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1003 Submissions

[265] viXra:1003.0275 [pdf] replaced on 30 May 2010

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

Authors: S. Halayka
Comments: 7 Pages. Added reference McDonald JR, Miller WA. Coupling Non-Gravitational Fields with Simplicial Spacetimes

Using a 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.
Category: Quantum Gravity and String Theory

[264] viXra:1003.0274 [pdf] submitted on 31 Mar 2010

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.
Category: Number Theory

[263] viXra:1003.0273 [pdf] submitted on 31 Mar 2010

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.
Category: Number Theory

[262] viXra:1003.0272 [pdf] replaced on 3 Apr 2010

Eight Solved and Eight Open Problems in Elementary Geometry

Authors: Florentin Smarandache
Comments: 12 pages

In this paper we review nine previous proposed and solved problems of elementary 2D geometry [4] and [6], and we extend them either from triangles to polygons or polyhedrons,or from circles to spheres (from 2D-space to 3D-space), and make some comments about them.
Category: Geometry

[261] viXra:1003.0271 [pdf] submitted on 8 Mar 2010

Three Conjectures and Two Open Generalized Problems in Number Theory

Authors: Florentin Smarandache
Comments: 3 pages

On a Problem with Primes.
Category: Number Theory

[260] viXra:1003.0270 [pdf] submitted on 8 Mar 2010

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.
Category: Mind Science

[259] viXra:1003.0269 [pdf] submitted on 8 Mar 2010

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.
Category: Set Theory and Logic

[258] viXra:1003.0268 [pdf] replaced on 12 Apr 2010

Essay on the Proclivities of Particularity and Generality

Authors: Stephen P. Smith
Comments: 15 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.
Category: Linguistics

[257] viXra:1003.0267 [pdf] submitted on 30 Mar 2010

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.
Category: Topology

[256] viXra:1003.0265 [pdf] submitted on 30 Mar 2010

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.
Category: Classical Physics

[255] viXra:1003.0264 [pdf] submitted on 30 Mar 2010

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.
Category: Number Theory

[254] viXra:1003.0263 [pdf] submitted on 30 Mar 2010

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.
Category: Number Theory

[253] viXra:1003.0262 [pdf] submitted on 30 Mar 2010

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.
Category: Number Theory

[252] viXra:1003.0261 [pdf] submitted on 30 Mar 2010

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.
Category: Number Theory

[251] viXra:1003.0260 [pdf] submitted on 30 Mar 2010

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
Category: Number Theory

[250] viXra:1003.0259 [pdf] submitted on 28 Mar 2010

Analytical Proof of the Taylor Equation Including Taylor's Constant Sγ 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).
Category: Classical Physics

[249] viXra:1003.0258 [pdf] submitted on 28 Mar 2010

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.
Category: Number Theory

[248] viXra:1003.0257 [pdf] submitted on 8 Mar 2010

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.
Category: Artificial Intelligence

[247] viXra:1003.0256 [pdf] submitted on 8 Mar 2010

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)].
Category: Geometry

[246] viXra:1003.0255 [pdf] submitted on 26 Mar 2010

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 (note: it is TEM, TE, TM or evanescent. I mean "radar signal" in a wide sense, ie for ex. also into a waveguide). This is done by deriving a spinor representation of the TE TM through the Dirac equation for plane wave, starting rigorously from Maxwell's equations without any use of equivalent V, I as in previous papers. As a byproduct the representation is extended to the TEM. Then I introduce a tentative procedure to express the deflection of the field in a different direction, and its variation in frequency, and rest mass. This is accomplished through the interaction with SU(2)xU(1) gauge fields ie electroweak interactions. Some simple but illustrative examples are given. The ideas set out here need of course further research.
Category: Quantum Physics

[245] viXra:1003.0254 [pdf] submitted on 26 Mar 2010

Smarandache's Cevian Triangle Theorem in The Einstein Reletivistic Velocity Model of Hyperbolic Geometry

Authors: Cătălin Barbu
Comments: 4 pages

In this note, we present a proof of Smarandache's cevian triangle hyperbolic theorem in the Einstein relativistic velocity model of hyperbolic geometry.
Category: Geometry

[244] viXra:1003.0253 [pdf] submitted on 26 Mar 2010

On to What Effect LHC Experiment Should Arrive

Authors: Dainis Zeps
Comments: 12 pages

We consider idea of hierarchical multitime notion and of the cone of creation. Following this idea, the time used in traditional sense is only a single projection of time in the multitime. Multitime must have inner dimension upwards turning it into hierarchical structure which acts as what we call global cone of creation. On our time projection, evolution of species and BB, both global and local, in SM are examples of local cones of creation. Higgs field as symmetry breaking accounts for complementary worlds on other projections of time in multitime. We argue that time is form of referencing within matter and doesn't have any sense without matter. These are the hypothetical assumptions which may be tested, when LHC experiment shall go on.
Category: History and Philosophy of Physics

[243] viXra:1003.0252 [pdf] replaced on 2013-04-22 14:06:13

Ornamental Sign Language in the First Order Tracery Belts

Authors: Modris Tenisons, Dainis Zeps
Comments: 19 Pages. Corrected version

We consider an ornamental sign language of first order where principles of sieve displacement, of asymmetric building blocks as a base of ornament symmetry, color exchangeability and side equivalence principles work. Generic aspects of sieve and a genesis of ornamental pattern and ornament signs in it are discussed. Hemiolia principle for ornamental genesis is introduced. The discoverer of most of these principles were artist Modris Tenisons [4, 5, 6, 7 (refs. 23, 24), 8 (ref. 65)]. Here we apply a systematical research using simplest mathematical arguments. We come to conclusions that mathematical argument in arising ornament is of much more significance than simply symmetries in it as in an image. We are after to inquire how ornament arises from global aspects intertwined with these local. We raise an argument of sign’s origin from code rather from image, and its eventual impact on research of ornamental patterns, and on research of human prehension of sign and its connection with consciousness.
Category: Artificial Intelligence

[242] viXra:1003.0251 [pdf] submitted on 8 Mar 2010

Introduction to Poly-Emporium Theory in Economics

Authors: V. Christianto, Florentin Smarandache
Comments: 11 pages

We propose the poly-emporium theory. A search done in Google on May 3rd, 2008, for the term "poly-emporium" returned no entry, so we introduce it for the first time.
Category: Economics and Finance

[241] viXra:1003.0250 [pdf] submitted on 8 Mar 2010

Introduction to the mu-Bit

Authors: Florentin Smarandache, V. Christianto
Comments: 3 pages

Mu-bit is defined here as 'multi-space bit'. It is different from standard meaning of bit in conventional computation, because in Smarandache's multi-space theory, the bit is created simultaneously at multi-spaces. This new 'bit' term is different from multi-valued-bit already known in computer technology, for example as MVLong [8][9]. This new concept is also different from qu-bit from quantum computation terminology [10]. We know that using quantum mechanics logic we could introduce new way of computation with 'qubit' (quantum bit), but the logic remains Neumann. Now from the viewpoint of m-valued multi-space logic, we introduce a new term: 'mu-bit' (from ' multi-space bit').
Category: Digital Signal Processing

[240] viXra:1003.0249 [pdf] submitted on 8 Mar 2010

Numerical Result of Supersymmetric Klein-Gordon Equation. Plausible Observation of Supersymmetric-Meson

Authors: V. Christianto, Florentin Smarandache
Comments: 5 pages

In the context of some recent papers suggesting CT-symmetric QM in order to generalize PT-symmetric QM, in this paper we present an idea that there is quite compelling reasoning to argue in favour of supersymmetric extension of Klein-Gordon equation. Its numerical solutions in some simplest conditions are presented. Since the potential corresponding to this supersymmetric KGE is neither Coulomb, Yukawa, nor Hulthen potential [2a], then one can expect to observe a new type of matter, which may be called 'supersymmetric-meson'. Its presence may be expected in particular in the process of breaking of Coulomb barrier in low energy schemes. Further observation is of course recommended in order to refute or verify this proposition.
Category: Quantum Physics

[239] viXra:1003.0248 [pdf] submitted on 8 Mar 2010

Graph Distance, Optimal Communication and Group Stability: A Preliminary Conjecture

Authors: Florentin Smarandache, V. Christianto
Comments: 4 pages

In recent years, there has been a rapid increase in the literature which discusses new phenomenon associated to social network. One of the well-known phenomenon in this regards is known as 'six degrees of separation' [1], which implies that one can always keep a communication with each other anywhere within a six-step. A number of experiments has verified this hypothesis, either in the context of offline communication (postal mail), or online communication (email, etc.). In this article, we argue that by introducing this known 'six degrees of separation' into the context of group instability problem, one can find a new type of wisdom in organization. Therefore, we offer a new conjecture, which may be called 'Group stability conjectures based on Graph/Network distance." To our knowledge this conjecture has not been discussed elsewhere, and therefore may be useful for further research, in particular in the area of organization development and group stability studies. The purpose of this article was of course not to draw a conclusive theory, but to suggest further study of this proposed conjecture.
Category: Social Science

[238] viXra:1003.0247 [pdf] replaced on 30 Mar 2010

Deceleration Parameter Q(Z) in 4D and 5D Geometries, and Implications of Graviton Mass in Mimicking Dark Energy in Both Geometries

Authors: Andrew Beckwith
Comments: 5 pages, 1 figure. Re done to make equivalence of Beckwith DM/DE and brane world conditions shown as the same as Yurov.s 2002 conditions. Actual conference submission for the Beyond the Standard Model 2010, by Dr. Andrew Beckwith. Heavily referenced by Dr. Beckwith in PIERS 2010, XIAN, on March 22, at 11 a.m. in room D with two other presenters, Dr. Cruise of Birmingham University, and Dr. Li of Chongquing University, as given by http://piers.mit.edu/piers2010xian/files/FinalProgram.pdf. Note that Dr. Grishkuk, of Cardiff University did not attend. Conference entry for proceedings as edited by Dr. H. V. Klaptor-Kleingross, as given for http://www.phy.uct.ac.za/beyond2010/

The case for a four-dimensional graviton mass (non zero) influencing reacceleration of the universe in both four and five dimensions is stated, with particular emphasis on the question whether 4D and 5D geometries as given here yield new physical insight as to cosmological evolution. Both cases give equivalent reacceleration one billion years ago, which leads to the question whether other criteria can determine the relative benefits of adding additional dimensions to cosmology models.
Category: Relativity and Cosmology

[237] viXra:1003.0246 [pdf] submitted on 25 Mar 2010

Theory of First Force

Authors: Willi Penker
Comments: 3 pages

The effects of forces are well known; however, the basic mechanisms of how forces work and are transmitted remain unexplained. This essay is meant to determine these basic mechanisms.
Category: Quantum Gravity and String Theory

[236] viXra:1003.0245 [pdf] submitted on 25 Mar 2010

Smarandache's Pedal Polygon Theorem in The Poincaré Disc Model of Hyperbolic Geometry

Authors: Cătălin Barbu
Comments: 4 pages

In this note, we present a proof of the hyperbolic a Smarandache's pedal polygon theorem in the Poincaré disc model of hyperbolic geometry.
Category: Geometry

[235] viXra:1003.0244 [pdf] submitted on 3 Mar 2010

We Tell Students To Distrust Common Sense, Then We Criticize Them For Their Inability To Use Common Sense: a Comment on Archiv:1003.4288

Authors: Ron Bourgoin
Comments: 2 pages

The authors of Archiv:1003.4288 study a student named "Jim". "Jim" displays a propensity for believing his mathematical solutions rather than what his common sense tells him. He is a student taking an introductory physics class. The authors wonder why mathematical solutions take precedence over common sense. In this brief note we cite as the root cause of the problem the fact that we tell our students to distrust their common sense. When we arrive at relativity theory, for example, we inform our students that common sense is useless in relativity theory. We tell them that common sense is useless in quantum mechanics. Is it any wonder our students believe whatever the math tells them?
Category: Mind Science

[234] viXra:1003.0243 [pdf] replaced on 2012-03-20 18:35:37

Is There Life After Death?

Authors: John A. Gowan
Comments: 11 Pages.

Our sense of individual immortality is a consequence of the self-awareness of the Universe caught knowingly in the act of looking at itself through human eyes. I am how the Universe becomes self-aware and experiences itself. The immortality of the Universe is therefore quite naturally intuited to be my own. The Universe is a conservation domain: all parts of the Universe are immortal or otherwise conserved. Our true immortality is the eternal nature of the Universe itself - including its capacity to continuously evolve and create information, life, and self-knowledge. Human life oscillates between a generalized (genomic) and a specific (individual) expression. The creation of a new human being is remarkably analogous to the creation of a new elementary particle: both processes require a symmetric energy state which recapitulates the original environmental conditions of its specialized domain.
Category: General Science and Philosophy

[233] viXra:1003.0242 [pdf] submitted on 8 Mar 2010

On the Meaning of Imaginary Part of Solution of Biquaternion Klein-Gordon Equation

Authors: V. Christianto, Florentin Smarandache
Comments: 4 pages

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation has solution containing imaginary part, which differs appreciably from known solution of KGE. In the present article we discuss some possible interpretation of this imaginary part of the solution of biquaternionic KGE (BQKGE). Further observation is of course recommended in order to refute or verify this proposition.
Category: Quantum Physics

[232] viXra:1003.0240 [pdf] submitted on 8 Mar 2010

Introduction to Biquaternion Number, Schrödinger Equation, and Fractal Graph

Authors: V. Christianto, Florentin Smarandache
Comments: 8 pages

It is known that quaternion number has wide application in theoretical physics and engineering fields alike, in particular to describe Maxwell electrodynamics. In the meantime, recently this quaternion number has also been used to draw fractal graph. The present note is intended as an introduction to this very interesting study, i.e. to find linkage between quaternion/biquaternion number, quantum mechanical equation (Schrödinger equation) and fractal graph. Hopefully this note will be found useful for subsequent study.
Category: Quantum Physics

[231] viXra:1003.0239 [pdf] submitted on 8 Mar 2010

Of Intent, Citation Game, and Scale-Free Networks: a Heuristic Argument

Authors: V. Christianto, Florentin Smarandache
Comments: 11 pages

A heuristic argument was presented in favor of hypothesis that scientific communication corresponds to a process known as scale-free network. As a result, it is argued that scientific referencing through citation follows the same process, therefore it could be expected that this shall also exhibit fractality as observed in various phenomena associated with scale-free networks. This argument appears conceivable because the process of citation involves a decision-making, coined here as 'citation game.' In this regard, it is recommended to conduct citation analysis to measure the fractality of this process. While at present this heuristic argument cannot be considered as conclusive, further research is recommended to verify or refute this hypothesis.
Category: General Science and Philosophy

[230] viXra:1003.0237 [pdf] submitted on 8 Mar 2010

A Note on Exchange Rate Management and Gravity Equation: Developing Country's Viewpoint

Authors: V. Christianto, Florentin Smarandache
Comments: 6 pages

In the last few decades, the flexible exchange rate has become the predominating policy implemented by most countries in the World, except only a few countries who can keep their exchange rates fixed. The predominating position can be attributed mainly to Milton Friedman's strong support. What is less known, nonetheless, is a hidden premise that the flexible exchange rate policy will help fiscal policy in the sense that only governments who do not manage the fiscal policy properly will get 'punished' by exchange rate decreases. But as the US-Japan experience showed [1], this widely-held assumption is often not realistic. The same experience has been observed in other countries too, i.e. that financial liberalization including flexible exchange rate often became precursor of financial instability [2]. While in the past year, in Indonesia for particular, the exchange rate remains stable, it does not mean that it would be free from troubles in the future. Therefore it is worthwhile to explore some other choices for better exchange rate policy. In the present paper will discuss, albeit in somewhat 'crude' manner, some long-term approaches which have been discussed in the literature, and also not-so conventional approaches which may be suitable for short term purposes. The basic proposition in the present paper is that we argue in favor of returning to fixed (or pegging) exchange rate, but of course it is not realistic to promote this policy for the short-term future. Therefore we explore some unconventional alternatives for short-term. It is our hope that the proposition would be useful to explore further by the economics policy makers.
Category: Economics and Finance

[229] viXra:1003.0235 [pdf] replaced on 26 May 2010

Justification of the Zeta Regularization Procedure for the Integrals ∫xm-Sdx

Authors: Jose Javier Garcia Moreta
Comments: 15 pages

In this paper we review and try to justify some results we gave before concerning the zeta regularization of integrals ∫xm-sdx via the zeta regularization of the divergent series Σxm-sdx and the zeta function ζ(m - s)
Category: Number Theory

[228] viXra:1003.0234 [pdf] replaced on 26 Mar 2010

The Hardy-Littlewood Prime K-Tuple Conjecture is False

Authors: Chun-Xuan Jiang
Comments: 7 pages

Using Jiang function we prove Jiang prime -tuple theorem. We prove that the Hardy-Littlewood prime-tuple conjecture is false. Jiang prime -tuple theorem can replace the Hardy-Littlewood prime-tuple conjecture.
Category: Number Theory

[227] viXra:1003.0233 [pdf] submitted on 7 Mar 2010

Sequences of Numbers Involved in Unsolved Problems

Authors: Florentin Smarandache
Comments: 141 pages

Over 300 sequences and many unsolved problems and conjectures related to them are presented herein.
Category: Number Theory

[226] viXra:1003.0232 [pdf] submitted on 7 Mar 2010

Fuzzy Cognitive Maps and Neutrosophic Cognitive Maps

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 213 pages

In a world of chaotic alignments, traditional logic with its strict boundaries of truth and falsity has not imbued itself with the capability of reflecting the reality. 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. Neutrosophy is a new branch of philosophy that studies the origin, nature and scope of neutralities, as well as their interactions with different ideational spectra. This was introduced by one of the authors, Florentin Smarandache. A few of the mentionable characteristics of this mode of thinking are [90-94]: It proposes new philosophical theses, principles, laws, methods, formulas and movements; it reveals that the world is full of indeterminacy; it interprets the uninterpretable; regards, from many different angles, old concepts, systems and proves that an idea which is true in a given referential system, may be false in another, and vice versa; attempts to make peace in the war of ideas, and to make war in the peaceful ideas! The main principle of neutrosophy is: Between an idea and its opposite , there is a continuum-power spectrum of Neutralities. This philosophy forms the basis of Neutrosophic logic.
Category:
Artificial Intelligence

[225] viXra:1003.0231 [pdf] submitted on 7 Mar 2010

Smarandache Special Definite Algebraic Structures

Authors: W. B. Vasantha Kandasamy
Comments: 141 pages

In this book we introduce the notion of Smarandache special definite algebraic structures. We can also call them equivalently as Smarandache definite special algebraic structures. These new structures are defined as those strong algebraic structures which have in them a proper subset which is a weak algebraic structure. For instance, the existence of a semigroup in a group or a semifield in a field or a semiring in a ring. It is interesting to note that these concepts cannot be defined when the algebraic structure has finite cardinality i.e., when the algebraic structure has finite number of elements in it.
Category: Algebra

[224] viXra:1003.0230 [pdf] submitted on 7 Mar 2010

Applications of Smarandache Function, and Prime and Coprime Functions

Authors: Sebastián Martín Ruiz
Comments: 25 pages

The Smarandache function is defined as follows: S(n)= the smallest positive integer such that S(n)! is divisible by n. [1] In this article we are going to see that the value this function takes when n is a perfect number of the form n = 2k - 1.(2k - 1) , p = 2k - 1 being a prime number.
Category: Number Theory

[223] viXra:1003.0229 [pdf] submitted on 7 Mar 2010

Smarandache Multi-Space Theory

Authors: Linfan Mao
Comments: 275 pages

A Smarandache multi-space is a union of n different spaces equipped with some different structures for an integer n ≥ 2, which can be used both for discrete or connected spaces, particularly for geometries and spacetimes in theoretical physics.
Category: Combinatorics and Graph Theory

[222] viXra:1003.0228 [pdf] submitted on 7 Mar 2010

Generalized Partitions and New Ideas On Number Theory and Smarandache Sequences

Authors: Amarnath Murthy, Charles Ashbacher
Comments: 219 pages

This book arose out of a collection of papers written by Amarnath Murthy. The papers deal with mathematical ideas derived from the work of Florentin Smarandache, a man who seems to have no end of ideas. Most of the papers were published in Smarandache Notions Journal and there was a great deal of overlap. My intent in transforming the papers into a coherent book was to remove the duplications, organize the material based on topic and clean up some of the most obvious errors. However, I made no attempt to verify every statement, so the mathematical work is almost exclusively that of Murthy.
Category: Number Theory

[221] viXra:1003.0227 [pdf] replaced on 26 Jun 2011

Automorphismgroups of Maps, Surfaces and Smarandache Geometries

Authors: Linfan Mao
Comments: 399 pages.

