viXra.org e-printsPreprints from viXra.org site
http://viXra.org/
Thu Oct 19 18:07:12 BST 2017Thu Oct 19 18:07:12 BST 2017<![CDATA[Alter Coherence of Light]]>
http://viXra.org/abs/1710.0222
2017-10-19 07:14:52Condensed Matter reference: viXra:1710.0222v1 title: Alter Coherence of Light authors: George Rajna category: Condensed Matter type: submission date: 2017-10-19 07:14:52 abstract:
Brown University researchers have demonstrated for the first time a method of substantially changing the spatial coherence of light. [12] Researchers at the University of Central Florida have generated what is being deemed the fastest light pulse ever developed. [11] Physicists at Chalmers University of Technology and Free University of Brussels have now found a method to significantly enhance optical force. [10] Nature Communications today published research by a team comprising Scottish and South African researchers, demonstrating entanglement swapping and teleportation of orbital angular momentum 'patterns' of light. [9] While physicists are continually looking for ways to unify the theory of relativity, which describes large-scale phenomena, with quantum theory, which describes small-scale phenomena, computer scientists are searching for technologies to build the quantum computer using Quantum Information. In August 2013, the achievement of "fully deterministic" quantum teleportation, using a hybrid technique, was reported. On 29 May 2014, scientists announced a reliable way of transferring data by quantum teleportation. Quantum teleportation of data had been done before but with highly unreliable methods. The accelerating electrons explain not only the Maxwell Equations and the Special Relativity, but the Heisenberg Uncertainty Relation, the Wave-Particle Duality and the electron's spin also, building the Bridge between the Classical and Quantum Theories. The Planck Distribution Law of the electromagnetic oscillators explains the electron/proton mass rate and the Weak and Strong Interactions by the diffraction patterns. The Weak Interaction changes the diffraction patterns by moving the electric charge from one side to the other side of the diffraction pattern, which violates the CP and Time reversal symmetry. The diffraction patterns and the locality of the self-maintaining electromagnetic potential explains also the Quantum Entanglement, giving it as a natural part of the Relativistic Quantum Theory and making possible to build the Quantum Computer with the help of Quantum Information.
]]> <![CDATA[Elementary Formulas for Pi]]>
http://viXra.org/abs/1710.0221
2017-10-19 07:26:39General Mathematics reference: viXra:1710.0221v1 title: Elementary Formulas for Pi authors: Edgar Valdebenito category: General Mathematics type: submission date: 2017-10-19 07:26:39 abstract:
This note presents some formulas for pi=3.141592...
]]> <![CDATA[Mistakes and Contradictions in the Michelson Morley Experiment]]>
http://viXra.org/abs/1710.0220
2017-10-19 09:46:07Classical Physics reference: viXra:1710.0220v1 title: Mistakes and Contradictions in the Michelson Morley Experiment authors: Walter Ruh category: Classical Physics type: submission date: 2017-10-19 09:46:07 abstract:
In the following, it is shown that the Michelson & Morley experiment is subject to heavy mistakes. All considerations are based on the original publication, »AMERICAN JOURNAL OF SCIENCE, ARTICLE XXXVI On the Relative Motion of the Earth and the Luminiferous Ether, by ALBERT A. MICHELSON and EDWARD W. MORLEY".
1. The experiment presents measurements and expects results in the evening at around 18:00. This is wrong! Anyone with a knowledge of the earth's rotation and the course around the sun can see that the Michelson and Morley experiment makes sense only at the high noon and at midnight. The "ether wind" is only at this time in the measurable direction to the measuring device. In the evening and in the morning, the ether wind is in any case perpendicular (from top to bottom or from bottom to top) to the horizontal measuring device.
2. The light path, as described, cannot be correct. The perpendicular deflected light path can never be against the "ether wind".
3. Intellectual bases for the experiment are incomplete and therefore incorrect. The assumptions and conditions do not correspond with the mathematics for this experiment.
At the end is only one conclusion possible: The Michelson and Morley experiment is very roughly mistaken and therefore the results must be considered irrelevant.
]]> <![CDATA[Construction of Planar Multilayer Dyadic Green’s Functions by Fourier Expansion Method — Part I: Isotropic Media]]>
http://viXra.org/abs/1710.0219
2017-10-17 19:41:10Mathematical Physics reference: viXra:1710.0219v1 title: Construction of Planar Multilayer Dyadic Green’s Functions by Fourier Expansion Method — Part I: Isotropic Media authors: Huai-Yi Xie category: Mathematical Physics type: submission date: 2017-10-17 19:41:10 abstract:
In this paper, we have derived planar multilayer dyadic Green’s functions by Fourier expansion method and have checked its correctness by comparing results for reflected electric fields from dipole emissions near such structures available in previous literature. Furthermore, we show how these dyadic Green’s functions can be applied to calculate reflected fields from a dipole source with arbitrary orientations. We believe our formulation will be powerful in the modeling of molecular fluorescence near these structures.
]]> <![CDATA[Kilonova Merger Black Holes as the Origin of Ejected Quasar-Based Dark Matter Black Hole Halo Population.]]>
http://viXra.org/abs/1710.0216
2017-10-18 04:25:40Quantum Gravity and String Theory reference: viXra:1710.0216v1 title: Kilonova Merger Black Holes as the Origin of Ejected Quasar-Based Dark Matter Black Hole Halo Population. authors: Leo Vuyk category: Quantum Gravity and String Theory type: submission date: 2017-10-18 04:25:40 abstract:
Our Galaxy halo seems to be crowded with small KiloNova dark matter black holes.
