream publications, nor does his or her protégé. But the paradigm shifter and his or her protégé cause revolutions, which are what determine directions and the future course of physics. How do we find those mentors and their protégés? Shouldn't that relationship be one we foster and encourage rather than stifle?

Nonlinear Theory of Elementary Particles 2. the Photon Theory

Authors: A.G. Kyriakos
Comments: 11 Pages.

In the proposed article the photon theory is examined from the point of view of the nonlinear theory of elementary particles ( http://vixra.org/abs/1005.0019 ).

Warp Drive Basic Science Written for "Aficionados". Chapter II Jose Natario.

Authors: Fernando Loup
Comments: 22 Pages. This work develops the Natario Warp Drive from ther arXiv paper gr-qc/0110086.

Natario Warp Drive is one of the most exciting Spacetimes of General Relativity.It was the second Spacetime Metric able to develop Superluminal Velocities.However in the literature about Warp Drives the Natario Spacetime is only marginally quoted.Almost all the available literature covers the Alcubierre Warp Drive. It is our intention to present here the fully developed Natario Warp Drive Spacetime and its very interesting features.Our presentation is given in a more accessible mathematical formalism following the style of the current Warp Drive literature destined to graduate students of physics since the original Natario Warp Drive paper of 2001 was presented in a sophisticated mathematical formalism not accessible to average students. Like the Alcubierre Warp Drive Spaceime that requires a continuous function f(rs) in order to be completely analyzed or described we introduce here the Natario Shape Function n(r) that allows ourselves to study the amazing physical features of the Natario Warp Drive. The non-existence of a continuous Shape Function for the Natario Warp Drive in the original 2001 work was the reason why Natario Warp Drive was not covered by the standard literature in the same degree of coverage dedicated to the Alcubierre Warp Drive. We hope to change the situation because the Natario Warp Drive looks very promising.

Inquiry as to if Higher Dimensions Can be Used to Unify DM and DE, if Massive Gravitons Are Stable.

Authors: Andrew Beckwith
Comments: 5 pages, one figure. Initial work for possible submission to the DSU 2010 conference proceedings. Contains answer to question asked by Dr. Debasish Majumdar of the Saha institute, India, as to massive graviton stability which the author tried to answer.

The following questions are raised in this document. First, can there be a stable (massive) graviton? If so, does this massive graviton, as modeled by KK DM, with a modification of slight 4 dimensional space mass, contribute to DE, at least in terms of re acceleration ? The answer, if one assumes that the square of a frequency for graviton mass is real valued and greater than zero appears to be affirmative. The author, when considering a joint DM - DE model finds evidence that re acceleration of the universe one billion years ago in a higher dimensional setting can be justified in terms of a slight modification of standard KK DM models, if one considers how an information exchange between present to prior universes occurs, which the author thinks mandates more than four dimensional space time geometry.

Photon Field and Infinity

Authors: John L. O'Sullivan
Comments: 6 pages

Existences have tangible dimensions and intangible dimensions. The tangible dimensions have finite energy responsible for mass and universal space-time and the intangible dimensions have infinite energy without beginning or end. This report will show the relation between mass and infinity where the speed of light is common to both giving an understanding of time and matter in the electromagnetic wave field.

What Can be Said About ( Massive) Graviton Stability? & is there DM Generated DE ?

Authors: Andrew Beckwith
Comments: 39 pages, talk for Rudn 10, Moscow, June 30, 2010. 3 figures. Divided into two themes . 1st :Criteria for Massive graviton stability, and 2nd : Applications of a massive graviton, if stable, to a modification of KK DM to possibly insure DE re acceleration 1 billion years ago

Delineating conditions for the existence of a stable (massive) graviton mass, and its possible role in mimicking DE one billion years ago in the re acceleration of the universe

A Theorem About Simultaneous Orthological and Homological Triangles

Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 13 pages.

In this paper we prove that if P₁,P₂ are isogonal points in the triangle ABC , and if A₁B₁C₁ and A₂B₂C₂ are their ponder triangle such that the triangles ABC and A₁B₁C₁ are homological (the lines AA₁ , BB₁ , CC₁ are concurrent), then the triangles ABC and A₂B₂C₂ are also homological.

Hipotese de Smarandache: Evidencias, Implicacoes E Aplicacoes

Authors: Leonardo F. D. da Motta
Comments: 5 pages, Paper in Portugues.

Paper about the Smarandache Hypothesis that there is no speed barrier in the universe and one can construct any speed.

Can a Massive Graviton be a Stable Particle ?

Authors: Andrew Beckwith
Comments: 6 pages, no figures. Relies upon determining if a frequency, for a graviton is, when squared positive definite, and real valued. The idea may be part of a Rudn 10 presentation June 30, in Moscow, along with a brief introduction to the author's ideas about a joint DM-DE model, heavily dependent upon this concept of stable gravitons with very small mass. If not used in Rudn 10, it will be part of a poster in Rencontres De Blois, in July 15-20, 2010

This document is due to a question asked in the Dark Side of the Universe conference, 2010, in Leon, Mexico, when a researcher from India asked the author about how to obtain a stability analysis of massive gravitons. The answer to this question involves an extension of the usual Pauli_Fiertz Langrangian, with non zero graviton mass contributing to a relationship between the trace of a re done GR stress-energy tensor ( assuming non zero graviton mass) , and the trace of a re done symmetric tensor, times a tiny mass for a 4 dimensional graviton. The resulting analysis makes use of Visser's treatment of a stress energy tensor, with experimental applications discussed in the resulting analysis. If the square of frequency of a massive graviton is real valued and greater than zero, stability can be possibly confirmed experimentally.

Planetary Orbits (According to "Hypothesis on MATTER")

Authors: Nainan K. Varghese
Comments: 28 pages, Originally published in General Science Journal

In any system of bodies, relativistic considerations can provide only those parameters of the constituent bodies, which are related to their relative positions. Use of a reference frame, related to a static central body, causes a planetary orbit to appear as closed geometrical figure around the central body. As the central body, itself is a moving body, this does not reflect physical reality. Although they help to explain apparent phenomena, all properties attributed to elliptical/circular planetary orbital path are unreal. Real physical actions are restricted to real entities and they have to be understood with reference to an absolute reference. Since, elliptical shape of a planetary orbit is an imaginary aspect; it has its limitations to explain real actions in nature. Due to constant motions of free bodies in space, it is practically impossible for a free body to orbit around another. However, they may orbit about each other and follow a common median path in space. Mechanism of orbit-formation and the limitations of orbiting bodies, described in this article, are based on a radically different dynamics from an alternative concept put forward in 'Hypothesis on MATTER'. A planet's parameters, during initial entry into its datum orbit, determine size and eccentricity of its apparent orbit. Only those bodies, which approach the central body from the rear, on the outer side of its curved path, through a small window in space can form stable orbits. Hence, it is imperative that all bodies of a planetary system orbit in the same sense and are (almost) in the same plane. Perihelion/aphelion of an orbital path could be anywhere in the orbit, but the point at which the orbiting body has its highest/lowest linear speeds are fixed in relation to the central body's path. All natural planets, whose perihelion are in front of their point of entry; arrive from outside the planetary system.

The New Prime Theorem (141)-(190)

Authors: Chun-Xuan Jiang
Comments: 60 pages

Using Jiang function we prove that the new prime theorems (141)-(190) contain infinitely many prime solutions and no prime solutions.

Probabilistic Interpretation of Quantum Mechanics with Schrödinger Quantization Rule

Authors: Saurav Dwivedi
Comments: 4 pages, To be published in "Physics Essays"

We quantize the probabilistic interpretation of quantum mechanics using Schrödinger quantization rule. We describe the probability of getting a quantum object in configuration space as the eigenvalue (image) of quantum mechanical probability (operator) satisfying Schrödinger probability eigenvalue equation. The deduction is used to obtain quantum description of systems which would be used to quantize many classical and quantum (differential) problems.

The Primary Gas and the Postulates of Quantum Mechanics-Vii

Authors: V.A.Induchoodan Menon
Comments: 11 pages

The author shows that that for each quantum mechanical property of a micro-system there is a corresponding thermodynamic one in the primary gas. He further shows that the basic postulates of quantum mechanics have equivalents in the primary gas approach based on statistical mechanics provided time is accorded directional symmetry. He shows that the interference pattern obtained in Young's double slit experiment could be explained in terms of the primary gas approach using the directional symmetry of time.

A Very Special Case, a Brief Comment About the Michelson / Morley Experiment

Authors: Roald C. Maximo
Comments: 2 pages

Very often, in the history of science, amazingly simple phenomena, when initially misunderstood, may become laden with prejudice and somewhat mystical connotations and, since then, are passed on from generation to generation for no better reason then magister dixit. One example already discussed here [1] has been stellar aberration. But there is nevertheless a very special case where in trying to explain the null result of the Michelson and Morley experiment scientists, just to keep up to their prejudices, chose the weirdest explanations; instrument length contraction or ether drag !

Five Properties of the Smarandache Double Factorial Function

Authors: Felice Russo
Comments: 3 pages

In this paper some properties of the Smarandache double factorial function have been analyzed.

An Economics Model for the Smarandache Anti-Geometry

Authors: Roberto Torretti
Comments: 3 pages

The Smarandache anti-geometry is a non-euclidean geometry that denies all Hilbert's twenty axioms, each axiom being denied in many ways in the same space. In this paper one finds an economics model to this geometry by making the following correlations: (i) A point is the balance in a particular checking account, expressed in U.S. currency. (Points are denoted by capital letters). (ii) A line is a person, who can be a human being. (Lines are denoted by lower case italics). (iii) A plane is a U.S. bank, affiliated to the FDIC. (Planes are denoted by lower case boldface letters).

About Very Perfect Numbers

Authors: Mihály Bencze, Florin Popovici, Florentin Smarandache
Comments: 3 pages

In this short paper we prove that the square of an odd prime number cannot be a very perfect number.

Smarandache Idempotents in Loop Rings Z_tL_n(m) of the Loops L_n(m):

Authors: W.B.Vasantha, Moon K. Chetry
Comments: 9 pages

In this paper we establish the existance of S-idempotents in case of loop rings Z_tL_n(m) for a special class of loops L_n(m); over the ring of modulo integers Z_t for a specific value of t. These loops satisfy the conditions g_i² = 1 for every g_i ε L_n(m). We prove Z_tL_n(m) has an S-idempotent when t is a perfect number or when t is of the form 2ⁱp or 3ⁱp (where p is an odd prime) or in general when t = p₁ⁱp₂ (p₁ and p₂ are distinct odd primes). It is important to note that we are able to prove only the existance of a single S-idempotent; however we leave it as an open problem wheather such loop rings have more than one S-idempotent. This paper has three sections. In section one, we give the basic notions about the loops L_n(m) and recall the definition of S-idempotents in rings. In section two, we establish the existance of S-idempotents in the loop ring Z_tL_n(m). In the final section, we suggest some interesting problems based on our study.

No-Time-Dilation Corrected Supernovae 1a and GRBs Data and Low-Energy Quantum Gravity

Authors: Michael A. Ivanov
Comments: 5 pages, 2 figures, Latex. Poster contribution to the VI Int. Workshop on the Dark side of the Universe (DSU2010), Guanajuato U., Leon, Mexico, 1-6 June, 2010.

Earlier it was shown that in the model of low-energy quantum gravity by the author, observations of Supernovae 1a and GRBs, which are corrected by observers for characteristic for the standard cosmological model time dilation, may be fitted with the theoretical luminosity distance curve only up to z ~ 0:5; for higher redshifts the predicted luminosity distance is essentially bigger. The model itself has not time dilation due to another redshift mechanism. It is shown here that a correction of observations for no time dilation leads to a good accordance of observations and theoretical predictions for all achieved redshifts.

Hypothesis on Matter

Authors: Nainan K. Varghese
Comments: 14 pages

'Hypothesis on MATTER' is a revolutionary new concept, which explains all physical phenomena based on just one type of (postulated) basic particle - the Quantum of matter. Conception and development of this model is founded on the conviction that there can be only one type of basic entities. They provide substance and create all other real entities in nature. All (apparent) interactions and diverse properties of superior entities are logical developments from inherent properties of the (postulated) quanta of matter. Quanta of matter, by their natural interactions, creates and structure all other entities including an allencompassing medium. A wide array of physical phenomena are explained in the book [1]; from the origin of 3D matter to gravity and subatomic interactions to cosmological events, based on the simple mechanical interactions of quanta of matter. There is no more any need to envisage 'actions at a distance' or to invoke irrational assumptions like diversity of natural forces, mass-energy equivalence, duality of light or constancy of its speed, dual nature of electric charge, singularities, big bang, etc. This new concept will radically alter our understanding of the physical universe and at the same time, explain complex physical phenomena with simple 'Cause and Effect' relationships.

Perspectives About Density of Universal Cosmic Mass, Density of Space and the a-Temporal Gravitation

Authors: Davide Fiscaletti
Comments: 12 pages

Clocks are measuring systems for the numerical order, speed and frequency of material changes that run into space. Time does not run into space on its own, time exists only as numerical order, speed and frequency of material change. Stellar objects and particles move into space only and not into time. Gravitational interaction between material objects is the result of curvature of space that is determined by the granular structure of space. Density of the elementary grains of space depends on density of universal cosmic mass, higher is the density of universal cosmic mass lower is the density of grains of empty space. Density of empty space is the physical basis of its curvature. Material objects have a tendency to move into direction of lower density and higher curvature of space. Gravitational interaction mass-space-mass is immediate: the presence of a mass causes change of density of space, change of density of space causes gravitational motion. A mass acts on another mass indirectly via the change of density of empty space. Gravitational interaction between two masses is immediate: no time, namely no duration of motion of a particle or wave in space is needed to transmit gravitational interaction from one to another material object.

Numerical Order of Physical Events Has no Duration

Authors: Davide Fiscaletti, Amrit Sorli
Comments: 8 pages

With clocks we measure numerical order t0,t1,t2,...,tn of a physical event. A sequence t_n-1 is "before" a sequence t_n equivalently to natural number n-1 is before natural number n. Numerical order t0,t1,t2,...,tn of a physical event has no duration. It runs in a timeless space where physical time is run of clocks. Duration of an event is a result of experiencing its measurement with a clock through the frame of psychological time "past-present-future" but events happen exclusively in space.

About Immediate Physical Phenomena and Space as a Direct Medium of Information

Authors: Davide Fiscaletti
Comments: 11 pages

For several physical phenomena elapsed clock run t for them to happen is zero. These events can be appropriately defined as "immediate physical phenomena" and support the view that, at a fundamental level, time exists only as a run of clocks in a timeless space. Immediate physical phenomena are carried directly by space which functions as a direct information medium. The perspective is opened that the quanta of space that build quantum space assume a crucial role as regards these phenomena.

Surmounting the Cartesian Cut: Torsion Fields, the Extended Photon, Quantum Jumps, the Klein Bottle, Multivalued Logic, the Time Operator Chronomes, Perception, Semiotics, Neurology and Cognition

Authors: Diego L. Rapoport
Comments: 79 pages

We present a conception that surmounts the Cartesian Cut -prevailing in science-based on a representation of the fusion of the physical 'objective' and the 'subjective' realms. We introduce a mathematical-physics and philosophical theory for the physical realm and its mapping to the cognitive and perceptual realms and a philosophical reflection on the bearings of this fusion in cosmology, cognitive sciences, human and natural systems and its relations with a time operator and the existence of time cycles in Nature's and human systems. This conception surges from the self-referential construction of spacetime through torsion fields and its singularities; in particular the photon's self-referential character, basic to the embodiment of cognition ; we shall elaborate this in detail in perception and neurology.

It's my Lap to Run, But I am not the Best

Authors: Ron Bourgoin
Comments: 2 pages

There comes a time in life when it's our turn to run the lap. We are handed the baton in life's 4 x 100 meter relay. Perhaps there are others who would do a better job, but they didn't show up for the race.

Spacetime Deformations Theory

Authors: Jacek Safuta
Comments: 9 pages

The spacetime deformations theory unifies general relativity with quantum mechanics i.e. unifies all interactions, answers the questions: why particles have mass and what they are, answers the question: what is energy, unifies force fields and matter, implies new theories like spacetime deformations evolution. This is a theory of principle (universal theory delivering description of nature) and not constructive theory (describing particular phenomenon using specific equations). The theory is falsifiable, background independent (space has no fixed geometry), not generating singularities or boundaries. This is hard to believe but a belief has nothing to with it. The real intellectual challenge is to falsify the theory.

A Class of Orthohomological Triangles

Authors: Claudiu Coandă, Florentin Smarandache, Ion Pătraşcu
Comments: 5 pages

In this article we propose to determine the triangles' class... (see paper for full abstract)

The Hyperbolic Menelaus Theorem in the Poincaré Disc Model of Hyperbolic Geometry

Authors: Florentin Smarandache, Catalin Barbu
Comments: 4 pages

In this note, we present the hyperbolic Menelaus theorem in the Poincaré disc of hyperbolic geometry.

Detector of Aether Operating on Transverse Doppler Effect

Authors: V.V. Demjanov
Comments: 7 pages

Rotating the source of light around the point lying on the light's beam we can observe the transverse Doppler effect by a spectrometer located in the center of rotation. The anomalous shift of the electromagnetic wave's frequency was found from this experiment (performed in 1969-1974 years) that appeared to be much higher than anticipated from the standard relativistic expression taking into account solely the linear velocity of rotation of the source in the laboratory. The interpretation of the experimental observations admitting absolute motion of the Earth and respective accounting for reality of the Lorentz contraction and time dilation enabled us to determine the speed of the Earth relative to luminiferous aether. It appeared to be somewhat above 400 km/s that agrees well with the value formerly found by me using three methods of determining the speed of "aether wind" by Michelson-type interferometers thoroughly accounted for refractive indices of optical media.

The New Prime Theorem (131)-(140)

Authors: Chun-Xuan Jiang
Comments: 14 pages

Using Jiang function we prove that the new prime theorems (131)-(140) contain infinitely many prime solutions and no prime solutions.

Fractal Operators in Non-Equilibrium Field Theory

Authors: Ervin Goldfain
Comments: 19 pages, This contribution represents a sequel to CSF 28, (2006), 913-922.

Relativistic quantum field theory (QFT) describes fundamental interactions between elementary particles occurring in an energy range up to several hundreds GeV. Extending QFT beyond this range needs to account for the imbalance produced by unsuppressed quantum fluctuations and for the emergence of non-equilibrium phase transitions. Our underlying premise is that fractal operators become mandatory tools when exploring evolution from low-energy physics to the non-equilibrium regime of QFT. Canonical quantization using fractal operators leads to the concept of "complexon", a fractional extension of quantum excitations and a likely candidate for non-baryonic Dark Matter. A discussion on the duality between this new field-theoretic framework and General Relativity is included.