Automorphism groups survey similarities on mathematical systems, which appear nearly in all mathematical branches, such as those of algebra, combinatorics, geometry, ... and theoretical physics, theoretical chemistry, etc. In geometry, configurations with high symmetry born symmetrical patterns, a kind of beautiful pictures in aesthetics. Naturally, automorphism groups enable one to distinguish systems by similarity. More automorphisms imply more symmetries of that system. This fact has established the fundamental role of automorphism groups in modern sciences. So it is important for graduate students knowing automorphism groups with applications.
Category: Combinatorics and Graph Theory

[220] viXra:1003.0225 [pdf] submitted on 7 Mar 2010

Geometric Theorems, Diophantine Equations, and Arithmetic Functions

Authors: József Sándor
Comments: 302 pages

This book contains short notes or articles, as well as studies on several topics of Geometry and Number theory. The material is divided into five chapters: Geometric theorems; Diophantine equations; Arithmetic functions; Divisibility properties of numbers and functions; and Some irrationality results. Chapter 1 deals essentially with geometric inequalities for the remarkable elements of triangles or tetrahedrons. Other themes have an arithmetic character (as 9-12) on number theoretic problems in Geometry
Category: Number Theory

[219] viXra:1003.0224 [pdf] submitted on 7 Mar 2010

Introduction to Neutrosophic Logic

Authors: Charles Ashbacher
Comments: 145 pages

As someone who works heavily in both math and computers, I can truly appreciate the role that logic plays in our modern world. One cannot understand the foundations of mathematics while lacking knowledge of the basics of logic and how proofs are constructed. Two of the first classes I took as a graduate student in mathematics were in the foundations of mathematics, and hardly a day goes by where I do not use some topic from those courses.
Category: Set Theory and Logic

[218] viXra:1003.0223 [pdf] submitted on 7 Mar 2010

Smarandache Geometries & Map Theory with Applications(i)

Authors: Linfan Mao
Comments: 215 pages

SMARANDACHE GEOMETRIES & MAP THEORY WITH APPLICATIONS
Category: Combinatorics and Graph Theory

[217] viXra:1003.0222 [pdf] submitted on 21 Mar 2010

On the Scale Factor of the Universe and Redshift.

Authors: John Hunter
Comments: 6 pages

It is proposed that there has been a longstanding misunderstanding of the relationship between scale factor of the universe and redshift. It is shown how value of omega(matter) of one quarter of the true value, (hence the apparent dark energy phenomenon) can result from such a misconception. Predictions for the magnitudes of supernovae against redshift are made and found to be in good agreement with supernovae data, without dark energy.
Category: Relativity and Cosmology

[216] viXra:1003.0221 [pdf] replaced on 27 Jun 2011

Combinatorial Geometry with Applications to Field Theory

Authors: Linfan Mao
Comments: 502 pages.

Accompanied with humanity into the 21st century, a highlight trend for developing a science is its overlap and hybrid, and harmoniously with other sciences, which enables one to handle complex systems in the WORLD. This is also for developing mathematics. As a powerful tool for dealing with relations among objectives, combinatorics, including combinatorial theory and graph theory mushroomed in last century. Its related with algebra, probability theory and geometry has made it to an important subject in mathematics and interesting results emerged in large number without metrics. Today, the time is come for applying combinatorial technique to other mathematics and other sciences besides just to find combinatorial behavior for objectives. That is the motivation of this book, i.e., to survey mathematics and fields by combinatorial principle.
Category: Combinatorics and Graph Theory

[215] viXra:1003.0220 [pdf] submitted on 7 Mar 2010

Pluckings from the Tree of Smarandache Sequences and Functions

Authors: Charles Ashbacher
Comments: 80 pages

In writing a book, one encounters and overcomes many obstacles. Not the least of which is the occasional case of writer's block. This is especially true in mathematics where sometimes the answer is currently and may for all time be unknown. There is nothing worse than writing yourself into a corner where your only exit is to build a door by solving unsolved problems. In any case, it is my hope that you will read this volume and come away thinking that I have overcome enough of those obstacles to make the book worthwhile. As always, your comments and criticisms are welcome. Feel free to contact me using any of the addresses listed below, although e-mail is the preferred method.
Category: Number Theory

[214] viXra:1003.0219 [pdf] submitted on 7 Mar 2010

Smarandache Sequences, Stereograms and Series

Authors: Charles Ashbacher
Comments: 135 pages

This is the fifth book that I have written that expands on the ideas of Florentin Smarandache. In addition, I have edited two others that also deal with the areas of mathematics under the Smarandache Notions umbrella. All of this is a credit to the breadth and depth of his mathematical achievement. Therefore, I once again must commend and thank him for providing so much material to work with. I also would like to thank J. McGray for her encouragement and patience as I struggled to make this book a reality. The material cited in this book can be found at the website http://www.gallup.unm.edu/~smarandache/. The deepest thanks go to my mother Paula Ashbacher, who encouraged me to play sports, but in the off chance that I would never learn to hit the curve ball, also insisted that I read books. This proved to be a wise career strategy. Finally, I would like to express my deep love for Kathy Brogla, my partner/soul mate/best friend. So pretty and vivacious, she makes life fun, exciting and a joy to experience every single day. She is a remarkable woman and I am so blessed to have her in my life. Kathy is also the creator of the image on the front cover.
Category: Number Theory

[213] viXra:1003.0218 [pdf] submitted on 7 Mar 2010

G-Dimensional Theory & the Smarandache Quantum Paradoxes: Comparative Logic and Modern Quantum Theory

Authors: L. Stephen Young
Comments: 44 pages

The Smarandache Quantum Paradoxes ["Nature", Vol. 413, No. 6854] and Smarandache Hypothesis (FTL) are defined as a formal set of (anti-logic) statements inclusive in modern quantum theory. To determine whether they constitute theoretical artifacts or can be considered true physical paradoxes, G Dimensional Theory, a unique, logical and physically congruent system of physics, at significant variance with modern and classical theory, is presented in Sections 3-4. A comparative analysis of the Smarandache quantum paradoxes within context of the two theories follows in Section 5.
Category: Quantum Physics

[212] viXra:1003.0217 [pdf] submitted on 7 Mar 2010

Mainly Natural Numbers

Authors: Henry Ibstedt
Comments: 97 pages

This book consists of a selection of papers most of which were produced during the period 1999-2002. They have been inspired by questions raised in recent articles in current Mathematics journals and in Florentin Smarandache's wellknown publication Only Problems, Not Solutions.
Category: Number Theory

[211] viXra:1003.0216 [pdf] submitted on 7 Mar 2010

The Smarandache Function

Authors: C. Dumitrescu, V. Seleacu
Comments: 137 pages

The function named in the title of this book is originated from the exiled Romanian mathematician Florentin Smarandache.
Category: Number Theory

[210] viXra:1003.0215 [pdf] replaced on 6 Mar 2010

The Aesthetics of Paradoxism

Authors: Titu Popescu
Comments: 100 pages, v1 in Romainian, V2 in English Translated by P. Georgelin, F. Smarandache, and L. Popescu

In the history of thought and creation, the decisive events, the great and significant moments, the strongly affirmative stages - then the imposition of the optimizing novelties - have depended on the name and prestige of a personality. Referring to those, we personalize further on. The examples are extremely numerous, even in our nearest past. When we mention a creation - in the largest sense of the term - with the name of the personality who illustrates it most extensively at a given time, we state precisely the specific importance of it; we give it, with other words, the identity to which we can refer continuously with full knowledge and without causing any confusion among the receivers. The facts are called with the name of the man who produced them, and in this way we can compose a parallel onomastic dictionary, in which the work is included in the person's space, keeping its content. The consecrated proper names evolve through quickly imposed habits, a large range of increments that announce the essential outline of their peak production. No space for ambiguity remains when we address to readers or listeners who are somewhat acquainted with the subject and we use such terms as Aristotelianism, Platonism, Kantianism, Hegelianism, Proustianism, Eminescianism, Barbianism, etc. We have even the advantage of a centered communication when we suggest with a sole notion the work as well as its dominant features, linked with the renown of the concerned author.
Category: History and Philosophy of Physics

[209] viXra:1003.0214 [pdf] submitted on 18 Mar 2010

Nom Associative SU(3)L X U(1)N Gauge Model and Predictions

Authors: N. Mebarki, M. Boussahel
Comments: 38 pages

A classical gauge model based on the Lie group SU(3)L X U(1)N with exotic quarks is reformulated within the formalism of non-associative geometry associated to an L-cycle. The N charges of the fermionic particles and the related parameters constraints are uniquely determinedalgebraic consequences. Moreover, the number of scalar particles are dictated by the non-associativity of the geometry. As a byproduct of this formalism, the scalar, charged and neutral gauge bosons masses as well as the mixing angles are derived. Furthermore, various expressions of the vector and axial couplings of the quarks and leptons with the neutral gauge bosons and lower bounds of the very heavy gauge bosons are also obtained.
Category: High Energy Particle Physics

[208] viXra:1003.0213 [pdf] submitted on 18 Mar 2010

Smarandache Φ-Theorem

Authors: Zhang Wenpeng
Comments: 1 page

Fermat's and Euler's theorem on congruencies are generalized to the case when the integers a and m are not necessarily co-prime.
Category: Relativity and Cosmology

[207] viXra:1003.0212 [pdf] submitted on 18 Mar 2010

On the Origins of the Stellar Initial Mass Function

Authors: Golden Gadzirayi Nyambuya
Comments: 12 pages, 2 figures, submitted to MNRAS-MJ.

In this reading, a new theoreticalmodel of star and cluster formation is posited. Thismodel seeks to set a mathematical framework to understand the origins of the stellar Initial Mass Function and within this framework, explain star and cluster formation from a unified perspective by tieing together into a single garment three important observational facts: (1) that the most massive stars of most observed clusters of stars are preferentially found in their centers; (2) Larson's 1982 empirical observation that the maximum stellar mass is related to the total mass of the parent cloud; (3) that clump masses in giant molecular clouds exhibit a power mass spectrum law akin to that found in star clusters and this behavior is also true for molecular clouds as well. Key to this model is the way the cloud fragments to form cores from which the new stars are born. We show that the recently proposed azimuthally symmetric theory of gravitation has two scale of fragmentation where one is the scale that leads to cloud collapse and the other is the scale on which the cloud fragments. The collapse and fragmentation takes place simultaneously. If the proposed model is anything to go by, then, one can safely posit that the slope of the IMF can be explained from two things: the star formation rate of the cores from which these stars form and the density index describing the density profile. Additionally and more importantly, if the present is anything to by, then, fragmentation of molecular clouds is posited as being a result of them possessing some spin angular momentum.
Category: Relativity and Cosmology

[206] viXra:1003.0211 [pdf] submitted on 18 Mar 2010

Goldbach Conjecture (A): Upper Bound Estimation and Lower Bound Estimation

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

We have sieve method formula of π(N) and sieve method formula of r2(N). By these sieve method formula, we can obtain (see paper for equation)
Category: Number Theory

[205] viXra:1003.0210 [pdf] submitted on 18 Mar 2010

About Speed and Time

Authors: Roald C. Maximo
Comments: 3 pages

In this short essay, I am starting from very basic concepts to try, step by step, to establish a valid physical relation between speed, energy and time. My intention, just from the start, is to by pass the Theory of Relativity and also avoid the application of the Lorentz transformation as canned good. If it has to be part of the solution it shall also arise spontaneously during the formulations as it ended up being the case.
Category: Relativity and Cosmology

[204] viXra:1003.0209 [pdf] submitted on 6 Mar 2010

Advances and Applications of DSmT for Information Fusion Collected Works Volume 2

Authors: Florentin Smarandache, Jean Dezert
Comments: 461 pages

This second book devoted on advances and applications of Dezert-Smarandache Theory (DSmT) for information fusion collects recent papers from different researchers working in engineering and mathematics. Part 1 of this book presents the current state-of-the-art on theoretical investigations while, Part 2 presents several applications of this new theory. Some ideas in this book are still under current development or improvements, but we think it is important to propose them in order to share ideas and motivate new debates with people interested in new reasoning methods and information fusion. So, we hope that this second volume on DSmT will continue to stir up some interests to researchers and engineers working in data fusion and in artificial intelligence.
Category: Artificial Intelligence

[203] viXra:1003.0208 [pdf] submitted on 6 Mar 2010

Advances and Applications of DSmT for Information Fusion Collected Works Volume 1

Authors: Florentin Smarandache, Jean Dezert
Comments: 438 pages

This book is devoted to an emerging branch of Information Fusion based on new approach for modelling the fusion problematic when the information provided by the sources is both uncertain and (highly) conflicting. This approach, known in literature as DSmT (standing for Dezert-Smarandache Theory), proposes new useful rules of combinations. We gathered in this volume a presentation of DSmT from the beginning to the latest development. Part 1 of this book presents the current state-of-the-art on theoretical investigations while Part 2 presents several applications of this new theory. We hope that this first book on DSmT will stir up some interests to researchers and engineers working in data fusion and in artificial intelligence. Many simple but didactic examples are proposed throughout the book. As a young emerging theory, DSmT is probably not exempt from improvements and its development will continue to evolve over the years. We just want through this book to propose a new look at the Information Fusion problematic and open a new track to attack the combination of information.
Category: Artificial Intelligence

[202] viXra:1003.0205 [pdf] submitted on 6 Mar 2010

Numerical Solution of Schrödinger Equation with PT-Symmetric Periodic Potential, and Its Gamow Integral

Authors: V. Christianto, Florentin Smarandache
Comments: 8 pages

In a number of preceding papers we introduced a new PT-symmetric periodic potential, derived from biquaternion radial Klein-Gordon equation. In the present paper we will review our preceding result, and continue with numerical solution of Gamow integral for that periodic potential. And then we also compare with other periodic potentials which are already known, such as Posch-Teller or Rosen-Morse potential. We also discuss a number of recent development in the context of condensed matter nuclear science, in particular those experiments which are carried out by Prof. A. Takahashi and his team from Kobe University. There is hint to describe his team's experiment as 'mesofusion' (or mesoscopic fusion). We then analyze possibility to enhance the performance of Takahashi's mesofusion experiment under external pulse field. Further experiments are of course recommended in order to verify or refute the propositions outlined herein.
Category: Quantum Physics

[201] viXra:1003.0204 [pdf] replaced on 2014-03-13 04:08:55

Introduction to Smarandache-Christianto (SC) Potential

Authors: Florentin Smarandache, V. Christianto
Comments: 3 Pages.

A new type of potential for nucleus, which is different from Coulomb potential or Yukawa potential. This new potential may have effect for radius range within r = 5 - 10 fm.
Category: General Mathematics

[200] viXra:1003.0203 [pdf] submitted on 6 Mar 2010

Is There Iso-PT Symmetric Potential in Nature?

Authors: V. Christianto, Florentin Smarandache
Comments: 6 pages

In recent years there are new interests on special symmetry in physical systems, called PT-symmetry with various ramifications. Along with the isodual symmetry popularized by RM Santilli, these ideas form one of cornerstone in hadron physics. In the present article, we argue that it is plausible to generalise both ideas to become iso-PT symmetry which indicate there should be new potential obeying this symmetry. We also discuss some possible interpretation of the imaginary solution of the solution of biquaternionic KGE (BQKGE); which indicate the plausible existence of the propose iso-PT symmetry. Further observation is of course recommended in order to refute or verify this proposition.
Category: Quantum Physics

[199] viXra:1003.0202 [pdf] submitted on 17 Mar 2010

The Higgs Boson/Quantum Gravity/Cosmological Constant Connections

Authors: James R. Bogan
Comments: 7 pages

We suggest discovery targets for the Higgs boson and a Tev mass scale for quantum gravity, in terms of the cosmological constant, and ultimately, the electron.
Category: High Energy Particle Physics

[198] viXra:1003.0201 [pdf] submitted on 6 Mar 2010

Cultural Advantages in China: Tale of Six Cities

Authors: Fu Yuhua, Florentin Smarandache, V. Christianto
Comments: 96 pages

Nowadays, plenty of factories from Europe and other developed countries have been relocated to this country, considering its tremendous economic scale and rapid growth rate during the past three decades. But most of what happens inside the China nowadays is deeply hidden from the outside world ("the foreigners" as China people would call). This fact is partly because most reports on China were written by the so-called fly-high experts who are busy completing their reports despite a busy schedule. Very few books or reports were written by people inside, or at least "foreigners" who spent a few years in China. Therefore in this book, we took a different approach, by inviting local scientists and other writers to describe what happens surround them.
Category: Economics and Finance

[197] viXra:1003.0200 [pdf] submitted on 6 Mar 2010

Cultural Advantage for Cities an Alternative for Developing Countries

Authors: V. Christianto, Florentin Smarandache
Comments: 63 pages

After more than a decade Michael Porter's book Competitive Advantage of Nations stays ahead of the other books, in particular as alternative framework from the comparative advantage idea inspired by Adam Smith. This small book is merely an alternative proposition, a postscript perhaps, to Porter's book, with basic idea that one cannot rely merely on industrial processes alone to keep stay ahead of market changes. Hence, for cities in developing countries the municipal shall find out their city's best resources, and develop their city starting from there, instead of striving blindly in the conventional industrial path.
Category: Economics and Finance

[196] viXra:1003.0199 [pdf] submitted on 6 Mar 2010

New Classes of Codes for Cryptologists and Computer Scientists

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 206 pages

Historically a code refers to a cryptosystem that deals with linguistic units: words, phrases etc. We do not discuss such codes in this book. Here codes are message carriers or information storages or information transmitters which in time of need should not be decoded or read by an enemy or an intruder. When we use very abstract mathematics in using a specific code, it is difficult for non-mathematicians to make use of it. At the same time, one cannot compromise with the capacity of the codes. So the authors in this book have introduced several classes of codes which are explained very non-technically so that a strong foundation in higher mathematics is not needed. The authors also give an easy method to detect and correct errors that occur during transmission. Further some of the codes are so constructed to mislead the intruder. False n-codes, whole n-codes can serve this purpose.
Category: Number Theory

[195] viXra:1003.0198 [pdf] submitted on 6 Mar 2010

Six Conjectures Which Generalize or Are Related to Andrica's Conjecture

Authors: Florentin Smarandache
Comments: 3 pages

TSix conjectures on pairs of consecutive primes are listed below together with examples in each case.
Category: Number Theory

[194] viXra:1003.0197 [pdf] submitted on 6 Mar 2010

Application of Probabilistic PCR5 Fusion Rule for Multisensor Target Tracking

Authors: Aloïs Kirchnera, Frédéric Dambrevilleb, Francis Celeste, Florentin Smarandache, Jean Dezert
Comments: 9 pages

This paper defines and implements a non-Bayesian fusion rule for combining densities of probabilities estimated by local (non-linear) filters for tracking a moving target by passive sensors. This rule is the restriction to a strict probabilistic paradigm of the recent and efficient Proportional Conflict Redistribution rule no 5 (PCR5) developed in the DSmT framework for fusing basic belief assignments. A sampling method for probabilistic PCR5 (p-PCR5) is defined. It is shown that p-PCR5 is more robust to an erroneous modeling and allows to keep the modes of local densities and preserve as much as possible the whole information inherent to each densities to combine. In particular, p-PCR5 is able of maintaining multiple hypotheses/modes after fusion, when the hypotheses are too distant in regards to their deviations. This new p-PCR5 rule has been tested on a simple example of distributed non-linear filtering application to show the interest of such approach for future developments. The non-linear distributed filter is implemented through a basic particles filtering technique. The results obtained in our simulations show the ability of this p-PCR5-based filter to track the target even when the models are not well consistent in regards to the initialization and real cinematic. Keywords: Filtering, Robust estimation, non-Bayesian fusion rule, PCR5, Particle filtering.
Category: Artificial Intelligence

[193] viXra:1003.0196 [pdf] submitted on 6 Mar 2010

Qualitative Belief Conditioning Rules (QBCR)

Authors: Florentin Smarandache, Jean Dezert
Comments: 13 pages

In this paper we extend the new family of (quantitative) Belief Conditioning Rules (BCR) recently developed in the Dezert-Smarandache Theory (DSmT) to their qualitative counterpart for belief revision. Since the revision of quantitative as well as qualitative belief assignment given the occurrence of a new event (the conditioning constraint) can be done in many possible ways, we present here only what we consider as the most appealing Qualitative Belief Conditioning Rules (QBCR) which allow to revise the belief directly with words and linguistic labels and thus avoids the introduction of ad-hoc translations of quantitative beliefs into quantitative ones for solving the problem.
Category: Artificial Intelligence

[192] viXra:1003.0195 [pdf] submitted on 6 Mar 2010

Enrichment of Qualitative Beliefs for Reasoning Under Uncertainty

Authors: Xin-De Li, Xinhan Huang, Florentin Smarandache, Jean Dezert
Comments: 12 pages

This paper deals with enriched qualitative belief functions for reasoning under uncertainty and for combining information expressed in natural language through linguistic labels. In this work, two possible enrichments (quantitative and/or qualitative) of linguistic labels are considered and operators (addition, multiplication, division, etc) for dealing with them are proposed and explained. We denote them qe-operators, qe standing for "qualitative-enriched" operators. These operators can be seen as a direct extension of the classical qualitative operators (q-operators) proposed recently in the Dezert-Smarandache Theory of plausible and paradoxist reasoning (DSmT). q-operators are also justified in details in this paper. The quantitative enrichment of linguistic label is a numerical supporting degree in [0,∞), while the qualitative enrichment takes its values in a finite ordered set of linguistic values. Quantitative enrichment is less precise than qualitative enrichment, but it is expected more close with what human experts can easily provide when expressing linguistic labels with supporting degrees. Two simple examples are given to show how the fusion of qualitative-enriched belief assignments can be done.
Category: Artificial Intelligence

[191] viXra:1003.0194 [pdf] submitted on 16 Mar 2010

Applications of Euclidian Snyder Geometry to Space Time Physics & Deceleration Parameter ( DE Replacement?) Analysis of Linkage Between 1st, 2nd Inflation?