Halton Arp was the first astronomer who observed accelerating QSO objects ( Quasi Stellar Objects) ejected out of the galaxy into the halo sphere.
According to Quantum FFF Theory we postulate that dark matter is the same as black holes, small or large, which are assumed to accelerate by the pushing plasma tail away from local gravity centers as a base for universal complexity.
A second postulation, is that the Big Bang was the evaporation and splitting of a former Big Crunch black hole nucleus of compressed Axion Higgs particles. This Big Crunch real particle based nucleus created the oscillating Axion /Higgs field vacuum lattice and numerous chunky nuclei of massive dark matter black holes.
The oscillating vacuum Lattice is supposed to represent a dynamic reference frame and the so called Dark Energy or Zero Point Energy acting as the motor for all Fermion spin and as the transfer medium for all photon information, leading to local lightspeed and local time.
The local lattice length is called Planck length, which is assumed to vary dependent on the distance to local vacuum absorbers in the form of black hole nuclei, which grow continuously, in contrast with the so called Hawking evaporation of black holes.
The energetic vacuum lattice is also assumed to act as a Gravity Quantum Dipole Repeller because gravitons are not supposed to attract- but repel Fermions, however with less impulse than the vacuum dark energy particles.
As a consequence, Feynman diagrams become more complex than before.
Recent measurements by Yehuda Hoffman et al. did show the large scale repelling effect of “empty space” in opposition of the “attracting gravity effect” of super clusters which he called “Dipole Repeller” effect.
This seems to be a great support for the dual Quantum gravity proposal of Quantum FFF Theory, as opposing quantum push effects between vacuum particles and gravitons on Fermion around massive objects.
Recently I found that the merging of galaxy clusters itself show dynamic observational signs of a contraction of the vacuum inside the merging galaxy clusters by the anomalous central clustering of the dark matter black hole content which seems to be stripped from the individual galaxy clusters located at the borders of the new super cluster.
( see Abell 520 and bullet cluster: “no inertia effect of dark matter black holes”.)
Then we also may assume that the universal vacuum between galaxy clusters should be also subjected to this absorption process, ( which is supposed to be the origin of the Hubble redshift by the local reduction of the light speed) as a sign for universal contraction and negative entropy, leading to a cyclic universe.
]]> <![CDATA[An Elegant Solution to the Cosmological Constant Problem based on The Bohm-Poisson Equation]]>
http://viXra.org/abs/1710.0215
2017-10-18 04:43:32Quantum Gravity and String Theory reference: viXra:1710.0215v1 title: An Elegant Solution to the Cosmological Constant Problem based on The Bohm-Poisson Equation authors: Carlos Castro category: Quantum Gravity and String Theory type: submission date: 2017-10-18 04:43:32 abstract:
After applying the recently proposed Bohm-Poisson equation [1] to the observable Universe as a $whole$,
and by introducing an ultraviolet (Planck) and infrared (Hubble) scale, one can naturally obtain a value for the vacuum energy density of the $same$ $magnitude$ as
the extremely small observed vacuum energy density, and explain the origins of its $repulsive$ gravitational nature. Because Bohm's formulation of QM is by construction non-local, it is this non-locality which casts light into the crucial ultraviolet/infrared entanglement of the Planck/Hubble scales which was required in order to obtain the observed value of the vacuum energy density.
]]> <![CDATA[Role of Main Components in the Rheology of Heavy Oil (In Russian)]]>
http://viXra.org/abs/1710.0214
2017-10-18 06:19:34Chemistry reference: viXra:1710.0214v1 title: Role of Main Components in the Rheology of Heavy Oil (In Russian) authors: S. O. Ilyin category: Chemistry type: submission date: 2017-10-18 06:19:34 abstract:
A series of rheological properties of the main components (saturated compounds, light and heavy aromatic compounds, resins and asphaltenes), extracted from a typical sample of heavy oil extracted in tatarstan (russia), were consistently investigated. The viscosity and viscoelastic characteristics of these components are measured in a wide range of temperatures and deformation conditions, as well as their solutions in tetralin. Saturated hydrocarbons behave in a manner similar to paraffin oil, i. E. Demonstrate viscous-plastic behavior at low temperatures. For light aromatic compounds, non-newtonian behavior is characteristic, and heavy aromatic compounds, as well as resins and asphaltenes, behave like newtonian fluids. In their totality, the anomalous-rheological effects practically do not affect the rheology of heavy oil, which can be regarded as a newtonian fluid over a wide range of temperatures. The most significant value for the viscosity of heavy oil is the interaction of resins and asphaltenes. Concentration dependences of the viscosity of these components are qualitatively similar, but the viscosity of solutions of asphaltenes at high concentrations is much higher than the viscosity of equicomponent resin solutions. This reflects a lower critical concentration of asphaltenes, at which their formation occurs (up to the formation of graphene), compared to resins. An investigation of the rheology of the model "artificial" oil, from which the resins were removed, but contained a different amount of asphaltenes, showed that in this case the viscosity was higher than in the original oil. This indicates a stabilizing effect of the resins, which most likely contribute to the formation of emulsions, preventing further structure formation of the asphaltenes.