M-Theory

Authors: Min-Young Yun
Comments: 55 pages

The behavior of smallest unit that creating from superstring and quark is indeterminate, but can be described as one equation according to macroscopic-rules. So, it is easy to understand in all ages and countries, at any times and places. Newborns speak out the easiest word 'Mom' at the first time they speaking, which Decided the title of the theory.

Smarandache Zero Divisors

Authors: W.B.Vasantha Kandasamy
Comments: 5 pages

In this paper, we study the notion of Smarandache zero divisor in semigroups and rings. We illustrate them with examples and prove some interesting results about them.

A New Equation for the Load Balance Scheduling Based on the Smarandache F-Inferior Part Function

Authors: Tatiana Tabirca, Sabin Tabirca
Comments: 6 pages

This article represents an extension of [Tabirca, 2000a]. A new equation for upper bounds is obtained based on the Smarandache f-inferior part function. An example involving upper diagonal matrices is given in order to illustrate that the new equation provide a better computation.

Faster Than Light?

Authors: Felice Russo
Comments: 3 pages

The hypothesis formulated by Smarandache on the possibility that no barriers exist in the Universe for an object to travel at any speed is here shortly analyzed.

On the Mean Value of the Additive Analogue of Smarandache Function

Authors: Yi Yuan, Zhang Wenpeng
Comments: 3 pages

see paper for abstract

An Introduction to the Smarandache Square Complementary Function

Authors: Felice Russo
Comments: 13 pages

In this paper the main properties of Smarandache Square Complementary function has been analyzed. Several problems still unsolved are reported too.

Some New Results Concerning the Smarandache Ceil Function

Authors: Sabin Tabirca, Tatiana Tabirca
Comments: 7 pages

In this article we present two new results concerning the Smarandache Ceil function. The first result proposes an equation for the number of fixed-point number of the Smarandache ceil function. Based on this result we prove that the average of the Smarandache ceil function is Θ(n) .

Factors and Primes in Two Smarandache Sequences

Authors: Ralf W. Stephan
Comments: 7 pages

Using a personal computer and freely available software, the author factored some members of the Smarandache consecutive sequence and the reverse Smarandache sequence. Nearly complete factorizations are given up to Sm(80) and RSm(80). Both sequences were excessively searched for prime members, with only one prime found up to Sm(840) and RSm(750): RSm(82) = 828180...10987654321.

Smarandache Neutrosophic Algebraic Structures

Authors: W. B. Vasantha Kandasamy
Comments: 203 pages

In this book for the first time we introduce the notion of Smarandache neutrosophic algebraic structures. Smarandache algebraic structures had been introduced in a series of 10 books. The study of Smarandache algebraic structures has caused a shift of paradigm in the study of algebraic structures.

The New Prime Theorem (45)-(70)

Authors: Chun-Xuan Jiang
Comments: 33 pages

Using Jiang function we prove that the new prime theorems (45)-(70) contain infinitely many prime solutions and no prime solutions.

Enery Content of Gravitation as a Way to Quantify Both Entropy and Information Generation in the Early Universe

Authors: Andrew Beckwith
Comments: 8 pages, 1 figure. Represents a concept which may be presented in future conferences once fully developed.

Based upon Alcubierre's formalism about energy flux of gravitational waves, as well as Saunder's treatment of temperature dependence of the Hubble parameter in the early universe , we initiate a particle count treatment of gravitons, and subsequent entropy generation which gives , via the standard model treatment of the FRW metric a way to explain/ justify a value of entropy of the order of S ~ 10⁶ - 10⁷ at the very onset of inflation.

Mathematics is Physics

Authors: Dainis Zeps
Comments: 16 pages

In series of articles we continue to advance idea that mathematics and physics is the same. We bring forward two basic assumptions as principles. First is the primacy of life as opposed to dominating reductionism, and second - immaturity of epistemology. Second principle says that we have reached stage of epistemology where we have stepped outside simple perceptibility only on level of individuality (since Aristotle) but not on level of collective mind. The last stage have reached only most of religious teachings but not physical science that is still under oppressive influence of reductionism. This causes that what we call research in physical science turns out to be simply instrumental improvement of perception within visional confinement we call field of information. We discuss and try to apply principle that within field of information we can't invent or discover anything that doesn't existing.

Learning to Cooperate for Progress in Physics

Authors: Jonathan J. Dickau
Comments: 11 pages. The author plans to present this paper at the 11th Frontiers of Fundamental Physics conference, which is in Paris, France July 6-9, 2010.

At the 10^th Frontiers of Fundamental Physics symposium, Gerard 't Hooft stated that, for some of the advances we hope to see in Physics in the future, there must be a great deal of cooperation between researchers from different disciplines, as well as mathematicians, programmers, technologists, and others. Accomplishing this requires a new mindset; however, as so much of our past progress has come out of a fiercely competitive process - especially since a critical review of our ideas about reality remains an essential part of making progress and checking our progress. We must also address the fact that some frameworks appear incompatible, as with relativity and quantum mechanics, which remain at odds despite years of attempts to find a quantum gravity theory. I explore the idea that playful exploration, using both left-brained and right-brained approaches to learning, allows resolution of conflicting ideas by taking advantage of our innate developmental strategies. It may thus foster the kind of interdisciplinary cooperation we are hoping to see.

Block Universe

Authors: Amrit S. Sorli
Comments: 11 page

According to the formalism d = v*t fourth dimension of space-time X₄ = i*c*t is spatial too. Time is not a fourth dimension of space-time. Material change i.e. motion run in a timeless space. Fundamental unit of numeric order t₀,t₁,t₂,...,t_n of material change is Planck time t_p . We measure numeric order of material change with clocks. Material change t_n-1 is "before" material change t_n equivalently as natural number n-1 is "before" natural number n. Numeric order of material change runs in a timeless 4D space and has no duration. Space-time is a timeless phenomenon.

A Brief and Elementary Note on Redshift

Authors: José Francisco García Juliá
Comments: 5 Pages.

A reasonable explanation of both redshifts: cosmological (without expansion of the universe) and intrinsic, is given using a single tired light mechanism. In the first case, the redshift is produced because the light interacts with microwaves. In the second, the interaction is with radio waves. And all this is compatible with a static universe with a space temperature of 2.7 ^oK.

The Sieve Method of the Number of Solutions of Goldbach Conjecture (A)

Authors: Tong Xin Ping
Comments: 3 Pages, In Chinese

We can find all solutions of Goldbach conjecture (A) ling in the closed interval [pr+1, N-pr-1], and we can obtain expression of the number of solutions of Goldbach conjecture (A).

Mapping Penrose-Rindler Null Tetrads to the Advanced and Retarded Wheeler-Feynman-Aharonov Destiny & History Null Tetrads

Authors: Jack Sarfatti
Comments: 3 pages

This is a short mathematical note clarifying the use of Cramer's Transactional Interpretation in the Spinor Qubit Pre-Geometry of Wheeler's IT FROM BIT.

Quantum Smarandache Paradoxes

Authors: Gheorghe Niculescu
Comments: 2 pages

In this paper one presents four of the smarandacheian paradoxes in physics found in various physics sites or printed material.

Smarandache Hypothesis: Evidences, Implications and Applications

Authors: Leonardo F. D. da Motta
Comments: 5 pages

In 1972, Smarandache proposed that there is not a limit speed on the nature, based on the EPR-Bell (Einstein, Podolsky, Rosen, Bell) paradox. Although it appears that this paradox was solved recently, there are many other evidences that guide us to believe that Smarandache Hypothesis is right on quantum mechanics and even on the new unification theories. If Smarandache Hypothesis turns to be right under any circumstance, some concepts of modern physics would have to be "refit" to agree with Smarandache Hypothesis. Moreover, when the meaning of Smarandache Hypothesis become completely understood, a revolution on technology, specially in communication, will arise.

Seven Conjectures in Geometry and Number Theory

Authors: Florentin Smarandache
Comments: 2 pages

In this short paper we propose four conjectures in synthetic geometry that generalize Erdos-Mordell Theorem, and three conjectures in number theory that generalize Fermat Numbers.

The Relativity of Time. the Time of the Relativity

Authors: Xavier Terri Castañé
Comments: 5 pages

Demonstration without mathematical formulas of the theory of special and general relativity of Einstein is false.

Where Does Universal Expansion Equal Gravitational Attraction?

Authors: Chris O'Loughlin
Comments: 9 pages

A comparison of the attractive motion experienced by masses due to gravitational interaction over relatively short distances with the recessional motion of masses at relatively large distances (that adhere to the velocity increases described by Hubble's v = Hr relation) is presented to demonstrate the similarities between the two motions. Based on the similarities of the two motions, and the observation that gravitational acceleration decreases as distance increases while recessional acceleration decreases as distance decreases the distance at which the two accelerations are equal in magnitude but in opposite directions resulting in zero net acceleration is calculated and compared to similar results provided by Chernin et al. [1]. The summation of the attractive gravitational acceleration and the recessional acceleration is presented and plotted depicting a smooth, continuous transition from gravitational attraction to universal expansion. The underlying cause of these accelerations is not addressed.

The New Prime Theorem (44)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function J₂(ω) we prove that jPⁿ + 9 - j contain infinitely many prime solutions.

The New Prime Theorem (43)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that jP⁸ + k - j contain infinitely many prime solutions.

The New Prime Theorem (42)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that jP⁷ + k - j contain infinitely many prime solutions.

The New Prime Theorem (41)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that jP⁶ + k - j contain infinitely many prime solutions.

The New Prime Theorem (40)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that jP⁵ + k - j contain infinitely many prime solutions.

The New Prime Theorem (39)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that if J₂(ω) ≠ 0 then there are infinitely many primes P such that each of jP⁴ + k - j is a prime, J₂(ω) = 0 then there are finite primes P such that each of jP⁴ + k - j is a prime.

Infinite Smarandache Groupoids

Authors: A.K.S. Chandra Sekhar Rao
Comments: 6 pages

It is proved that there are infinitely many infinite Smarandache Groupoids.

The Evaporation of Common Sense

Authors: Ron Bourgoin
Comments: 3 pages

Common sense left the human mind a hundred years ago. It was forced out by relativity theory. This wildly imaginative work of fiction displaced all the logic humankind had labored so long to establish. People loved it. They were set free of the constraints of disciplined thought. But today we have a problem: relativity and all it has sprouted has taken us down a blind alley.

Multi-Criteria Decision Making Based on DSmT-Ahp

Authors: Jean Dezert, Jean-Marc Tacnet, Mireille Batton-Hubert, Florentin Smarandache
Comments: 6 pages

In this paper, we present an extension of the multicriteria decision making based on the Analytic Hierarchy Process (AHP) which incorporates uncertain knowledge matrices for generating basic belief assignments (bba's). The combination of priority vectors corresponding to bba's related to each (sub)-criterion is performed using the Proportional Conflict Redistribution rule no. 5 proposed in Dezert-Smarandache Theory (DSmT) of plausible and paradoxical reasoning. The method presented here, called DSmT-AHP, is illustrated on very simple examples.

Non Bayesian Conditioning and Deconditioning

Authors: Jean Dezert, Florentin Smarandache
Comments: 6 pages

In this paper, we present a Non-Bayesian conditioning rule for belief revision. This rule is truly Non-Bayesian in the sense that it doesn't satisfy the common adopted principle that when a prior belief is Bayesian, after conditioning by X, Bel(X|X) must be equal to one. Our new conditioning rule for belief revision is based on the proportional conflict redistribution rule of combination developed in DSmT (Dezert-Smarandache Theory) which abandons Bayes' conditioning principle. Such Non-Bayesian conditioning allows to take into account judiciously the level of conflict between the prior belief available and the conditional evidence. We also introduce the deconditioning problem and show that this problem admits a unique solution in the case of Bayesian prior; a solution which is not possible to obtain when classical Shafer and Bayes conditioning rules are used. Several simple examples are also presented to compare the results between this new Non-Bayesian conditioning and the classical one.

An Experimental Evidence of Energy Non-Conservation

Authors: Yu Liang, Qichang Liang, Xiaodong Liu
Comments: 5 pages

According to Maxwell's theory, the displacement current in vacuum can produce electromotive force on conducting current. However, the displacement current in vacuum does not experience electromotive force from conducting current. The asymmetrical electromotive forces result in non-conserved energy transmission between any two coils involving displacement current and conducting current. In this work, we designed and performed the measurements for such effect. We observed the explicit evidences of non-conserved energy transmission between a toroid solenoid and a parallel plate capacitor. The measured energy increase is well predicted by the numerical estimation.

Fusion of Masses Defined on Infinite Countable Frames of Discernment

Authors: Florentin Smarandache, Arnaud Martin
Comments: 5 pages

In this paper we introduce for the first time the fusion of information on infinite discrete frames of discernment and we give general results of the fusion of two such masses using the Dempster's rule and the PCR5 rule for Bayesian and non-Bayesian cases.

Degree of Uncertainty of a Set and of a Mass

Authors: Florentin Smarandache, Arnaud Martin
Comments: 9 pages

In this paper we use extend Harley's measure of uncertainty of a set and of mass to the degree of uncertainty of a set and of a mass (bba).

The Theory of Distributions Applied to Divergent Integrals of the Form (See Paper for Equation)

Authors: Jose Javier Garcia Moreta
Comments: 9 pages

In this paper we review some results on the regularization of divergent integrals of the form ... (see paper for full abstract)

Relating the Physical Structure and Properties of Quantum Space-Time to Elementary Particles, Gravity, and Relativistic Phenomena

Authors: Gary Heen
Comments: 22 pages

Modern theory states that matter and energy in their most basic form exist in discrete amounts, or quanta. The author proffers that space-time also exists as discrete quanta, and derives a physical model of space-time and elementary particles. The hypothesis for this space-time model is that the quanta for matter and space-time are convertible states of the same elementary building block: the quantum mass unit.

Relativistic Gravitational Effects Start Above Photon Scale

Authors: Amrit S. Sorli
Comments: 1 page

Constancy of the light velocity in areas of space with different gravity implies that relativistic gravitational effects start on the scale above photon. At the photon scale and below physical phenomena have no relativistic gravitational effects.

The Basis of Quantum Mechanics' Compatibility with Relativity Whose Impairment Gives Rise to the Klein-Gordon and Dirac Equations

Authors: Steven Kenneth Kauffmann
Comments: 13 pages, Also archived as arXiv:1005.2641 [physics.gen-ph].

Solitary-particle quantum mechanics' inherent compatibility with special relativity is implicit in Schrödinger's postulated wave-function rule for the operator quantization of the particle's canonical threemomentum, taken together with his famed time-dependent wave-function equation that analogously treats the operator quantization of its Hamiltonian. The resulting formally four-vector equation system assures proper relativistic covariance for any solitary-particle Hamiltonian operator which, together with its canonical three-momentum operator, is a Lorentz-covariant four-vector operator. This, of course, is always the case for the quantization of the Hamiltonian of a properly relativistic classical theory, so the strong correspondence principle definitely remains valid in the relativistic domain. Klein-Gordon theory impairs this four-vector equation by iterating and contracting it, thereby injecting extraneous negative-energy solutions that are not orthogonal to their positive-energy counterparts of the same momentum, thus destroying the basis of the quantum probability interpretation. Klein-Gordon theory, which thus depends on the square of the Hamiltonian operator, is as well thereby cut adrift from Heisenberg's equations of motion. Dirac theory confuses the space-time symmetry of the four-vector equation system with such symmetry for its time component alone, which it fatuously imposes, thereby breaching the strong correspondence principle for the free particle and imposing the starkly unphysical momentum-independence of velocity. Physically sensible alternatives, with external electromagnetic fields, to the Klein-Gordon and Dirac equations are derived, and the simple, elegant symmetry-based approach to antiparticles is pointed out.

Product of Distributions and Zeta Regularization of Divergent Integrals ∫ X^m-Sdx and Fourier Transforms

Authors: Jose Javier Garcia Moreta
Comments: 9 pages

Using the theory of distributions and Zeta regularization we manage to give a definition of product for Dirac delta distributions, we show how the fact of one can be define a coherent and finite product of dDirac delta distributions is related to the regularization of divergent integrals ... (see paper for full abstract)

Set Linear Algebra and Set Fuzzy Linear Algebra

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K Ilanthenral
Comments: 345 pages.

In this book, the authors define the new notion of set vector spaces which is the most generalized form of vector spaces. Set vector spaces make use of the least number of algebraic operations, therefore, even a non-mathematician is comfortable working with it. It is with the passage of time, that we can think of set linear algebras as a paradigm shift from linear algebras. Here, the authors have also given the fuzzy parallels of these new classes of set linear algebras. This book abounds with examples to enable the reader to understand these new concepts easily. Laborious theorems and proofs are avoided to make this book approachable for nonmathematicians. The concepts introduced in this book can be easily put to use by coding theorists, cryptologists, computer scientists, and socio-scientists. Another special feature of this book is the final chapter containing 304 problems. The authors have suggested so many problems to make the students and researchers obtain a better grasp of the subject. This book is divided into seven chapters. The first chapter briefly recalls some of the basic concepts in order to make this book self-contained. Chapter two introduces the notion of set vector spaces which is the most generalized concept of vector spaces. Set vector spaces lends itself to define new classes of vector spaces like semigroup vector spaces and group vector 6 spaces. These are also generalization of vector spaces. The fuzzy analogue of these concepts are given in Chapter three. In Chapter four, set vector spaces are generalized to biset bivector spaces and not set vector spaces. This is done taking into account the advanced information technology age in which we live. As mathematicians, we have to realize that our computer-dominated world needs special types of sets and algebraic structures. Set n-vector spaces and their generalizations are carried out in Chapter five. Fuzzy n-set vector spaces are introduced in the sixth chapter. The seventh chapter suggests more than three hundred problems. When a researcher sets forth to solve them, she/he will certainly gain a deeper understanding of these new notions.

Smarandache Semirings and Semifields

Authors: W. B. Vasantha Kandasamy
Comments: 4 pages.

In this paper we study the notion of Smarandache semirings and semifields and obtain some interesting results about them. We show that not every semiring is a Smarandache semiring. We similarly prove that not every semifield is a Smarandache semifield. We give several examples to make the concept lucid. Further, we propose an open problem about the existence of Smarandache semiring S of finite order.

Randomness and Optimal Estimation in Data Sampling

Authors: M. Khoshnevisan, S. Saxena, H. P. Singh, S. Singh, Florentin Smarandache
Comments: 63 pages.

The purpose of this book is to postulate some theories and test them numerically. Estimation is often a difficult task and it has wide application in social sciences and financial market. In order to obtain the optimum efficiency for some classes of estimators, we have devoted this book into three specialized sections.

The Smarandache P and S Persistence of a Prime

Authors: Felice Russo
Comments: 5 pages.

The Smarandache P and S persistence of a prime

Relativistic Mass Macrobodies

Authors: Vladislav Konovalov
Comments: 2 pages.