Authors: Andrew Beckwith
Comments: A. Yurov; arXiv : hep-th/028129 v1, 19 Aug, 2002 material added to the analysis presented in S.A. at Beyond the Standard Model. 50 pages

presentation of 7 new pages with respect to linkage between 1st and 2nd inflation, 1st 10-35 seconds after big bang, and 2nd one billion years ago
Category: Relativity and Cosmology

[190] viXra:1003.0193 [pdf] replaced on 29 Mar 2010

DE-Celeration Parameter Q(Z) and Inflaton φ(t). I.e. How to Link Early Universe Inflation with re Acceleration? Links to Radi of the Universe Formalism?

Authors: Andrew Beckwith
Comments: 16 pages, four figures. Re statement of prior submission, with specific commentary as given in Appendix B, and also the radius of the Universe question , as can be ascertained via modeling included. This material added, to make presentation conform more closely to the Xian, PRC PIERS presentation given in 2010, March 22, at 11 a.m. which did emphasize, at the end the importance of material in Appendix B, as well as the given conclusion, and the radius of the Universe question, as of Eq. (38), as very important to applications of GW/ graviton based astronomy/ astro physics. Appendix B in particular delves into how massless graviton Field equations, and their small mass graviton versions do not connect, in the limit of mass of a graviton approaching zero.

The case for a four dimensional graviton mass (non zero) influencing reacceleration of the universe in five dimensions is stated; with emphasis upon if five dimensional geometries as given below give us new physical insight as to cosmological evolution. A calculated inflaton φ(t) may partly reemerge after fading out in the aftermath of inflation. The inflaton 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 at red shit value of Z ~ .423. A final statement as to how and why the radius of the universe question may be affected by these deliberations is presented , in terms of if the graviton is either purely a field theoretic , or semi classical object, as via t'Hoofts deterministic QM is presented in the end, as an open question.
Category: Relativity and Cosmology

[189] viXra:1003.0192 [pdf] replaced on 19 Aug 2011

Funcoids and Reloids

Authors: Victor Porton
Comments: 53 pages

It is a part of my Algebraic General Topology research. In this article, I introduce the concepts of funcoids, which generalize proximity spaces and reloids, which generalize uniform spaces. The concept of funcoid is generalized concept of proximity, the concept of reloid is cleared from superfluous details (generalized) concept of uniformity. Also funcoids generalize pretopologies and preclosures. Also funcoids and reloids are generalizations of binary relations whose domains and ranges are filters (instead of sets). Also funcoids and reloids can be considered as a generalization of (oriented) graphs, this provides us with a common generalization of analysis and discrete mathematics. The concept of continuity is defined by an algebraic formula (instead of old messy epsilondelta notation) for arbitrarymorphisms (including funcoids and reloids) of a partially ordered category. In one formula are generalized continuity, proximity continuity, and uniform continuity.
Category: Topology

[188] viXra:1003.0191 [pdf] submitted on 16 Mar 2010

On a Heuristic Approach to Mechanics and Electrodynamics of Moving Bodies

Authors: Leonid I. Filippov
Comments: In Russian, 33 pages, 12 figures

Determination to make the Einstein's treatment of simultaneity and relativistic notions of length and time interval measurement more intuitive and illustrative led to creation of a model in which light impulses are substituted with sound signals. The model uncovers the substance of Einstein's mathematical constructs and the mechanisms that give rise to relativistic effects. Consistent application of the model resulted in new constructions. The paper examines known mechanical and electromagnetic phenomena that can be clarified by this model. The use of such an approach leads to the notion of a distinguished frame of reference. In particular, the theory calls for the existence of electromagnetic interaction that contradicts the principle of relativity. The paper contains a description of an experimental apparatus built to test this prediction, as well as the results of the experiments.
Category: Relativity and Cosmology

[187] viXra:1003.0190 [pdf] submitted on 16 Mar 2010

A Brief Note on "Un-Particle" Physics

Authors: Ervin Goldfain
Comments: 1 page, Published in "Progress in Physics" vol. 3 (2008).

The possibility of a hidden sector of particle physics that lies beyond the energy range of the Standard Model has been recently advocated by many authors. A bizarre implication of this conjecture is the emergence of a continuous spectrum of massless fields with non-integral scaling dimensions called "un-particles". The purpose of this Letter is to show that the idea of "un-particles" was considered in at least two previous independent publications, prior to its first claimed disclosure.
Category: High Energy Particle Physics

[186] viXra:1003.0189 [pdf] submitted on 16 Mar 2010

Euclid-Euler-Jiang Prime Theorem

Authors: Chun-Xuan Jiang
Comments: 13 pages

Santilli's prime chains: (see paper for equations) There exist infinitely many primes such that are primes for arbitrary length . It is the Book proof. This is a generalization of Euclid-Euler proof for the existence of infinitely many primes. Therefore Euclid-Euler-Jiang theorem in the distribution of primes is advanced. It is the Book theorem.
Category: Number Theory

[185] viXra:1003.0188 [pdf] submitted on 16 Mar 2010

There Are Infinitely Many Prime Triplets

Authors: Chun-Xuan Jiang
Comments: 5 pages

Using Jiang's function we prove that there are infinitely many primes such that 3P-2 and 3P+2 are primes.
Category: Number Theory

[184] viXra:1003.0187 [pdf] submitted on 6 Mar 2010

A Generalization of a Leibniz Geometrical Theorem

Authors: Mihály Bencze, Florin Popovici, Florentin Smarandache
Comments: 5 pages

In this article we present a generalization of a Leibniz's theorem in geometry and an application of this.
Category: Geometry

[183] viXra:1003.0186 [pdf] submitted on 6 Mar 2010

Inequalities for Integer and Fractional Parts

Authors: Mihály Bencze, Florentin Smarandache
Comments: 8 pages

In this paper we present some new inequalities relative to integer and functional parts.
Category: Number Theory

[182] viXra:1003.0185 [pdf] submitted on 6 Mar 2010

On Recent Discovery of New Planetoids in the Solar System and Quantization of Celestial System

Authors: V. Christianto, Florentin Smarandache
Comments: 8 pages

The present note revised the preceding article discussing new discovery of a new planetoid in the solar system. Some recent discoveries have been included, and its implications in the context of quantization of celestial system are discussed, in particular from the viewpoint of superfluid dynamics. In effect, it seems that there are reasons to argue in favor of gravitation-related phenomena from boson condensation.
Category: Astrophysics

[181] viXra:1003.0184 [pdf] submitted on 6 Mar 2010

Cultural Advantage as an Alternative Framework: An Introduction

Authors: Florentin Smarandache, V. Christianto
Comments: 11 pages

Despite the economics jargon on 'rational choice', nowadays the entire world has nothing else to choose except to succumb under the spell of magic words of modern economics, i.e. 'neoliberalism', 'financial liberalization', 'free market' (laissez-faire), and 'globalization'. All of these can be shown to be part of a preconception, i.e. far beyond the 'neutral' idea of natural sciences. In Fritjof Capra's book 'Turning Point' (Bantam Books, 1982) these phenomena are summarized as follows: economics thinking have started by assuming that in economics sciences one can achieve the same generality and universality that physicists enjoy in doing Natural Sciences. In other words, economists try to become through their work 'hard science' rather than recognizing that in economics the subject of their study is human/people which is far from being predictable, either as individual or as society. In our humble opinion, economics is a mixture of both, hard and soft sciences. In order to show this, we introduce a new study, called Poly-Emporium Theory, where we show that phenomena from hard science and soft science co-exist and interact in economics. Poly-Emporium Theory is the study of interactions among many (big and small) firms in the market, and it is different from oligopoly since poly-emporium takes into consideration the small firms too (not only the big firms that dominate the market as in oligopoly). The above logic of thinking is the starting point to submit a new idea, under the heading of 'Cultural Advantage.' The first book in the series has title: Cultural Advantage for Cities: An alternative for Developing Countries. This presentation summarizes its basic ideas, with a hope that these ideas may be found interesting to develop further. For clarity the readers are referred to the book.
Category: Economics and Finance

[180] viXra:1003.0183 [pdf] submitted on 6 Mar 2010

A Note On Testing Of Hypothesis

Authors: Rajesh Singh, Jayant Singh, Florentin Smarandache
Comments: 5 pages

In this paper problem of testing of hypothesis is discussed when the samples have been drawn from normal distribution. The study of hypothesis testing is also extended to Baye's set up.
Category: Statistics

[179] viXra:1003.0182 [pdf] submitted on 6 Mar 2010

Structural Dynamics of Various Causes of Migration in Jaipur

Authors: Jayant Singh, Hansraj Yadav, Florentin Smarandache
Comments: 22 pages

Jaipur urban area has grown tremendously in last three decades. Composition of People migrating due to various reasons has display a meticulous trend. Dominance of people moving due to marriages is getting sturdy whereas Jaipur city is losing its luster in attracting persons for education and business. Short duration migration from Jaipur district to urban area has gone down to a very low level. Flow of migrants from Rural areas to Jaipur outpaced the migrants from urban areas and its composition from various in terms long and short distances migration has substantially changed over two consecutive decades. Movements of males and females were differ on many criterion as male moving faster than females for employment & education and females move faster than male for marriages and moving along family was found evident in short, medium and long distances migration. Gender gap in people migration from different reasons was observed and a gender specific trend was seen favour. Short duration migration and migration due to education & employment is not as prominence as it was two decade back
Category: Social Science

[178] viXra:1003.0181 [pdf] submitted on 6 Mar 2010

Proportional Conflict Redistribution Rules for Information Fusion

Authors: Florentin Smarandache, Jean Dezert
Comments: 41 pages

In this paper we propose five versions of a Proportional Conflict Redistribution rule (PCR) for information fusion together with several examples. From PCR1 to PCR2, PCR3, PCR4, PCR5 one increases the complexity of the rules and also the exactitude of the redistribution of conflicting masses. PCR1 restricted from the hyper-power set to the power set and without degenerate cases gives the same result as the Weighted Average Operator (WAO) proposed recently by Jøsang, Daniel and Vannoorenberghe but does not satisfy the neutrality property of vacuous belief assignment. That's why improved PCR rules are proposed in this paper. PCR4 is an improvement of minC and Dempster's rules. The PCR rules redistribute the conflicting mass, after the conjunctive rule has been applied, proportionally with some functions depending on the masses assigned to their corresponding columns in the mass matrix. There are infinitely many ways these functions (weighting factors) can be chosen depending on the complexity one wants to deal with in specific applications and fusion systems. Any fusion combination rule is at some degree ad-hoc.
Category: Artificial Intelligence

[177] viXra:1003.0180 [pdf] submitted on 6 Mar 2010

Smarandache Type Function Obtained by Duality

Authors: C. Dumitrescu, N. Vîrlan, Şt. Zamfir, E. Rădescu, N. Rădescu, Florentin Smarandache
Comments: 15 pages

In this paper we extended the Smarandache function from the set N* of positive integers to the set Q of rational numbers. Using the inversion formula, this function is also regarded as a generating function. We put in evidence a procedure to construct a (numerical) function starting from a given function in two particular cases. Also connections between the Smarandache function and Euler's totient function as with Riemann's zeta function are established.
Category: Number Theory

[176] viXra:1003.0179 [pdf] replaced on 16 Jul 2010

Prime Sieve Using Multiplication Operation Table

Authors: Jongsoo Park
Comments: 76 pages

Ben Green and Terence Tao showed that for any positive integer k, there exist infinitely many arithmetic progressions of length k consisting only of prime numbers. [14] Four parallel proofs of Szemer'edi's theorem have been achieved; one by direct combinatorics, one by ergodic theory, one by hypergraph theory, and one by Fourier analysis and additive combinatorics. Even with so many proofs, Professor T. Tao points out that with this problem, there remains a sense that our understanding of this result is incomplete; for instance, none of the approaches were powerful enough to detect progressions in the primes, mainly due to the sparsity of the prime sequence. [22] Oliver Lonsdale Atkin introduced a prime sieve using irreducible binary quadratic forms and modular arithmetic; the algorithm enumerates representations of integers by certain binary quadratic forms. A way that uses modular arithmetic is widely known: 6n+δ, 12n+δ, 30n+δ, 60n+δ.[31] In this paper, we assert that the composite number of the 12n+1, 5, 7, 11 series as selected by a Modular Arithmetic and Multiplication Table are not random but consist of very structural and regular arithmetic progression groups.
Category: Number Theory

[175] viXra:1003.0178 [pdf] submitted on 6 Mar 2010

On Solving General Linear Equations in the Set of Natural Numbers

Authors: Florentin Smarandache
Comments: 4 pages

The utility of this article is that it establishes if the number of the natural solutions of a general linear equation is limited or not. We will show also a method of solving, using integer numbers, the equation ax - by = c (which represents a generalization of lemmas 1 and 2 of [4]), an example of solving a linear equation with 3 unknowns in N, and some considerations on solving, using natural numbers, equations with n unknowns.
Category: Number Theory

[174] viXra:1003.0177 [pdf] submitted on 6 Mar 2010

Criteria of Primality

Authors: Florentin Smarandache
Comments: 4 pages

In this article we present four necessary and sufficient conditions for a natural number to be prime.
Category: Number Theory

[173] viXra:1003.0176 [pdf] submitted on 15 Mar 2010

Gravitational Limits

Authors: Willi Penker
Comments: 3 pages

The theory of black holes states that without the energy set free by nuclear fusion, the gravity of a big star will always be stronger than all other forces, causing it to collapse and ending in a singularity. During such a collapse, however, gravity itself should free enough binding energy to ultimately prevent the star from collapsing to a state where its escape velocity reaches the speed of light.
Category: Relativity and Cosmology

[172] viXra:1003.0175 [pdf] submitted on 15 Mar 2010

Do Thermodynamic Entropy and Quantum Non-locality Have a Common Basis?

Authors: Jonathan J. Dickau
Comments: 6 pages, The author notes that revisions are needed for this paper to be rigorously accurate, but wishes to foster conversation on this topic.

Both researchers and educators have expressed displeasure with the definition of entropy as a measure of disorder. Instead, it is argued by Leff, Lambert, and others that the increase of entropy can be far more accurately described using terms such as 'dispersal of energy,' 'spreading and sharing of energy,' and 'spatial and temporal spreading.' In decoherence theory, a similar metaphor is used to describe the phenomena involved with quantum non-locality, superposition, and entanglement. Specifically the wavefunction of a quantum entity, such as a sub-atomic particle or photon is not seen to collapse but rather is transferred through interactions to a system and/or its environment. This suggests there may be a common basis for entropy and non-locality. I explore the idea that energy is motive and extensive by nature, and that all its forms of expression involve motion, action, and propagation, which clearly leads to its being spread and shared when unconstrained, among the available microstates of its local system and the larger environment. Thus a single description, focusing on this universal quality of energy, explains both 2nd Law entropy and quantum non-locality.
Category: Quantum Physics

[171] viXra:1003.0174 [pdf] submitted on 6 Mar 2010

Redesigning Decision Matrix Method with an Indeterminacy-Based Inference Process

Authors: Jose L. Salmeron, Florentin Smarandache
Comments: 12 pages

For academics and practitioners concerned with computers, business and mathematics, one central issue is supporting decision makers. In this paper, we propose a generalization of Decision Matrix Method (DMM), using Neutrosophic logic. It emerges as an alternative to the existing logics and it represents a mathematical model of uncertainty and indeterminacy. This paper proposes the Neutrosophic Decision Matrix Method as a more realistic tool for decision making. In addition, a de-neutrosophication process is included.
Category: Artificial Intelligence

[170] viXra:1003.0173 [pdf] submitted on 6 Mar 2010

Linguistic-Mathematical Statistics in Rebus, Lyrics, Juridical Texts, Fancies and Paradoxes

Authors: Florentin Smarandache
Comments: 44 pages

This is a collection of linguistic-mathematical approaches to Romanian rebus, poetical and juridical texts, and proposes fancies, recreational math problems, and paradoxes. We study the frequencies of letters, syllables, vowels in various poetry, grill definitions in rebus, and rebus rules. We also compare the scientific language, lyrical language, and puzzles' language, and compute the Shannon entropy and Onicescu informational energy.
Category: Linguistics

[169] viXra:1003.0172 [pdf] submitted on 6 Mar 2010

A General Family of Estimators for Estimating Population Mean Using Known Value of Some Population Parameter(s)

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

A general family of estimators for estimating the population mean of the variable under study, which make use of known value of certain population parameter(s), is proposed. Under Simple Random Sampling Without Replacement (SRSWOR) scheme, the expressions of bias and mean-squared error (MSE) up to first order of approximation are derived. Some well known estimators have been shown as particular member of this family. An empirical study is carried out to illustrate the performance of the constructed estimator over others.
Category: Statistics

[168] viXra:1003.0171 [pdf] submitted on 6 Mar 2010

Deducibility Theorems in Boolean Logic

Authors: Florentin Smarandache
Comments: 4 pages

In this paper we give two theorems from the Propositional Calculus of the Boolean Logic with their consequences and applications and we prove them axiomatically.
Category: Set Theory and Logic

[167] viXra:1003.0170 [pdf] submitted on 14 Mar 2010

Diophantine Equation (See Paper) Has Infinitely Many Prime Solutions

Authors: Chun-Xuan Jiang
Comments: 18 pages

By using the arithmetic function J2n+1(ω) we prove that Diophantine equation (see paper) has infinitely many prime solutions.It is the Book proof. The J2n+1(ω) ushers in a new era in the prime numbers theory.
Category: Number Theory

[166] viXra:1003.0169 [pdf] submitted on 14 Mar 2010

Comparison of the Algorithmic and Axiomatic Approaches to the Construction of Quantum Field Theory

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

Two possibilities of the quantum theory construction, indicated by Feynman, are examined. The special features of the structure of the Standard Model (SM) are enumerated, which attest to the fact that SM is not an axiomatic, but an algorithmic theory. Deficiencies of SM and possibilities of overcoming these deficiencies are indicated. The structure of the nonlinear quantum field theory (NQFT) as an axiomatic theory, which makes it possible to overcome deficiencies in the Standard Model, is presented.
Category: High Energy Particle Physics

[165] viXra:1003.0168 [pdf] submitted on 6 Mar 2010

K-Nomial Coefficients

Authors: Florentin Smarandache
Comments: 4 pages

In this article we will widen the concepts of "binomial coefficients" and "trinomial coefficients" to the concept of "k-nomial coefficients", and one obtains some general properties of these. As an application, we will generalize the" triangle of Pascal".
Category: Algebra

[164] viXra:1003.0167 [pdf] submitted on 6 Mar 2010

A Class of Recursive Sets

Authors: Florentin Smarandache
Comments: 7 pages

In this article one builds a class of recursive sets, one establishes properties of these sets and one proposes applications. This article widens some results of [1].
Category: Set Theory and Logic

[163] viXra:1003.0166 [pdf] replaced on 20 Mar 2010

A Self-Recurrence Method for Generalizing Known Scientific Results

Authors: Florentin Smarandache
Comments: 7 pages

A great number of articles widen known scientific results (theorems, inequalities, math/physics/chemical etc. propositions, formulas), and this is due to a simple procedure, of which it is good to say a few words: Let suppose that we want to generalizes a known mathematical proposition P(a) , where a is a constant, to the proposition P(n) , where n is a variable which belongs to subset of N . To prove that P is true for n by recurrence means the following: the first step is trivial, since it is about the known result P(a) (and thus it was already verified before by other mathematicians!). To pass from P(n) to P(n + 1) , one uses too P(a) : therefore one widens a proposition by using the proposition itself, in other words the found generalization will be paradoxically proved with the help of the particular case from which one started! We present below the generalizations of Hölder, Minkovski, and respectively Tchebychev inequalities.
Category: Functions and Analysis