]]> <![CDATA[Nuclear Quantum Gravity – A First Review]]>
http://viXra.org/abs/1710.0212
2017-10-18 11:28:03Quantum Gravity and String Theory reference: viXra:1710.0212v1 title: Nuclear Quantum Gravity – A First Review authors: U. V. S. Seshavatharam , S. Lakshminarayana category: Quantum Gravity and String Theory type: submission date: 2017-10-18 11:28:03 abstract:
To have a unified model of nuclear quantum gravity, it seems quite reasonable to consider a large nuclear gravitational constant, $G_s
\cong 3.3\pm 0.03
times 10^{28}$ $m^3/kg/sec^2$. In this context, we show practical applications pertaining to micro physics as well as macro physics. We would like to suggest that: (1) $G_s$ plays a crucial role in understanding quantum theory of light, photoelectric work functions, superconductivity, nuclear binding energy, nuclear root mean square charge radii, neutron-proton mass difference, nuclear stability, nuclear magnetic dipole moments, weak coupling angle, Fermi’s weak coupling constant, proton melting point and total energy of electron in Hydrogen atom etc.; (2) Nuclear binding energy can be understood with a single energy coefficient of magnitude 10 MeV. (3) Newtonian gravitational constant $G_N$ and the proposed $G_s$ play a joint role in understanding neutron star mass generation as well as proton mass generation; and (4) Considering $G_s$ as a characteristic feature of magnetism, celestial bodies ‘mass dependent’ magnetic dipole moments can be estimated.
]]> <![CDATA[What is Behind Coulomb]]>
http://viXra.org/abs/1710.0211
2017-10-18 13:34:47Classical Physics reference: viXra:1710.0211v1 title: What is Behind Coulomb authors: Walter Ruh category: Classical Physics type: submission date: 2017-10-18 13:34:47 abstract:
Starting from the deviation «of the good order» that Coulomb / Ampere disappears in energies, it was shown that behind the in the abstract unit Coulomb is a real value, composed of kilograms, meters and seconds. This gives the field equations a real substance which can represent power and energy in real terms. The results are indicative of a (forbidden) "model medium" without concluding that a medium exists in reality. The logic and physical beauty of this system is overwhelming.
Ausgehend von der stossenden Abweichung «von der guten Ordnung», dass Coulomb/Ampere bei Energierechnungen verschwindet wurde aufgezeigt, dass hinter der abstrakten Einheit Coulomb ein realer Wert, zusammengesetzt aus Kilogramm, Metern und Sekunden zu finden ist. Dadurch bekommen die Feldgleichungen eine reale Substanz welche Leistung und Energie real darstellen kann.
Die Resultate ergeben Indizien auf ein (verbotenes) "Modell-Medium", ohne zu folgern, dass ein Medium in Realität existiert. Die Logik und physikalische Schönheit dieser Systematik ist überwältigend.
]]> <![CDATA[Importance of Manchester Coding Using Micro-Controllers/Related Data Processing Mechanisms – An Interesting Insight into Manchester Coding & Smart Watch Applications.]]>
http://viXra.org/abs/1710.0210
2017-10-18 14:30:33Digital Signal Processing reference: viXra:1710.0210v1 title: Importance of Manchester Coding Using Micro-Controllers/Related Data Processing Mechanisms – An Interesting Insight into Manchester Coding & Smart Watch Applications. authors: N.T.Kumar,Thiago R,Sandro B,Vinicius R,Lisane V,Vanderlei P category: Digital Signal Processing type: submission date: 2017-10-18 14:30:33 abstract:
Smart Watches are modern devices involving cutting edge technologies in all aspects of working and
communicating with the surrounding environments by detecting parameters and also providing a means
to transmit the related data for further processing via Computers/Tablets/Smart Phones etc..We wish to
highlight the importance of “Manchester Coding” in the context of Smart Watches based on Micro-
controllers for example SAML21 Series from ATMEL.
]]> <![CDATA[Prime Numbers as a Function of a Geometric Progression]]>
http://viXra.org/abs/1710.0209
2017-10-18 15:14:30Number Theory reference: viXra:1710.0209v1 title: Prime Numbers as a Function of a Geometric Progression authors: Leif R. Uppström, Daniel Uppström category: Number Theory type: submission date: 2017-10-18 15:14:30 abstract:
In mathematical literature it is asked for a computable function or efficient algorithm to find all, or at least a large subset, of the prime numbers. This paper shows that all primes can be characerised by their reciprocal period length L and its figure value R. These parameters are given for each prime after inversion to an infinitely repeated period and are used to group all primes into disjoint sets that arise as a function of a geometric progression. This theory suggests new ways to enumerate and find large primes.
]]> <![CDATA[The Recursive Future Equation Based On The Ananda-Damayanthi Normalized Similarity Measure. {File Closing Version 4}. ISSN 1751-3030]]>
http://viXra.org/abs/1710.0208
2017-10-18 23:07:44Artificial Intelligence reference: viXra:1710.0208v1 title: The Recursive Future Equation Based On The Ananda-Damayanthi Normalized Similarity Measure. {File Closing Version 4}. ISSN 1751-3030 authors: Ramesh Chandra Bagadi category: Artificial Intelligence type: submission date: 2017-10-18 23:07:44 abstract:
In this research Technical Note the author have presented a Recursive Future Average Of A Time Series Data Based on Cosine Similarity.