The relativistic growth of mass macrobodies differs from microparticles

Smarandache Pseudo-Ideals

Authors: W. B. Vasantha Kandasamy
Comments: 5 pages

In this paper we study the Smarandache pseudo-ideals of a Smarandache ring. We prove every ideal is a Smarandache pseudo-ideal in a Smarandache ring but every Smarandache pseudo-ideal in general is not an ideal. Further we show that every polynomial ring over a field and group rings FG of the group G over any field are Smarandache rings. We pose some interesting problems about them.

Santilli's Isoprime Theory

Authors: Chun-Xuan Jiang
Comments: 16 Pages

We establish the Santilli's isomathematics based on the generalization of the modern mathematics. (see paper for rest of abstract with equations)

Applications of Euclidian Snyder Geometry to Space Time Physics & Deceleration Parameter ( DM Generated DE Replacement?)

Authors: Andrew Beckwith
Comments: 55 pages. 30 minute talk for the Dark Side of the Universe conference, Leon, Mexico, June 1st to June 6th, 2010

Contains specific elaboration of material on Glinkas quantum gas hypothesis, as far as a counting algorithm, and also attempts to show possible commonality between semi classical theories, and brane world interpretations ( higher dimensions) while addressing the issue of what are the implications of a small graviton mass in 4 dimensions, i.e. the violations of the correspondence/ complimentarity principle.

The Galois Solvable Fourth Roots of Reality

Authors: Jack Sarfatti
Comments: 8 pages

Local observers are defined by orthonormal "non-holonomic" (aka "non-coordinate") tetrad gravity fields (Cartan's "moving frames"). The tetrads are spin 1 vector fields under the 6-parameter homogeneous Lorentz group SO1,3 of Einstein's 1905 special relativity. You can think of the tetrad gravity fields as the square roots of Einstein's 1916 spin 2 metric tensor gravity fields. We will see that we must also allow for spin 0 and spin 1 gravity because the spin 1 tetrads, in turn, are Einstein-Podolsky-Rosen entangled quantum states of pairs of 2-component Penrose-Rindler qubits in the quantum pregeometry. The Wheeler-Feynman qubits are the square roots of the advanced and retarded null tetrads and can therefore be called the Galois solvable fourth roots of reality. The spherical wavefront tetrads are then formally the Bell pair states of quantum information theory. Penrose's Cartesian tetrads are a different choice from mine here. The different tetrad choices correspond to the different contours around the photon propagator poles in the complex energy plane of quantum electrodynamics. Both of his spinors in his spin frame are retarded in the same light cone, e.g. the forward cone. It seems that Penrose and Rindler implicitly answered Wheeler's question of how IT comes from BIT, but no one realized it until now.

Geometrical Axioms Refuting the Continuum-Hypothesis

Authors: Dm. Vatolin
Comments: 15 pages, Russian.

This article formulates three geometrical axioms from which it follows that the continuum power is greater then any well-ordered set power.

Partition of a Set Which Contains an Infinite Arithmetic (Respectively Geometric) Progression

Authors: Florentin Smarandache
Comments: 3 pages

We prove that for any partition of a set which contains an infinite arithmetic (respectively geometric) progression into two subsets, at least one of these subsets contains an infinite number of triplets such that each triplet is an arithmetic (respectively geometric) progression.

Fuzzy and Neutrosophic Analysis of Periyar's Views on Untouchability

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Kandasamy
Comments: 385 pages

K.R.Narayanan was a lauded hero and a distinguished victim of his Dalit background. Even in an international platform when he was on an official visit to Paris, the media headlines blazed, 'An Untouchable at Elysee'. He was visibly upset and it proved that a Dalit who rose up to such heights was never spared from the pangs of outcaste-ness and untouchability, which is based on birth. Thus, if the erstwhile first citizen of India faces such humiliation, what will be the plight of the last man who is a Dalit? As one of the world's largest socio-economically oppressed, culturally subjugated and politically marginalized group of people, the 138 million Dalits in India suffer not only from the excesses of the traditional oppressor castes, but also from State Oppression - which includes, but is not limited to, authoritarianism, police brutality, economic embargo, criminalization of activists, electoral violence, repressive laws that aim to curb fundamental rights, and the non-implementation of laws that safeguard Dalit rights. The Dalits were considered untouchable for thousands of years by the Hindu society until the Constitution of India officially abolished the practice of untouchability in 1950.

Paradoxism's Main Roots

Authors: Florin Vasiliu
Comments: 62 pages

Paradoxism's Main Roots

Reservation for Other Backward Classes in Indian Central Government Institutions Like Iits, Iims and Aiims a Study of the Role of Media Using Fuzzy Super FRM Models

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Kandasamy
Comments: 16 pages

The new notions of super column FRM model, super row FRM model and mixed super FRM model are introduced in this book. These three models are introduced specially to analyze the biased role of the print media on 27 percent reservation for the Other Backward Classes (OBCs) in educational institutions run by the Indian Central Government. This book has four chapters. In chapter one the authors introduce the three types of super FRM models. Chapter two uses these three new super fuzzy models to study the role of media which feverishly argued against 27 percent reservation for OBCs in Central Government-run institutions in India. The experts we consulted were divided into 19 groups depending on their profession. These groups of experts gave their opinion and comments on the news-items that appeared about reservations in dailies and weekly magazines, and the gist of these lengthy discussions form the third chapter of this book. The fourth chapter gives the conclusions based on our study. Our study was conducted from April 2006 to March 2007, at which point of time the Supreme Court of India stayed the 27 percent reservation for OBCs in the IITs, IIMs and AIIMS. After the aforesaid injunction from the Supreme Court, the experts did not wish to give their opinion since the matter was sub-judice. The authors deeply acknowledge the service of each and every expert who contributed their opinion and thus made this book a possibility. We have analyzed the data using the opinion of the experts who formed a heterogeneous group consisting of administrators, lawyers, OBC/SC/ST students, upper caste students and Brahmin students, educationalists, university vice-chancellors, directors, professors, teachers, retired Judges, principals of colleges, parents, journalists, members of the public, politicians, doctors, engineers, NGOs and government staff.

Some Smarandache Problems

Authors: Mladen V. Vassilev-Missana, Krassimir T. Atanassov
Comments: 67 pages, Book in Romanian, French and English. Proposed and solved problems for students' mathematical competitions in number theory, algebra, geometry, trigonometry, calculus.

During the five years since publishing [2], we have obtained many new results related to the Smarandache problems. We are happy to have the opportunity to present them in this book for the enjoyment of a wider audience of readers. The problems in Chapter two have also been solved and published separately by the authors, but it makes sense to collate them here so that they can be better seen in perspective as a whole, particularly in relation to the problems elucidated in Chapter one. Many of the problems, and more especially the techniques employed in their solution, have wider applicability than just the Smarandache problems, and so they should be of more general interest to other mathematicians, particularly both professional and amateur number theorists.

Solved Problems of Geometry and Trigonometry for College Students.

Authors: Florentin Smarandache
Comments: 171 pages

Solved problems of geometry and trigonometry for college students.

Tetron Model Building

Authors: Bodo Lampe
Comments: 12 pages, 1 figure

Spin models are considered on a discretized inner symmetry space with tetrahedral symmetry as possible dynamical schemes for the tetron model. Parity violation, which corresponds to a change of sign for odd permutations, is shown to dictate the form of the Hamiltonian. It is further argued that such spin models can be obtained from more fundamental principles by considering a (7+1)-dimensional spacetime with octonion multiplication.

Big Bang ? a Critical Review

Authors: Ashwini Kumar Lal
Comments: 22 pages, 5 figures, published in Journal of Cosmology, 2010, Vol 6, pp.1533-1547.

Inflationary Big Bang model is the generally accepted theory for the origin of universe. Nonetheless, findings of the observational astronomy as also the revelations in the field of fundamental physics over the past two decades question validity of the 'Big Bang' model as a viable theory for origin of the universe. This paper examines a few of the various factors which undermine the theory of the big Bang, including the organization of galactic superstructures, the Cosmic Microwave Background, distant galaxies, gravitational waves, redshifts, and the age of local galaxies.

Theory Cannot Choose from Its Several Possible Interpretations

Authors: Ron Bourgoin
Comments: 3 pages

A theory can be interpreted several different ways. Which interpretation is "the correct interpretation" is well nigh impossible to determine. For that reason, we select the one that best fits our concept of what reality is. That means we choose on the basis of metaphysics.

Only Problems not Solutions

Authors: Florentin Smarandache
Comments: 112 pages

The development of mathematics continues in a rapid rhythm, some unsolved problems are elucidated and simultaneously new open problems to be solved appear.

Estimation of Mean in Presence of Non Response Using Exponential Estimator

Authors: Rajesh Singh, Mukesh Kumar, Manoj K. Chaudhary, Florentin Smarandache
Comments: 11 pages

This paper considers the problem of estimating the population mean using information on auxiliary variable in presence of non response. Exponential ratio and exponential product type estimators have been suggested and their properties are studied. An empirical study is carried out to support the theoretical results.

A Method of Solving Certain Nonlinear Diophantine Equations

Authors: Florentin Smarandache
Comments: 2 pages

In this paper we propose a method of solving a Nonlinear Diophantine Equation by converting it into a System of Diophantine Linear Equations.

N-Linear Algebra of Type II

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 231 pages

This book is a continuation of the book n-linear algebra of type I and its applications. Most of the properties that could not be derived or defined for n-linear algebra of type I is made possible in this new structure: n-linear algebra of type II which is introduced in this book. In case of n-linear algebra of type II, we are in a position to define linear functionals which is one of the marked difference between the n-vector spaces of type I and II. However all the applications mentioned in n-linear algebras of type I can be appropriately extended to n-linear algebras of type II. Another use of n-linear algebra (n-vector spaces) of type II is that when this structure is used in coding theory we can have different types of codes built over different finite fields whereas this is not possible in the case of n-vector spaces of type I. Finally in the case of n-vector spaces of type II we can obtain neigen values from distinct fields; hence, the n-characteristic polynomials formed in them are in distinct different fields. An attractive feature of this book is that the authors have suggested 120 problems for the reader to pursue in order to understand this new notion. This book has three chapters. In the first chapter the notion of n-vector spaces of type II are introduced. This chapter gives over 50 theorems. Chapter two introduces the notion of n-inner product vector spaces of type II, n-bilinear forms and n-linear functionals. The final chapter 6 suggests over a hundred problems. It is important that the reader should be well versed with not only linear algebra but also nlinear algebras of type I.

N-Linear Algebra of Type I and Its Applications

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 120 pages

With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several related results which are analogues of the classical linear algebra theorems. In case of n-vector spaces we can define several types of linear transformations. The notion of n-best approximations can be used for error correction in coding theory. The notion of n-eigen values can be used in deterministic modal superposition principle for undamped structures, which can find its applications in finite element analysis of mechanical structures with uncertain parameters. Further it is suggested that the concept of nmatrices can be used in real world problems which adopts fuzzy models like Fuzzy Cognitive Maps, Fuzzy Relational Equations and Bidirectional Associative Memories. The applications of 6 these algebraic structures are given in Chapter 3. Chapter four gives some problem to make the subject easily understandable. The authors deeply acknowledge the unflinching support of Dr.K.Kandasamy, Meena and Kama.

Fuzzy Interval Matrices, Neutrosophic Interval Matrices and Their Applications

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 304 pages

The new concept of fuzzy interval matrices has been introduced in this book for the first time. The authors have not only introduced the notion of fuzzy interval matrices, interval neutrosophic matrices and fuzzy neutrosophic interval matrices but have also demonstrated some of its applications when the data under study is an unsupervised one and when several experts analyze the problem. Further, the authors have introduced in this book multiexpert models using these three new types of interval matrices. The new multi expert models dealt in this book are FCIMs, FRIMs, FCInMs, FRInMs, IBAMs, IBBAMs, nIBAMs, FAIMs, FAnIMS, etc. Illustrative examples are given so that the reader can follow these concepts easily. This book has three chapters. The first chapter is introductory in nature and makes the book a self-contained one. Chapter two introduces the concept of fuzzy interval matrices. Also the notion of fuzzy interval matrices, neutrosophic interval matrices and fuzzy neutrosophic interval matrices, can find applications to Markov chains and Leontief economic models. Chapter three gives the application of fuzzy interval matrices and neutrosophic interval matrices to real-world problems by constructing the models already mentioned. Further these models are mainly useful when the data is an unsupervised one and when one needs a multi-expert model. The new concept of fuzzy interval matrices and neutrosophic interval matrices will find their applications in engineering, medical, industrial, social and psychological problems. We have given a long list of references to help the interested reader.

Proposing the Existence of a New Symmetry Called the Wick Symmetry-Representation of a Particle as a Primary Gas vi

Authors: V.A.Induchoodan Menon
Comments: 21 pages

The author discusses the similarity between the expression for the state function of the primary gas representing a particle and that of the wave function. It is observed that the only difference between these two expressions is that in the former time appears as a real function while in the latter it appears as an imaginary function. He shows that the primary gas approach which treats time as a real and the quantum mechanical approach which treats time as imaginary are two ways of representing the same reality and points to a new symmetry called the Wick symmetry. He shows that the probability postulate of quantum mechanics can be understood in a very simple and natural manner based on the primary gas representation of the particle. It is shown that the zero point energy of the quantum mechanics is nothing but the energy of the thermal bath formed by the vacuum fluctuations in the Higgs field. He shows that the quantum mechanics is nothing but the thermodynamics of the primary gas where time has not lost its directional symmetry.

New Prime K-Tuple Theorem (20)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any there are infinitely many primes P such that each of jP^P₀ + j+1 is a prime.

New Prime K-Tuple Theorem (19)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any there are infinitely many primes P such that each of P^P₀ + 4ⁿ is a prime.

New Prime K-Tuple Theorem (18)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any there are infinitely many primes kPsuch that each of P^P₀ + (2j)² is a prime.

New Prime K-Tuple Theorem (17)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any there are infinitely many primes kPsuch that each of P^P₀ + j(j+1) is a prime.

New Prime K-Tuple Theorem (16)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of jP⁵ + j +1 is a prime.

New Prime K-Tuple Theorem (15)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P⁵ + 4ⁿ is a prime.

New Prime K-Tuple Theorem (14)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P⁵ + (2j)² is a prime.

New Prime K-Tuple Theorem (13)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P⁵ + j( j +1) is a prime.

Our Artificial Reality Created by Theory

Authors: Ron Bourgoin
Comments: 2 pages

Theory is a template, a schematic of what we think reality is. We see reality according to the template. What does not conform to the template is excised. For that reason, much that occurs in the world is not seen. That is how we miss the great discoveries going on right under our noses.

Covariant Isolation from an Abelian Gauge Field of Its Nondynamical Potential, Which, When Fed Back, Can Transform Into a "Confining Yukawa"

Authors: Steven Kenneth Kauffmann
Comments: 12 pages, Also archived as arXiv:1005.1101 [physics.gen-ph]

For Abelian gauge theory a properly relativistic gauge is developed by supplementing the Lorentz condition with causal determination of the time component of the four-vector potential by retarded Coulomb transformation of the charge density. This causal Lorentz gauge agrees with the Coulomb gauge for static charge densities, but allows the four-vector potential to have a longitudinal component that is determined by the time derivative of the four-vector potential's time component. Just as in Coulomb gauge, the two transverse components of the four-vector potential are its sole dynamical part. The four-vector potential in this gauge covariantly separates into a dynamical transverse four-vector potential and a nondynamical timelike/longitudinal four-vector potential, where each of these two satisfies the Lorentz condition. In fact, analogous partition of the conserved four-current shows each to satisfy a Lorentz-condition Maxwellequation system with its own conserved four-current. Because of this complete separation, either of these four-vector potentials can be tinkered with without affecting its counterpart. Since it satisfies the Lorentz condition, the nondynamical four-vector potential times a constant with dimension of inverse length squared is itself a conserved four-current, and so can be fed back into its own source current, which transforms its time component into an extended Yukawa, with both exponentially decaying and exponentially growing components. The latter might be the mechanism of quark-gluon confinement: in non-Abelian color gauge theory the Yukawa mixture ratio ought to be tied to color, with palpable consequences for "colorful" hot quark-gluon plasmas.

New Prime K-Tuple Theorem (12)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of jP³ + j + 1 is a prime.

New Prime K-Tuple Theorem (11)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P³ + 4ⁿ is a prime.

New Prime K-Tuple Theorem (10)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P³ + (2 j)² is a prime.

New Prime K-Tuple Theorem (9)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove that P, P¹⁵ + j(j+1)(j=1,...,7) contain no prime solutions.

New Prime K-Tuple Theorem (8)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove that P, P⁹ + j(j+1)(j=1,...,7) contain no prime solutions.

New Prime K-Tuple Theorem (7)

Authors: Chun-Xuan Jiang
Comments: 2 Pages

Using Jiang function we prove for any k there are infinitely many primes P such that each of P³ + j( j + 1) is a prime.

A Theory of Unified Gravitation

Authors: Gil Raviv
Comments: 255 Pages.

The theory presented here, entitled the theory of unified gravitation, holds that the nuclear strong interaction and gravitation are one and the same force. Detailed and relatively simple mathematics are shown to lead to an explicit strong/gravitational force equation that relies on only three independent parameters, identical to the parameters used in Newton's gravitational theory. The theory is applied on various distance scales to explain a broad range of phenomena, and is shown to provide an unparalleled level of agreement with observations, without requiring an assumption of dark matter, dark energy or inflation. Most notable is its ability to reproduce the morphologies of various types of galaxies and nebulae, as well as the complex structure of Saturn's main body of rings. Additional large-scale phenomena explained by unified gravitation include

• The constant rotation curve observed in spiral galaxies
• The nature of density waves in spiral galaxies
• The mechanism underlying star formation and fragmentation
• The parameters that determine galactic (or nebular) morphology and classification
• The clustering of nearby galaxies, repulsion between distant galaxies, and the creation of galactic voids
• The accelerated expansion of the universe
• The cause of the observed redshift periodicity
• The mechanism responsible for the creation of galactic and stellar wind
• The sudden expansion of gas and matter observed in novae and supernovae
• The formation of planetary ring systems and the composition of planets
• The mechanism responsible for the creation of the planetary and galactic magnetic fields
• A possible mechanism for the creation of the solar corona
• The process of ionization that produces the vast amount of plasma in the universe.

Proof of the 3n+1 Problem for N ≥ 1

Authors: Steffen Bode
Comments: 6 Pages.

I establish the existence of a unique binary pattern inherent to the 3n+1 step, and then use this binary pattern to prove the 3n+1 problem for all positive integers.

Warp Drive Basic Science Written for "Aficionados". Chapter I Miguel Alcubierre.