[162] viXra:1003.0165 [pdf] submitted on 6 Mar 2010

A Neutrosophic Description Logic

Authors: Haibin Wang, André Rogatko, Florentin Smarandache, Rajshekhar Sunderraman
Comments: 19 pages

Description Logics (DLs) are appropriate, widely used, logics for managing structured knowledge. They allow reasoning about individuals and concepts, i.e. set of individuals with common properties. Typically, DLs are limited to dealing with crisp, well defined concepts. That is, concepts for which the problem whether an individual is an instance of it is a yes/no question. More often than not, the concepts encountered in the real world do not have a precisely defined criteria of membership: we may say that an individual is an instance of a concept only to a certain degree, depending on the individual's properties. The DLs that deal with such fuzzy concepts are called fuzzy DLs. In order to deal with fuzzy, incomplete, indeterminate and inconsistent concepts, we need to extend the capabilities of fuzzy DLs further. In this paper we will present an extension of fuzzy ALC, combining Smarandache's neutrosophic logic with a classical DL. In particular, concepts become neutrosophic (here neutrosophic means fuzzy, incomplete, indeterminate and inconsistent), thus, reasoning about such neutrosophic concepts is supported. We will define its syntax, its semantics, describe its properties and present a constraint propagation calculus for reasoning in it.
Category: Artificial Intelligence

[161] viXra:1003.0164 [pdf] submitted on 6 Mar 2010

Generalizations of Ceva's Theorem and Applications

Authors: Florentin Smarandache
Comments: 7 pages

In these paragraphs one presents three generalizations of the famous theorem of Ceva
Category: Geometry

[160] viXra:1003.0163 [pdf] submitted on 6 Mar 2010

A Generalization of Euler's Theorem on Congruencies

Authors: Florentin Smarandache
Comments: 7 pages

In the paragraphs which follow we will prove a result which replaces the theorem of Euler: "If (a,m) = 1, then aφ(m) = 1 (mod m)", for the case when a and m are not relatively primes.
Category: Number Theory

[159] viXra:1003.0162 [pdf] submitted on 6 Mar 2010

A Generalization in Space of Jung's Theorem

Authors: Florentin Smarandache
Comments: 2 pages

In this short note we will prove a generalization of Joung's theorem in space.
Category: Geometry

[158] viXra:1003.0161 [pdf] submitted on 6 Mar 2010

DSmT: a New Paradigm Shift for Information Fusion

Authors: Jean Dezert, Florentin Smarandache
Comments: 11 pages

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been and still remains of primal importance for the development of reliable information fusion systems. In this short survey paper, we present the theory of plausible and paradoxical reasoning, known as DSmT (Dezert-Smarandache Theory) in literature, developed for dealing with imprecise, uncertain and potentially highly conflicting sources of information. DSmT is a new paradigm shift for information fusion and recent publications have shown the interest and the potential ability of DSmT to solve fusion problems where Dempster's rule used in Dempster-Shafer Theory (DST) provides counter-intuitive results or fails to provide useful result at all. This paper is focused on the foundations of DSmT and on its main rules of combination (classic, hybrid and Proportional Conflict Redistribution rules). Shafer's model on which is based DST appears as a particular and specific case of DSm hybrid model which can be easily handled by DSmT as well. Several simple but illustrative examples are given throughout this paper to show the interest and the generality of this new theory.
Category: Artificial Intelligence

[157] viXra:1003.0159 [pdf] submitted on 6 Mar 2010

An Introduction to the DSm Theory for the Combination of Paradoxical, Uncertain, and Imprecise Sources of Information

Authors: Florentin Smarandache, Jean Dezert
Comments: 21 pages

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this introduction, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT) in the literature, developed for dealing with imprecise, uncertain and paradoxical sources of information. We focus our presentation here rather on the foundations of DSmT, and on the two important new rules of combination, than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout the presentation to show the efficiency and the generality of this new approach.
Category: Artificial Intelligence

[156] viXra:1003.0158 [pdf] replaced on 2 Apr 2010

The Trapped Light ie Towards an Electromagnetic Theory of Elementary Particles

Authors: Giuliano Bettini
Comments: 17 pages, slightly amended

Examines the possibility of a purely electromagnetic formation of the physical world, and in particular electron. For this purpose presents a number of parallels between elementary particles and radar signals and radar target.
Category: Quantum Physics

[155] viXra:1003.0157 [pdf] submitted on 6 Mar 2010

Fusion of Qualitative Beliefs Using DSmT

Authors: Florentin Smarandache, Jean Dezert
Comments: 13 pages

This paper introduces the notion of qualitative belief assignment to model beliefs of human experts expressed in natural language (with linguistic labels). We show how qualitative beliefs can be efficiently combined using an extension of Dezert-Smarandache Theory (DSmT) of plausible and paradoxical quantitative reasoning to qualitative reasoning. We propose a new arithmetic on linguistic labels which allows a direct extension of classical DSm fusion rule or DSm Hybrid rules. An approximate qualitative PCR5 rule is also proposed jointly with a Qualitative Average Operator. We also show how crisp or interval mappings can be used to deal indirectly with linguistic labels. A very simple example is provided to illustrate our qualitative fusion rules.
Category: Artificial Intelligence

[154] viXra:1003.0156 [pdf] submitted on 6 Mar 2010

Target Type Tracking with PCR5 and Dempster's Rules: a Comparative Analysis

Authors: Jean Dezert, Albena Tchamova, Florentin Smarandache, Pavlina Konstantinova
Comments: 10 pages

In this paper we consider and analyze the behavior of two combinational rules for temporal (sequential) attribute data fusion for target type estimation. Our comparative analysis is based on Dempster's fusion rule proposed in Dempster-Shafer Theory (DST) and on the Proportional Conflict Redistribution rule no. 5 (PCR5) recently proposed in Dezert-Smarandache Theory (DSmT). We show through very simple scenario and Monte-Carlo simulation, how PCR5 allows a very efficient Target Type Tracking and reduces drastically the latency delay for correct Target Type decision with respect to Demspter's rule. For cases presenting some short Target Type switches, Demspter's rule is proved to be unable to detect the switches and thus to track correctly the Target Type changes. The approach proposed here is totally new, efficient and promising to be incorporated in real-time Generalized Data Association - Multi Target Tracking systems (GDA-MTT) and provides an important result on the behavior of PCR5 with respect to Dempster's rule. The MatLab source code is provided in [5].
Category: Artificial Intelligence

[153] viXra:1003.0155 [pdf] submitted on 6 Mar 2010

Processing Uncertainty and Indeterminacy in Information Systems Projects Success Mapping

Authors: Jose L. Salmeron, Florentin Smarandache
Comments: 13 pages

IS projects success is a complex concept, and its evaluation is complicated, unstructured and not readily quantifiable. Numerous scientific publications address the issue of success in the IS field as well as in other fields. But, little efforts have been done for processing indeterminacy and uncertainty in success research. This paper shows a formal method for mapping success using Neutrosophic Success Map. This is an emerging tool for processing indeterminacy and uncertainty in success research. EIS success have been analyzed using this tool.
Category: Artificial Intelligence

[152] viXra:1003.0154 [pdf] submitted on 6 Mar 2010

The Combination of Paradoxical, Uncertain and Imprecise Sources of Information based on DSmT and Neutro-Fuzzy Inference

Authors: Florentin Smarandache, Jean Dezert
Comments: 20 pages

The management and combination of uncertain, imprecise, fuzzy and even paradoxical or high conflicting sources of information has always been, and still remains today, of primal importance for the development of reliable modern information systems involving artificial reasoning. In this chapter, we present a survey of our recent theory of plausible and paradoxical reasoning, known as Dezert-Smarandache Theory (DSmT) in the literature, developed for dealing with imprecise, uncertain and paradoxical sources of information. We focus our presentation here rather on the foundations of DSmT, and on the two important new rules of combination, than on browsing specific applications of DSmT available in literature. Several simple examples are given throughout the presentation to show the efficiency and the generality of this new approach. The last part of this chapter concerns the presentation of the neutrosophic logic, the neutro-fuzzy inference and its connection with DSmT. Fuzzy logic and neutrosophic logic are useful tools in decision making after fusioning the information using the DSm hybrid rule of combination of masses.
Category: Artificial Intelligence

[151] viXra:1003.0153 [pdf] submitted on 6 Mar 2010

Conjectures on Partitions of Integers as Summations of Primes

Authors: Florentin Smarandache
Comments: 3 pages

In this short note many conjectures on partitions of integers as summations of prime numbers are presented, which are extension of Goldbach conjecture.
Category: Number Theory

[150] viXra:1003.0152 [pdf] submitted on 6 Mar 2010

The Generalized Pignistic Transformation

Authors: Jean Dezert, Florentin Smarandache, Milan Daniel
Comments: 11 pages

This paper presents in detail the generalized pignistic transformation (GPT) succinctly developed in the Dezert-Smarandache Theory (DSmT) framework as a tool for decision process. The GPT allows to provide a subjective probability measure from any generalized basic belief assignment given by any corpus of evidence. We mainly focus our presentation on the 3D case and provide the complete result obtained by the GPT and its validation drawn from the probability theory.
Category: Artificial Intelligence

[149] viXra:1003.0151 [pdf] submitted on 6 Mar 2010

A Method of Solving a Diophantine Equation of Second Degree with N Variables

Authors: Florentin Smarandache
Comments: 11 pages

A METHOD OF SOLVING A DIOPHANTINE EQUATION OF SECOND DEGREE WITH N VARIABLES
Category: Number Theory

[148] viXra:1003.0150 [pdf] submitted on 6 Mar 2010

On the Tweety Penguin Triangle Problem

Authors: Jean Dezert, Florentin Smarandache
Comments: 17 pages

In this paper, one studies the famous well-known and challenging Tweety Penguin Triangle Problem (TPTP or TP2) pointed out by Judea Pearl in one of his books. We first present the solution of the TP2 based on the fallacious Bayesian reasoning and prove that reasoning cannot be used to conclude on the ability of the penguin-bird Tweety to fly or not to fly. Then we present in details the counter-intuitive solution obtained from the Dempster-Shafer Theory (DST). Finally, we show how the solution can be obtained with our new theory of plausible and paradoxical reasoning (DSmT)
Category: Artificial Intelligence

[147] viXra:1003.0149 [pdf] submitted on 6 Mar 2010

Infinite Classes of Counter-Examples to the Dempster's Rule of Combination

Authors: Jean Dezert, Florentin Smarandache
Comments: 13 pages

This paper presents several classes of fusion problems which cannot be directly attacked by the classical mathematical theory of evidence, also known as the Dempster-Shafer Theory (DST) either because the Shafer's model for the frame of discernment is impossible to obtain or just because the Dempster's rule of combination fails to provide coherent results (or no result at all). We present and discuss the potentiality of the DSmT combined with its classical (or hybrid) rule of combination to attack these infinite classes of fusion problems.
Category: Artificial Intelligence

[146] viXra:1003.0148 [pdf] submitted on 6 Mar 2010

Combining Uncertain and Paradoxical Evidences for DSm Hybrid Models

Authors: Jean Dezert, Florentin Smarandache
Comments: 33 pages

This paper presents a general method for combining uncertain and paradoxical source of evidences for a wide class of fusion problems. From the foundations of the Dezert-Smarandache Theory (DSmT) we show how the DSm rule of combination can be adapted to take into account all possible integrity constraints (if any) of the problem under consideration due to the true nature of elements/concepts involved into it. We show how the Shafer's model can be considered as a specific DSm hybrid model and be easily handled by our approach and a new efficient rule of combination different from the Dempster's rule is obtained. Several simple examples are also provided to show the efficiency and the generality of the approach proposed in this work.
Category: Artificial Intelligence

[145] viXra:1003.0147 [pdf] submitted on 6 Mar 2010

On the Generation of Hyper-Powersets for the DSmT

Authors: Jean Dezert, Florentin Smarandache
Comments: 11 pages

The recent theory of plausible and paradoxical reasoning (DSmT) developed by the authors appears to be a nice promising theoretical tools to solve many information fusion problems where the Shafer's model cannot be used due to the intrinsic paradoxical nature of the elements of the frame of discernment and where a strong internal conflict between sources arises. The main idea of DSmT is to work on the hyper-powerset of the frame of discernment of the problem under consideration. Although the definition of hyper-powerset is well established, the major difficulty in practice is to generate such hyper-powersets in order to implement DSmT fusion rule on computers. We present in this paper a simple algorithm for generating hyper-powersets and discuss the limitations of our actual computers to generate such hyper-powersets when the dimension of the problem increases.
Category: Artificial Intelligence

[144] viXra:1003.0146 [pdf] submitted on 6 Mar 2010

Partial Ordering of Hyper-Powersets and Matrix Representation of Belief Functions Within DSmT

Authors: Jean Dezert, Florentin Smarandache
Comments: 13 pages

In this paper, we examine several issues for ordering or partially ordering elements of hyperpowertsets involved in the recent theory of plausible, uncertain and paradoxical reasoning (DSmT) developed by the authors. We will show the benefit of some of these issues to obtain a nice and useful matrix representation of belief functions.
Category: Artificial Intelligence

[143] viXra:1003.0145 [pdf] replaced on 16 Oct 2010

Non-equilibrium Dynamics as Source of Asymmetries in High Energy Physics

Authors: Ervin Goldfain
Comments: 16 pages, Paper published in Electronic Journal of Theoretical Physics. EJTP 7, No. 24 (2010) 219234

Understanding the origin of certain symmetry breaking scenarios in high-energy physics remains an open challenge. Here we argue that, at least in some cases, symmetry violation is an effect of non-equilibrium dynamics that is likely to develop somewhere above the energy scale of electroweak interaction. We also find that, imposing Poincare symmetry in non-equilibrium field theory, leads to fractalization of space-time continuum via period-doubling transition to chaos.
Category: High Energy Particle Physics

[142] viXra:1003.0144 [pdf] submitted on 12 Mar 2010

A Simple Calculation of a Possible Variation in the Speed of Light

Authors: Ioannis Iraklis Haranas
Comments: 3 pages, Published Journal of Theoretics

The idea of a possible variable light cosmology was recently investigated by certain authors. In our brief note an estimate for a possible variation in the speed of light can be calculated if fundamental relations of cosmology are used along with a plausible definition of the speed of light.
Category: Relativity and Cosmology

[141] viXra:1003.0143 [pdf] submitted on 12 Mar 2010

On the Measurement of Absolute Velocities

Authors: Alex Ceapa
Comments: 4 pages, Published:Journal of Theoretics Oct/Nov 2002 Vol.4, No.5

Inertial observers can not only measure their absolute velocities but that of light as well, thereby being able to shed insight into the principle of the constancy of light velocity. The light speeds c±v, though considered to conflict with this principle, are shown herein to not be true physical entities.
Category: Relativity and Cosmology

[140] viXra:1003.0142 [pdf] submitted on 12 Mar 2010

Anisotropic Cosmological Models with a Generalized Chaplygin Gas

Authors: N. Mebarki
Comments: 10 pages, Presented at Invisible Universe International Conference, 29 June-10 July 2009, Paris, France

Anisotropic cosmological models with a generalized Chaplygin gas in a Finsler space-time geometry are considered and a class of exact solutions as well as cosmological parameters behaviors are studied. Moreover, the viability and stability criteria for a general solution are also discussed.
Category: Relativity and Cosmology

[139] viXra:1003.0141 [pdf] submitted on 12 Mar 2010

Higher Oreder Curvature Gravity in Finsler Geometry

Authors: N. Mebarki, M. Y. Boudjada
Comments: 3 pages, Presented in the 12th Marcel Grossmann Meeting 12-18 July 2009, Paris, France

In Finslerian space-time, a higher order curvature cosmological model of gravity is proposed and a class of cosmological solutions is obtained. Moreover, the viability and stability near critical points are also discussed.
Category: Relativity and Cosmology

[138] viXra:1003.0140 [pdf] submitted on 12 Mar 2010

New Seiberg-Witten Fields Maps Through Weyl Symmetrization and The Pure Geometric Extension of The Standard Model

Authors: N. Mebarki, F. Khelili, O. Benabbes
Comments: 20 pages, Published in EJTP No22 (2009)5-28

A unified description of a symmetrized and anti-symmetrized Moyal star product of the non-commutative infinitesimal gauge transformations is presented and the corresponding Seiberg-Witten maps are derived. Moreover, the noncommutative covariant derivative, field strenght tensor as well as gauge transformations are shown to be consistently constructed not on the enveloping but on the Lie and/or Poisson algebra. As an application, a pure geometric extension of the standard model is shown explicitly.
Category: High Energy Particle Physics

[137] viXra:1003.0139 [pdf] submitted on 12 Mar 2010

Gaps Among Products of m Primes

Authors: Chun-Xuan Jiang
Comments: 9 pages

Using Jiang function J2(ω) we prove gaps among products of m prime: d(x) = d(x + 1) = d(x + 5 - 3) = d(x + 7 - 3) = ... = d(x + Pn - 3) = m > 1 infinitely-often, where Pn denotes the n - th prime.
Category: Number Theory

[136] viXra:1003.0138 [pdf] submitted on 12 Mar 2010

To Demonstrate That Gravity Is Action-at-a-distance

Authors: Chun-Xuan Jiang
Comments: 14 pages

In this paper we explain the behavior of the entire universe from the smallest to the largest scales. We found the only tachyonic string theory (other string theories all are guesses), find an equation that changed the universe: F-bar = -mc2/R, establish the expansion theory of the universe without dark matter and dark energy, and prove that the principle of equivalence is nonexistent. We demonstrate that gravity is action-at-a-distance and that a gravitational wave is unobservable.We suggest a new universe model.
Category: Quantum Gravity and String Theory

[135] viXra:1003.0137 [pdf] submitted on 6 Mar 2010

Empirical Study in Finite Correlation Coefficient in Two Phase Estimation

Authors: M. Khoshnevisan, F. Kaymram, Housila P. Singh, Rajesh Singh, Florentin Smarandache
Comments: 10 pages

This paper proposes a class of estimators for population correlation coefficient when information about the population mean and population variance of one of the variables is not avaliable but information about these parameters of another variable (auxiliary) is avaliable, in two phase sampling and analyzes its properties. Optimum estimator in the class is identified with its variance formula. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters.Following Singh (1982) and Srivastava and Jhajj (1983), it has been shown that when these population parameters are replaced by their consistent estimates the resulting class of estimators has the same asymptotic variance as that of optimum estimator. An empirical study is carried out to demonstrate the performance of the constructed estimators.
Category: Statistics

[134] viXra:1003.0136 [pdf] submitted on 6 Mar 2010

Econometric Analysis on Efficiency of Estimator

Authors: M. Khoshnevisan, F. Kaymram, Housila P. Singh, Rajesh Singh, Florentin Smarandache
Comments: 11 pages

This paper investigates the efficiency of an alternative to ratio estimator under the super population model with uncorrelated errors and a gammadistributed auxiliary variable. Comparisons with usual ratio and unbiased estimators are also made.
Category: Statistics

[133] viXra:1003.0135 [pdf] submitted on 6 Mar 2010

Optimal Plant Layout Design for Process-focused Systems

Authors: M. Khoshnevisan, Sukanto Bhattacharya, Florentin Smarandache
Comments: 13 pages

In this paper we have proposed a semi-heuristic optimization algorithm for designing optimal plant layouts in process-focused manufacturing/service facilities. Our proposed algorithm marries the well-known CRAFT (Computerized Relative Allocation of Facilities Technique) with the Hungarian assignment algorithm. Being a semi-heuristic search, our algorithm is likely to be more efficient in terms of computer CPU engagement time as it tends to converge on the global optimum faster than the traditional CRAFT algorithm - a pure heuristic. We also present a numerical illustration of our algorithm.
Category: Data Structures and Algorithms

[132] viXra:1003.0134 [pdf] submitted on 6 Mar 2010

Definitions Derived from Neutrosophics

Authors: Florentin Smarandache
Comments: 15 pages

Thirty-three new definitions are presented, derived from neutrosophic set, neutrosophic probability, neutrosophic statistics, and neutrosophic logic. Each one is independent, short, with references and cross references like in a dictionary style.
Category: Data Structures and Algorithms

[131] viXra:1003.0133 [pdf] submitted on 6 Mar 2010

Utility of Choice: An Information Theoretic Approach to Investment Decision-making

Authors: M. Khoshnevisan, Florentin Smarandache, Sukanto Bhattacharya
Comments: 18 pages

In this paper we have devised an alternative methodological approach for quantifying utility in terms of expected information content of the decisionmaker's choice set. We have proposed an extension to the concept of utility by incorporating extrinsic utility; which we have defined as the utility derived from the element of choice afforded to the decision-maker by the availability of an object within his or her object set. We have subsequently applied this extended utility concept to the case of investor utility derived from a structured, financial product - an custom-made investment portfolio incorporating an endogenous capital-guarantee through inclusion of cash as a risk-free asset, based on the Black-Scholes derivative-pricing formulation. We have also provided instances of potential application of information and coding theory in the realms of financial decision-making with such structured portfolios, in terms of transmission of product information.
Category: Economics and Finance