]]> <![CDATA[A Conjecture On The Nature Of Time]]>
http://viXra.org/abs/1710.0207
2017-10-18 23:30:00Quantum Physics reference: viXra:1710.0207v1 title: A Conjecture On The Nature Of Time authors: Felix M Lev category: Quantum Physics type: submission date: 2017-10-18 23:30:00 abstract:
In our previous publications we argue that finite mathematics is fundamental, classical mathematics (involving such notions as infinitely small/large, continuity etc.) is a degenerate special case of finite one, and ultimate quantum theory will be based on finite mathematics. We consider a finite quantum theory (FQT) based on a finite field or ring with a large characteristic $p$ and show that standard continuous quantum theory is a special case of FQT in the formal limit $p\to\infty$. Space and time are purely classical notions and are not present in FQT at all. In the present paper we discuss how classical equations of motions arise as a consequence of the fact that $p$ changes, i.e. $p$ is the evolution parameter.
]]> <![CDATA[Proton and Antiproton Share Fundamental Properties]]>
http://viXra.org/abs/1710.0206
2017-10-19 01:55:50High Energy Particle Physics reference: viXra:1710.0206v1 title: Proton and Antiproton Share Fundamental Properties authors: George Rajna category: High Energy Particle Physics type: submission date: 2017-10-19 01:55:50 abstract:
An asymmetry must exist here somewhere but we simply do not understand where the difference is. What is the source of the symmetry break? [13] They have successfully deciphered the total angular momentum (spin) of the nucleon, determining how it's shared among its constituents. [12] The resulting values for the Rydberg constant and the proton radius are in excellent agreement with the muonic results (Nature 466, 213 (2010)), but disagree by 3.3 standard deviations with the average of the previous determinations from regular hydrogen. [11] In a stringent test of a fundamental property of the standard model of particle physics, known as CPT symmetry, researchers from the RIKEN-led BASE collaboration at CERN have made the most precise measurements so far of the charge-to-mass ratio of protons and their antimatter counterparts, antiprotons. [10] The puzzle comes from experiments that aimed to determine how quarks, the building blocks of the proton, are arranged inside that particle. That information is locked inside a quantity that scientists refer to as the proton's electric form factor. The electric form factor describes the spatial distribution of the quarks inside the proton by mapping the charge that the quarks carry. [9] Taking into account the Planck Distribution Law of the electromagnetic oscillators, we can explain the electron/proton mass rate and the Weak and Strong Interactions. Lattice QCD gives the same results as the diffraction patterns of the electromagnetic oscillators, explaining the color confinement and the asymptotic freedom of the Strong Interactions.
]]> <![CDATA[An Approximation to the Prime Counting Function Through the Sum of Consecutive Prime Numbers]]>
http://viXra.org/abs/1710.0205
2017-10-19 02:50:41Number Theory reference: viXra:1710.0205v1 title: An Approximation to the Prime Counting Function Through the Sum of Consecutive Prime Numbers authors: Juan Moreno Borrallo category: Number Theory type: submission date: 2017-10-19 02:50:41 abstract:
In this paper it is proved that the sum of consecutive prime numbers under the square root of a given natural number is asymptotically equivalent to the prime counting function. Also, it is proved another asymptotic relationship between the sum of the first prime numbers up to the integer part of the square root of a given natural number and the prime counting function.
]]> <![CDATA[Solution of Maxwell's Equations for a Capacitor with Alternating Voltage]]>
http://viXra.org/abs/1710.0204
2017-10-15 09:03:46Classical Physics reference: viXra:1710.0204v1 title: Solution of Maxwell's Equations for a Capacitor with Alternating Voltage authors: Solomon I. Khmelnik category: Classical Physics type: submission date: 2017-10-15 09:03:46 abstract:
A solution of the Maxwell equations for a variable voltage capacitor with a variable voltage is given, which is a development of inconsistency (corresponding to the energy conservation law) solution of the Maxwell equations for vacuum. It is shown that in an electromagnetic wave propagating through a capacitor, the flux of electromagnetic energy does not change with time. It is shown that there exists a longitudinal (along the radius) standing electromagnetic wave. For a simple verification of the findings, detailed proof is given.
]]> <![CDATA[Solution of Maxwell's Equations for a Capacitor with Alternating Voltage \\ Решение уравнений Максвелла для конденсатора с переменным напряжением]]>
http://viXra.org/abs/1710.0203
2017-10-15 09:07:50Classical Physics reference: viXra:1710.0203v1 title: Solution of Maxwell's Equations for a Capacitor with Alternating Voltage \\ Решение уравнений Максвелла для конденсатора с переменным напряжением authors: Solomon I. Khmelnik category: Classical Physics type: submission date: 2017-10-15 09:07:50 abstract:
A solution of the Maxwell equations for a variable voltage capacitor with a variable voltage is given, which is a development of inconsistency (corresponding to the energy conservation law) solution of the Maxwell equations for vacuum. It is shown that in an electromagnetic wave propagating through a capacitor, the flux of electromagnetic energy does not change with time. It is shown that there exists a longitudinal (along the radius) standing electromagnetic wave. For a simple verification of the findings, detailed proof is given. \\ Приводится решение уравнений Максвелла для конденсатора с переменным напряжением, которое является развитием непротиворечивого (соответствующего закону сохранения энергии) решения уравнений Максвелла для вакуума. Показано, что в электромагнитной волне, распространяющейся через конденсатор, поток электромагнитной энергии не изменяется во времени. Показано, что существует продольная (вдоль радиуса) стоячая электромагнитная волна.
Для простой проверки полученных выводов приводится подробное доказательство.
]]> <![CDATA[Recurrence Relation for Calculating the Sequence of Primes]]>
http://viXra.org/abs/1710.0202
2017-10-15 09:49:16Number Theory reference: viXra:1710.0202v1 title: Recurrence Relation for Calculating the Sequence of Primes authors: I. N. Tukaev category: Number Theory type: submission date: 2017-10-15 09:49:16 abstract:
A recurrence relation is defined for calculating a sequence of prime numbers using the Riemann zeta function and the Euler product.