Authors: Fernando Loup
Comments: 37 Pages. The Warp Drive as a Dynamical Spacetime is one of the most interesting Spacetimes of General Relativity and is being heavily studied inside arXiv.org.See for example the arXiv papers 1001.4960, 0904.0141,0710.4474, gr-qc/0009013,gr.qc/0110086,gr.qc/9905084,gr.qc/9702026 or the Post Doctoral Dissertation Thesis gr-qc/9805037. We feel that it is time for viXra to have its own papers exclusively devoted to this Dynamical Spacetime:The Warp Drive

Alcubierre Warp Drive is one of the most exciting Spacetimes of General Relativity.It was the first Spacetime Metric able to develop Superluminal Velocities.However some physical problems associated to the Alcubierre Warp Drive seemed to deny the Superluminal Behaviour.We demonstrate in this work that these problems can be overcomed and we arrive at some interesting results although we used two different Shape Functions one continuous g(rs) as an alternative to the original Alcubierre f(rs) and a Piecewise Shape Function f_pc(rs) as an alternative to the Ford-Pfenning Piecewise Shape Function with a behaviour similar to the Natario Warp Drive producing effectively an Alcubierre Warp Drive without Expansion/Contraction of the Spacetime. We also introduce here the Casimir Warp Drive.

Considerations on New Functions in Number Theory

Authors: Florentin Smarandache
Comments: 20 pages

In this paper a small survey is presented on eighteen new functions and four new sequences, such as: Inferior/Superior f-Part, Fractional f-Part, Complementary function with respect with another function, S-Multiplicative, Primitive Function, Double Factorial Function, S-Prime and S-Coprime Functions, Smallest Power Function.

Analysis of Social Aspects of Migrant Labourers Living with Hiv/aids Using Fuzzy Theory and Neutrosophic Cognitive Maps

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 472 pages

Neutrosophic logic grew as an alternative to the existing topics and it represents a mathematical model of uncertainty, vagueness, ambiguity, imprecision, undefined-ness, unknown, incompleteness, inconsistency, redundancy and contradiction. Despite various attempts to reorient logic, there has remained an essential need for an alternative system that could infuse into itself a representation of the real world. Out of this need arose the system of neutrosophy and its connected logic, neutrosophic logic. This new logic, which allows also the concept of indeterminacy to play a role in any real-world problem, was introduced first by one of the authors Florentin Smarandache.

Neutrosophic Rings

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 154 pages

In this book we define the new notion of neutrosophic rings. The motivation for this study is two-fold. Firstly, the classes of neutrosophic rings defined in this book are generalization of the two well-known classes of rings: group rings and semigroup rings. The study of these generalized neutrosophic rings will give more results for researchers interested in group rings and semigroup rings. Secondly, the notion of neutrosophic polynomial rings will cause a paradigm shift in the general polynomial rings. This study has to make several changes in case of neutrosophic polynomial rings. This would give solutions to polynomial equations for which the roots can be indeterminates. Further, the notion of neutrosophic matrix rings is defined in this book. Already these neutrosophic matrixes have been applied and used in the neutrosophic models like neutrosophic cognitive maps (NCMs), neutrosophic relational maps (NRMs) and so on.

Confidence Intervals for the Pythagorean Formula in Baseball

Authors: David D. Tung
Comments: 27 Pages.

In this paper, we will investigate the problem of obtaining confidence intervals for a baseball team's Pythagorean expectation, i.e. their expected winning percentage and expected games won. We study this problem from two different perspectives. First, in the framework of regression models, we obtain confidence intervals for prediction, i.e. more formally, prediction intervals for a new observation, on the basis of historical binomial data for Major League Baseball teams from the 1901 through 2009 seasons, and apply this to the 2009 MLB regular season. We also obtain a Scheffé-type simultaneous prediction band and use it to tabulate predicted winning percentages and their prediction intervals, corresponding to a range of values for log(RS=RA). Second, parametric bootstrap simulation is introduced as a data-driven, computer-intensive approach to numerically computing confidence intervals for a team's expected winning percentage. Under the assumption that runs scored per game and runs allowed per game are random variables following independent Weibull distributions, we numerically calculate confidence intervals for the Pythagorean expectation via parametric bootstrap simulation on the basis of each team's runs scored per game and runs allowed per game from the 2009 MLB regular season. The interval estimates, from either framework, allow us to infer with better certainty as to which teams are performing above or below expectations. It is seen that the bootstrap confidence intervals appear to be better at detecting which teams are performing above or below expectations than the prediction intervals obtained in the regression framework.

Nonlinear Theory of Elementary Particles 1. Choice of Axiomatics and Mathematical Apparatus of Theory

Authors: A.G. Kyriakos
Comments: 12 Pages.

In the previous paper (http://vixra.org/abs/1003.0169), which can be considered as an introduction to the nonlinear theory, we have shown that the Standard Model (S?) is not an axiomatic, but an algorithmic theory. In the proposed article the simplest (minimum) axiomatics is examined from the point of view of the possible forms of its mathematical representation.

Using Noetics to Determine the Geometric Limits of 3-Body Alignments that Produce Subtle Energies

Authors: Jeffrey S. Keen
Comments: 7 pages, 5 Figures.

Attempting to link quantum physics with general relativity is one current approach to the comprehension of the structure of the universe. However, this could be an impossible objective as recent theories suggest that gravity is not a fundamental force but a consequence of the way information about material objects is organised in space time (e.g. Reference 27). In this theory, gravity is analogous to the flow of water, and involves a holographic universe, information, entropy, and chaos theory. However, such theories do not explain acts of observations affecting the results of scientific experiments. Many researchers, (e.g. Reference 51), including the author, believe that understanding the structure of the universe lies not just in physics and the above concepts, but in addition involves consciousness and cognitive neuroscience together with understanding the nature and perception of information. As Noetics and dowsing involve all the latter factors, it is proving to be a powerful and relevant research tool. This paper combines these considerations in a non-orthodox, but heuristic approach, linked by geometry. A previous paper, (See Reference 24: http://vixra.org/abs/1001.0004), identified that geometric alignments of three bodies, be they 3 pebbles, 3 circles drawn on paper, or 3 astronomical bodies produce a subtle energy beam that can be detected by the mind and measured. Intriguingly, this beam has a divergence angle involving the inverse of the Fine Structure Constant (137). It has also been shown to instantaneously communicate conscious information across the solar system. These facts suggest, together with other findings, that this "consciousness beam" is linked to the structure of the universe. This avenue of research is now further developed, by quantifying the limits of the alignment of the 3-bodies that is required to produce the subtle energy beam. The findings are that for observations made near the outer of the 3 bodies, the alignment must be less than arcsine 1/4. But for observations near the middle body, this alignment must be within arcsine1/5. This article is a summary of the concepts which are augmented on the author's website http://www.jeffreykeen.co.uk/

About an Identity and Its Applications

Authors: Mihály Bencze, Florentin Smarandache
Comments: 2 pages

About an Identity and its Applications

Generalization of a Remarkable Theorem

Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 3 pages

In [1] Professor Claudiu Coandă proves the following theorem using the barycentric coordinates.

On Relating a 10-Dimensional and 11-Dimensional Duality Model of Quantized Space-Time to Elementary Particles

Authors: Gary Heen
Comments: 8 pages

It is suggested in this paper that space-time and matter are both derived from a common entity, the quantum mass unit. A 10-dimensional and 11-dimensional duality model of the quantum mass unit is presented diagrammatically, and a mathematical argument is put forth indicating how energetic photons interact with space-time, converting space-time into virtual particle pairs of matter and anti-matter.

Tuning and What it Means to Physics

Authors: Ron Bourgoin
Comments: 3 pages

In the 60s, the word was relevance; now it's tuning. For physics, it means striking a resonance between the world of making a profit and the preparation of physicists. The international effort is designed to solicit the input of industry in restructuring the physics curriculum. This spells trouble for physics departments.

The End of Science

Authors: Vladislav Konovalov
Comments: 4 pages.

The numerous errors, stored fundamental physics, have stopped its development

Deceleration Parameter Q(z) and the Role of Nucleated GW 'gravition Gas' in the Development of DE Alternatives

Authors: Andrew Beckwith
Comments: 7 pages, 2 figures, 3 tables. Possible talk for the following conference "*Fundamental Frontiers of Physics*" which will take place in Paris, France from the 6th to the 9th of July, 2010.

The case for a four dimensional graviton mass (non zero) influencing reacceleration of the universe in five dimensions is stated, with particular emphasis upon if five dimensional geometries as given below give us new physical insight as to cosmological evolution. A comparison with the quantum gas hypothesis of Glinka shows how stochastic GW/ gravitons may emerge in vacuum nucleated space, with emphasis upon comparing their number in phase space, as compared with different strain values

The Neutrosophic Research Method in Scientific and Humanistic Fields

Authors: Florentin Smarandache
Comments: 2 pages

The Neutrosophic Research Method is a generalization of Hegel's dialectic, and suggests that scientific and humanistic research will progress via studying not only the opposite ideas but the neutral ideas related to them as well in order to have a bigger picture of the whole problem to solve.

Another Explanation of the Redshifts of the Pair Quasar-Galaxy NGC 7319

Authors: José Francisco García Juliá
Comments: 2 Pages.

The excess of redshift of the quasar might be produced in its interior by the transference of heat from the light waves to the radio waves.

Concept and Method of Physimatics, Logic of Existence and the Logical Time Formula

Authors: Robert Gallinat
Comments: 12 pages

Conceptual approach and heuristic method for an investigation of the possible algebraic structure of the interdependence between mathematical and physical reality and about the connection between local, non-local and global properties in physics and mathematics, expressed by a General N-fold algebra

The Improved of the Chen Jing Run Theorem

Authors: Tong Xin Ping
Comments: 3 Pages, In Chinese

Chen Jing Run proved that "On the representation of a large even integer as the sum of a prime and the product of at most two primes" and lower bound estimations of the number of solutions. Jiang Chun Xuan, Tong Xin Ping proved that "An even integer as the sum of a prime and the product of two primes" and compute formula of the number of solutions. This paper compares the accuracy of the three formulas

Smarandache Near-Rings and Their Generalizations

Authors: W. B. Vasantha Kandasamy
Comments: 5 pages

In this paper we study the Smarandache semi-near-ring and nearring, homomorphism, also the Anti-Smarandache semi-near-ring. We obtain some interesting results about them, give many examples, and pose some problems. We also define Smarandache semi-near-ring homomorphism.

Neutrality and Many-Valued Logics

Authors: Andrew Schumann, Florentin Smarandache
Comments: 121 pages

This book written by A. Schumann & F. Smarandache is devoted to advances of non-Archimedean multiple-validity idea and its applications to logical reasoning. Leibnitz was the first who proposed Archimedes' axiom to be rejected. He postulated infinitesimals (infinitely small numbers) of the unit interval [0, 1] which are larger than zero, but smaller than each positive real number. Robinson applied this idea into modern mathematics in [117] and developed so-called non-standard analysis. In the framework of non-standard analysis there were obtained many interesting results examined in [37], [38], [74], [117].

Basic Neutrosophic Algebraic Structures and Their Application to Fuzzy and Neutrosophic Models

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 149 pages

Study of neutrosophic algebraic structures is very recent. The introduction of neutrosophic theory has put forth a significant concept by giving representation to indeterminates. Uncertainty or indeterminacy happen to be one of the major factors in almost all real-world problems. When uncertainty is modeled we use fuzzy theory and when indeterminacy is involved we use neutrosophic theory. Most of the fuzzy models which deal with the analysis and study of unsupervised data make use of the directed graphs or bipartite graphs. Thus the use of graphs has become inevitable in fuzzy models. The neutrosophic models are fuzzy models that permit the factor of indeterminacy. It also plays a significant role, and utilizes the concept of neutrosophic graphs. Thus neutrosophic graphs and neutrosophic bipartite graphs plays the role of representing the neutrosophic models. Thus to construct the neutrosophic graphs one needs some of the neutrosophic algebraic structures viz. neutrosophic fields, neutrosophic vector spaces and neutrosophic matrices. So we for the first time introduce and study these concepts. As our analysis in this book is application of neutrosophic algebraic structure we found it deem fit to first introduce and study neutrosophic graphs and their applications to neutrosophic models.

Smarandache Non-Associative (Sna-) Rings

Authors: W. B. Vasantha Kandasamy
Comments: 13 pages

In this paper we introduce the concept of Smarandache non-associative rings, which we shortly denote as SNA-rings as derived from the general definition of a Smarandache Structure (i.e., a set A embedded with a week structure W such that a proper subset B in A is embedded with a stronger structure S). Till date the concept of SNA-rings are not studied or introduced in the Smarandache algebraic literature. The only non-associative structures found in Smarandache algebraic notions so far are Smarandache groupoids and Smarandache loops introduced in 2001 and 2002. But they are algebraic structures with only a single binary operation defined on them that is nonassociative. But SNA-rings are non-associative structures on which are defined two binary operations one associative and other being non-associative and addition distributes over multiplication both from the right and left. Further to understand the concept of SNA-rings one should be well versed with the concept of group rings, semigroup rings, loop rings and groupoid rings. The notion of groupoid rings is new and has been introduced in this paper. This concept of groupoid rings can alone provide examples of SNA-rings without unit since all other rings happens to be either associative or nonassociative rings with unit. We define SNA subrings, SNA ideals, SNA Moufang rings, SNA Bol rings, SNA commutative rings, SNA non-commutative rings and SNA alternative rings. Examples are given of each of these structures and some open problems are suggested at the end.

N-Algebraic Structures and S-N-Algebraic Structures

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 209 pages

In this book, for the first time we introduce the notions of Ngroups, N-semigroups, N-loops and N-groupoids. We also define a mixed N-algebraic structure. We expect the reader to be well versed in group theory and have at least basic knowledge about Smarandache groupoids, Smarandache loops, Smarandache semigroups and bialgebraic structures and Smarandache bialgebraic structures.

Almost Unbiased Estimator for Estimating Population Mean Using Known Value of Some Population Parameter(s)

Authors: Rajesh Singh, Mukesh Kumar, Florentin Smarandache
Comments: 14 pages

In this paper we have proposed an almost unbiased estimator using known value of some population parameter(s). Various existing estimators are shown particular members of the proposed estimator. Under simple random sampling without replacement (SRSWOR) scheme the expressions for bias and mean square error (MSE) are derived. The study is extended to the two phase sampling. Empirical study is carried out to demonstrate the superiority of the proposed estimator.

Quantum Corrections to the Gravitational Potential and Orbital Motion

Authors: Ioannis Iraklis Haranas, Vasile Mioc
Comments: 3 pages, Submitted to the ROAJ, Vol. 20 , No. 2, 2010

GRT predicts the existence of relativistic corrections to the static Newtonian potential, which can be calculated and verified experimentally. The idea leading to quantum corrections at large distances consists of the interactions of massless particles, which only involve their coupling energies at low energies. Using the quantum correction term of the potential we obtain the perturbing quantum acceleration function. Next, with the help of the Newton-Euler planetary equations, we calculate the time rates of changes of the orbital elements per revolution for three different orbits around the primary. For one solar mass primary and an orbit with semimajor axis and eccentricity equal to that of Mercury we obtain that Δω_qu = 1.517x10^{-81 o}/cy, while ΔM_qu = -1.840x10^-46 rev/cy.

On a Concatenation Problem

Authors: Henry Ibstedt
Comments: 13 pages.

This article has been inspired by questions asked by Charles Ashbacher in the Journal of Recreational Mathematics, vol. 29.2. It concerns the Smarandache Deconstructive Sequence. This sequence is a special case of a more general concatenation and sequencing procedure which is the subject of this study. Answers are given to the above questions. The properties of this kind of sequences are studied with particular emphasis on the divisibility of their terms by primes.

Introduction to N-Adaptive Fuzzy Models to Analyze Public Opinion on Aids

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 236 pages.

AIDS is not simply a physical malady, it is also an artifact of social and sexual transgression, violated taboo, fractured identity-political and personal projections. Its key words are primarily the property of the powerful. AIDS: Keywords - is my attempt to identify and contest some of the assumptions underlying our current 'knowledge'. In this effort I am joined by many AIDS activists including people living with AIDS - Acquired Immuno Deficiency Syndrome.

General Combination Rules for Qualitative and Quantitative Beliefs

Authors: Arnaud martin, Christophie Osswald, Jean Desert, Florentin Smarandache
Comments: 23 pages.

Martin and Osswald [15] have recently proposed many generalizations of combination rules on quantitative beliefs in order to manage the conflict and to consider the specificity of the responses of the experts. Since the experts express themselves usually in natural language with linguistic labels, Smarandache and Dezert [13] have introduced a mathematical framework for dealing directly also with qualitative beliefs. In this paper we recall some element of our previous works and propose the new combination rules, developed for the fusion of both qualitative or quantitative beliefs.

An Introduction to the Smarandache Geometries

Authors: L. Kuciuk, M. Antholy
Comments: 23 pages.

In this paper we make a presentation of these exciting geometries and present a model for a particular one.

On the 5D Extra-Force According to Basini-Capozziello-Ponce De Leon Formalism and Three Important Features: Chung-Freese Superluminal Braneworld,strong Gravitational Fields and the Pioneer Anomaly.

Authors: Fernando Loup
Comments: 91 Pages. This work was sent to arXiv.org as arXiv:0710.0924 in 4 October 2007 to celebrate the 50th Anniversary of the Space Race and the launch of the Sputnik I (4 October 1957). It suffered major modifications in order to be accepted for publication. Versions #1 and #2 can be considered as a different paper from versions #3 and #4 It was published in the book Space Exploration Research Chapter IX from Nova Scientific Publishers ISBN 978-1-60692-264-4 2009. It was also published in the Volume 14 Issue 3-4 (Journal of Magnetohydrodynamics, Plasma and Space Research) ISSN: 1083-4729 The published versions are the #3 and #4 from arXiv.org - The versions #1 and #2 contains a mathematical description about how to solve the pathologies of the Einstein Field Equation known as the Superluminal Alcubierre Warp Drive. It also contains a Memorial to Serguei Pavlovitch Korolev(the creator of the Sputnik I) and a Memorial to all the Cosmonauts and Astronauts that died in Outer Space in the spaceships Soyuz I,Soyuz XI,Apollo I,Challenger and Columbia…the first 50 years of the Space Race We feel that this work in the unpublished version #1 and #2 deserves to be placed on viXra as a valid paper to overcome the limitations of the Superluminal Alcubierre Warp Drive Spacetime specially the part of the Horizons and the causally disconnected portions of the Spacetime inside the Warp Drive bubble.We use something that resembles the Apollo spacecrafts This version is exactly equal without changes to the version #2 stored in arXiv.org This paper was inspired in a TV series from the British Broadcasting Corporation called "The Space Race"

We use the 5D Extra Dimensional Force according to Basini-Capozziello-Ponce De Leon, Overduin-Wesson and Mashoon-Wesson-Liu Formalisms to study the behaviour of the Chung-Freese Superluminal BraneWorld compared to the Alcubierre Warp Drive and we arrive at some interesting results from the point of view of the Alcubierre ansatz although we used two different Shape Functions one continuous g(rs) as an alternative to the original Alcubierre f(rs) and a Piecewise Shape Function fpc(rs) with a behaviour similar to the Natario Warp Drive. We introduce here the Casimir Warp Drive.We also demonstrate that in flat 5D Minkowsky Spacetime or weak Gravitational Fields we cannot tell if we live in a 5D or a 4D Universe according to Basini-Capozziello-Ponce De Leon,Overduin-Wesson and Mashoon-Wesson-Liu Dimensional Reduction but in the extreme conditions of Strong Gravitational Fields we demonstrate that the effects of the 5D Extra Dimension becomes visible and perhaps the study of the extreme conditions in Black Holes can tell if we live in a Higher Dimensional Universe.We use a 5D Maartens-Clarkson Schwarzschild Cosmic Black String centered in the Sun coupled to the 5D Extra Force from Ponce De Leon together with Mashoon-Wesson-Liu and the definitions of Basini-Capozziello and Bertolami-Paramos for the Warp Fields in order to demonstrate that the Anomalous Effect disturbing two American space probes known as the Pioneer Anomaly is a force of 5D Extra Dimensional Nature.As a matter of fact the Pioneer Anomaly is the first experimental evidence of the "Fifth Force" predicted years ago by Mashoon-Wesson-Liu and we also demonstrate that this Extra Force is coming from the Sun.