[130] viXra:1003.0132 [pdf] submitted on 6 Mar 2010

A Proposed Artificial Neural Network Classifier to Identify Tumor Metastases Part I

Authors: M. Khoshnevisan, Sukanto Bhattacharya, Florentin Smarandache
Comments: 14 pages

In this paper we propose a classification scheme to isolate truly benign tumors from those that initially start off as benign but subsequently show metastases. A non-parametric artificial neural network methodology has been chosen because of the analytical difficulties associated with extraction of closed-form stochastic-likelihood parameters given the extremely complicated and possibly non-linear behavior of the state variables. This is intended as the first of a three-part research output. In this paper, we have proposed and justified the computational schema. In the second part we shall set up a working model of our schema and pilot-test it with clinical data while in the concluding part we shall give an in-depth analysis of the numerical output and model findings and compare it to existing methods of tumor growth modeling and malignancy prediction.
Category: Quantitative Biology

[129] viXra:1003.0131 [pdf] submitted on 6 Mar 2010

Computational Exploration of Investor Utilities Underlying a Portfolio Insurance Strategy

Authors: M. Khoshnevisan, Florentin Smarandache, Sukanto Bhattacharya
Comments: 24 pages

In this paper we take a look at a simple portfolio insurance strategy using a protective put and computationally derive the investor's governing utility structures underlying such a strategy under alternative market scenarios. Investor utility is deemed to increase with an increase in the excess equity generated by the portfolio insurance strategy over a simple investment strategy without any insurance. Three alternative market scenarios (probability spaces) have been explored - "Down", "Neutral" and "Up", categorized according to whether the price of the underlying security is most likely to go down, stay unchanged or go up. The methodology used is computational, primarily based on simulation and numerical extrapolation. The Arrow-Pratt measure of risk aversion has been used to determine how the investors react towards risk under the different scenarios.
Category: Economics and Finance

[128] viXra:1003.0130 [pdf] submitted on 6 Mar 2010

A Family of Estimators of Population Mean Using Multiauxiliary Information in Presence of Measurement Errors

Authors: Jack Allen, Housila P. Singh, Florentin Smarandache
Comments: 16 pages

This paper proposes a family of estimators of population mean using information on several auxiliary variables and analyzes its properties in the presence of measurement errors.
Category: Statistics

[127] viXra:1003.0129 [pdf] submitted on 6 Mar 2010

Fuzziness and Funds Allocation in Portfolio Optimization

Authors: Jack Allen, Sukanto Bhattacharya, Florentin Smarandache
Comments: 21 pages

Each individual investor is different, with different financial goals, different levels of risk tolerance and different personal preferences. From the point of view of investment management, these characteristics are often defined as objectives and constraints. Objectives can be the type of return being sought, while constraints include factors such as time horizon, how liquid the investor is, any personal tax situation and how risk is handled. It's really a balancing act between risk and return with each investor having unique requirements, as well as a unique financial outlook - essentially a constrained utility maximization objective. To analyze how well a customer fits into a particular investor class, one investment house has even designed a structured questionnaire with about two-dozen questions that each has to be answered with values from 1 to 5. The questions range from personal background (age, marital state, number of children, job type, education type, etc.) to what the customer expects from an investment (capital protection, tax shelter, liquid assets, etc.). A fuzzy logic system has been designed for the evaluation of the answers to the above questions. We have investigated the notion of fuzziness with respect to funds allocation.
Category: Economics and Finance

[126] viXra:1003.0128 [pdf] submitted on 6 Mar 2010

Estimation of Weibull Shape Parameter by Shrinkage Towards an Interval Under Failure Censored Sampling

Authors: Housila P. Singh, Sharad Saxena, Jack Allen, Sarjinder Singh, Florentin Smarandache
Comments: 20 pages

This paper is speculated to propose a class of shrinkage estimators for shape parameter β in failure censored samples from two-parameter Weibull distribution when some 'apriori' or guessed interval containing the parameter β is available in addition to sample information and analyses their properties. Some estimators are generated from the proposed class and compared with the minimum mean squared error (MMSE) estimator. Numerical computations in terms of percent relative efficiency and absolute relative bias indicate that certain of these estimators substantially improve the MMSE estimator in some guessed interval of the parameter space of β, especially for censored samples with small sizes. Subsequently, a modified class of shrinkage estimators is proposed with its properties.
Category: Statistics

[125] viXra:1003.0127 [pdf] submitted on 11 Mar 2010

Nonlinear Dynamics, Field Theory and Collider Phenomenology

Authors: Ervin Goldfain
Comments: 9 pages, This paper is a condensed version of an article published in a nonlinear dynamics journal in 2009

Both theory and experiment strongly suggest that new phenomena await discovery above the energy range of the standard model for particle physics (SM). We argue that a correct description of physics in the Terascale sector needs to account for the unquenched randomness induced by short-distance fluctuations. The existence of unparticles, alleged to emerge at the next-generation colliders, is motivated by a dynamic setting that is far-of-equilibrium and able to sustain a rich spectrum of complex phenomena.
Category: High Energy Particle Physics

[124] viXra:1003.0126 [pdf] submitted on 11 Mar 2010

The Meaning of Mass

Authors: Alex Ceapa
Comments: 2 pages, Published in Journal of Theoretics, vol.6-3, June/July 2004

Der Waerden obtained the spinorial transcription of the Dirac equation from the relativistic energy-momentum relationship. The recent validation of the principle of the physical determination of equations in the special relativity theory enables us to deduce the meaning of mass from his results.
Category: Relativity and Cosmology

[123] viXra:1003.0125 [pdf] replaced on 2013-04-22 14:03:34

The Learning of Ancient Languages as (super)Human Effort

Authors: Dainis Zeps
Comments: 9 Pages. Corrected version

Problems around teaching ancient languages are discussed. It is suggested to assume that learning and teaching of languages require some superhuman effort. Author’s experience of teaching ancient languages and producing electronic educational tools both for text version and for Internet in Faculty of Theology in University of Latvia is described. Problems around cognitive models of reasoning and place of languages there are discussed.
Category: Linguistics

[122] viXra:1003.0123 [pdf] replaced on 11 Mar 2010

Objections to Quantum Gravity Theories based on Causal Dynamical Triangulation

Authors: Ervin Goldfain
Comments: 2 pages, Letters submitted to the Editors of Classical and Quantum Gravity (v1) and Physics Review Letters (v2).

This memo is in regards to the recently published contribution by Ambjorn J. et al. "Planckian Birth of Quantum de Sitter Universe" PRL 100, 091304 (2008). The article claims that "causal dynamical triangulation" enables a consistent regularization of quantum gravity. A "quantum universe" emerging from a nonperturbative sum over geometries is alleged to recover "with high accuracy a fourdimensional de Sitter space-time". On closer examination, the approach is built on many objectionable premises
Category: Quantum Gravity and String Theory

[121] viXra:1003.0122 [pdf] submitted on 6 Mar 2010

A Generalized Numeration Base

Authors: Florentin Smarandache
Comments: 6 pages

A Generalized Numeration Base is defined in this paper, and then particular cases are presented, such as Prime Base, Square Base, m-Power Base, Factorial Base, and operations in these bases.
Category: Number Theory

[120] viXra:1003.0121 [pdf] submitted on 6 Mar 2010

G Add-On, Digital, Sieve, General Periodical, and Non-Arithmetic Sequences

Authors: Florentin Smarandache
Comments: 14 pages

Other new sequences are introduced in number theory, and for each one a general question: how many primes each sequence has.
Category: Number Theory

[119] viXra:1003.0120 [pdf] submitted on 6 Mar 2010

Another Set of Sequences, Sub-Sequences, and Sequences of Sequences

Authors: Florentin Smarandache
Comments: 42 pages

New sequences in number theory are showed below with definitions, examples, solved or open questions and references for each case.
Category: Number Theory

[118] viXra:1003.0119 [pdf] submitted on 6 Mar 2010

Funny Problems!

Authors: Florentin Smarandache
Comments: 6 pages

Thirty original and collected problems, puzzles, and paradoxes in mathematics and physics are explained in this paper, taught by the author to the elementary and high school teachers at the University of New Mexico - Gallup in 1997-8 and afterwards. They have a more educational interest because make the students think different!
Category: Set Theory and Logic

[117] viXra:1003.0118 [pdf] submitted on 6 Mar 2010

Numerology

Authors: Florentin Smarandache
Comments: 16 pages

A collection of original sequences, open questions, and problems are mentioned below.
Category: Number Theory

[116] viXra:1003.0117 [pdf] submitted on 6 Mar 2010

Linguistic Paradoxes and Tautologies

Authors: Florentin Smarandache
Comments: 12 pages

Classes of linguistic paradoxes are introduced with examples and explanations. They are part of the author's work on the Paradoxist Philosophy based on mathematical logic. The general cases exposed below are modeled on the English language structure in a rigid way. In order to find nice particular examples of such paradoxes one grammatically adjusts the sentences.
Category: Set Theory and Logic

[115] viXra:1003.0116 [pdf] submitted on 6 Mar 2010

Mixed Noneuclidean Geometries

Authors: Florentin Smarandache
Comments: 23 pages

The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the apparently unscientific ideas into scientific ones, and to develop their study (The Theory of Imperfections). And finally, to interconnect opposite (and not only) human fields of knowledge into as-heterogeneous-as-possible another fields.
Category: Geometry

[114] viXra:1003.0115 [pdf] submitted on 6 Mar 2010

Special Algebraic Structures

Authors: Florentin Smarandache
Comments: 4 pages

New notions are introduced in algebra in order to better study the congruences in number theory. For example, the <special semigroups> make an important such contribution.
Category: Algebra

[113] viXra:1003.0114 [pdf] submitted on 6 Mar 2010

On Rugina's System of Thought

Authors: Florentin Smarandache
Comments: 30 pages

In this article one investigates Rugina's Orientation Table and one gives particular examples for several of its seven models. Leon Walras's Economics of Stable Equilibrium and Keynes's Economics of Disequilibrium are combined in Rugina's Orientation Table in systems which are s% stable and 100-s% unstable, where s may be 100, 95, 65, 50, 35, 5, and 0. The Classical Logic and Modern Logic are united in Rugina's Integrated Logic, and then generalized in the Neutrosophic Logic.
Category: Artificial Intelligence

[112] viXra:1003.0113 [pdf] submitted on 6 Mar 2010

Improvement in Estimating the Population Mean Using Exponential Estimator in Simple Random Sampling

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 6 pages

This study proposes some exponential ratio-type estimators for estimating the population mean of the variable under study ... (see paper for full abstract)
Category: Statistics

[111] viXra:1003.0112 [pdf] submitted on 6 Mar 2010

Convergence of a Family of Series

Authors: Florentin Smarandache
Comments: 4 pages

In this article we will construct a family of expressions ε(n). For each element E(n) from ε(n), the convergence of the series Σ E(n) can be determined in accordance to the theorems of this article.
Category: Number Theory

[110] viXra:1003.0111 [pdf] submitted on 6 Mar 2010

A Numerical Function in the Congruence Theory

Authors: Florentin Smarandache
Comments: 8 pages

In this paper we define a function L which will allow us to (separately or simultaneously) generalize many theorems from Number Theory obtained by Wilson, Fermat, Euler, Gauss, Lagrange, Leibniz, Moser, and Sierpinski.
Category: Number Theory

[109] viXra:1003.0110 [pdf] submitted on 6 Mar 2010

Comments on "A New Combination of Evidence Based on Compromise"

Authors: Jean Dezert, Arnaud Martin, Florentin Smarandache
Comments: 5 pages

Comments on "A new combination of evidence based on compromise"
Category: Artificial Intelligence

[108] viXra:1003.0109 [pdf] submitted on 6 Mar 2010

A General Class of Estimators of Population Median Using Two Auxiliary Variables in Double Sampling

Authors: Jack Allen, Housila P. Singh, Sarjinder Singh, Florentin Smarandache
Comments: 21 pages

In this paper we have suggested two classes of estimators for population median MY of the study character Y using information on two auxiliary characters X and Z in double sampling. It has been shown that the suggested classes of estimators are more efficient than the one suggested by Singh et al (2001). Estimators based on estimated optimum values have been also considered with their properties. The optimum values of the first phase and second phase sample sizes are also obtained for the fixed cost of survey.
Category: Statistics

[107] viXra:1003.0108 [pdf] submitted on 6 Mar 2010

A Class of DSm Conditioning Rules

Authors: Florentin Smarandache, Mark Alford
Comments: 9 pages

In this paper we introduce two new DSm fusion conditioning rules with example, and as a generalization of them a class of DSm fusion conditioning rules, and then extend them to a class of DSm conditioning rules.
Category: Artificial Intelligence

[106] viXra:1003.0107 [pdf] submitted on 6 Mar 2010

A General Theorem for the Characterization of N Prime Numbers Simultaneously

Authors: Florentin Smarandache
Comments: 9 pages

This article presents a necessary and sufficient theorem for N numbers, coprime two by two, to be prime simultaneously. It generalizes V. Popa's theorem [3], as well as I. Cucurezeanu's theorem ([1], p. 165), Clement's theorem, S. Patrizio's theorems [2], etc. Particularly, this General Theorem offers different characterizations for twin primes, for quadruple primes, etc.
Category: Number Theory

[105] viXra:1003.0106 [pdf] submitted on 10 Mar 2010

Some Results due to a Possible Cosmic Quantum Mechanics in Astrophysics

Authors: Ioannis Iraklis Haranas
Comments: 6 pages, Publisher Journal of Theoretics, vol. 4, no. 1, 2001.

Recent observations confirm quantized galactic redshifts and hint a possible new form of quantum mechanics, which could probably explain these observed properties of the galaxies. This brief contribution investigates a possible relation between the new cosmic Planck constant hg and other fundamental constants of physics.
Category: Astrophysics

[104] viXra:1003.0105 [pdf] submitted on 10 Mar 2010

Orthogonal Polynomials, Moment Problem and the Riemann XI-Function ξ(1/2 + Iz)

Authors: Jose Javier Garcia Moreta
Comments: 12 Pages.

In this paper we study a set of orthogonal Polynomials with respect a certain given measure related to the Taylor series expansion of the Xi-function , this paper is based on a previous conjecture by Carlon and Gaston related to the fact that Riemann Hypothesis (with simple zeros) is equivalent to the limit for a certain set of orthogonal Polynomials, we study the 'Hamburger moment problem' for even 'n' and 0 for n odd here the moments are related to the power series expansion of Xi-function , we also give the integral representation for the generating function , in terms of the Laplace transform of , and in the end of the paper we study the connection of our orthogonal polynomial set with the Kernel , through all the paper we will use the simplified notation (see paper for abstract with equations)
Category: Functions and Analysis

[103] viXra:1003.0104 [pdf] replaced on 12 Mar 2010

Messenger Particles and Relativity

Authors: John R. McWhinnie
Comments: 13 pages

This article is an attempt to expose the role played by messenger particles in physics. The concept of the "messenger particle" has long been considered in physics. The latest research shows evidence that the four fundamental forces of nature ,Gravitation, Electromagnetic and the Weak and Strong Nuclear forces are all created by messenger particles. This hypotheses is leading to a new way of thinking about the fundamental sub-atomic wave/particles that are the building blocks of our universe. Some of the latest evidence actually shows that in order to understand what is happening with these messenger particles it is necessary to perceive them as information carriers. The four messenger particles that are thought to exist are the Graviton (not yet discovered) , Photon, Weak Guage Boson and the Gluon. This paper shall be concerned with the Photon as an information carrier.
Category: Relativity and Cosmology

[102] viXra:1003.0103 [pdf] submitted on 6 Mar 2010

About the Characteristic Function of a Set

Authors: Mihály Bencze, Florentin Smarandache
Comments: 11 pages

In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory found in undergraduate studies.
Category: Number Theory

[101] viXra:1003.0102 [pdf] submitted on 6 Mar 2010

On Carmichaël's Conjecture

Authors: Florentin Smarandache
Comments: 4 pages

On Carmichaël's conjecture
Category: Number Theory

[100] viXra:1003.0101 [pdf] submitted on 6 Mar 2010

A New Class Fusion Rule for Solving Blackman's Association Problem

Authors: Albena Tchamova, Jean Dezert, Florentin Smarandache
Comments: 6 pages

This paper presents a new approach for solving the paradoxical Blackman's Association Problem. It utilizes the recently defined new class fusion rule based on fuzzy Tconorm/ T-norm operators together with Dezert-Smarandache theory based, relative variations of generalized pignistic probabilities measure of correct associations, defined from a partial ordering function of hyper-power set. The ability of this approach to solve the problem against the classical Dempster-Shafer's method, proposed in the literature is proven. It is shown that the approach improves the separation power of the decision process for this association problem.
Category: Artificial Intelligence

[99] viXra:1003.0100 [pdf] submitted on 6 Mar 2010

On the Blackman's Association Problem

Authors: Jean Dezert, Florentin Smarandache, Albena Tchamova
Comments: 11 pages

Modern multitarget-multisensor tracking systems involve the development of reliable methods for the data association and the fusion of multiple sensor information, and more specifically the partioning of observations into tracks. This paper discusses and compares the application of Dempster-Shafer Theory (DST) and the Dezert-Smarandache Theory (DSmT) methods to the fusion of multiple sensor attributes for target identification purpose. We focus our attention on the paradoxical Blackman's association problem and propose several approaches to outperfom Blackman's solution. We clarify some preconceived ideas about the use of degree of conflict between sources as potential criterion for partitioning evidences.
Category: Artificial Intelligence

[98] viXra:1003.0099 [pdf] submitted on 6 Mar 2010

Methods in Industrial Biotechnology for Chemical Engineers

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache
Comments: 126 pages

Industrial Biotechnology is an interdisciplinary topic to which tools of modern biotechnology are applied for finding proper proportion of raw mix of chemicals, determination of set points, finding the flow rates etc., This study is significant as it results in better economy, quality product and control of pollution. The authors in this book have given only methods of industrial biotechnology mainly to help researchers, students and chemical engineers. Since biotechnology concerns practical and diverse applications including production of new drugs, clearing up pollution etc. we have in this book given methods to control pollution in chemical industries as it has become a great health threat in India. In some cases, the damage due to environmental pollution outweighs the benefits of the product.
Category: Chemistry

[97] viXra:1003.0098 [pdf] submitted on 6 Mar 2010

Applications of Bimatrices to Some Fuzzy and Neutrosophic Models

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral
Comments: 273 pages

Graphs and matrices play a vital role in the analysis and study of several of the real world problems which are based only on unsupervised data. The fuzzy and neutrosophic tools like fuzzy cognitive maps invented by Kosko and neutrosophic cognitive maps introduced by us help in the analysis of such real world problems and they happen to be mathematical tools which can give the hidden pattern of the problem under investigation. This book, in order to generalize the two models, has systematically invented mathematical tools like bimatrices, trimatrices, n-matrices, bigraphs, trigraphs and n-graphs and describe some of its properties. These concepts are also extended neutrosophically in this book.
Category: Algebra

[96] viXra:1003.0097 [pdf] submitted on 6 Mar 2010

Introduction to Bimatrices

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral
Comments: 181 pages

Matrix theory has been one of the most utilised concepts in fuzzy models and neutrosophic models. From solving equations to characterising linear transformations or linear operators, matrices are used. Matrices find their applications in several real models. In fact it is not an exaggeration if one says that matrix theory and linear algebra (i.e. vector spaces) form an inseparable component of each other.
Category: Algebra

[95] viXra:1003.0096 [pdf] submitted on 6 Mar 2010

Introduction to Linear Bialgebra

Authors: W. B. Vasantha Kandasamy, Florentin Smarandache, K. Ilanthenral
Comments: 238 pages

The algebraic structure, linear algebra happens to be one of the subjects which yields itself to applications to several fields like coding or communication theory, Markov chains, representation of groups and graphs, Leontief economic models and so on. This book has for the first time, introduced a new algebraic structure called linear bialgebra, which is also a very powerful algebraic tool that can yield itself to applications.
Category: Algebra

[94] viXra:1003.0095 [pdf] submitted on 6 Mar 2010

About Bernoulli's Numbers

Authors: Mihály Bencze, Florentin Smarandache
Comments: 3 pages

Many methods to compute the sum of the first n natural numbers of the same powers (see [4]) are well known. In this article we present a simple proof of the method from [3].
Category: Number Theory

[93] viXra:1003.0094 [pdf] submitted on 6 Mar 2010

Belief Conditioning Rules

Authors: Florentin Smarandache, Jean Dezert
Comments: 27 pages

In this paper we propose a new family of Belief Conditioning Rules (BCR) for belief revision. These rules are not directly related with the fusion of several sources of evidence but with the revision of a belief assignment available at a given time according to the new truth (i.e. conditioning constraint) one has about the space of solutions of the problem.
Category: Artificial Intelligence

[92] viXra:1003.0093 [pdf] submitted on 6 Mar 2010

Bases of Solutions for Linear Congruences

Authors: Florentin Smarandache
Comments: 5 pages

In this article we establish some properties regarding the solutions of a linear congruence, bases of solutions of a linear congruence, and the finding of other solutions starting from these bases. This article is a continuation of my article "On linear congruences".
Category: Number Theory

[91] viXra:1003.0092 [pdf] submitted on 6 Mar 2010

Auxiliary Information and a Priori Values in Construction of Improved Estimators

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 75 pages

This volume is a collection of six papers on the use of auxiliary information and a priori values in construction of improved estimators. The work included here will be of immense application for researchers and students who employ auxiliary information in any form.
Category: Statistics

[90] viXra:1003.0091 [pdf] submitted on 6 Mar 2010

Ratio Estimators in Simple Random Sampling Using Information on Auxiliary Attribute

Authors: Rajesh Singh, Pankaj Chauhan, Nirmala Sawan, Florentin Smarandache
Comments: 7 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.
Category: Statistics

[89] viXra:1003.0090 [pdf] submitted on 8 Mar 2010

Observation of Anomalous Potential Electric Energy in Distilled Water Under Solar Heating

Authors: Florentin Smarandache, V. Christianto
Comments: 9 pages

In this paper, we describe a very simple experiment with distilled water which could exhibit anomalous potential electrical energy with very minimum preparation energy. While this observed excess energy here is less impressive than [1][2] and the material used is also far less exotic than common LENR-CANR experiments, from the viewpoint of minimum preparation requirement - and therefore less barrier for rapid implementation--, it seems that further experiments could be recommended in order to verify and also to explore various implications of this new proposition.
Category: Chemistry

[88] viXra:1003.0089 [pdf] replaced on 12 May 2010

Complete Exposition of Non-Primes Generated from a Geometric Revolving Approach by 8x8 Sets of Related Series, and thereby ad negativo Exposition of a Systematic Pattern for the Totality of Prime Numbers

Authors: Stein E. Johansen
Comments: 41 pages, Submitted to Journal of Calcutta Mathematical Society, Nov 18, 2009.