]]> <![CDATA[Automatic Intelligent Translation of Videos]]>
http://viXra.org/abs/1710.0201
2017-10-15 11:44:37Data Structures and Algorithms reference: viXra:1710.0201v1 title: Automatic Intelligent Translation of Videos authors: Shivam Bansal category: Data Structures and Algorithms type: submission date: 2017-10-15 11:44:37 abstract:
There are a lot of educational videos online which are in English and inaccessible to 80% population of the world. This paper presents a process to translate a video into another language by creating its transcript and using TTS to produce synthesized fragments of speech. It introduces an algorithm which synthesyses intelligent, synchronized, and easily understandable audio by combining those fragments of speech. This algorithm is also compared to an algorithm from another research paper on the basis of performance.
]]> <![CDATA[Inertia]]>
http://viXra.org/abs/1710.0200
2017-10-15 13:08:02Quantum Gravity and String Theory reference: viXra:1710.0200v1 title: Inertia authors: Andrey N. Smirnov category: Quantum Gravity and String Theory type: submission date: 2017-10-15 13:08:02 abstract:
We consider how inertia appears in the theory of emergent space-time-matter. The phenomenon of inertia is explained for the case of the presence of reflection symmetry (parity) in the wave function. This symmetry is broken only in weak interactions. For the case of weak interaction, there is no explanation for inertia, but there is an assumption that the development of a mathematical model based on the construction of universes from the field of the Metauniverse will justify the inertia for such a case.
]]> <![CDATA[Salary Fluctuation Theory]]>
http://viXra.org/abs/1710.0199
2017-10-15 14:47:30Economics and Finance reference: viXra:1710.0199v1 title: Salary Fluctuation Theory authors: Chuanli Chen category: Economics and Finance type: submission date: 2017-10-15 14:47:30 abstract:
In this paper, based on my previous price theory, I will put forward my own labor
market price determination theory, I will discuss the determination of price under
different situations.
]]> <![CDATA[Intuitive Geometric Significance of Pauli Matrices and Others in a Plane]]>
http://viXra.org/abs/1710.0198
2017-10-15 23:37:12Mathematical Physics reference: viXra:1710.0198v1 title: Intuitive Geometric Significance of Pauli Matrices and Others in a Plane authors: Hongbing Zhang category: Mathematical Physics type: submission date: 2017-10-15 23:37:12 abstract:
The geometric significance of complex numbers is well known, such as the meaning of imaginary unit i is to rotate a vector with pi/2, etc. In this article, we will try to find some intuitive geometric significances of Pauli matrices, split-complex numbers, SU(2), SO(3), and their relations, and some other operators often used in quantum physics, including a new method to lead to the spinor-space and Dirac equation.
]]> <![CDATA[General Brachistochrone Curve]]>
http://viXra.org/abs/1710.0197
2017-10-15 23:42:10Mathematical Physics reference: viXra:1710.0197v1 title: General Brachistochrone Curve authors: Hongbing Zhang category: Mathematical Physics type: submission date: 2017-10-15 23:42:10 abstract:
In history, the problem of Johann Bernoulli's Brachistochrone Curve (BBC) was assumed the case that the force of gravity on the falling body is constant, for example, the case of near the surface of the Earth. In this article, we will propose and solve a new problem of the General Brachistochrone Curve (GBC), in case of the body falling in a large space of Newton gravity field, or in stronger Newton gravity field, in which the force of gravity is inversely proportional to the square of the height above the center of the star or planet.
]]> <![CDATA[Matrix-Representations of Tensors]]>
http://viXra.org/abs/1710.0196
2017-10-15 23:46:11Mathematical Physics reference: viXra:1710.0196v1 title: Matrix-Representations of Tensors authors: Hongbing Zhang category: Mathematical Physics type: submission date: 2017-10-15 23:46:11 abstract:
The metric tensor of Minkowski space-time, the electromagnetic field tensor, etc., are usually represented by 4x4 matrices in many textbooks, but in this paper we will demonstrate that this form of matrix-representation is unreasonable. We will introduce more reasonable rules of matrix-form for representing any (p,q)-type tensor.
]]> <![CDATA[Interest Theory]]>
http://viXra.org/abs/1710.0195
2017-10-16 01:23:27Economics and Finance reference: viXra:1710.0195v1 title: Interest Theory authors: Chuanli Chen category: Economics and Finance type: submission date: 2017-10-16 01:23:27 abstract:
In this paper I will put forward my own interest theory. I will discuss the factors that
could influence the real interest rate. I will discuss the relationship between the
interest, money supply and money demand.
]]> <![CDATA[A Framework for Pest Analysis Based on Neutrosophic Cognitive Map: Case Study in a Vertical Farming Initiative]]>
http://viXra.org/abs/1710.0194
2017-10-16 05:22:01General Mathematics reference: viXra:1710.0194v1 title: A Framework for Pest Analysis Based on Neutrosophic Cognitive Map: Case Study in a Vertical Farming Initiative authors: Wilmer Ortiz Choez, Marcos Quinteros Cortázar, Shirley Huerta Cruz, Katiuska Rubira Carvache category: General Mathematics type: submission date: 2017-10-16 05:22:01 abstract:
Recently, neutrosophic cognitive maps and its
application in decision making have become a topic of great importance for researchers and practitioners alike. In this paper, a new model PEST analysis is presented based on neutrosophic cognitive maps static analysis. The proposed framework is composed of five activities, identifying PEST factors and
sub-factors, modelling interrelation among PEST
factors, calculate centrality measures, factor classification, and factors ranking. A case study developed in environment analysis for a vertical farming project was presented, ranking factor based in interrelation and incorporating indeterminacy in the analysis. Further works will concentrate extending the model for incorporating scenario analysis.