The New Prime Theorem (38)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that there are infinitely many primes P such that each of jP³ + k - j is a prime.

The New Prime Theorem (37)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that there are infinitely many primes P such that each of jP³ + 7 - j is a prime.

The New Prime Theorem (36)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that there are infinitely many primes P such that each of jP³ + 5 - j is a prime.

The New Prime Theorem (35)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that there are infinitely many primes P such that 2P³ + 1 and P³ + 2 are all prime.

The New Prime Theorem (34)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that if J₂ (ω) ≠ 0 then there are infinitely many primes P such that each of jP² + k - j is a prime, if J₂ (ω) = 0 then there are finitely many primes P such that each of jP² + k - j is a prime.

The Meaning of the Singularity: 2. Astro-Sociology: Predicting the Presence of Twin Planets (Extended Version)

Authors: Alon Retter
Comments: 17 pages.

This paper presents a remarkable analogy between the human society and Astronomy. Please keep an open mind as the resemblance is not only qualitative but also quantitative. We point out many similarities between stars and people, such as properties of grouping - single stars vs. singles, binary stars vs. couples, cities vs. clusters, countries vs. galaxies, etc. Men and women are linked with cool and hot stars. We match planets with children and attribute the two genders to gas and solid planets. Moons are related with pets or grandchildren, asteroids with germs / viruses, accretion disks with bellies and jets with pukes. Suicide attempts in people are associated with supernovae in stars. Inflation is connected with the rapid growth of the embryo, and the time the universe became transparent to light is linked with the human birth. A simple analogue to the cosmic background radiation is the bellybutton, and the universe acceleration is coupled with the pace increase in modern life. The mean values of the distributions of star multiples and the number of US households are almost identical (2.04 and 2.03). Moreover, an amazing resemblance between the two curves is evident (Fig. 1). The distribution of gas (or solid) planets is similar to that of boys (or girls) as well, and the fit could improve once selection effects are considered. Monte Carlo simulations suggest that our results are significant at a confidence level higher of ~99.9%! The surprising linkage between humanity and stars can lead to many predictions. It is proposed that about a third of stars harbor planets. We predict that stars are equally divided between hot and cool stars and planets between gas and solid planets. The presence of four gas and four solid planets in the solar system supports our prediction. We also forecast that the mean number of planets around host stars should be near two, larger around binaries than in single stars and higher in hot stars than in cool stars. We vision the presence of twin planets that share the same orbit. The wealth of known extra-solar planets should already contain a few such systems. We forecast the presence of a new astronomical phenomenon, which we alias 'planova' - an eruption in a planet that may destroy it, and speculate about the presence of planet jets. The ideas and results of this paper are clearly unusual and unbelievable. A brief explanation to our findings is presented in the discussion and further developed in forthcoming papers.

The Meaning of the Singularity: 2. Astro-Sociology: Predicting the Presence of Twin Planets (Short Version)

Authors: Alon Retter
Comments: 7 pages.

We present a remarkable analogy between the human society and Astronomy. Please keep an open mind as the resemblance is both qualitative and quantitative. We link stars and children with persons and planets. The two genders are matched with cool and hot stars and with gas and solid planets. The mean values of the distributions of star multiples and US households are almost identical. Moreover, an amazing resemblance between the two curves is evident. In addition, the distribution of gas / solid planets is similar to that of boys / girls as well, and the fit could improve once selection effects are considered. Monte Carlo simulations suggest that our results are significant at a confidence level of 99.9%! We thus predict that about a third of stars harbor planets and that stars are equally divided between hot and cool stars and planets between gas and solid planets. The presence of 4 gas and 4 solid planets in the solar system supports our prediction. We forecast that the mean number of planets around host stars should be near two, and vision the presence of twin planets that share the same orbit. The wealth of known extra-solar planets should already contain a few such systems.

The Meaning of the Singularity: 1. a Single Particle Universe

Authors: Alon Retter
Comments: 6 pages.

We examine the basic term 'particle'. We start by exploring a universe that contains a single particle. In such a universe there is no meaning for motion, energy, space and time. Only for a two particles universe the physical quantities can be measured. However, the determination of the physical quantities implies that the particles are not separated from each other! We thus propose that all particles are interconnected. This novel perception naturally explains the two well known paradoxes: the twin-electrons experiment and Schrödinger's cat. In fact, we argue that the twinelectrons experiment is an actual proof for global non-detachment. We state that it cannot be shown that a particle is elementary. If one is divided by two numerous times, zero is never reached. There must be a jump into zero - the singularity. The sought Higgs particle is simply the singularity itself, which cannot be found, having no properties.

How Acoustic Resonance Can Reduce the Average Velocity in a Falling Body?

Authors: V. Torres-Zúñiga
Comments: 9 pages, figures in color. Manuscript to be submitted to Revista de la Sociedad Mexicana de Física E

In this article, a simple experiment is described for correcting the misconception that acoustic pressure and levitation effects are hard to observe in school laboratories. Analysis of the free fall velocity of a toy parachute within a vertical tube, driven by sound in a range of frequencies around the resonant condition, exhibits the resonance frequency, the node pressure zones, and the optimal conditions to obtain acoustical levitation of a light body.

A Fifth Smarandache Friendly Prime Pair

Authors: Philip Gibbs
Comments: 1 page

A Smarandache friendly prime pair is a pair of prime numbers (p,q), p < q, such that the product pq is equal to the sum of all primes from p to q inclusive. Previously four such pairs were known: (2,5), (3,13), (5,31) and (7,53). A fifth one is found by a brute force search.

On a Problem Concerning the Smarandache Friendly Prime Pairs

Authors: Felice Russo
Comments: 3 pages.

In this paper a question posed in [1] and concerning the Smarandache friendly prime pairs is analysed.

Computational Modeling in Applied Problems: Collected Papers on Econometrics, Operations Research, Game Theory and Simulation

Authors: Florentin Smarandache, Sukanto Bhattacharya, Mohammad Khoshnevisan
Comments: 109 pages.

Computational models pervade all branches of the exact sciences and have in recent times also started to prove to be of immense utility in some of the traditionally 'soft' sciences like ecology, sociology and politics. This volume is a collection of a few cuttingedge research papers on the application of variety of computational models and tools in the analysis, interpretation and solution of vexing real-world problems and issues in economics, management, ecology and global politics by some prolific researchers in the field.

The New Prime Theorem (33)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove x² + y⁴ (J. Friedlander and H. Iwaniec, The polynomial x² + y⁴ Captures its primes, Ann. Math., 148(1998) 945-1040)

The New Prime Theorem (32)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove x³ + 2y³ (D. R. Heath-Brown, prime represented by x³ + 2y³, Acta Math., 186(2001)1-84).

Equivalence of Maxwell's Source-Free Equations to the Time-Dependent Schrödinger Equation for a Solitary Particle with Two Polarizations and Hamiltonian |cp|

Authors: Steven Kenneth Kauffmann
Comments: 17 pages, Also archived as arXiv:1004.1820 [physics.gen-ph].

It was pointed out in a previous paper that although neither the Klein-Gordon equation nor the Dirac Hamiltonian produces sound solitary free-particle relativistic quantum mechanics, the natural square-root relativistic Hamiltonian for a nonzero-mass free particle does achieve this. Failures of the Klein-Gordon and Dirac theories are reviewed: the solitary Dirac free particle has, inter alia, an invariant speed well in excess of c and staggering spontaneous Compton acceleration, but no pathologies whatsoever arise from the square-root relativistic Hamiltonian. Dirac's key misapprehension of the underlying four-vector character of the time-dependent, configuration-representation Schrödinger equation for a solitary particle is laid bare, as is the invalidity of the standard "proof" that the nonrelativistic limit of the Dirac equation is the Pauli equation. Lorentz boosts from the particle rest frame point uniquely to the square-root Hamiltonian, but these don't exist for a massless particle. Instead, Maxwell's equations are dissected in spatial Fourier transform to separate nondynamical longitudinal from dynamical transverse field degrees of freedom. Upon their decoupling in the absence of sources, the transverse field components are seen to obey two identical time-dependent Schrödinger equations (owing to two linear polarizations), which have the massless freeparticle diagonalized square-root Hamiltonian. Those fields are readily modfied to conform to the attributes of solitary-photon wave functions. The wave functions' relations to the potentials in radiation gauge are also worked out. The exercise is then repeated without the considerable benefit of the spatial Fourier transform.

Condensed Light a Reinterpration of Quantum Mechanics and Relativity

Authors: Niels Vandamme
Comments: 7 pages

This paper propounds several hypotheses which offer an alternate explanation to some of the real or purported effects encountered in quantum mechanics and relativity, giving a mechanical explanation for the absolute speed of light, the conversion of matter to energy, and the observed superluminal expansion of the universe.

The New Prime Theorem (31)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove and P₁ = P⁹ ± m and P₁ = (2P)⁹ ± n

The New Prime Theorem (30)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove and P₁ = P^P0 ± m and P₁ = (2P)^p0 ± n

The New Prime Theorem (29)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove and P₁ = P⁵ ± m and P₁ = (2P)⁵ ± n

The New Prime Theorem (28)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that 1P = P ± m and 1 P = 2P ± n have infinitely many

Corrections to the wu-Sprung Potential for the Riemann Zeros and a New Hamiltonian Whose Energies Are the Prime Numbers

Authors: Jose Javier Garcia Moreta
Comments: 7 pages

We review the Wu-Sprung potential adding a correction involving a fractional derivative of Riemann Zeta function, we study a global semiclassical analysis in order to fit a Hamiltonian H=T+V fitting to the Riemann zeros and another new Hamiltonian whose energy levels are precisely the prime numbers, through these paper we use the notation log_e (x) = ln(x) = log(x) for the logarithm , also unles we specify Σ_γ h(γ) means that we sum over ALL the imaginary parts of the nontrivial zero on both the upper and lower complex plane.

The Hundred Year Detour: a Comment on Arxiv:1004.2901

Authors: Ron Bourgoin
Comments: 3 pages

Arxiv:1004.2901 exposes a chink in the armor. It seems that joining general relativity with quantum mechanics is like trying to fit a square peg in a round hole. Obviously there's something terribly wrong with one of the theories. Since quantum mechanics has been far too successful in too many areas, it is felt general relativity has to go.

Multispace & Multistructure. Neutrosophic Transdisciplinarity

Authors: Florentin Smarandache
Comments: 802 pages.

The fourth volume, in my book series of "Collected Papers", includes 100 published and unpublished articles, notes, (preliminary) drafts containing just ideas to be further investigated, scientific souvenirs, scientific blogs, project proposals, small experiments, solved and unsolved problems and conjectures, updated or alternative versions of previous papers, short or long humanistic essays, letters to the editors - all collected in the previous three decades (1980-2010) - but most of them are from the last decade (2000-2010), some of them being lost and found, yet others are extended, diversified, improved versions.

Some Characterisations of α-Cut in Intuitionistic Fuzzy Set Theory

Authors: V. Veeramani, Roque Batulan
Comments: 7 pages

This paper contains the Basic Definitions of an Intuitionstic Fuzzy Set theory and operations on it. Mainly we discussed the basic concepts of α - cut with examples and Characterisations.

The New Prime Theorem (27)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture P: m² +1 and m² + 3 [4].

The New Prime Theorem (26)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture N: x³ + y³ + z³ [4].

The New Prime Theorem (25)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove Hardy-Littlewood conjecture M: x³ + y³ + k [4].

The New Prime Theorem (24)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove Hardy-Littlewood conjecture K: x³ + k [4].

The New Prime Theorem (23)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture F: am² + bm+ c [4].

The New Prime Theorem (22)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture B: P, P + k [4].

The New Prime Theorem (21)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove binary Goldbach conjecture and N = P1 + ... + Pn [4]

The New Prime Theorem (20)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that Jiang prime k -tuple theorem is true[1-3] and Hardy-Littlewood prime k -tuple conjecture is false[4-8]. The tool of additive prime number theory is basically the Hardy-Littlewood prime tuple conjecutre, but can not prove and count any prime problems[6].

Non Standard DE & DM, with Deceleration Parameter Q(z) in Five Dimensions

Authors: Andrew Beckwith
Comments: 4 pages, one figure. Actual ( minus the address ) submission for the following conference : extended abstract of 4 pages for possibly being placed in C. Corda's section namely , "Second Big Challenge Symposium - The Big Challenge of Cosmological Understanding: Gravitation, Dark Matter and Dark Energy. Towards New Scenarios" during the 8th International Conference of Numerical Analysis and Applied Mathematics, at Hotel Rodos Palace, Rhodes, Greece, 19-25 September 2010.

The case for a four dimensional graviton mass (non zero) influencing reacceleration of the universe in five dimensions is stated, with particular emphasis upon if five dimensional geometries as given below give us new physical insight as to cosmological evolution. We postulate that a calculated inflaton φ(t) may re-emerge after fading out in the aftermath of inflation. The inflaton may be a contributing factor to, with non zero graviton mass, in re acceleration of the universe a billion years ago. Many theorists assume that the inflaton is the source of entropy. The inflaton also may be the source of re acceleration of the universe, especially if the effects of a re emergent inflaton are in tandem with the appearance of macro effects of a small graviton mass, leading to a speed up of the rate of expansion of the universe one billion years ago, at red shit value of Z ~ .423

Deceleration Parameter Q(Z) in Five Dimensions, and Can a Partial re Appearance of Quinessence φ(t) Play a Role in an Increase in re Acceleration at Z ~. 423?

Authors: Andrew Beckwith
Comments: 4 pages, 1 figure. extended abstract of 3-4 pages for possibly being placed in C. Corda's section namely , "Second Big Challenge Symposium - The Big Challenge of Cosmological Understanding: Gravitation, Dark Matter and Dark Energy. Towards New Scenarios" during the 8th International Conference of Numerical Analysis and Applied Mathematics, at Hotel Rodos Palace, Rhodes, Greece, 19-25 September 2010.

The case for a four dimensional graviton mass (non zero) influencing reacceleration of the universe in five dimensions is stated, with particular emphasis upon if five dimensional geometries as given below give us new physical insight as to cosmological evolution. One noticeable datum, that a calculated inflaton φ(t) re-emerged after fading out in the aftermath of inflation. The inflaton is a contributing factor to, with non zero graviton mass, in re acceleration of the universe a billion years ago. The inflaton also may be the source of re acceleration of the universe, especially if the effects of a re emergent inflaton are in tandem with the appearance of macro effects of a small graviton mass, leading to a speed up of the rate of expansion of the universe one billion years ago, at red shit value of Z ~ .423

Signs of Supersymmetry

Authors: Bernard Riley
Comments: 10 pages

Particles resulting from the breaking of symmetries are arranged symmetrically about mass levels that descend in geometric progression from the Planck Mass within three sequences, of common ratio 1/π, 2/π and 1/e. Particles arranged in this way include the weak gauge bosons W^± and Z⁰, the quark weak isospin doublets u-d, s-c and b-t, and all hadronic isospin doublets. Many pairs of hadrons with some common quark content also form symmetric partnerships. Often, the mass difference characterising a partnership is precisely equal to the mass of a level. The spin-0 partners of the quarks and charged leptons are identified. The mass sequences may derive from the geometry of compact extra spaces of Planck scale.

Why Create When there is no Recognition, no Reward?

Authors: Ron Bourgoin
Comments: 2 pages

Why run the race when there is no trophy? The creative human being is often not recognized, not rewarded. What to do?

The Quantum Uncertainty Principle, Gravitational Waves, and Black Holes

Authors: Willi Penker
Comments: 2 pages

Following the basic rules of the uncertainty principle, gravitation itself becomes uncertain and even massive black holes go into superposition without the possibility of ending up in a real singularity.

Contextuality: a Philosophical Paradigm, with Applications to Philosophy of Cognitive Science

Authors: Carlos Gershenson
Comments: 12 pages.

We develop on the idea that everything is related, inside, and therefore determined by a context. This stance, which at first might seem obvious, has several important consequences. This paper first presents ideas on Contextuality, for then applying them to problems in philosophy of cognitive science. Because of space limitations, for the second part we will assume that the reader is familiar with the literature of philosophy of cognitive science, but if this is not the case, it would not be a limitation for understanding the main ideas of this paper. We do not argue that Contextuality is a panaceic answer for explaining everything, but we do argue that everything is inside a context. And because this is always, we sometimes ignore it, but we believe that many problems are dissolved with a contextual approach, noticing things we ignore because of their obviousity. We first give a notion of context. We present the idea that errors are just incongruencies inside a context. We also present previous ideas of absolute being, relative being, and lessincompleteness. We state that all logics, and also truth judgements, are contextdependant, and we develop a "Context-dependant Logic". We apply ideas of Contextuality to problems in semantics, the problem of "where is the mind", and the study of consciousness.

Processes of Consciousness

Authors: Flavian Vasile
Comments: 9 pages.

This paper presents consciousness as the sum of describable processes, without limiting it only to verbal understanding. Consciousness is presented as a buffer space of the unconscious, accessed by any mental decision-taking processes. Consciousness is composed of sequential outputs of non-conscious processes that form, as frames in a picture, the impression of our ego continuity. The functional consequences of this point of view are then further discussed.

A Note on Neutrosophy

Authors: Huang, Cheng-Gui
Comments: 1 pages.

I claim that Neutrosophy, by Professor Florentin Smarandache, is a deep thought in human culture. That gives advantage to break the mechanical understanding of human culture. For example, according to the mechanical theory: existence and non-existence could not be simultaneously. Actually existence and non-existence are simultaneously. Everyone knows that human life is like a way in the empty space of a bird flying. Everyone can not see himself a second ago, everyone can not see himself for the time being and everyone can not see himself a second future. Everyone could not know what is the existence of self. Everyone is also difficult to say the non-existence of self. So the existence and non-existence of self are simultaneously. And the existence and nonexistence of everything are simultaneously, where, the law of excluded middle does not apply. These basic facts express the depth of Smarandache's Neutrosophy. He has a lot of friends in ancient and in nowadays, in the West and in the East.