We present a certain geometrical interpretation of the natural numbers, where these numbers appear as joint products of 5- and 3-multiples located at specified positions in a revolving chamber. Numbers without factors 2, 3 or 5 appear at eight such positions, and any prime number larger than 7 manifests at one of these eight positions after a specified amount of rotations of the chamber. Our approach determines the sets of rotations constituting primes at the respective eight positions, as the complements of the sets of rotations constituting non-primes at the respective eight positions. These sets of rotations constituting non-primes are exhibited from a basic 8x8-matrix of the mutual products originating from the eight prime numbers located at the eight positions in the original chamber. This 8x8-matrix is proven to generate all non-primes located at the eight positions in strict rotation regularities of the chamber. These regularities are expressed in relation to the multiple 112 as an anchoring reference point and by means of convenient translations between certain classes of multiples. We find the expressions of rotations generating all non-primes located at same position in the chamber as a set of eight related series. The total set of non-primes located at the eight positions is exposed as eight such sets of eight series, and with each of the series completely characterized by four simple variables when compared to a reference series anchored in 112. This represents a complete exposition of non-primes generated by a quite simple mathematical structure. Ad negativo this also represents a complete exposition of all prime numbers as the union of the eight complement sets for these eight non-prime sets of eight series.
Category: Number Theory

[87] viXra:1003.0088 [pdf] submitted on 8 Mar 2010

A Different Derivation of the Calogero Conjecture

Authors: Ioannis Iraklis Haranas
Comments: 5 pages, Publisher Journal of Theoretics, vol. 4, no. 1, 2001.

In a study by F. Calogero [1] entitled "Cosmic origin of quantization" an expression was derived for the variability of h with time, and its consequences if any, of such an idea in cosmology were examined. In this paper we will offer a different derivation of the Calogero conjecture based on a postulate concerning a variable speed of light, [2] in conjuction with Weinberg's relationship for the mass of an elementary particle.
Category: Astrophysics

[86] viXra:1003.0087 [pdf] submitted on 8 Mar 2010

Santilli's Isomathematical Theory for Changing Modern Mathematics

Authors: Chun-Xuan Jiang
Comments: 7 pages, Dedicated to the 30-th anniversary of China reform and opening

We establish the Santilli's isomathematics based on the generalization of the modern mathematics. (more see paper)
Category: Number Theory

[85] viXra:1003.0086 [pdf] submitted on 8 Mar 2010

Fermat's Last Theorem Has Been Proved(2)

Authors: Chun-Xuan Jiang
Comments: 5 pages

In this paper we prove that it is sufficient to prove S13 + S23 = 1 for Fermat's last theorem using the complex hyperbolic functions in the hypercomplex variable theory. More than 200 years ago Euler gave a proof of S13 + S23 = 1. Fermat's last theorem has been proved.
Category: Number Theory

[84] viXra:1003.0084 [pdf] submitted on 8 Mar 2010

The Approximate Solutions of Blasius Equation

Authors: Chun-Xuan Jiang
Comments: 4 pages

We find Blasius function to satisfy the boundary condition f'(∞) = 1 and obtain the approximate solutions of Blasius equation.
Category: Number Theory

[83] viXra:1003.0083 [pdf] submitted on 5 Mar 2010

Artificial Intelligence and Responsive Optimization

Authors: M. Khoshnevisan, Sukanto Bhattacharya, Florentin Smarandache
Comments: 87 pages

The purpose of this book is to apply the Artificial Intelligence and control systems to different real models.
Category: Artificial Intelligence

[82] viXra:1003.0082 [pdf] replaced on 6 Mar 2010

Neutrosophy in Arabic Philosophy

Authors: Florentin Smarandache, Salah Osman
Comments: 293 pages, v1 in Arabic, v2 in English

Neutrosophy is ascribed to Dr. Florentin Smarandache, professor of mathematics and sciences, and head of its department at the University of New Mexico - Gallup (USA). The main aim of this book is to provide the reader with the philosophy of neutrosophy and its application to the Arabic-Islamic thought. So the book is divided into two parts; the first belongs to prof. Smarandache, in which he exposes his philosophy of neutrosophy. The second belongs to Dr. Salah Osman, assistant professor of logic and the philosophy of science in Minufiya university - in which he applies the philosophy of neutrosophy to the Arabic-Islamic thought.
Category: General Science and Philosophy

[81] viXra:1003.0081 [pdf] submitted on 8 Mar 2010

Complex Dynamics and the High-energy Regime of Quantum Field Theory

Authors: Ervin Goldfain
Comments: 13 pages, This paper was published in IJNSNS 6(3), pp. 223-234, 2005

The standard model embodies our current knowledge of elementary particle physics and represents a well-tested framework for the study of non-gravitational phenomena at low energies. It is built on the foundations of relativistic quantum field theory (QFT), which provides the correct description of electroweak and strong interactions involving leptons and quarks. It is generally believed that, extending the validity of QFT to energies on or beyond the TeV range must include the unavoidable signature of vacuum fluctuations and strong-field gravity. We argue that an effective approach to the high-energy regime of QFT demands the tools of complex dynamics and fractal operators. The unexpected consequences of using fractal operators to model complexity beyond the current range of QFT are outlined and discussed.
Category: High Energy Particle Physics

[80] viXra:1003.0080 [pdf] replaced on 11 Apr 2010

On Nonlinear Quantum Mechanics, Noncommutative Phase Spaces, Fractal-Scale Calculus and Vacuum Energy

Authors: Carlos Castro
Comments: 18 pages, has been submitted to Foundations of Physics

A novel (to our knowledge) Generalized Nonlinear Schrödinger equation based on the modifications of Nottale-Cresson's fractal-scale calculus and resulting from the noncommutativity of the phase space coordinates is explicitly derived. The modifications to the ground state energy of a harmonic oscillator yields the observed value of the vacuum energy density. In the concluding remarks we discuss how nonlinear and nonlocal QM wave equations arise naturally from this fractal-scale calculus formalism which may have a key role in the final formulation of Quantum Gravity.
Category: Quantum Gravity and String Theory

[79] viXra:1003.0079 [pdf] submitted on 7 Mar 2010

Linear Algebra and Smarandache Linear Algebra

Authors: W. B. Vasantha Kandasamy
Comments: 175 pages

While I began researching for this book on linear algebra, I was a little startled. Though, it is an accepted phenomenon, that mathematicians are rarely the ones to react surprised, this serious search left me that way for a variety of reasons. First, several of the linear algebra books that my institute library stocked (and it is a really good library) were old and crumbly and dated as far back as 1913 with the most 'new' books only being the ones published in the 1960s.
Category: Algebra

[78] viXra:1003.0078 [pdf] submitted on 7 Mar 2010

Smarandache Fuzzy Algebra

Authors: W. B. Vasantha Kandasamy
Comments: 455 pages

In 1965, Lofti A. Zadeh introduced the notion of a fuzzy subset of a set as a method for representing uncertainty. It provoked, at first (and as expected), a strong negative reaction from some influential scientists and mathematicians - many of whom turned openly hostile. However, despite the controversy, the subject also attracted the attention of other mathematicians and in the following years, the field grew enormously, finding applications in areas as diverse as washing machines to handwriting recognition. In its trajectory of stupendous growth, it has also come to include the theory of fuzzy algebra and for the past five decades, several researchers have been working on concepts like fuzzy semigroup, fuzzy groups, fuzzy rings, fuzzy ideals, fuzzy semirings, fuzzy near-rings and so on.
Category: Algebra

[77] viXra:1003.0077 [pdf] submitted on 7 Mar 2010

Bialgebraic Structures and Smarandache Bialgebraic Structures

Authors: W. B. Vasantha Kandasamy
Comments: 272 pages

The study of bialgebraic structures started very recently. Till date there are no books solely dealing with bistructures. The study of bigroups was carried out in 1994-1996. Further research on bigroups and fuzzy bigroups was published in 1998. In the year 1999, bivector spaces was introduced. In 2001, concept of free De Morgan bisemigroups and bisemilattices was studied. It is said by Zoltan Esik that these bialgebraic structures like bigroupoids, bisemigroups, binear rings help in the construction of finite machines or finite automaton and semi automaton. The notion of non-associative bialgebraic structures was first introduced in the year 2002. The concept of bialgebraic structures which we define and study are slightly different from the bistructures using category theory of Girard's classical linear logic. We do not approach the bialgebraic structures using category theory or linear logic.
Category: Algebra

[76] viXra:1003.0076 [pdf] submitted on 7 Mar 2010

Smarandache Non-Associative Rings

Authors: W. B. Vasantha Kandasamy
Comments: 201 pages

An associative ring is just realized or built using reals or complex; finite or infinite by defining two binary operations on it. But on the contrary when we want to define or study or even introduce a non-associative ring we need two separate algebraic structures say a commutative ring with 1 (or a field) together with a loop or a groupoid or a vector space or a linear algebra. The two non-associative well-known algebras viz. Lie algebras and Jordan algebras are mainly built using a vector space over a field satisfying special identities called the Jacobi identity and Jordan identity respectively. Study of these algebras started as early as 1940s. Hence the study of non-associative algebras or even non-associative rings boils down to the study of properties of vector spaces or linear algebras over fields.
Category: Algebra

[75] viXra:1003.0075 [pdf] submitted on 7 Mar 2010

Smarandache Near-Rings

Authors: W. B. Vasantha Kandasamy
Comments: 201 pages

Near-rings are one of the generalized structures of rings. The study and research on near-rings is very systematic and continuous. Near-ring newsletters containing complete and updated bibliography on the subject are published periodically by a team of mathematicians (Editors: Yuen Fong, Alan Oswald, Gunter Pilz and K. C. Smith) with financial assistance from the National Cheng Kung University, Taiwan. These newsletters give an overall picture of the research carried out and the recent advancements and new concepts in the field. Conferences devoted solely to near-rings are held once every two years. There are about half a dozen books on near-rings apart from the conference proceedings. Above all there is a online searchable database and bibliography on near-rings. As a result the author feels it is very essential to have a book on Smarandache near-rings where the Smarandache analogues of the near-ring concepts are developed. The reader is expected to have a good background both in algebra and in near-rings; for, several results are to be proved by the reader as an exercise.
Category: Algebra

[74] viXra:1003.0074 [pdf] submitted on 7 Mar 2010

Smarandache Rings

Authors: W. B. Vasantha Kandasamy
Comments: 222 pages

Over the past 25 years, I have been immersed in research in Algebra and more particularly in ring theory. I embarked on writing this book on Smarandache rings (Srings) specially to motivate both ring theorists and Smarandache algebraists to develop and study several important and innovative properties about S-rings.
Category: Algebra

[73] viXra:1003.0073 [pdf] submitted on 7 Mar 2010

Smarandache Loops

Authors: W. B. Vasantha Kandasamy
Comments: 129 pages

The theory of loops (groups without associativity), though researched by several mathematicians has not found a sound expression, for books, be it research level or otherwise, solely dealing with the properties of loops are absent. This is in marked contrast with group theory where books are abundantly available for all levels: as graduate texts and as advanced research books.
Category: Algebra

[72] viXra:1003.0072 [pdf] submitted on 7 Mar 2010

Smarandache Semirings, Semifields, and Semivector Spaces

Authors: W. B. Vasantha Kandasamy
Comments: 122 pages

Smarandache notions, which can be undoubtedly characterized as interesting mathematics, has the capacity of being utilized to analyse, study and introduce, naturally, the concepts of several structures by means of extension or identification as a substructure. Several researchers around the world working on Smarandache notions have systematically carried out this study. This is the first book on the Smarandache algebraic structures that have two binary operations.
Category: Algebra

[71] viXra:1003.0071 [pdf] submitted on 7 Mar 2010

Groupoids and Smarandache Groupoids

Authors: W. B. Vasantha Kandasamy
Comments: 115 pages

The study of Smarandache Algebraic Structure was initiated in the year 1998 by Raul Padilla following a paper written by Florentin Smarandache called "Special Algebraic Structures". In his research, Padilla treated the Smarandache algebraic structures mainly with associative binary operation. Since then the subject has been pursued by a growing number of researchers and now it would be better if one gets a coherent account of the basic and main results in these algebraic structures. This book aims to give a systematic development of the basic non-associative algebraic structures viz. Smarandache groupoids. Smarandache groupoids exhibits simultaneously the properties of a semigroup and a groupoid. Such a combined study of an associative and a non associative structure has not been so far carried out. Except for the introduction of smarandacheian notions by Prof. Florentin Smarandache such types of studies would have been completely absent in the mathematical world.
Category: Algebra

[70] viXra:1003.0070 [pdf] submitted on 7 Mar 2010

Smarandache Semigroups

Authors: W. B. Vasantha Kandasamy
Comments: 95 pages

The main motivation and desire for writing this book, is the direct appreciation and attraction towards the Smarandache notions in general and Smarandache algebraic structures in particular. The Smarandache semigroups exhibit properties of both a group and a semigroup simultaneously. This book is a piece of work on Smarandache semigroups and assumes the reader to have a good background on group theory; we give some recollection about groups and some of its properties just for quick reference.
Category: Algebra

[69] viXra:1003.0069 [pdf] submitted on 6 Mar 2010

Applications of Wallis Theorem

Authors: Mihály Bencze, Florentin Smarandache
Comments: 2 pages

In this paper we present theorems and applications of Wallis theorem related to trigonometric integrals.
Category: Number Theory

[68] viXra:1003.0068 [pdf] submitted on 6 Mar 2010

On Diophantine Equation X2 = 2Y4 1

Authors: Florentin Smarandache
Comments: 2 pages

In this note we present a method of solving this Diophantine equation, method which is different from Ljunggren's, Mordell's, and R.K.Guy's.
Category: Number Theory

[67] viXra:1003.0067 [pdf] submitted on 6 Mar 2010

Algorithms for Solving Linear Congruences and Systems of Linear Congruences

Authors: Florentin Smarandache
Comments: 9 pages

In this article we determine several theorems and methods for solving linear congruences and systems of linear congruences and we find the number of distinct solutions. Many examples of solving congruences are given.
Category: Number Theory

[66] viXra:1003.0066 [pdf] replaced on 6 Mar 2010

Theory and Problems on Algebraic Structures.

Authors: Ion Goian, Raisa Grigor, Vasile Marin, Florentin Smarandache
Comments: 119 pages, v1 in Romanian language, v2 in Russian language.

Theory and problems on algebraic structures.
Category: Algebra

[65] viXra:1003.0065 [pdf] submitted on 6 Mar 2010

Logic: a Misleading Concept. a Contradiction Study Toward Agent's Logic Ontology

Authors: Feng Liu, Florentin Smarandache
Comments: 10 pages

The paper presents a fresh new comprehensive ideology on Neutrosophic Logic based on contradiction study in a broad sense: general critics on conventional logic by examining the essence of logic, fresh insights on logic definition based on Chinese philosophical survey, and a novel and genetic logic model as the elementary cell against Von Neumann oriented ones based on this novel definition. As for the logic definition, the paper illustrates that logic is rather a tradeoff between different factors than truth and false abstraction. It is stressed that the kernel of any intelligent system is exactly a contradiction model. The paper aims to solve the chaos of logic and exhibit the potential power of neutrosophy: a new branch of scientific philosophy.
Category: Set Theory and Logic

[64] viXra:1003.0064 [pdf] submitted on 6 Mar 2010

Adaptative Combination Rule and Proportional Conflict Redistribution Rule for Information Fusion

Authors: M. C. Florea, J. Dezert, P. Valin, Florentin Smarandache, Anne-Laure Jousselme
Comments: 8 pages

This paper presents two new promising combination rules for the fusion of uncertain and potentially highly conflicting sources of evidences in the theory of belief functions established first in Dempster-Shafer Theory (DST) and then recently extended in Dezert-Smarandache Theory (DSmT). Our work is to provide here new issues to palliate the well-known limitations of Dempster's rule and to work beyond its limits of applicability. Since the famous Zadeh's criticism of Dempster's rule in 1979, many researchers have proposed new interesting alternative rules of combination to palliate the weakness of Dempster's rule in order to provide acceptable results specially in highly conflicting situations. In this work, we present two new combination rules: the class of Adaptive Combination Rules (ACR) and a new efficient Proportional Conflict Redistribution (PCR) rule. Both rules allow to deal with highly conflicting sources for static and dynamic fusion applications. We present some interesting properties for ACR and PCR rules and discuss some simulation results obtained with both rules for Zadeh's problem and for a target identification problem.
Category: Artificial Intelligence

[63] viXra:1003.0063 [pdf] submitted on 6 Mar 2010

About Factorial Sums

Authors: Mihály Bencze, Florentin Smarandache
Comments: 3 pages

In this paper, we present some new inequalities for factorial sum.
Category: Number Theory

[62] viXra:1003.0062 [pdf] submitted on 6 Mar 2010

Intentionally and Unintentionally. On Both, A and Non-A, in Neutrosophy

Authors: Feng Liu, Florentin Smarandache
Comments: 7 pages

The paper presents a fresh new start on the neutrality of neutrosophy in that "both A and Non-A" as an alternative to describe Neuter-A in that we conceptualize things in both intentional and unintentional background. This unity of opposites constitutes both objective world and subjective world. The whole induction of such argument is based on the intensive study on Buddhism and Daoism including I-ching. In addition, a framework of contradiction oriented learning philosophy inspired from the Later Trigrams of King Wen in I-ching is meanwhile presented. It is shown that although A and Non-A are logically inconsistent, but they are philosophically consistent in the sense that Non-A can be the unintentionally instead of negation that leads to confusion. It is also shown that Buddhism and Daoism play an important role in neutrosophy, and should be extended in the way of neutrosophy to all sciences according to the original intention of neutrosophy.
Category: Set Theory and Logic

[61] viXra:1003.0061 [pdf] submitted on 6 Mar 2010

Thirty-Six Unsolved Problems in Number Theory

Authors: Florentin Smarandache
Comments: 38 pages

Partially or totally unsolved questions in number theory and geometry especially, such as coloration problems, elementary geometric conjectures, partitions, generalized periods of a number, length of a generalized period, arithmetic and geometric progressions are exposed.
Category: Number Theory

[60] viXra:1003.0060 [pdf] submitted on 6 Mar 2010

DSmT Qualitative Reasoning Based on 2-Tuple Linguistic Representation Model

Authors: Xin-De Li, Xian-Zhong Dai, Jean Dezert, Florentin Smarandache
Comments: 6 pages