]]> <![CDATA[Competencies Evaluation Based on Single Valued Neutrosophic Numbers and Decision Analysis Schema]]>
http://viXra.org/abs/1710.0193
2017-10-16 05:23:34General Mathematics reference: viXra:1710.0193v1 title: Competencies Evaluation Based on Single Valued Neutrosophic Numbers and Decision Analysis Schema authors: Evelyn Jazmín Henríquez Antepara, Oscar Omar Apolinario Arzube, Jorge Arturo Chicala Arroyave, Eduardo Antonio Alvarado Unamuno, Maikel Leyva Vazquez category: General Mathematics type: submission date: 2017-10-16 05:23:34 abstract:
Recently, neutrosophic sets and its application
to decision making have become a topic of significant im-portance for researchers and practitioners. The present work addresses one of the most complex aspects of the formative process based on competencies: evaluation. In this paper, a new method for competencies evaluation is
developed in a multicriteria framework.
]]> <![CDATA[Covering-Based Rough Single Valued Neutrosophic Sets]]>
http://viXra.org/abs/1710.0192
2017-10-16 05:24:39General Mathematics reference: viXra:1710.0192v1 title: Covering-Based Rough Single Valued Neutrosophic Sets authors: Yingcang Ma, Wanying Zhou, Qing Wan category: General Mathematics type: submission date: 2017-10-16 05:24:39 abstract:
Rough sets theory is a powerful tool to deal with uncertainty and incompleteness of knowledge in information systems. Wang et al. proposed single valued neutrosophic sets as an extension of intuitionistic fuzzy sets to deal with real-world problems. In this paper, we propose the covering-based rough single valued neutrosophic sets by combining covering-based rough sets and single valued neutrosophic sets.
]]> <![CDATA[Decision Support Based on Single Valued Neutrosophic Number for Information System Project Selection]]>
http://viXra.org/abs/1710.0191
2017-10-16 05:25:46General Mathematics reference: viXra:1710.0191v1 title: Decision Support Based on Single Valued Neutrosophic Number for Information System Project Selection authors: Silvia Liliana Tejada Yepez category: General Mathematics type: submission date: 2017-10-16 05:25:46 abstract:
Neutrosophic sets and its application to decision support have become a topic of great importance for researchers and practitioners alike. In this paper, a new model for decision making in the selection of information system projects is presented based on single valued neutrosophic number (SVN-numbers) allowing the use of linguistic variables with multiples points of view from experts.
]]> <![CDATA[More On P-Union and P-Intersection of Neutrosophic Soft Cubic Set]]>
http://viXra.org/abs/1710.0190
2017-10-16 05:26:53General Mathematics reference: viXra:1710.0190v1 title: More On P-Union and P-Intersection of Neutrosophic Soft Cubic Set authors: R. Anitha Cruz, F. Nirmala Irudayam category: General Mathematics type: submission date: 2017-10-16 05:26:53 abstract:
The P-union, P-intersection, P-OR and P-AND
of neutrosophic soft cubic sets are introduced and their related properties are investigated. We show that the Punion and the P-intersection of two internal neutrosophic soft cubic sets are also internal neutrosophic soft cubic sets.
]]> <![CDATA[Neutrosophy for Software Requirement Prioritization]]>
http://viXra.org/abs/1710.0189
2017-10-16 05:35:31General Mathematics reference: viXra:1710.0189v1 title: Neutrosophy for Software Requirement Prioritization authors: Ronald Barriga Dias, Wilmer Ortiz Choez, Inelda Martillo Alcivar, Wilber Ortiz Aguilar category: General Mathematics type: submission date: 2017-10-16 05:35:31 abstract:
Software engineers are involved in complex decisions that require multiples viewpoints. A specific case is the requirement prioritization process. This process is used to decide which software requirement to develop in certain release from a group of candidate requirements. Criteria involved in this process can involve indeterminacy. In this paper a software requirement prioritization model is develop based SVN numbers. Finally, an illustrative example is presented in order to show the proposed model.
]]> <![CDATA[On New Measures of Uncertainty for Neutrosophic Sets]]>
http://viXra.org/abs/1710.0188
2017-10-16 05:36:23General Mathematics reference: viXra:1710.0188v1 title: On New Measures of Uncertainty for Neutrosophic Sets authors: Pinaki Majumdar category: General Mathematics type: submission date: 2017-10-16 05:36:23 abstract:
The notion of entropy of single valued
neutrosophic sets (SVNS) was first introduced by
Majumdar and Samanta in [10]. In this paper some
problems with the earlier definition of entropy has been pointed out and a new modified definition of entropy for SVNS has been proposed.