Notion of Neutrosophic Risk and Financial Markets Prediction

Authors: Sukanto Bhattacharya
Comments: 7 pages.

The efficient market hypothesis based primarily on the statistical principle of Bayesian inference has been proved to be only a special-case scenario. The generalized financial market, modeled as a binary, stochastic system capable of attaining one of two possible states ...

Neutrosophy in Situation Analysis

Authors: Anne-Laure Jousselme, Patrick Maupin
Comments: 7 pages.

In situation analysis (SA), an agent observing a scene receives information from heterogeneous sources of information including for example remote sensing devices, human reports and databases. The aim of this agent is to reach a certain level of awareness of the situation in order to make decisions. For the purpose of applications, this state of awareness can be conceived as a state of knowledge in the classical epistemic logic sense. Considering the logical connection between belief and knowledge, the challenge for the designer is to transform the raw, imprecise, conflictual and often paradoxical information received from the different sources into statements understandable by both man and machines. Hence, quantitative (i.e. measuring the world) and qualitative (i.e. reasoning about the structure of the world) information processing coexist in SA. A great challenge in SA is the conciliation of both aspects in mathematical and logical frameworks. As a consequence, SA applications need frameworks general enough to take into account the different types of uncertainty and information present in the SA context, doubled with a semantics allowing meaningful reasoning on situations. The aim of this paper is to evaluate the capacity of neutrosophic logic and Dezert- Smarandache theory (DSmT) to cope with the ontological and epistemological problems of SA.

The Israel-Palestine Question a Case for Application of Neutrosophic Game Theory

Authors: Sukanto Bhattacharya, Florentin Smarandache, Mohammad Khoshnevisan
Comments: 10 pages.

In our present paper, we have explored the possibilities and developed arguments for an application of principles of neutrosophic game theory as a generalization of the fuzzy game theory model to a better understanding of the Israel-Palestine problem in terms of the goals and governing strategies of either side. We build on an earlier attempted justification of a game theoretic explanation of this problem by Yakir Plessner (2001) and go on to argue in favour of a neutrosophic adaptation of the standard 2x2 zero-sum game theoretic model in order to identify an optimal outcome

Toward Excitation and Inhibition in Neutrosophic Logic

Authors: Feng Liu
Comments: 8 pages.

Logic should have been defined as the unity of contradiction between logic director and logic implementation. Chinese Daoism asserts that everything is defined in the unity of opposites, namely yin and yang, accordingly yang conducts change and yin brings it up (I-Ching, also known as Book of Changes). In this way logic is redefined in an indeterminate style to facilitate "both A and Anti-A" etc. in neutrosophics of logic. The unity of opposites is also described as neutrality in neutrosophy. An intermediate multi-referential model of excitation and inhibition is developed to derive a multiagent architecture of logic, based on Chinese yin-yang philosophy. This methodology of excitation/inhibition suggests a rhymed way of logic, leading to a dynamic methodology of weight strategy that links logic with neural network approach. It also confirms the crucial role of indeterminacy in logic as a fatal criticism to classical mathematics and current basis of science.

Truth and Absolute Truth in Neutrosophic Logic

Authors: Feng Liu
Comments: 12 pages.

As a philosophical analysis of some fatal paradoxes, the paper distinguishes the conceptual difference between representation of truth and source of truth, and leads to the conclusion that in order to acquire the genuine source of truth, independently of specific representations possibly belonging to different worlds, one is necessary to ignore all the ideas, logics, conceptions, philosophies and representable knowledge even himself belonging to those misleading worlds, returning to his infant nature, as a preliminary step for his cultivation of unconstrained wisdom. It also carries out some coordinative crucial issues as natural-doctrine, minded-unwitting, logic-infancy, conception-deconception, determinacy-indeterminacy. The paper tries to verify the role of neutrosophy and neutrosophic logic in religious issues and open a gateway toward the oriental classics, excavating the lost treasure.

Analyzing if a Graviton Gas Acts Like a Cosmological Vacuum State and 'cosmological' Constant Parameter

Authors: Andrew Beckwith
Comments: 20 pages, 5 figures. Meant as a thought experiment which when cleaned up will be a companion piece to the question of the nature of cosmological constants, as presented in viXra:1004.0079

If a non zero graviton mass exists, the question arises if a release of gravitons, possibly as a "Graviton gas" at the onset of inflation could be an initial vacuum state. Pros and cons to this idea are raised, in part based upon bose gases. The analysis starts with Volovik's 1condensed matter treatment of GR, and ends with consequences, which the author sees, if the supposition is true.

Quantizing Time and Space from the Standing Wave to the Primary Gas Structure of a Particle V

Authors: V.A.Induchoodan Menon
Comments: 25 pages

The author introduces the concept of a primary gas which is an abstract gas where the microstates are occupied successively in time unlike in the case of a real gas where the microstates are occupied simultaneously. He shows that a single plane wave associated with a standing wave formed by the confinement of a luminal wave could be treated as the microstate of the primary gas that represents a particle. This approach makes it possible to understand the dynamics of a particle in terms of the thermodynamics of the primary gas. In this approach, time and space turn out to be the intrinsic properties of the primary gas that represents a particle and the quantized nature of time and space emerges from it in a natural manner. It is shown that the action (with a negative sign) of a particle could be identified with the entropy of the primary gas and the principle of least action is nothing but the second law of thermodynamics. The author shows that the uncertainty relation of quantum mechanics can be derived directly from the equation for fluctuations and he explains the statistical basis of the virtual interactions.

The Implicit Function in the Hardy-Littewood Conjecture

Authors: Tong Xin Ping
Comments: 6 Pages, In Chinese

(see paper)

Existence and Number of Solutions of Diophantine Quadratic Equations with Two Unknowns in Z and N

Authors: Florentin Smarandache
Comments: 2 pages.

In this short note we study the existence and number of solutions in the set of integers (Z) and in the set of natural numbers (N) of Diophantine equations of second degree with two unknowns of the general form ax² - by² = c .

Smarandache Spaces as a New Extension of the Basic Space-Time of General Relativity

Authors: Dmitri Rabounski
Comments: 2 pages.

This short letter manifests how Smarandache geometries can be employed in order to extend the "classical" (Riemannian geometry) basis of the General Theory of Relativity through joining the properties of two or more (different) geometries in the same single space. Perspectives in this way seem much profitly: the basic space-time of General Relativity can be extended to not only metric geometries, but even to non-metric ones (where no distances can be measured), or to spaces of the mixed kind which possess the properties of both metric and non-metric spaces (the latter should be referred to as "semi-metric spaces"). If both metric and non-metric properties possessed at the same (at least one) point of a space, it is one of Smarandache geometries, and should be referred to as "Smarandache semi-metric space". Such spaces can be introduced according to the mathematical apparatus of physically observable quantities (chronometric invariants), if considering a breaking of the observable space metric on the continuous background of the fundamental metric tensor.

Global Totalitarianism and the Crisis of Neo-Lib Movement

Authors: Florentin Smarandache
Comments: 10 pages.

During the past decades there are growing concerns on the escalation and massive deprivation of the public life's quality, which some researchers attribute these as effects of the so-called 'Globalization'. To cite a few books, Prof. J. Stiglitz's book "Globalization and its Discontent" has sparked debate all over the world. A somewhat less known book which is worth to mention here is N. Hertz's book "The Silent Takeover." The present article may not offer something new compared to the aforementioned 'standard literature' in the critical analysis of globalization, but we discuss some hints on deep the root causes of the problems related to globalization, not only at phenomenological-social level but also at mathematical foundations of economics theory itself, namely the notion of 'utility'.

New Classes of Neutrosophic Linear Algebras

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral
Comments: 288 pages.

In this book we introduce mainly three new classes of linear algebras; neutrosophic group linear algebras, neutrosophic semigroup linear algebras and neutrosophic set linear algebras. The authors also define the fuzzy analogue of these three structures.

Quark Lepton Braids and Heterotic Supersymmetry

Authors: M. D. Sheppeard
Comments: 8 pages. submitted to JPA

A unique matrix is easily assigned to each Bilson-Thompson braid diagram. The quark and lepton matrices are then related to bosons via a twisted quantum Fourier transform, for which fermion and boson multiplets fit the dimension structure of heterotic strings.

Morphology, Linear and Nonlinear Optical Response of Octopolar Chromophores Embedded in a Silica Sonogel Matrix

Authors: V. Torres-Zúñiga, O.G. Morales-Saavedra, G. Hennrich, J.O. Flores-Flores, R. Ortega-Martínez
Comments: 15 pages. Manuscript submitted and accepted for publication as an article in Mol. Cryst. Liq. Cryst.

In this work, a liquid crystalline octopolar molecule 1,3,5-tris(ethynylphenyl)benzene-(1) was successfully embedded as dopant chromophore within a SiO2 based sonogel network in order to prepare stable solid state hybrid materials with intense second harmonic generation (SHG). This recently synthesized octopolar compound exhibit a centrosymmetric C₃-symmetry structure, which is constituted by an electron-rich core and electron-poor periphery groups. The sonogel method, induced by energetic ultrasonic (US) waves applied at the TEOS/H₂O reactant mixture interface has proven to be a suitable route in the manufacture of monolithic hybrid systems suitable for optical characterizations. The octopolar-based hybrid samples were comprehensively studied in their morphology, spectroscopic, linear and second-order nonlinear optical (NLO) properties, according to several characterization techniques: epimicroscopy, AFM, UV-Vis- and fluorescence (PL) spectroscopies, and the NLO-SHG-technique. Epimicroscopy, photoluminiscent and absorption spectra evidence an optimal and homogeneous inclusion of the octopolar compounds within the glassy sonogel network. Without necessity of molecular poling processes, the effective quadratic-NLO susceptibility χ_effS⁽²⁾ of the hybrid was estimated to 13.6x10^-3 pm/V at 1064 nm by SHG-transmission experiments recorded far-off of the resonance regime.

The Tsallis Entropy and the Boltzmann Entropy Applicable to the Same Classic Generalized System

Authors: Xiangjun Feng
Comments: 3 pages and 3 figures. This paper has been published in the on-line journal of World Chinese Forum On Science of General Systems (WCFSGS), ISSN 1936-7260. Report Number: 300-P-10-04-01. Journal Reference: WCFSGS VOL 6, NO. S1 ( A SPECIAL EDITION ON NONEXTENSIVE MECHANICS ), APRIL 2010, ISSN 1936 - 7260.

It is demonstrated clearly that for the same classic generalized system the Tsallis power-laws with both the q > 1 and the q < 1 can be induced by the constraint of the constant harmonic mean for the so-called reciprocal energies r E and at the same time the Boltzmann distribution or the negative exponential probability distribution can be generated with the constraint of the constant arithmetic mean for the generalized energies E . The author thus argues that there might be no definite "extensive system" or "classic system" and there are only "classic physical parameters" and "classic constraints". For any physical system or generalized system, it is the non-natural constraints which determine both the forms of the entropies and the non-uniform equilibrium distributions.

Consequences of Squeezing Initially Coherent (Semi Classical) States with Regards to Finding if the Cosmological Constant Is, or is not a 'vacuum' Field

Authors: Andrew Beckwith
Comments: 30 pages, 5 figures. One of two subject areas submitted to the conference 11th annual international meeting "Fundamental Frontiers of Physics" which will take place in the capital of France, Paris, from the 6th to the 9th of July, 2010.

The following document is to prepare an analysis on if the cosmological constant is a vacuum field. Candidates for how to analyze this issue come up in terms of brane theory, modified treatments of WdM theory (pseudo time component added) and/ or how to look at squeezing of vacuum states, as initially coherent semi classical constructions, or string theory versions of coherent states. The article presents a thought experiment if there is a non zero graviton mass, and at the end, in the conclusion states experimental modeling criteria which may indicate if a non zero graviton mass is measurable, which would indicate the existence, de facto of a possible replacement for DE, based upon non zero mass gravitons, and indications for a replacement for a cosmological constant.

The "Measurement Problem" in Quantum Physics Can be Partly Resolved with Analysis of Relatedness Between Space-Time, Physical Time and Psychological Time

Authors: Amrit S. Sorli
Comments: 5 pages

Clocks are systems for measuring frequency, velocity, duration and numerical order t₀,t₁,t₂,...,t_n of physical events. Time t obtained with clocks is not a forth dimension X₄ of space, time t is only a component of X₄ = i * c * t. This view of clock/time as a measuring system sees physical phenomena running exclusively in space and not in time. This view is supported with several experiments which confirm that time t of physical event can be zero. Time is not part of space; time is run of clocks in space. Past, present and future exist as a psychological time in the mind only not in the universe. We experience motion i.e. change in the space through the frame of psychological time. We "project" linear psychological time "past-present-future" into the space, however it is not there. Observer who distinguishes between space-time, physical time and psychological time is aware that in quantum measurement he only measures physical events in space and not in time. Clock/time is merely a measuring device. With this understanding observer's observation, measurement and experience of quantum phenomena are closer to their real nature. Stream of numerical order of quantum phenomena t₀,t₁,t₂,...,t_n runs in space only and not in time. Stream of quantum phenomena has no duration on its own. Duration is result of measurement.

On the Relation Between Mathematics, Natural Sciences, and Scientific Inquiry

Authors: V. Christianto, Florentin Smarandache
Comments: 17 pages

Some ratio estimators for estimating the population mean of the variable under study, which make use of information regarding the population proportion possessing certain attribute, are proposed. Under simple random sampling without replacement (SRSWOR) scheme, the expressions of bias and mean-squared error (MSE) up to the first order of approximation are derived. The results obtained have been illustrated numerically by taking some empirical population considered in the literature.

Improved Exponential Estimator for Population Variance Using Two Auxiliary Variables

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 8 pages

In this paper exponential ratio and exponential product type estimators using two auxiliary variables are proposed for estimating unknown population variance S_y². Problem is extended to the case of two-phase sampling. Theoretical results are supported by an empirical study.

Bifurcations and Pattern Formation in Particle Physics: a Model Study

Authors: Ervin Goldfain
Comments: 17 pages, This contribution is a sequel to EPL, 82 (2008), 11001. Its content has been updated and expanded with research findings from 2008 up to the present.

Quantum field theories, regardless of their content, lead to a finite or infinite number of coupled nonlinear field equations. In general, solving these equations in analytic form or managing them through lattice-based computations has been met with limited success. We argue that the theory of nonlinear dynamical systems offers a fresh approach to this challenge. Working from the universal route to chaos in coupled systems of differential equations, we find that: a) particles acquire mass as plane wave solutions of the complex Ginzburg-Landau equation (CGLE), without any reference to the hypothetical Higgs scalar; b) the U(1) x SU(2) and SU(3) gauge groups, as well as leptons and quarks, are sequentially generated

Somme Remarks About Starlight Aberration

Authors: Roald C. Maximo
Comments: 2 pages

Many physicists still do not accept the obvious conclusion that (c + v) and (c - v) are valid solutions when applied to moving observers. There are actually well known experimental proofs to validate those expressions. Besides the Sagnac effect, one experiment that has been hidden and given no publicity was a measurement of the orbital periods of the Jovian satellite (Io) performed by Ole C. Römer that shows just such a velocity composition as the Earth approaches the planet or recedes in its orbit. [1] But, perhaps due to the pervading lato sensu interpretation of the second postulate of the Special Theory of Relativity in connection with the currently generalized opinion that any physical theory, to be valid, must conform to the TR, many physicists are reluctant to accept it. Whenever such a situation arises, they are eager to draw the Lorentz transformation from their pockets and apply it in some way to alleviate the discomfort.

The Wave Structure of the Electric Field

Authors: Michael Harney
Comments: 5 pages

Maxwell's equations describe the interactions of the electromagnetic field at a macroscopic level. In the 1920s, Louis DeBroglie demonstrated that every moving particle (including an electron) has a wave nature, and we know from Einstein that every wave has a particle nature, which we call the photon. Later in the 1930s, Paul Dirac's development of the famous Dirac equation showed the quantum nature of the electron at relativistic speeds. Then in 1948 Richard Feynman and Julian Schwinger extended these concepts in the development of quantum electrodynamics which gives a full accounting (although a very strange one) of how an electron can borrow energy from the vacuum of space and return it legally as long it does so within limits of the uncertainty principle.

Application of Wheeler-Feynman Absorber Theory to Laser Power Output

Authors: Michael Harney, Michael Weber, Milo Wolff
Comments: 2 pages

The method described is designed to increase laser output power using a concept from Wheeler-Feynman absorber theory [1,2] and the work of Tetrode [3], where photons are modeled as sources of energy that must also have a sink (an electron) to be absorbed. According to Wheeler-Feynman and Tetrode, if an electron is not present to absorb the photon, then the photon can never be emitted. In Wheeler-Feynman absorber theory, advanced and retarded potentials resemble time-reversal equations because there must be communication faster than light between the source-photon and the sink-electron, reasoned Feynman, so that the source photon's atom would know whether to emit a photon. This enigma was resolved by Milo Wolff in his work "Exploring the Physics of the Unknown Universe" [4], where he describes the use of spherical scalar in-waves and out-waves that travel at c and whose local speed is based on local-mass density. The in-out waves form electrons and also allows communication between them.

The New Prime Theorem (19)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove that such that (see paper) has infinitely many prime solutions.

The New Prime Theorem (18)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove Hardy-Littlewood conjecture E : x² + 1

The New Prime Theorem (17)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove that such that P_n = 2 P₁P₂ ... P_n-1 has infinitely many prime solutions.

The New Prime Theorem (16)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove that there exist infinitely many primes P such that each of (j)ⁿ P + (k - j)ⁿ is a prime.

The New Prime Theorem (15)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove that there exist infinitely many primes P such that each of (j)³ P + (k - j)³ is a prime.

The New Prime Theorem (14)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that there exist infinitely many primes P such that each of (j)² P + (k - j)² is a prime.

S-Denying a Theory

Authors: Florentin Smarandache
Comments: 8 pages

In this paper we introduce the operators of validation and invalidation of a proposition, and we extend the operator of S-denying a proposition, or an axiomatic system, from the geometric space to respectively any theory in any domain of knowledge, and show six examples in geometry, in mathematical analysis, and in topology.

Improvement in Estimating Population Mean Using Two Auxiliary Variables in Two-Phase Sampling

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 11 pages

This study proposes improved chain-ratio type estimator for estimating population mean using some known values of population parameter(s) of the second auxiliary character. The proposed estimators have been compared with two-phase ratio estimator and some other chain type estimators. The performances of the proposed estimators have been supposed with a numerical illustration.