Most of modern systems for information retrieval, fusion and management have to deal more and more with information expressed quatitatively (by linguistic labels) since human reports are better and easier expressed in natural language than with numbers. In this paper, we propose to use Herrera-Martínez' 2-Tuple linguistic representation model (i.e. equidistant linguistic labels with a numeric value assessment) for reasoning with uncertain and qualitative information in Dezert-Smarandache Theory (DSmT) framework to preserve the precision and the efficiency of the fusion of linguistic information expressing the expert's qualitative beliefs. We present operators to deal with the 2-Tuples and show from a simple example how qualitative DSmT-based fusion rules can be used for qualitative reasoning and fusioning under uncertainty.
Category: Artificial Intelligence

[59] viXra:1003.0059 [pdf] submitted on 6 Mar 2010

Combination of Qualitative Information with 2-Tuple Linguistic Representation in Dezert-Smarandache Theory

Authors: Xin-De Li, Florentin Smarandache, Xian-Zhong Dai
Comments: 12 pages

Modern systems for information retrieval, fusion and management need to deal more and more with information coming from human experts usually expressed qualitatively in natural language with linguistic labels. In this paper, we propose and use two new 2-Tuple linguistic representation models (i.e., a distribution function model (DFM) and an improved Herrera-Martínez's model) jointly with the fusion rules developed in Dezert-Smarandache Theory (DSmT), in order to combine efficiently qualitative information expressed in term of qualitative belief functions. The two models both preserve the precision and improve the efficiency of the fusion of linguistic information expressing the global expert's opinion. However, DFM is more general and efficient than the latter, especially for unbalanced linguistic labels. Some simple examples are also provided to show how the 2-Tuple qualitative fusion rules are performed and their advantages.
Category: Artificial Intelligence

[58] viXra:1003.0058 [pdf] submitted on 6 Mar 2010

The Dual of the Orthopole Theorem

Authors: Ion Pătraşcu
Comments: 5 pages, Translated by Prof. Florentin Smarandache

In this article we prove the theorems of the orthopole and we obtain, through duality, its dual, and then some interesting specific examples of the dual of the theorem of the orthopole.
Category: Geometry

[57] viXra:1003.0057 [pdf] submitted on 6 Mar 2010

DE Longchamps' Point, Line and Circle

Authors: Ion Pătraşcu
Comments: 7 pages, Translated by Prof. Florentin Smarandache

The purpose of this article is to familiarize the reader with these notions, emphasizing on connections between them.
Category: Geometry

[56] viXra:1003.0056 [pdf] submitted on 6 Mar 2010

The Dual Theorem Relative to the Simson's Line

Authors: Ion Pătraşcu
Comments: 5 pages, Translated by Prof. Florentin Smarandache

In this article we elementarily prove some theorems on the poles and polars theory, we present the transformation using duality and we apply this transformation to obtain the dual theorem relative to the Samson's line.
Category: Geometry

[55] viXra:1003.0055 [pdf] submitted on 6 Mar 2010

On PT-Symmetric Periodic Potential, Quark Confinement, and Other Impossible Pursuits

Authors: V. Christianto, Florentin Smarandache
Comments: 3 pages

As we know, it has been quite common nowadays for particle physicists to think of six impossible things before breakfast, just like what their cosmology fellows used to do. In the present paper, we discuss a number of those impossible things, including PT-symmetric periodic potential, its link with condensed matter nuclear science, and possible neat link with Quark confinement theory. In recent years, the PT-symmetry and its related periodic potential have gained considerable interests among physicists. We begin with a review of some results from a preceding paper discussing derivation of PT-symmetric periodic potential from biquaternion Klein-Gordon equation and proceed further with the remaining issues. Further observation is of course recommended in order to refute or verify this proposition.
Category: High Energy Particle Physics

[54] viXra:1003.0054 [pdf] submitted on 6 Mar 2010

A Note of Extended Proca Equations and Superconductivity

Authors: V. Christianto, Florentin Smarandache, Frank Lichtenberg
Comments: 4 pages

It has been known for quite long time that the electrodynamics of Maxwell equations can be extended and generalized further into Proca equations. The implications of introducing Proca equations include an alternative description of superconductivity, via extending London equations. In the light of another paper suggesting that Maxwell equations can be written using quaternion numbers, then we discuss a plausible extension of Proca equation using biquaternion number. Further implications and experiments are recommended.
Category: Condensed Matter

[53] viXra:1003.0053 [pdf] submitted on 6 Mar 2010

On Emergent Physics, "Unparticles" and Exotic "Unmatter" States

Authors: Ervin Goldfain, Florentin Smarandache
Comments: 6 pages

Emergent physics refers to the formation and evolution of collective patterns in systems that are nonlinear and out-of-equilibrium. This type of large-scale behavior often develops as a result of simple interactions at the component level and involves a dynamic interplay between order and randomness. On account of its universality, there are credible hints that emergence may play a leading role in the Tera-ElectronVolt (TeV) sector of particle physics. Following this path, we examine the possibility of hypothetical highenergy states that have fractional number of quanta per state and consist of arbitrary mixtures of particles and antiparticles. These states are similar to "un-particles", massless fields of non-integral scaling dimensions that were recently conjectured to emerge in the TeV sector of particle physics. They are also linked to "unmatter", exotic clusters of matter and antimatter introduced few years ago in the context of Neutrosophy. The connection between 'unmatter' and 'unparticle' is explained in details in this paper. Unparticles have very odd properties which result from the fact that they represent fractional field quanta. Unparticles are manifested as mixed states that contain arbitrary mixtures of particles and antiparticles (therefore they simultaneously evolve "forward" and "backward" in time). From this, the connection with unmatter. Using the fractal operators of differentiation and integration we get the connection between unparticle and unmatter. 'Unmatter' was coined by F. Smarandache in 2004 who published three papers on the subject.
Category: Condensed Matter

[52] viXra:1003.0052 [pdf] submitted on 6 Mar 2010

International Injustice in Science

Authors: Florentin Smarandache
Comments: 2 pages

In the scientific research, it is important to keep our freedom of thinking and not being yoked by others' theories without checking them, no matter where they come from. Cogito, ergo sum (I think, therefore I am), said Descartes (1596-1650), and this Latin aphorism became his first principle in philosophy.
Category: History and Philosophy of Physics

[51] viXra:1003.0051 [pdf] submitted on 6 Mar 2010

The Neutrosophic Logic View to Schrödinger's Cat Paradox, Revisited

Authors: Florentin Smarandache, V. Christianto
Comments: 5 pages

The present article discusses Neutrosophic logic view to Schrödinger's cat paradox. We argue that this paradox involves some degree of indeterminacy (unknown) which Neutrosophic logic can take into consideration, whereas other methods including Fuzzy logic cannot. To make this proposition clear, we revisit our previous paper by offering an illustration using modified coin tossing problem, known as Parrondo's game.
Category: Quantum Physics

[50] viXra:1003.0050 [pdf] submitted on 6 Mar 2010

Kaluza-Klein-Carmeli Metric from Quaternion-Clifford Space, Lorentz' Force, and Some Observables

Authors: V. Christianto, Florentin Smarandache
Comments: 7 pages

It was known for quite long time that a quaternion space can be generalized to a Clifford space, and vice versa; but how to find its neat link with more convenient metric form in the General Relativity theory, has not been explored extensively. We begin with a representation of group with non-zero quaternions to derive closed FLRW metric [1], and from there obtains Carmeli metric, which can be extended further to become 5D and 6D metric (which we propose to call Kaluza-Klein-Carmeli metric). Thereafter we discuss some plausible implications of this metric, beyond describing a galaxy's spiraling motion and redshift data as these have been done by Carmeli and Hartnett [4, 5, 6]. In subsequent section we explain Podkletnov's rotating disc experiment. We also note possible implications to quantum gravity. Further observations are of course recommended in order to refute or verify this proposition.
Category: Quantum Physics

[49] viXra:1003.0049 [pdf] submitted on 6 Mar 2010

Numerical Solution of Radial Biquaternion Klein-Gordon Equation

Authors: V. Christianto, Florentin Smarandache
Comments: 2 pages

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation has solution containing imaginary part, which differs appreciably from known solution of KGE. In the present article we present numerical /computer solution of radial biquaternionic KGE (radialBQKGE); which differs appreciably from conventional Yukawa potential. Further observation is of course recommended in order to refute or verify this proposition.
Category: Quantum Physics

[48] viXra:1003.0048 [pdf] submitted on 6 Mar 2010

Thirty Unsolved Problems in the Physics of Elementary Particles

Authors: V. Christianto, Florentin Smarandache
Comments: 3 pages

Unlike what some physicists and graduate students used to think, that physics science has come to the point that the only improvement needed is merely like adding more numbers in decimal place for the masses of elementary particles or gravitational constant, there is a number of unsolved problems in this field that may require that the whole theory shall be reassessed. In the present article we discuss thirty of those unsolved problems and their likely implications. In the first section we will discuss some well-known problems in cosmology and particle physics, and then other unsolved problems will be discussed in next section.
Category: High Energy Particle Physics

[47] viXra:1003.0047 [pdf] submitted on 6 Mar 2010

Yang-Mills Field from Quaternion Space Geometry, and Its Klein-Gordon Representation

Authors: Alexander Yefremov, Florentin Smarandache, V. Christianto
Comments: 9 pages

Analysis of covariant derivatives of vectors in quaternion (Q-) spaces performed using Q-unit spinor-splitting technique and use of SL(2C)-invariance of quaternion multiplication reveals close connexion of Q-geometry objects and Yang-Mills (YM) field principle characteristics. In particular, it is shown that Q-connexion (with quaternion non-metricity) and related curvature of 4 dimensional (4D) space-times with 3D Q-space sections are formally equivalent to respectively YM-field potential and strength, traditionally emerging from the minimal action assumption. Plausible links between YM field equation and Klein-Gordon equation, in particular via its known isomorphism with Duffin-Kemmer equation, are also discussed.
Category: Quantum Physics

[46] viXra:1003.0046 [pdf] submitted on 6 Mar 2010

Reply to "Notes on Pioneer Anomaly Explanation by Satellite-Shift Formula of Quaternion Relativity"

Authors: V. Christianto, Florentin Smarandache
Comments: 3 pages

In the present article we would like to make a few comments on a recent paper by A. Yefremov in this journal [1]. It is interesting to note here that he concludes his analysis by pointing out that using full machinery of Quaternion Relativity it is possible to explain Pioneer XI anomaly with excellent agreement compared with observed data, and explain around 45% of Pioneer X anomalous acceleration. We argue that perhaps it will be necessary to consider extension of Lorentz transformation to Finsler-Berwald metric, as discussed by a number of authors in the past few years. In this regard, it would be interesting to see if the use of extended Lorentz transformation could also elucidate the long-lasting problem known as Ehrenfest paradox. Further observation is of course recommended in order to refute or verify this proposition.
Category: Astrophysics

[45] viXra:1003.0045 [pdf] submitted on 6 Mar 2010

Numerical Solution of Time-Dependent Gravitational Schrödinger Equation

Authors: V. Christianto, Diego L. Rapoport, Florentin Smarandache
Comments: 5 pages

In recent years, there are attempts to describe quantization of planetary distance based on time-independent gravitational Schrödinger equation, including Rubcic & Rubcic's method and also Nottale's Scale Relativity method. Nonetheless, there is no solution yet for time-dependent gravitational Schrödinger equation (TDGSE). In the present paper, a numerical solution of time-dependent gravitational Schrödinger equation is presented, apparently for the first time. This numerical solution leads to gravitational Bohr-radius, as expected. In the subsequent section, we also discuss plausible extension of this gravitational Schrödinger equation to include the effect of phion condensate via Gross-Pitaevskii equation, as described recently by Moffat. Alternatively one can consider this condensate from the viewpoint of Bogoliubov-deGennes theory, which can be approximated with coupled time-independent gravitational Schrödinger equation. Further observation is of course recommended in order to refute or verify this proposition.
Category: Astrophysics

[44] viXra:1003.0044 [pdf] submitted on 6 Mar 2010

Less Mundane Explanation of Pioneer Anomaly from Q-Relativity

Authors: Florentin Smarandache, V. Christianto
Comments: 4 pages

There have been various explanations of Pioneer blueshift anomaly in the past few years; nonetheless no explanation has been offered from the viewpoint of Q-relativity physics. In the present paper it is argued that Pioneer anomalous blueshift may be caused by Pioneer spacecraft experiencing angular shift induced by similar Qrelativity effect which may also affect Jupiter satellites. By taking into consideration "aether drift" effect, the proposed method as described herein could explain Pioneer blueshift anomaly within ~ 0.26% error range, which speaks for itself. Another new proposition of redshift quantization is also proposed from gravitational Bohr-radius which is consistent with Bohr-Sommerfeld quantization. Further observation is of course recommended in order to refute or verify this proposition.
Category: Astrophysics

[43] viXra:1003.0043 [pdf] submitted on 6 Mar 2010

Plausible Explanation of Quantization of Intrinsic Redshift from Hall Effect and Weyl Quantization

Authors: Florentin Smarandache, V. Christianto
Comments: 4 pages

Using phion condensate model as described by Moffat [1], we consider a plausible explanation of (Tifft) intrinsic redshift quantization as described by Bell [6] as result of Hall effect in rotating frame. We also discuss another alternative to explain redshift quantization from the viewpoint of Weyl quantization, which could yield Bohr-Sommerfeld quantization.
Category: Quantum Physics

[42] viXra:1003.0042 [pdf] submitted on 6 Mar 2010

A Note on Geometric and Information Fusion Interpretation of Bell's Theorem and Quantum Measurement

Authors: Florentin Smarandache, V. Christianto
Comments: 5 pages

In this paper we present four possible extensions of Bell's Theorem: Bayesian and Fuzzy Bayesian intrepretation, Information Fusion interpretation, Geometric interpretation, and the viewpoint of photon fluid as medium for quantum interaction.
Category: Quantum Physics

[41] viXra:1003.0041 [pdf] submitted on 6 Mar 2010

Schrödinger Equation and the Quantization of Celestial Systems

Authors: Florentin Smarandache, V. Christianto
Comments: 5 pages

In the present article, we argue that it is possible to generalize Schrödinger equation to describe quantization of celestial systems. While this hypothesis has been described by some authors, including Nottale, here we argue that such a macroquantization was formed by topological superfluid vortice. We also provide derivation of Schrödinger equation from Gross-Pitaevskii-Ginzburg equation, which supports this superfluid dynamics interpretation.
Category: Quantum Physics

[40] viXra:1003.0040 [pdf] submitted on 6 Mar 2010

The Neutrosophic Logic View to Schrödinger's Cat Paradox

Authors: Florentin Smarandache, V. Christianto
Comments: 5 pages

This article discusses Neutrosophic Logic interpretation of the Schrodinger's cat paradox. We argue that this paradox involves some degree of indeterminacy (unknown) which Neutrosophic Logic could take into consideration, whereas other methods including Fuzzy Logic could not. For a balanced discussion, other interpretations have also been discussed.
Category: Quantum Physics

[39] viXra:1003.0039 [pdf] submitted on 6 Mar 2010

Unmatter Entities Inside Nuclei, Predicted by the Brightsen Nucleon Cluster Model

Authors: Florentin Smarandache, Dmitri Rabounski
Comments: 5 pages

Applying the R. A. Brightsen Nucleon Cluster Model of the atomic nucleus we discuss how unmatter entities (the conjugations of matter and antimatter) may be formed as clusters inside a nucleus. The model supports a hypothesis that antimatter nucleon clusters are present as a parton (sensu Feynman) superposition within the spatial confinement of the proton (1H1), the neutron, and the deuteron (1H2). If model predictions can be confirmed both mathematically and experimentally, a new physics is suggested. A proposed experiment is connected to othopositronium annihilation anomalies, which, being related to one of known unmatter entity, orthopositronium (built on electron and positron), opens a way to expand the Standard Model.
Category: Nuclear and Atomic Physics

[38] viXra:1003.0038 [pdf] submitted on 6 Mar 2010

Verifying Unmatter by Experiments, More Types of Unmatter, and a Quantum Chromodynamics Formula

Authors: Florentin Smarandache
Comments: 4 pages

As shown, experiments registered unmatter: a new kind of matter whose atoms include both nucleons and anti-nucleons, while their life span was very short, no more than 10-20sec. Stable states of unmatter can be built on quarks and anti-quarks: applying the unmatter principle here it is obtained a quantum chromodynamics formula that gives many combinations of unmatter built on quarks and anti-quarks.
Category: High Energy Particle Physics

[37] viXra:1003.0037 [pdf] submitted on 6 Mar 2010

Entangled States and Quantum Causality Threshold in the General Theory of Relativity

Authors: Dmitri Rabounski, Larissa Borissova, Florentin Smarandache
Comments: 7 pages

This article shows, Synge-Weber's classical problem statement about two particles interacting by a signal can be reduced to the case where the same particle is located in two different points A and B of the basic space-time in the same moment of time, so the states A and B are entangled. This particle, being actual two particles in the entangled states A and B, can interact with itself radiating a photon (signal) in the point A and absorbing it in the point B. That is our goal, to introduce entangled states into General Relativity. Under specific physical conditions the entangled particles in General Relativity can reach a state where neither particle A nor particle B can be the cause of future events. We call this specific state Quantum Causality Threshold.
Category: Quantum Physics

[36] viXra:1003.0036 [pdf] submitted on 6 Mar 2010

There Is No Speed Barrier for a Wave Phase Nor for Entangled Particles

Authors: Florentin Smarandache
Comments: 2 pages

In this short paper, as an extension and consequence of Einstein-Podolski-Rosen paradox and Bell's inequality, one promotes the hypothesis (it has been called the Smarandache Hypothesis [1, 2, 3]) that: There is no speed barrier in the Universe and one can construct arbitrary speeds, and also one asks if it is possible to have an infinite speed (instantaneous transmission)? Future research: to study the composition of faster-than-light velocities and what happens with the laws of physics at faster-thanlight velocities?
Category: Quantum Physics

[35] viXra:1003.0035 [pdf] submitted on 6 Mar 2010

A New Form of Matter-Unmatter, Composed of Particles and Anti-Particles

Authors: Florentin Smarandache
Comments: 3 pages

Besides matter and antimatter there must exist unmatter (as a new form of matter) in accordance with the neutrosophy theory that between an entity <A> and its opposite <AntiA> there exist intermediate entities <NeutA>. Unmatter is neither matter nor antimatter, but something in between. An atom of unmatter is formed either by (1): electrons, protons, and antineutrons, or by (2): antielectrons, antiprotons, and neutrons. At CERN it will be possible to test the production of unmatter. The existence of unmatter in the universe has a similar chance to that of the antimatter, and its production also difficult for present technologies.
Category: Condensed Matter

[34] viXra:1003.0034 [pdf] submitted on 6 Mar 2010

Quantum Quasi-Paradoxes and Quantum Sorites Paradoxes

Authors: Florentin Smarandache
Comments: 2 pages

There can be generated many paradoxes or quasi-paradoxes that may occur from the combination of quantum and non-quantum worlds in physics. Even the passage from the micro-cosmos to the macro-cosmos, and reciprocally, can generate unsolved questions or counter-intuitive ideas. We define a quasi-paradox as a statement which has a prima facie self-contradictory support or an explicit contradiction, but which is not completely proven as a paradox. We present herein four elementary quantum quasi-paradoxes and their corresponding quantum Sorites paradoxes, which form a class of quantum quasi-paradoxes.
Category: Quantum Physics

[33] viXra:1003.0033 [pdf] submitted on 6 Mar 2010

Essence Neutrosophy

Authors: Florentin Smarandache
Comments: 34 pages, In Russian language

Essence Neutrosophy
Category: Quantum Physics

[32] viXra:1003.0032 [pdf] submitted on 6 Mar 2010

Methods in the General Theory of Relativity

Authors: Dmitri Rabounski, Florentin Smarandache, Larissa Borissova
Comments: 107 pages, In Russian language

METHODS IN THE GENERAL THEORY OF RELATIVITY
Category: Relativity and Cosmology

[31] viXra:1003.0031 [pdf] submitted on 6 Mar 2010

Multi-Valued Logic, Neutrosophy, and Schrödinger Equation

Authors: Florentin Smarandache, V. Christianto
Comments: 109 pages

This book was intended to discuss some paradoxes in Quantum Mechanics from the viewpoint of Multi-Valued-logic pioneered by Lukasiewicz, and a recent concept Neutrosophic Logic. Essentially, this new concept offers new insights on the idea of 'identity', which too often it has been accepted as given. Neutrosophy itself was developed in attempt to generalize Fuzzy-Logic introduced by L. Zadeh. While some aspects of theoretical foundations of logic are discussed, this book is not intended solely for pure mathematicians, but instead for physicists in the hope that some of ideas presented herein will be found useful. The book is motivated by observation that despite almost eight decades, there is indication that some of those paradoxes known in Quantum Physics are not yet solved. In our knowledge, this is because the solution of those paradoxes requires re-examination of the foundations of logic itself, in particular on the notion of identity and multi-valuedness of entity. The book is also intended for young physicist fellows who think that somewhere there should be a 'complete' explanation of these paradoxes in Quantum Mechanics. If this book doesn't answer all of their questions, it is our hope that at least it offers a new alternative viewpoint for these old questions.
Category: Quantum Physics