]]> <![CDATA[An Extended Topsis for Multi-Attribute Decision Making Problems with Neutrosophic Cubic Information]]>
http://viXra.org/abs/1710.0186
2017-10-16 07:10:03General Mathematics reference: viXra:1710.0186v1 title: An Extended Topsis for Multi-Attribute Decision Making Problems with Neutrosophic Cubic Information authors: Surapati Pramanik, Partha Pratim Dey, Bibhas C. Giri, Florentin Smarandache category: General Mathematics type: submission date: 2017-10-16 07:10:03 abstract:
The paper proposes a new technique for dealing
with multi-attribute decision making problems
through an extended TOPSIS method under neutrosophic cubic environment. Neutrosophic cubic set is the generalized form of cubic set and is the hybridization of a neutrosophic
set with an interval neutrosophic set. In this
study, we have defined some operation rules for neutrosophic cubic sets and proposed the Euclidean distance between neutrosophic cubic sets.
]]> <![CDATA[Extension of Crisp Functions on Neutrosophic Sets]]>
http://viXra.org/abs/1710.0185
2017-10-16 07:11:01General Mathematics reference: viXra:1710.0185v1 title: Extension of Crisp Functions on Neutrosophic Sets authors: Sabu Sebastian, Florentin Smarandache category: General Mathematics type: submission date: 2017-10-16 07:11:01 abstract:
In this paper, we generalize the definition of
Neutrosophic sets and present a method for extending crisp functions on Neutrosophic sets and study some properties of such extended functions.
]]> <![CDATA[Multi Criteria Decision Making Using Correlation Coefficient Under Rough Neutrosophic Environment]]>
http://viXra.org/abs/1710.0184
2017-10-16 07:12:13General Mathematics reference: viXra:1710.0184v1 title: Multi Criteria Decision Making Using Correlation Coefficient Under Rough Neutrosophic Environment authors: Surapati Pramanik, Rumi Roy, Tapan Kumar Roy, Florentin Smarandache category: General Mathematics type: submission date: 2017-10-16 07:12:13 abstract:
In this paper, we define correlation coefficient
measure between any two rough neutrosophic sets. We also prove some of its basic properties. We develop a new multiple attribute group decision making method based on the proposed correlation coefficient measure.
]]> <![CDATA[Neutrosophic Regular Filters and Fuzzy Regular Filters in Pseudo-BCI Algebras]]>
http://viXra.org/abs/1710.0183
2017-10-16 07:13:21General Mathematics reference: viXra:1710.0183v1 title: Neutrosophic Regular Filters and Fuzzy Regular Filters in Pseudo-BCI Algebras authors: Xiaohong Zhang, Yingcang Ma, Florentin Smarandache category: General Mathematics type: submission date: 2017-10-16 07:13:21 abstract:
Neutrosophic set is a new mathematical tool
for handling problems involving imprecise, indeterminacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics.
]]> <![CDATA[Uniform Single Valued Neutrosophic Graphs]]>
http://viXra.org/abs/1710.0182
2017-10-16 07:15:08General Mathematics reference: viXra:1710.0182v1 title: Uniform Single Valued Neutrosophic Graphs authors: S. Broumi, A. Dey, A. Bakali, M. Talea, F. Smarandache, L. H. Son, D. Koley category: General Mathematics type: submission date: 2017-10-16 07:15:08 abstract:
In this paper, we propose a new concept named the uniform single valued neutrosophic graph. An illustrative example and some properties are examined. Next, we develop an algorithmic approach for computing the complement of the single valued neutrosophic graph. A numerical example is demonstrated for computing the complement of single valued neutrosophic graphs and uniform single valued neutrosophic graph.
]]> <![CDATA[Cargo Cult Science – Electromagnetic Harmonics and Heterodynes]]>
http://viXra.org/abs/1710.0181
2017-10-16 12:58:45Astrophysics reference: viXra:1710.0181v1 title: Cargo Cult Science – Electromagnetic Harmonics and Heterodynes authors: Frank H. Makinson category: Astrophysics type: submission date: 2017-10-16 12:58:45 abstract:
The process that produces harmonics and heterodynes are assumed to be well understood. The textbook definitions of these two terms are being tagged herein as cargo cult science because they are incomplete. Harmonics and heterodynes are an effect created when electromagnetic waves interact within a plasma of charged particles. The textbook descriptions of harmonics and heterodynes are based upon fundamental electromagnetic waves, sine waves that represent a single frequency, a special case. The textbook descriptions are based upon interactions that occur within electronic devices, which is a special case. For heterodynes, textbooks do not mention that the interaction within electronic devices are collinear, which is a special case. Radio astronomers are detecting signals coming from space that have spectral characteristics unlike anything taught in the textbooks. Contemporary radio astronomers would be the primary group of individuals that would be misled by the incomplete information provided in the textbooks.
]]> <![CDATA[Activation of Autophagy Process in Cancerous Cells at Quasi-Zero Gravity Environments]]>
http://viXra.org/abs/1710.0180
2017-10-16 13:00:37Physics of Biology reference: viXra:1710.0180v1 title: Activation of Autophagy Process in Cancerous Cells at Quasi-Zero Gravity Environments authors: Fran De Aquino category: Physics of Biology type: submission date: 2017-10-16 13:00:37 abstract:
Autophagy is a well-known process of cell death. In this work we show that it can be actived in cancerous cells at Quasi-Zero Gravity environments. The result is the total destruction of the cancerous cells without use of medicaments.