Optimum Statistical Test Procedure

Authors: Rajesh Singh, Jayant Singh, Florentin Smarandache
Comments: 16 pages

Optimum Statistical Test Procedure

Ratio-Product Type Exponential Estimator for Estimating Finite Population Mean Using Information on Auxiliary Attribute

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 15 pages

In practice, the information regarding the population proportion possessing certain attribute is easily available see Jhajj et.al. (2006). For estimating the population mean Y of the study variable y, following Bahl and Tuteja (1991), a ratio-product type exponential estimator has been proposed by using the known information of population proportion possessing an attribute (highly correlated with y) in simple random sampling. The expressions for the bias and the mean-squared error (MSE) of the estimator and its minimum value have been obtained. The proposed estimator has an improvement over mean per unit estimator, ratio and product type exponential estimators as well as Naik and Gupta (1996) estimators. The results have also been extended to the case of two phase sampling. The results obtained have been illustrated numerically by taking some empirical populations considered in the literature.

Almost Unbiased Exponential Estimator for the Finite Population Mean

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 12 pages

In this paper we have proposed an almost unbiased ratio and product type exponential estimator for the finite population mean Y-bar. It has been shown that Bahl and Tuteja (1991) ratio and product type exponential estimators are particular members of the proposed estimator. Empirical study is carried to demonstrate the superiority of the proposed estimator.

The New Prime Theorem (13)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove that n x aⁿ ± 1 has infinitely many prime solutions and n x 2ⁿ ± 1 have finite prime solutions.

The New Prime Theorem (12)

Authors: Chun-Xuan Jiang
Comments: 1 pages

Using Jiang function we prove that 3 x a³ ± 1 has infinitely many prime solutions

The New Prime Theorem (11)

Authors: Chun-Xuan Jiang
Comments: 1 pages

Using Jiang function we prove that 2 x a² ± 1 has infinitely many prime solutions

Importance of Sources Using the Repeated Fusion Method and the Proportional Conflict Redistribution Rules #5 and #6

Authors: Florentin Smarandache, Jean Dezert
Comments: 6 pages

We present in this paper some examples of how to compute by hand the PCR5 fusion rule for three sources, so the reader will better understand its mechanism. We also take into consideration the importance of sources, which is different from the classical discounting of sources.

Almost Unbiased Ratio and Product Type Estimator of Finite Population Variance Using the Knowledge of Kurtosis of an Auxiliary Variable in Sample Surveys

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 11 pages

It is well recognized that the use of auxiliary information in sample survey design results in efficient estimators of population parameters under some realistic conditions. Out of many ratio, product and regression methods of estimation are good examples in this context. Using the knowledge of kurtosis of an auxiliary variable Upadhyaya and Singh (1999) has suggested an estimator for population variance. In this paper, following the approach of Singh and Singh (1993), we have suggested almost unbiased ratio and product-type estimators for population variance.

District Level Analysis of Urbanization from Rural-to-Urban Migration in the Rajasthan State

Authors: Jayant Singh, Hansraj Yadav, Florentin Smarandache
Comments: 11 pages

Migration has various dimensions; urbanization due to migration is one of them. In Rajasthan State, District level analysis of urbanization due to migrants shows trend invariably for all the districts of the state though the contribution in urbanization by the migrants varies from district to district. In some districts the share of migrants moving to urban areas is very impressive though in others it is not that much high. The migrants' contribution in urbanization is on the rising over the decades. In this paper district level migration in the Rajasthan state is examined in relation to total urbanization and urbanization due to migration.

Alternatives to Pearson's and Spearman's Correlation Coefficients

Authors: Florentin Smarandache
Comments: 9 pages

This article presents several alternatives to Pearson's correlation coefficient and many examples. In the samples where the rank in a discrete variable counts more than the variable values, the mixture of Pearson's and Spearman's gives a better result.

Immediate Calculation of Some Poisson Type Integrals Using Supermathematics Circular ex-Centric Functions

Authors: Florentin Smarandache, Mircea Eugen Selariu
Comments: 10 pages

This article presents two methods, in parallel, of solving more complex integrals, among which is the Poisson's integral, in order to emphasize the obvious advantages of a new method of integration, which uses the supermathematics circular ex-centric functions. We will specially analyze the possibilities of easy passing/changing of the supermathematics circular ex-centric functions of a centric variable α to the same functions of ex-centric variable &theta. The angle α is the angle at the center point O(0,0), which represents the centric variable and θ is the angle at the ex-center E(k,ε), representing the ex-centric variable. These are the angles from which the points W₁ and W₂ are visible on the unity circle - resulted from the intersection of the unity/trigonometric circle with the revolving straight line d around the ex-centric E(k,&epsilon) - from O and from E, respectively.

A Simple Proportional Conflict Redistribution Rule

Authors: Florentin Smarandache, Jean Dezert
Comments: 21 pages

One proposes a first alternative rule of combination to WAO (Weighted Average Operator) proposed recently by Josang, Daniel and Vannoorenberghe, called Proportional Conflict Redistribution rule (denoted PCR1). PCR1 and WAO are particular cases of WO (the Weighted Operator) because the conflicting mass is redistributed with respect to some weighting factors. In this first PCR rule, the proportionalization is done for each non-empty set with respect to the non-zero sum of its corresponding mass matrix - instead of its mass column average as in WAO, but the results are the same as Ph. Smets has pointed out. Also, we extend WAO (which herein gives no solution) for the degenerate case when all column sums of all non-empty sets are zero, and then the conflicting mass is transferred to the non-empty disjunctive form of all non-empty sets together; but if this disjunctive form happens to be empty, then one considers an open world (i.e. the frame of discernment might contain new hypotheses) and thus all conflicting mass is transferred to the empty set. In addition to WAO, we propose a general formula for PCR1 (WAO for non-degenerate cases). Several numerical examples and comparisons with other rules for combination of evidence published in literature are presented too. Another distinction between these alternative rules is that WAO is defined on the power set, while PCR1 is on the hyper-power set (Dedekind's lattice). A nice feature of PCR1, is that it works not only on non-degenerate cases but also on degenerate cases as well appearing in dynamic fusion, while WAO gives the sum of masses in this cases less than 1 (WAO does not work in these cases). Meanwhile we show that PCR1 and WAO do not preserve unfortunately the neutrality property of the vacuous belief assignment though the fusion process. This severe drawback can however be easily circumvented by new PCR rules presented in a companion paper.

Single Valued Neutrosophic Sets

Authors: Haibin Wang, Florentin Smarandache, Yanqing Zhang, Rajshekhar Sunderraman
Comments: 4 pages

Neutrosophic set is a part of neutrosophy which studies the origin, nature, and scope of neutralities, as well as their interactions with different ideational spectra. Neutrosophic set is a powerful general formal framework that has been recently proposed. However, neutrosophic set needs to be specified from a technical point of view. To this effect, we define the settheoretic operators on an instance of neutrosophic set, we call it single valued neutrosophic set (SVNS). We provide various properties of SVNS, which are connected to the operations and relations over SVNS.

A Proof of Smarandache-Pătrașcu's Theorem Using Barycentric Coordinates

Authors: Claudiu Coandă
Comments: 4 pages

In this article we prove the Smarandache-Pătrașcu's Theorem in relation to the inscribed orthohomological triangles using the barycentric coordinates.

Toward an Exciting Rebuilding of Modern Physics

Authors: Alex Ceapa
Comments: 80 pages

At the time factors of unknown origin and physical meaning (like β in the Lorentz transformation, the Dirac matrices, etc.) are embedded in some underlying equations and, by way of consequence, the physical significance of the terms of these equations rests undisclosed, we validate the principle of the physical determination of equations in special relativity theory and relativistic quantum theory, as first step toward an exciting foundation of modern physics on this principle (yet all restraints of the principle are off in modern physics).

Non-Equilibrium Dynamics as Root Cause of Some Anomalies in Particle Physics

Authors: Ervin Goldfain
Comments: 16 pages, This contribution is a sequel to a paper published in Hadronic Journal, Vol. 31(6), p.179, 2008.

Despite its remarkable predictive power, the Standard Model for particle physics (SM) leaves out many open questions. Two representative examples are the issue of CP violation and the anomalous magnetic moment of leptons (AMM). Our work develops from the premise that the postulate of unitary evolution no longer holds near or above the scale of electroweak interaction or near the "new physics" sector of SM. Results suggest that CP violation in kaon physics and the AMM problem are manifestations of nonequilibrium dynamics. Numerical predictions are found to be in close agreement with experimental data.

Transformation of the Compton Effect and Fundamentals About Electromagnetism

Authors: Arman.V.zadeh
Comments: 21 pages

In this article we want to say about the Compton effect and the Zeeman effect. (Both of them are almost one effect). We know that both of them are about the light (electromagnetism waves) and some special particularity of that. For example the Zeeman effect is about the refraction of the light that when we put the source of the electromagnetism wave near the source of the magnetism or electrical field we'll see the breaking or refraction of the light and we can also that is possible that the light refract to some part for example three or four part but we should remember that these effect (Zeeman, Compton) aren't just for the light(the electromagnetism type) and of course they are a little about the light and some part of the light like the X-ray or β-ray or γ-ray or.... But it cant be impossible that these effects be correct also about the light.

Looking for Roots in All the Wrong Places: a Comment on Arxiv:1003.5008

Authors: Ron Bourgoin
Comments: 4 pages

The authors of ArXiv:1003.5008 tell us they are searching for the foundations of quantum mechanics, a theory they say was born early in the twentieth century. As a matter of fact, the theory was born in the eighteenth century.

The New Prime Theorem (10) there Are Finite Mersenne Primes and there Are Finite Repunits Primes

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove the finite Mersenne primes and the finite repunits primes.

The New Prime Theorem (9) there Are Finite Fermat Primes

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove the finite fermat primes.

The Prime Principle in Clusters and Nanostructures

Authors: Chun-Xuan Jiang
Comments: 7 pages

Why we have five fingers. We suggest two principles: (1) the prime principle and (2) the symmetric principle. We prove that 1, 3, 5, 7, 11, 23, 47, and 2, 4, 6, 10, 14, 22, 46, 94 are the most stable numbers, which are the basic building-blocks in clusters and nanostructures. The prime principle is the mathematical foundations for clusters and nanosciences. It is a theory of everything.

Prime Theorem: P₂ = AP₁ + b, Polignac Theorem and Goldbach Theorem

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove prime theorem: P₂ = aP₁ + b, Polignac theorem and Goldbach theorem.

K-Factorial

Authors: Florentin Smarandache
Comments: 1 pages

As a generalization of the factorial and double factorial one defines the kfactorial of n as the below product of all possible strictly positive factors (see paper)

Back and Forth Factorials

Authors: Florentin Smarandache
Comments: 2 pages

Back and Forth Factorials

Some Unsolved Problems, Questions, and Applications of the Brightsen Nucleon Cluster Model

Authors: Florentin Smarandache
Comments: 3 pages

According to the Brightsen Nucleon Cluster Model [1] all nuclides of beta stable isotopes can be described by three fundamental nucleon clusters {NPN,PNP,NP), with halo clusters (NN,PP,NNN) now experimentally observed. The Brightsen model builds on the early cluster models of the Resonating Group Structure of John Wheeler [2] and the Linus Pauling Close-Packed Spheron Model [3], which predict mathematically that the wave function of a composite nucleus can be viewed quantum mechanically as a combination of partial wave functions that correspond to the multiple ways nucleons (protons, neutrons) can be distributed into closepacked clusters, thus rejecting the standard model Hartree-Fock formalism of average field interactions between independent nucleons in nuclear shells. Presented in this section are a number of unsolved problems, questions, and future experimental pathways based on the Brightsen Nucleon Cluster Model formalism--many additional applications can be gleamed from careful study of the literature cited in the references provided

Souvenirs from the Empire of Numbers

Authors: Florentin Smarandache
Comments: 20 pages

Browsing through my fifth to twelfth grade years of preoccupation for creation I discovered a notebook of Number Theory. I liked to play with numbers as Tudor Arghezi (1880-1967) - our second national Romanian poet {after the genial poet Mihai Eminescu (1850-1889)} - played with words. I was so curious and amazed by the numbers' properties. Interesting theorems, equations, and inequalities! Such fascinating people who dedicated their research to numbers, just for the sake of science! I collected many results and tried to write a handbook of mathematicians and their results.

Rank Distance Bicodes and Their Generalization

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, N. Suresh Babu, R.S. Selvaraj
Comments: 152 pages

In this book the authors introduce the new notion of rank distance bicodes and generalize this concept to Rank Distance n-codes (RD n-codes), n, greater than or equal to three. This definition leads to several classes of new RD bicodes like semi circulant rank bicodes of type I and II, semicyclic circulant rank bicode, circulant rank bicodes, bidivisible bicode and so on. It is important to mention that these new classes of codes will not only multitask simultaneously but also they will be best suited to the present computerised era. Apart from this, these codes are best suited in cryptography.

Higgs Field and the Creation of Mass Standing Wave Structure of the Electron-IV

Authors: V.A.Induchoodan Menon
Comments: 12 pages

The author develops his idea of the standing electromagnetic half wave structure of the electron and proposes that the confinement of the wave is effected by the interactions with the Higgs field which can be explained on the basis of the uncertainty principle. These interactions allow vacuum to act like a thermal bath with the standing half wave in equilibrium with it. It is shown that this equilibrium is not destroyed even when it is in uniform translational motion. This invariance of the equilibrium to the velocity transformation is another way of looking at the theory of relativity.

The Moebius Strip. a Biology of Elementary Particles

Authors: Giuliano Bettini
Comments: 163 pages, In Italian

A book of semi qualitative ideas on electron, quarks and life. I quote from David Hestenes: "For many years I mulled over (...etc.). I was reluctant to publish my ideas, however, because the supporting arguments were mainly qualitative, and physics tradition demands a quantitative formulation which can be subjected to experimental test". We intend to make us an image purely electromagnetic of all interactions, and elementary particles, in particular electron, and quarks. This would force even the idea of a single universal vibration, a single field. The electron is interpreted as a small electric current carrying the elementary charge, elementary mass and Planck quantum of action. With the aid of a few math we identify the electron as one electromagnetic half wave closed on a Moebius strip. This is equivalent to a full wavelength making two turns on the border. It is also probably not totally irrelevant to note that this leads to interesting numerics on the fine structure constant. We identify a quark with a confined electromagnetic wave which is not sufficient in itself to complete a closed loop in space. So quarks are pictured as 1/3 and 2/3 of a full wavelength. A space model of their combination leads to the entire set of all and only the mesons and barions, in a unique way. In a quite spontaneous way colours theory is interpreted. Finally the various helices of quarks are interpreted as living organisms and similarities with a biological behaviour are showed. Arguments here are of course admittely primitive and mainly qualitative, also if supported with some math, but to my knowledge this overall conjecture has not been discussed elsewhere, and therefore may be useful for further research

The New Prime Theorem (8)

Authors: Chun-Xuan Jiang
Comments: 1 page

Using Jiang function we prove that x⁶ + 1091 has no prime solutions.

The New Prime Theorem (7)

Authors: Chun-Xuan Jiang
Comments: 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + 15 - j is a prime.

The New Prime Theorem (6)

Authors: Chun-Xuan Jiang
Comments: 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + 9 - j is a prime.

The New Prime Theorem (5)

Authors: Chun-Xuan Jiang
Comments: 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + k - j is a prime.

The New Prime Theorem (4)

Authors: Chun-Xuan Jiang
Comments: 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + 7 - j is a prime.

The New Prime Theorem (3)

Authors: Chun-Xuan Jiang
Comments: 1 page

Using Jiang function we prove that there exist infinitely many primes P such that each jP + 5 - j is a prime.

Disproofs of Riemann's Hypothesis

Authors: Chun-Xuan Jiang
Comments: 13 pages

As it is well known, the Riemann hypothesis on the zeros of the ζ(s) function has been assumed to be true in various basic developments of the 20-th century mathematics, although it has never been proved to be correct. The need for a resolution of this open historical problem has been voiced by several distinguished mathematicians. By using preceding works, in this paper we present comprehensive disproofs of the Riemann hypothesis. Moreover, in 1994 the author discovered the arithmetic function J_n(ω) that can replace Riemann's ζ(s) function in view of its proved features: if J_n(ω) ≠ 0, then the function has infinitely many prime solutions; and if J_n(ω) = 0, then the function has finitely many prime solutions. By using the Jiang J₂(ω) function we prove the twin prime theorem, Goldbach's theorem and the prime theorem of the form x² + 1. Due to the importance of resolving the historical open nature of the Riemann hypothesis, comments by interested colleagues are here solicited.

Foundations of Santilli's Isonumber Theory

Authors: Chun-Xuan Jiang
Comments: 413 pages

In my works (see the bibliography at the end of the Preface) I often expressed the view that the protracted lack of resolution of fundamental problems in science signals the needs of basically new mathematics. This is the case, for example, for: quantitative representations of biological structures; resolution of the vexing problem of grand-unification; invariant treatment of irreversibility at the classical and operator levels; identification of hadronic constituents definable in our spacetime; achievement of a classical representation of antimatter; and other basic open problems.

Neutrosophic Diagram and Classes of Neutrosophic Paradoxes

Authors: Florentin Smarandache
Comments: 14 pages

These paradoxes are called "neutrosophic" since they are based on indeterminacy (or neutrality, i.e. neither true nor false), which is the third component in neutrosophic logic. We generalize the Venn Diagram to a Neutrosophic Diagram, which deals with vague, inexact, ambiguous, illdefined ideas, statements, notions, entities with unclear borders. We define the neutrosophic truth table and introduce two neutrosophic operators (neuterization and antonymization operators) give many classes of neutrosophic paradoxes.

An Application of a Theorem of Orthohomological Triangles

Authors: Ion Pătraşcu, Florentin Smarandache
Comments: 3 pages

NIn this note we prove a problem given at a Romanian student mathematical competition, and we obtain an interesting result by using a Theorem of Orthohomological Triangles.

Neutrosophic Logic as a Theory of Everything in Logics

Authors: Florentin Smarandache
Comments: 3 pages

Neutrosophic Logic (NL) is a Theory of Everything in logics, since it is the most general so far. In the Neutrosophic Propositional Calculus a neutrosophic proposition has the truth value (T, I, F), where T is the degree of truth, I is the degree of indeterminacy (or neutral, i.e. neither truth nor falsehood), and F is the degree of falsehood, where T, I, F standard or non-standard subsets of the non-standard unit interval ]-0, 1+[. In addition, these values may vary over time, space, hidden parameters, etc. Therefore, NL is a triple-infinite logic but, by splitting the Indeterminacy, we prove in this article that NL is a n-infinite logic, with n = 1, 2, 3, 4, 5, 6, ... . Also, we present a total order on Neutrosophic Logic.

Blogs on Applications of Neutrosophics and Multispace in Sciences

Authors: Florentin Smarandache
Comments: 19 pages

The following blogs on applications of neutrosophics and multispace in sciences include meditations / reflections on science, comments, hypotheses, proposals, comparisons of ideas, possible projects, extensions or deviations or alternatives to classical knowledge, etc. selected from e-mails, letters, drafts, conversations, impressions, etc. We introduce the non-standard quaternion space and non-standard biquaternion space [and even a generalization of them to a general non-standard vector space of any dimension] as possible working spaces for connecting the micro- and macro-levels in physics. Neutrosophy is a MetaPhilosophy.