[30] viXra:1003.0030 [pdf] submitted on 6 Mar 2010

Today's Take on Einstein's Relativity

Authors: Homer B. Tilton, Florentin Smarandache
Comments: 109 pages, PROCEEDINGS OF THE CONFERENCE OF 18 FEB 2005

Einstein originally declared that the distortions of special relativity reflect real changes to the objects being remotely observed, then reconsidered. The first non sequitur is quoted here from Sachs
Category: Relativity and Cosmology

[29] viXra:1003.0029 [pdf] replaced on 6 Mar 2010

Declaration of Academic Freedom

Authors: Dmitri Rabounski
Comments: 4 pages, translated by Florentin Smarandache, v1 in French, v2 in Romanian

The author pledge for the freedom of scientists to expose and publish their papers.
Category: General Science and Philosophy

[28] viXra:1003.0028 [pdf] submitted on 6 Mar 2010

Quantum Causality Threshold and Paradoxes

Authors: Florentin Smarandache
Comments: 15 pages

In this paper we consider two entangled particles and study all the possibilities: when both are immobile, or one of them is immobile, or both are moving in different directions, or one of them is moving in a different direction. Then we study the causality between them and the paradoxes, which are generated. We define the Causality Threshold of a particle A with respect to another particle B.
Category: Quantum Physics

[27] viXra:1003.0027 [pdf] submitted on 6 Mar 2010

Unfolding the Labyrinth: Open Problems in Physics, Mathematics, Astrophysics, and Other Areas of Science

Authors: Florentin Smarandache, V. Christianto, Fu Yuhua, Radi I. Khrapko, J. Hutchison
Comments: 147 pages

The reader will find herein a collection of unsolved problems in mathematics and the physical sciences. Theoretical and experimental domains have each been given consideration. The authors have taken a liberal approach in their selection of problems and questions, and have not shied away from what might otherwise be called speculative, in order to enhance the opportunities for scientific discovery. Progress and development in our knowledge of the structure, form and function of the Universe, in the true sense of the word, its beauty and power, and its timeless presence and mystery, before which even the greatest intellect is awed and humbled, can spring forth only from an unshackled mind combined with a willingness to imagine beyond the boundaries imposed by that ossified authority by which science inevitably becomes, as history teaches us, barren and decrepit. Revealing the secrets of Nature, so that we truly see 'the sunlit plains extended, and at night the wondrous glory of the everlasting stars', requires far more than mere technical ability and mechanical dexterity learnt form books and consensus. The dustbin of scientific history is replete with discredited consensus and the grand reputations of erudite reactionaries. Only by boldly asking questions, fearlessly, despite opposition, and searching for answers where most have not looked for want of courage and independence of thought, can one hope to discover for one's self. From nothing else can creativity blossom and grow, and without which the garden of science can only aspire to an overpopulation of weeds.
Category: Mathematical Physics

[26] viXra:1003.0026 [pdf] submitted on 6 Mar 2010

Begin the Adventure How to Break the Light Barrier by A.d. 2079

Authors: Homer B. Tilton, Florentin Smarandache
Comments: 147 pages

Because of the almost universal failure to recognize the distinction between physical (reality-based, dynamical) and visual (appearance-based, kinematical) variables, a tremendous volume of mythology arose over the past 100 years centered around Einstein's reality view of the distortions of special relativity.
Category: Relativity and Cosmology

[25] viXra:1003.0025 [pdf] submitted on 6 Mar 2010

Quantization in Astrophysics, Brownian Motion, and Supersymmetry

Authors: Florentin Smarandache, V. Christianto
Comments: 516 pages

The present book discusses, among other things, various quantization phenomena found in Astrophysics and some related issues including Brownian Motion. With recent discoveries of exoplanets in our galaxy and beyond, this Astrophysics quantization issue has attracted numerous discussions in the past few years. Most chapters in this book come from published papers in various peer-reviewed journals, and they cover different methods to describe quantization, including Weyl geometry, Supersymmetry, generalized Schrödinger, and Cartan torsion method. In some chapters Navier-Stokes equations are also discussed, because it is likely that this theory will remain relevant in Astrophysics and Cosmology While much of the arguments presented in this book are theoretical, nonetheless we recommend further observation in order to verify or refute the propositions described herein. It is of our hope that this volume could open a new chapter in our knowledge on the formation and structure of Astrophysical systems. The present book is also intended for young physicist and math fellows who perhaps will find the arguments described here are at least worth pondering.
Category: Quantum Physics

[24] viXra:1003.0024 [pdf] submitted on 6 Mar 2010

Hadron Models and Related New Energy Issues

Authors: Florentin Smarandache, V. Christianto
Comments: 476 pages

The present book covers a wide-range of issues from alternative hadron models to their likely implications in New Energy research, including alternative interpretation of lowenergy reaction (coldfusion) phenomena.
Category: Condensed Matter

[23] viXra:1003.0023 [pdf] submitted on 6 Mar 2010

Neutrosophic Methods in General Relativity

Authors: Dmitri Rabounski, Florentin Smarandache, Larissa Borissova
Comments: 80 pages

In this work the authors apply concepts of Neutrosophic Logic to the General Theory of Relativity to obtain a generalisation of Einstein's fourdimensional pseudo-Riemannian differentiable manifold in terms of Smarandache Geometry (Smarandache manifolds), by which new classes of relativistic particles and non-quantum teleportation are developed. Fundamental features of Neutrosophic Logic are its denial of the Law of Excluded Middle, and open (or estimated) levels of truth, falsity and indeterminancy. Both Neutrosophic Logic and Smarandache Geometry were invented some years ago by one of the authors (F. Smarandache). The application of these purely mathematical theories to General Relativity reveals hitherto unknown possibilities for Einstein's theory. The issue of how closely the new theoretical possibilities account for physical phenomena, and indeed the viability of the concept of a fourdimensional space-time continuum itself as a fundamental model of Nature, must of course be explored by experiment.
Category: Relativity and Cosmology

[22] viXra:1003.0022 [pdf] submitted on 6 Mar 2010

A Study of the Schrödinger-Langevin Equation with PT-Symmetric Periodic Potential and its Application to Deuteron Cluster, and Relation to the Self-Organized Criticality Phenomena

Authors: V. Christianto, Florentin Smarandache
Comments: 5 pages

One of the most reported problem related to the CMNS (condensed matter nuclear science, or LENR), is the low probability of Coulomb barrier tunneling. It is supposed by standard physics that tunneling is only possible at high enough energy (by solving Gamow function). However, a recent study by A. Takahashi (2008, 2009) and experiment by Arata etc. (2008) seem to suggest that it is not impossible to achieve a working experiment to create the CMNS process. In accordance with Takahashi's EQPET/TSC model [1][2][3], the proposed study will find out some analytical and numerical solutions to the problem of barrier tunneling for cluster deuterium, in particular using Langevin method to solve the time-independent Schrödinger equation. It is hoped that the result can answer some of these mysteries.
Category: Condensed Matter

[21] viXra:1003.0021 [pdf] submitted on 6 Mar 2010

S-Denying of the Signature Conditions Expands General Relativity's Space

Authors: Dmitri Rabounski, Florentin Smarandache, Larissa Borissova
Comments: 7 pages

We apply the S-denying procedure to signature conditions in a four-dimensional pseudo-Riemannian space - i. e. we change one (or even all) of the conditions to be partially true and partially false. We obtain five kinds of expanded space-time for General Relativity. Kind I permits the space-time to be in collapse. Kind II permits the space-time to change its own signature. Kind III has peculiarities, linked to the third signature condition. Kind IV permits regions where the metric fully degenerates: there may be non-quantum teleportation, and a home for virtual photons. Kind V is common for kinds I, II, III, and IV.
Category: Relativity and Cosmology

[20] viXra:1003.0020 [pdf] submitted on 6 Mar 2010

Positive, Neutral and Negative Mass-Charges in General Relativity

Authors: Larissa Borissova, Florentin Smarandache
Comments: 4 pages

As shown, any four-dimensional proper vector has two observable projections onto time line, attributed to our world and the mirror world (for a mass-bearing particle, the projections posses are attributed to positive and negative mass-charges). As predicted, there should be a class of neutrally mass-charged particles that inhabit neither our world nor the mirror world. Inside the space-time area (membrane) the space rotates at the light speed, and all particles move at as well the light speed. So, the predicted particles of the neutrally mass-charged class should seem as light-like vortices.
Category: Relativity and Cosmology

[19] viXra:1003.0019 [pdf] submitted on 6 Mar 2010

A Note on Unified Statistics Including Fermi-Dirac, Bose-Einstein, and Tsallis Statistics, and Plausible Extension to Anisotropic Effect

Authors: V. Christianto, Florentin Smarandache
Comments: 4 pages

In the light of some recent hypotheses suggesting plausible unification of thermostatistics where Fermi-Dirac, Bose-Einstein and Tsallis statistics become its special subsets, we consider further plausible extension to include non-integer Hausdorff dimension, which becomes realization of fractal entropy concept. In the subsequent section, we also discuss plausible extension of this unified statistics to include anisotropic effect by using quaternion oscillator, which may be observed in the context of Cosmic Microwave Background Radiation. Further observation is of course recommended in order to refute or verify this proposition.
Category: Quantum Physics

[18] viXra:1003.0018 [pdf] submitted on 6 Mar 2010

A New Derivation of Biquaternion Schrödinger Equation and Plausible Implications

Authors: V. Christianto, Florentin Smarandache
Comments: 3 pages

In the preceding article we argue that biquaternionic extension of Klein-Gordon equation has solution containing imaginary part, which differs appreciably from known solution of KGE. In the present article we discuss some possible interpretation of this imaginary part of the solution of biquaternionic KGE (BQKGE); thereafter we offer a new derivation of biquaternion Schrödinger equation using this method. Further observation is of course recommended in order to refute or verify this proposition.
Category: Quantum Physics

[17] viXra:1003.0017 [pdf] submitted on 6 Mar 2010

An Exact Mapping from Navier-Stokes Equation to Schrödinger Equation via Riccati Equation

Authors: V. Christianto, Florentin Smarandache
Comments: 2 pages

In the present article we argue that it is possible to write down Schrödinger representation of Navier-Stokes equation via Riccati equation. The proposed approach, while differs appreciably from other method such as what is proposed by R. M. Kiehn, has an advantage, i.e. it enables us extend further to quaternionic and biquaternionic version of Navier-Stokes equation, for instance via Kravchenko's and Gibbon's route. Further observation is of course recommended in order to refute or verify this proposition.
Category: Classical Physics

[16] viXra:1003.0016 [pdf] submitted on 6 Mar 2010

A Note on Computer Solution of Wireless Energy Transmit via Magnetic Resonance

Authors: V. Christianto, Florentin Smarandache
Comments: 5 pages

In the present article we argue that it is possible to find numerical solution of coupled magnetic resonance equation for describing wireless energy transmit, as discussed recently by Karalis (2006) and Kurs et al. (2007). The proposed approach may be found useful in order to understand the phenomena of magnetic resonance. Further observation is of course recommended in order to refute or verify this proposition.
Category: Classical Physics

[15] viXra:1003.0015 [pdf] submitted on 6 Mar 2010

What Gravity Is. Some Recent Considerations

Authors: V. Christianto, Florentin Smarandache
Comments: 5 pages

It is well-known, that when it comes to discussions among physicists concerning the meaning and nature of gravitation, the room temperature can be so hot. Therefore, for the sake of clarity, it seems worth that all choices were put on a table, and we consider each choice's features and problems. The present article describes a nonexhaustive list of such gravitation theories for the purpose of inviting further and more clear discussions.
Category: Relativity and Cosmology

[14] viXra:1003.0014 [pdf] submitted on 6 Mar 2010

A Few Remarks on "The Length of Day: A Cosmological Perspective"

Authors: V. Christianto, Matti Pitkänen, Florentin Smarandache
Comments: 2 pages

An interesting hypothesis concerning the varying length of day has been formulated in this edition, proposed by A.I. Arbab, based on a proposition of varying gravitational constant, G. The main ideas are pointed out, and alternative frameworks are also discussed in particular with respect to the present common beliefs in astrophysics. Further observation is of course recommended in order to refute or verify this proposition.
Category: Relativity and Cosmology

[13] viXra:1003.0013 [pdf] submitted on 6 Mar 2010

Numerical Solution of Quantum Cosmological Model Simulating Boson and Fermion Creation

Authors: V. Christianto, Florentin Smarandache
Comments: 2 pages

A numerical solution of Wheeler-De Witt equation for a quantum cosmological model simulating boson and fermion creation in the early Universe evolution is presented. This solution is based on a Wheeler-DeWitt equation obtained by Krechet, Fil'chenkov, and Shikin, in the framework of quantum geometrodynamics for a Bianchi-I metric.
Category: Quantum Gravity and String Theory

[12] viXra:1003.0012 [pdf] submitted on 6 Mar 2010

On Some New Ideas in Hadron Physics

Authors: Florentin Smarandache, V. Christianto
Comments: 3 pages

We shortly review a series of novel ideas on the physics of hadrons and nuclear matter. Despite being vastly different in scope and content, these models share a common attribute, in that they offer unconventional viewpoints on infrared QCD and nuclear phenomena. In a sense, they are reminiscent of the plethora of formulations that have been developed over the years on classical gravitation: many seemingly disparate approaches can be effectively used to describe and explore the same physics.
Category: High Energy Particle Physics

[11] viXra:1003.0011 [pdf] replaced on 6 Mar 2010

On Some Novel Ideas in Hadron Physics. Part II

Authors: Florentin Smarandache, V. Christianto
Comments: 4 pages

As a continuation of the preceding section, we shortly review a series of novel ideas on the physics of hadrons. In the present paper, emphasis is given on some different approaches to the hadron physics, which may be called as 'programs' in the sense of Lakatos. For clarity, we only discuss geometrization program, symmetries/ unification program, and phenomenology of inter-quark potential program.
Category: High Energy Particle Physics

[10] viXra:1003.0010 [pdf] replaced on 6 Mar 2010

A Derivation of Maxwell Equations in Quaternion Space

Authors: V. Christianto, Florentin Smarandache
Comments: 6 pages

Quaternion space and its respective Quaternion Relativity (it also may be called as Rotational Relativity) has been defined in a number of papers including [1], and it can be shown that this new theory is capable to describe relativistic motion in elegant and straightforward way. Nonetheless there are subsequent theoretical developments which remains an open question, for instance to derive Maxwell equations in Q-space. Therefore the purpose of the present paper is to derive a consistent description of Maxwell equations in Q-space. First we consider a simplified method similar to the Feynman's derivation of Maxwell equations from Lorentz force. And then we present another derivation method using Dirac decomposition, introduced by Gersten (1999). Further observation is of course recommended in order to refute or verify some implication of this proposition.
Category: Classical Physics

[9] viXra:1003.0009 [pdf] submitted on 6 Mar 2010

Extension of the Big Bang Theory

Authors: Florentin Smarandache
Comments: 2 pages

In this note we propose the extension of the Big Bang Theory of the origin of the Universe to the model that there are cycles of beginning and ending.
Category: Quantum Physics

[8] viXra:1003.0008 [pdf] submitted on 5 Mar 2010

Our Ability to Research Comes Before Understanding of What We Research

Authors: Dainis Zeps
Comments: 11 pages, submitted to JCER

Impact of quantum mechanics on physical science epistemology and science at all is considered. We consider methodolically idea that science doesn't research its assumed objects but the ability to research, thus making itself not distinguishable from the cognitive science in the most general sense. Next idea is that what we discover firstly are the methods and the technologies understanding about which may come (if at all) much much later after we have learned to use these technologies in our life up to incredible level. Instrumentality rather than objectivity should be researched in science. In this sense quantum mechanical impact on sciences should be assessed. Using this approach, quantum consciousness should be quested for.
Category: History and Philosophy of Physics

[7] viXra:1003.0007 [pdf] replaced on 15 Mar 2010

Experiment to Test the Quantum Effect of a Waveguide (I)

Authors: Z.Y. Wang
Comments: 6 pages.

The waveguide can be regarded as a potential barrier to microwaves and we apply quantum mechanics to study the coefficient of reflection R and transmission T . An initial experimental result is also presented in this paper that the transverse momentum of the electromagnetic field in a waveguide is zero which is no longer in proportion to the transverse wave vector. We're preparing to detect under other conditions and will report as soon as possible.
Category: Quantum Physics

[6] viXra:1003.0006 [pdf] submitted on 4 Mar 2010

Deceleration Parameter Q(Z) in Five Dimensional Geometries, and Does a re Appearance of Quinessence φ(t) Play a Role in an Increase in Cosmological Acceleration at Z ~. 423?

Authors: Andrew Beckwith
Comments: Essay written for the Gravity Research Foundation 2010 Awards for Essays on Gravitation, Submitted March 4th, 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 calculated inflaton φ(t) may partly re-emerge after fading out in the aftermath of inflation. The inflaton may contribute 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 at red shit value of Z ~ .423
Category: Relativity and Cosmology

[5] viXra:1003.0005 [pdf] replaced on 25 Mar 2010

The un-Henging of Stonehenge

Authors: Constantinos Ragazas
Comments: 7 pages

In this paper we un-henge the mystery of Stonehenge and propose a simple and consistent explanation to all its puzzling enigmas. How the stones got there? How was it built? Why was it built? Why is it aligned with the summer solstice sunrise? When was it built? Who built it? We argue that Nature built Stonehenge while men directed its construction. Its original function was neither an astronomical observatory nor a healing religious center. Stonehenge acquired such attributes thousands of years later as people, even now, felt its grandeur and wonder. Though the method of its construction can be easily explained, loosening its magical hold on people's imagination may be a more difficult task.
Category: Archaeology

[4] viXra:1003.0004 [pdf] replaced on 8 Mar 2010

A Proof of Riemann Hypothesis Using the Growth of Mertens Function M(x)

Authors: Young-Mook Kang
Comments: 6 pages, Submitted to annals of mathematics

A study of growth of M(x) as x → ∞ is one of the most useful approach to the Riemann hypophotesis(RH). It is very known that the RH is equivalent to which M(x) = O(x1/2+ε) for ε > 0. Also Littlewood proved that "the RH is equivalent to the statement that limx → ∞ M(x)x-1/2-ε = 0, for every ε > 0".[1] To use growth of M(x) approaches zero as x → ∞, I simply prove that the Riemann hypothesis is valid. Now Riemann hypothesis is not hypothesis any longer.
Category: Number Theory

[3] viXra:1003.0003 [pdf] submitted on 3 Mar 2010

The Reaction Force of Emitted Radiation: a Comment on Arxiv:1003.0247

Authors: Ron Bourgoin
Comments: 2 pages

The authors of [arxiv:1003.0247] neglect to consider that the source of radiation is an accelerated electron, that an emitted photon reacts, or pushes back, on the electron that releases it. This is a linear process, therefore a nonlinear Schrödinger equation is not applicable.
Category: Quantum Physics

[2] viXra:1003.0002 [pdf] submitted on 3 Mar 2010

Gauss Planetary Equations in a Non-Singular Gravitational Potential

Authors: Ioannis Iraklis Haranas, Michael Harney
Comments: 6 pages, Submitted to the Journal of Gravitational Physics, p.6

We study the effects of a non-singular gravitational potential on satellite orbits by calculating the corresponding changes of its orbital elements, using Gauss' planetary equations. We derive two non-zero expressions for the changes of the argument of the perigee and the mean anomaly, and we compare them to those of the general relativity. Using the GRACE satellite system, we obtain numerical results from which we conclude that the effect of such a potential, on the perigee cannot be separated from that of general relativity. Furthermore, we conclude that the effect on the mean anomaly can probably be observed by today's technology.
Category: Relativity and Cosmology

[1] viXra:1003.0001 [pdf] submitted on 1 Mar 2010

Deceleration Parameter Q(Z) in Five Dimensional Geometries, and to What Degree a Partial re Appearance of Quinessence φ(t) May Play a Role in an Increase in Cosmological Acceleration at Z ~ .423

Authors: Andrew Beckwith
Comments: 10 pages, two figures. Source document for presentation to be made in Xian, PRC, March 23, at PIERS http://piers.mit.edu/piers2010xian/. Main contribution is reconciliation of re appearance of inllaton as generator of entropy with graviton count, a la. Y. Ng's 2008 result, with increase in q(z) increase in rate of acceleration of the universe one billion years ago.

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) may partly 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 shift value of Z ~ .423
Category: Relativity and Cosmology