Statistical Modelling of Primary Ewing Tumours of the Bone

Authors: Sreepurna Malakar, Florentin Smarandache, Sukanto Bhattacharya
Comments: 12 pages

This short technical paper advocates a bootstrapping algorithm from which we can form a statistically reliable opinion based on limited clinically observed data, regarding whether an osteo-hyperplasia could actually be a case of Ewing's osteosarcoma. The basic premise underlying our methodology is that a primary bone tumour, if it is indeed Ewing's osteosarcoma, cannot increase in volume beyond some critical limit without showing metastasis. We propose a statistical method to extrapolate such critical limit to primary tumour volume. Our model does not involve any physiological variables but rather is entirely based on time series observations of increase in primary tumour volume from the point of initial detection to the actual detection of metastases.

Back and Forth Summands

Authors: Florentin Smarandache
Comments: 2 pages

Back and Forth Summands

Self Knowledge and Knowledge Communication

Authors: Liu Feng, Florentin Smarandache
Comments: 6 pages

To deal with tough issues in knowledge management, the paper reexamines knowledge structure and has proposed a novel knowledge communication model based on the oriental cultural foundation. Knowledge discovery is not a simple addition or accumulation of information, but needs a feasible structural description. As an oriental approach, the paper constructs the structure on the bases of unity of opposites and their neutralities (as in neutrosophy; neutralities are the included middle of two opposites), which stresses the individualized self knowledge pattern or self knowledge structure. It signifies the dynamics in knowledge management - the principle of attraction between opposite natures and the neutralities in between them. It implies an identity in the opposites which serves as the impartial knowledge (since the opposites tend towards their neutralities), the completeness of knowledge, which is defined in the paper as imaginary part of knowledge.

Vectored Route-Length Minimization a Heuristic and an Open Conjecture

Authors: Florentin Smarandache, Sukanto Bhattacharya
Comments: 7 pages

We have posed a simple but interesting graph theoretic problem and posited a heuristic solution procedure, which we have christened as Vectored Route-length Minimization Search (VeRMinS). Basically, it constitutes of a re-casting of the classical "shortest route" problem within a strictly Euclidean space. We have only presented a heuristic solution process with the hope that a formal proof will eventually emerge as the problem receives wider exposure within mathematical circles.

Conditional Probability of Actually Detecting a Financial Fraud a Neutrosophic Extension to Benford's Law

Authors: Sukanto Bhattacharya, Kuldeep Kumar, Florentin Smarandache
Comments: 9 pages

This study actually draws from and builds on an earlier paper (Kumar and Bhattacharya, 2002). Here we have basically added a neutrosophic dimension to the problem of determining the conditional probability that a financial fraud has been actually committed, given that no Type I error occurred while rejecting the null hypothesis H₀: The observed first-digit frequencies approximate a Benford distribution; and accepting the alternative hypothesis H₁: The observed first-digit frequencies do not approximate a Benford distribution. We have also suggested a conceptual model to implement such a neutrosophic fraud detection system.

N-Norm and N-Conorm in Neutrosophic Logic and Set, and the Neutrosophic Topologies

Authors: Florentin Smarandache
Comments: 11 pages

In this paper we present the N-norms/N-conorms in neutrosophic logic and set as extensions of T-norms/T-conorms in fuzzy logic and set. Also, as an extension of the Intuitionistic Fuzzy Topology we present the Neutrosophic Topologies.

Neutrosophic Relational Data Model

Authors: Haibin Wang, Rajshekhar Sunderraman, Florentin Smarandache, André Rogatko
Comments: 25 pages

In this paper, we present a generalization of the relational data model based on interval neutrosophic set [1]. Our data model is capable of manipulating incomplete as well as inconsistent information. Fuzzy relation or intuitionistic fuzzy relation can only handle incomplete information. Associated with each relation are two membership functions one is called truth-membership function T which keeps track of the extent to which we believe the tuple is in the relation, another is called falsity-membership function F which keeps track of the extent to which we believe that it is not in the relation. A neutrosophic relation is inconsistent if there exists one tuple a such that T(α) + F(α) > 1. In order to handle inconsistent situation, we propose an operator called "split" to transform inconsistent neutrosophic relations into pseudo-consistent neutrosophic relations and do the set-theoretic and relation-theoretic operations on them and finally use another operator called "combine" to transform the result back to neutrosophic relation. For this data model, we define algebraic operators that are generalizations of the usual operators such as intersection, union, selection, join on fuzzy relations. Our data model can underlie any database and knowledge-base management system that deals with incomplete and inconsistent information.

A Triple Inequality with Series and Improper Integrals

Authors: Florentin Smarandache
Comments: 4 pages

As a consequence of the Integral Test we find a triple inequality which bounds up and down both a series with respect to its corresponding improper integral, and reciprocally an improper integral with respect to its corresponding series.

N-Ary Fuzzy Logic and Neutrosophic Logic Operators

Authors: Florentin Smarandache, V. Christianto
Comments: 15 pages

We extend Knuth's 16 Boolean binary logic operators to fuzzy logic and neutrosophic logic binary operators. Then we generalize them to n-ary fuzzy logic and neutrosophic logic operators using the smarandache codification of the Venn diagram and a defined vector neutrosophic law. In such way, new operators in neutrosophic logic/set/probability are built.

Gravity

Authors: Arman.V.zadeh
Comments: 10 pages

In this article we want to say about the gravity between the atoms to the new and special way. We know that the atom and the gravity between them are stable by moving the electron on the circuits around the nucleus(from the past articles) and know in this article we want to point to some interesting and new methods (at the new theory) to explain the events happened between the atoms and some materials in the gravity system. For this calculate some equation about the gravity.

Measurement of One-Way Speed of Light

Authors: Emil D. Gigov
Comments: 4 pages

Wave theory of light was tested by the Michelson's interferometer, whereas Newtonian corpuscular theory can be tested with the new interferometer, which can show whether the speed of light in empty space is variable during Doppler effect. Such measurement is possible due to the effect of Fizeau.

Strategy on T, i, F Operators.

Authors: Florentin Smarandache
Comments: 6 pages

The paper presents an initial explorations on T, I, F operations based on genetic concept hierarchy and genetic referential hierarchy, as a novel proposal to the indeterminacy issue in neutrosophic logic, in contrast to the T, I, F values inherited from conventional logics in which those values would fail to demonstrate the genetic aspect of a concept and accordingly loose the connection between generality and practicality. Based on the novel definition of logic and on the relativity of T, F concept, it illustrates that T, F are hierarchical operations which inter-consist and inter-complement each other, that "I" relates to a learning behavior profiled by an inspiration from I-ching, and that the neutralization operation, as the means to solve contradictions, will eventually come to the unification of opposites, leading to the fundamental issues in Buddhism and such alike. It also implies that Buddhism and Daoism are not religions.

Neutrosophic Set a Generalization of the Intuitionistic Fuzzy Set

Authors: Florentin Smarandache
Comments: 7 pages

In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.

Neutrosophic Logic a Generalization of the Intuitionistic Fuzzy Logic

Authors: Florentin Smarandache
Comments: 7 pages

In this paper one generalizes the intuitionistic fuzzy logic (IFL) and other logics to neutrosophic logic (NL). The differences between IFL and NL (and the corresponding intuitionistic fuzzy set and neutrosophic set) are pointed out.

Algebraic Generalization of Venn Diagram

Authors: Florentin Smarandache
Comments: 3 pages

It is easy to deal with a Venn Diagram for 1 ≤ n ≤ 3 sets. When n gets larger, the picture becomes more complicated, that's why we thought at the following codification. That's why we propose an easy and systematic algebraic way of dealing with the representation of intersections and unions of many sets.

Toward Dialectic Matter Element of Extenics Model

Authors: Florentin Smarandache
Comments: 10 pages

Based on the authors intensive investigation on the oriental dialectics, the paper presents a novel theoretical frame of matter element in the world leading science, extenics dealing with inconsistency or incompatibility, covering the widest range of application area from informatics, system engineering to management and finance. The dialectic matter-element is defined as the integral of all existing and prospecting ones based on all the infinite possible cognitive models. The novel model serves as the origin of constraint matter elements, the unity of both state description and cognitive action (cognition force with respect to neural science), a latent part of extenics, and possibly as essence of matter element. It explains, in a novel perspective, the origin of a name, and uncovers the source of contradiction and even the impetus of cognition.

Uniform and Partially Uniform Redistribution Rules

Authors: Florentin Smarandache, Jean Dezert
Comments: 4 pages

This short paper introduces two new fusion rules for combining quantitative basic belief assignments. These rules although very simple have not been proposed in literature so far and could serve as useful alternatives because of their low computation cost with respect to the recent advanced Proportional Conflict Redistribution rules developed in the DSmT framework.

Neutrosophic Logic Based Semantic Web Services Agent

Authors: Haibin Wang, Yan-Qing Zhang, Rajshekhar Sunderraman, Florentin Smarandache
Comments: 15 pages

In this paper we propose a framework called Semanic Web Services (see paper for full abstract)

Super-Mathematics Functions

Authors: Mircea Eugen Șelariu
Comments: 14 pages, translated from Romanian by Marian Nitu and Florentin Smarandache

In this paper we talk about the so-called Super-Mathematics Functions (SMF), which often constitute the base for generating technical, neo-geometrical, therefore less artistic objects. These functions are the results of 38 years of research, which began at University of Stuttgart in 1969. Since then, 42 related works have been published, written by over 19 authors, as shown in the References.

Polarization

Authors: Arman.V.zadeh
Comments: 9 pages

In this article we want to consider the polarization for matters and atoms. We know that if a special ray go down to the surface of a transparent matter and if it was not polarized when it beats to the transparent matter like glass and water it will reflex to polarized way (of course it be in a special angle from water to the ray or from ray to perpendicular line to the water. Now we want to say the reason of that which why effect this event. We know that the special angle is different for different matters like glass or water or... and that's because which the (n) or refracture index for different matters is different and we easily can get the special number for different matters but to this way that we should get the angle between the refracted ray and reflected way to 90^o and this subject that why we should take the angle to 90^o is a experiment number. So we can get the angle with the Snell law and Brewster law. And in this article we want to consider that why the angle should be 90^o (to theory way).

Magnetism

Authors: Arman.V.zadeh
Comments: 7 pages

This article is about the magnetism particular's of matters and here we try to say easily the magnetism effects of matters in the small system like atom also we try to say the magnetism field with the electrical field.

Can the External Directed Edges of a Complete Graph Form a Radially Symmetric Field at Long Distance?

Authors: S. Halayka
Comments: 5 Pages.

Using a simple numerical method, the external directed edges of a complete graph are tested for their level of fitness in terms of how well they form a radially symmetric field at long distance (e.g., a test for the inverse square law in 3D space). It is found that the external directed edges of a complete graph can very nearly form a radially symmetric field at long distance if the number of graph vertices is great enough.

The New Prime Theorem (2)

Authors: Chun-Xuan Jiang
Comments: 1 pages

Using Jiang function we prove that there exist infinitely many primes P such that P₁ and P₂ are all prime.

The New Prime Theorem (1)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jiang function we prove that there exist infinitely many primes P₁ such that a P₁ + b is prime.

Eight Solved and Eight Open Problems in Elementary Geometry

Authors: Florentin Smarandache
Comments: 9 pages

In this paper we review eight previous proposed and solved problems of elementary 2D geometry [1], and we extend them either from triangle to polygons or from 2D to 3D-space and make some comments about them.

Three Conjectures and Two Open Generalized Problems in Number Theory

Authors: Florentin Smarandache
Comments: 3 pages

On a Problem with Primes.

Improvement of Weber's and Fechner's Laws on Sensations and Stimuli

Authors: Florentin Smarandache
Comments: 3 pages

In this paper one uses a mathematical modeling of psychological processes and one improves the Weber's Law and Fechner's Law on sensations and stimuli.

The Smarandache's Class of Paradoxes

Authors: C. Le
Comments: 4 pages, edited by C. Le, and translated into German by Bernd Hutschenreuther

The Smarandache's Class of Paradoxes are semantic paradoxes of the form "All is <A>, the <nonA> too!", where <nonA> is what is not <A>. As a particular case, replacing <A> but an attribute (or, in general, by an idea) it is well know the Smarandache semantic paradox: "All is possible, the impossible too!" which is the motto of the Paradoxism movement in arts, letters, and sciences.

Essay on the Proclivities of Particularity and Generality

Authors: Stephen P. Smith
Comments: 13 pages

The proclivities of particularity and generality describe a polarity, held together by a naked emotionality that signifies a felt middle-term. This polarity indicates a type of circular reasoning, and can endlessly oscillate due to an equivocation that confuses particularity with generality that may block emotional energies and prevent resolution. Deduction and induction represent the same polarity, as does the frequentist and Bayesian interpretations of statistics. Reintroducing emotion back into logic returns an intuitionist logic and grammar, and this permits the resolution of felt tension. This intuitionism is tied to a time-sense that oscillates between foresight (to particularity) and hindsight (to generality). Emotionality is found relating to causation, agreeing with A.N. Whitehead. It is hypothesized that the intuitionist logic provides a universal grammar, or a vitalistic organizing principle, that has impacted on biological evolution. This agrees with panpsychism and panentheism.

Convergence of Funcoids

Authors: Victor Porton
Comments: 4 pages

Considered convergence and limit for funcoids (a generalization of proximity spaces). I also have defined (generalized) limit for arbitrary (not necessarily continuous) functions under certain conditions. This article is a part of my Algebraic General Topology research.

Problems of Physics of the XX-th Century

Authors: Andreï V. Serghienko
Comments: 3 pages.

The paper represents a philosophical review of problems of physics of the XX-th century.

Theory of Electromagnetism and the Light

Authors: Arman.V.zadeh
Comments: 14 pages

This article is about atoms and their particulars in equations. There are lots of equations from this subject that they have given by different scientists. For example one of those equations is the Planck equation that is for calculating the electron's momentum in the atom and we can add mechanic's statistic for some or all place's of electron in the atom.

New Prime K-Tuple Theorem (6)

Authors: Chun-Xuan Jiang
Comments: 1 pages

Using Jiang function we prove that for every positive integer k there exist infinitely many primes P such that each of P + 4ⁿ is prime.

New Prime K-Tuple Theorem (5)

Authors: Chun-Xuan Jiang
Comments: 1 pages

Using Jiang function we prove that for every positive integer k there exist infinitely many primes P₁ and P₂ such that each of 1 2 jP₁ + (j + 1)P₂ is prime.

New Prime K-Tuple Theorem (4)

Authors: Chun-Xuan Jiang
Comments: 1 pages

Using Jiang function we prove that for every positive integer k there exist infinitely many primes P such that each of P + (2j)² is prime.

New Prime K-Tuple Theorem (3)

Authors: Chun-Xuan Jiang
Comments: 1 pages

Using Jiang function we prove that for every positive integer k there exist infinitely many primes P such that each of jP + j +1 is prime.

New Prime K-Tuple Theorem (2)

Authors: Chun-Xuan Jiang
Comments: 3 pages

Using Jiang function we prove that for every positive integer k there exist infinitely many primes P such that each of P + j(j + 1) is prime

Analytical Proof of the Taylor Equation Including Taylor's Constant S_γ Which Previously Required Numerical Integration, with Applications

Authors: Nigel B. Cook
Comments: 3 pages, see paper for equations in abstract

British mathematician Sir Geoffrey I. Taylor in secret work for British civil defence in 1941 (declassified in 1950 and published in the Proceedings of the Royal Society, vol. 201A, pp. 159-186), derived the strong shock solution equation, namely distance, (equation) , where (equation) is the ambient (pre-shock) atmospheric density, t is time after explosion, E is the energy released and Sg is Taylor's calculated function of g, requiring a complex step-wise numerical integration. We present a proof of the equation (equation), implying that Taylor's so-called constant (equation), not requiring any complex integration. This is useful for close-in shock waves from nuclear explosions and supernovae explosions. We further obtain the general arrival time of the shock wave (equation), by noting two asymptotic solutions; namely, at very great distances, the blast decays into a sound wave so the arrival time t approaches the ratio of distance to sound velocity (equation), while at very close-in distances the strong shock equation previously derived becomes accurate, and there is also an easily included effect at intermediate distances due to the expansion of the hot air in reducing shock front arrival times. The errors of method made by Taylor for nuclear test explosions in air were also made by Russian mathematician Leonid I. Sedov who applied similar cumbersome numerical integrations in a 1946 paper (published in the Journal of Applied Mathematics and Mechanics, vol. 10, pp. 241-50).

New Prime K-Tuple Theorem(1)

Authors: Chun-Xuan Jiang
Comments: 2 pages

Using Jinag funciton we prove that there exist infinitely many primes P₁ and P₂ such that each of P₁ + jP₂ + j is prime and there exist infinitely many primes P₁ and P₂ such that each of P₁ + jP₂ + j is prime.

α-Discounting Method for Multi-Criteria Decision Making

Authors: Florentin Smarandache
Comments: 26 pages

In this paper we introduce a new procedure called α-Discounting Method for Multi-Criteria Decision Making (α-D MCDM), which is as an alternative and extension of Saaty's Analytical Hierarchy Process (AHP). It works for any set of preferences that can be transformed into a system of homogeneous linear equations. A degree of consistency (and implicitly a degree of inconsistency) of a decision-making problem are defined. α-D MCDM is generalized to a set of preferences that can be transformed into a system of linear and/or non-linear homogeneous and/or non-homogeneous equations and/or inequalities. Many consistent, weak inconsistent, and strong inconsistent examples are given.

Degree of Negation of an Axiom

Authors: Florentin Smarandache
Comments: 4 pages

In this article we present the two classical negations of Euclid's Fifth Postulate (done by Lobachevski-Bolyai-Gauss, and respectively by Riemann), and in addition of these we propose a partial negation (or a degree of negation) of an axiom in geometry. The most important contribution of this article is the introduction of the degree of negation (or partial negation) of an axiom and, more general, of a scientific or humanistic proposition (theorem, lemma, etc.) in any field - which works somehow like the negation in fuzzy logic (with a degree of truth, and a degree of falsehood) or like the negation in neutrosophic logic [with a degree of truth, a degree of falsehood, and a degree of neutrality (i.e. neither truth nor falsehood, but unknown, ambiguous, indeterminate)].

Quantum Similarities or Radar Scattering as a Gauge Theory

Authors: Giuliano Bettini
Comments: 48 pages

As a continuation of a preceding paper "The trapped light" a preliminary attempt of how to construct a spinor theory of radar scattering or radar signal-target interaction with the gauge theories of quantum mechanics is presented. This way radar signals and radar targets may become visible macroscopic objects to be put in analogy with Standard Model particles and interactions. The basic idea is that particles and forces are all of electromagnetic nature, light, and appear different due to the size and shape of interacting objects. For the purpose that we propose here, you must first deal with a generic radar signal in spinor form (no