]]> <![CDATA[Thermophysical Properties and Heat Transfer Using Nanofluids: a Review]]>
http://viXra.org/abs/1710.0179
2017-10-16 13:46:16Thermodynamics and Energy reference: viXra:1710.0179v1 title: Thermophysical Properties and Heat Transfer Using Nanofluids: a Review authors: Enrique Marcet Garcia, Eddy Martinez Padron, Marcelo Marcet Sanchez category: Thermodynamics and Energy type: submission date: 2017-10-16 13:46:16 abstract:
Nanofluids are considered to offer significantly more advantages in heat transfer than conventional fluids. Recently theoretical and experimental research papers appeared in the literature on thermophysical properties of nanofluids and enhancement of heat transfer using suspensions of nanoparticles. The aim of this review summarizes the results of research papers about thermophysical properties and forced convection heat transfer with nanofluids.
]]> <![CDATA[Gnuplantex: a Novel Free Software for Analyzing Texture and Color in Plants; Its Industrial Application.]]>
http://viXra.org/abs/1710.0178
2017-10-16 13:48:15Digital Signal Processing reference: viXra:1710.0178v1 title: Gnuplantex: a Novel Free Software for Analyzing Texture and Color in Plants; Its Industrial Application. authors: Enrique Marcet Garcia category: Digital Signal Processing type: submission date: 2017-10-16 13:48:15 abstract:
In many industrial applications where plants are used as raw material in the
production process, is important to perform a proper phytosanitary and quality
control. To perform these controls is possible by raw materials visual inspection,
however, to analyze texture and color in plants would allow
identifying/quantifying problems as: nutrient deficiencies; diseases (caused by
fungi, bacteria, etc.), as well as to identify problems in industrial process. The
aims of this paper are: (1) to develop free software (GPL) for texture analysis
(GLCM), color measurement (CIELab) and color-difference calculation using
CIEDE2000; (2) software application in the analysis of Moringa oleifera Lam
leaves. For programming the software we used Perl and wxBasic languages.
GNUplantex is easy-to-use software. It is available at:
http://www.2shared.com/file/tvzJPBy5/gnuplantex.html
]]> <![CDATA[Gravitational Waves GW150914 and Supernova Sn1987a]]>
http://viXra.org/abs/1710.0177
2017-10-16 14:04:05Astrophysics reference: viXra:1710.0177v1 title: Gravitational Waves GW150914 and Supernova Sn1987a authors: Nikitin A P category: Astrophysics type: submission date: 2017-10-16 14:04:05 abstract:
This article discusses two grand cosmological events: an explosion of blue supergiant - a star Sanduleak-69º 202 to form Supernova SN1987A, which remains unexplained, compared with at least a grand merger event black holes GW150914, from which the LIGO Collaboration account gravitational wave (GW). From the point of view of the theory of energy - electrodynamics, developed by the author, in physical terms, these two events are not fundamentally different: in all cases, the motion of matter must be radiated GW as part of the whole spectrum of radiation. It is predicted, along with the gravitational, neutrino and photon radiation from GW150914. By analogy with SN1987A, in the case of the merger of black holes after GW150914 GW signal through 10720 s ± 4000 s (~3h 00m 00s ± 1h 06m 40s) to come back to Earth the first neutrino signal (if option is possible that the first neutrino signal came earlier gravity) through 112.9·106 s (~3.6 years) after gravitational signal - the second neutrino signal through 66.031·106 s (~ 2.0924 years) after which the photon flash should be observed. Neutrino signals can be recorded on the IceCube Neutrino Observatory and other neutrino observatories.
]]> <![CDATA[The Middle Universe Revised]]>
http://viXra.org/abs/1710.0175
2017-10-17 00:49:32Astrophysics reference: viXra:1710.0175v1 title: The Middle Universe Revised authors: Justin White category: Astrophysics type: submission date: 2017-10-17 00:49:32 abstract:
The middle Universe is the universe we see rather than the speculative constructions of cosmology. Could the institutions of speculative astrophysics be handing down to us an inaccurate view of the universe. Schwarzschild's formula for a gravitational radius contains a mathematical fallacy. No black holes. Go figure.
]]> <![CDATA[Theorem of Prime Pair Distribution]]>
http://viXra.org/abs/1710.0174
2017-10-17 01:35:25Number Theory reference: viXra:1710.0174v1 title: Theorem of Prime Pair Distribution authors: Choe Ryujin category: Number Theory type: submission date: 2017-10-17 01:35:25 abstract:
Theorem of prime pair distribution
]]> <![CDATA[The Quantization of Space]]>
http://viXra.org/abs/1710.0173
2017-10-17 04:53:35History and Philosophy of Physics reference: viXra:1710.0173v1 title: The Quantization of Space authors: Uta Volkenborn, Heinz Volkenborn category: History and Philosophy of Physics type: submission date: 2017-10-17 04:53:35 abstract:
Abstract
The fine-structure constant α=1/137 demands a quantization of space. For this purpose, we refer to a volume constant of electromagnetic processes, which takes effect as a volume quantum. This involves not only a re-evaluation of the Dirac equation but also, and above all, a determination of Einstein’s velocity vector as the fundamental property of these processes. A prerequisite is the linking of the hydrogen spectrum with the hydrogen nucleus.
]]> <![CDATA[Projection Gravitation, a Projection Force from 5-Dimensional Space-Time Into 4-Dimensional Space-Time]]>
http://viXra.org/abs/1710.0172
2017-10-19 06:45:03Quantum Gravity and String Theory reference: viXra:1710.0172v2 title: Projection Gravitation, a Projection Force from 5-Dimensional Space-Time Into 4-Dimensional Space-Time authors: XiaoLin Li category: Quantum Gravity and String Theory type: replacement date: 2017-10-19 06:45:03 abstract:
A new gravity theory. Gravity is a projection force from 5-dimensional space-time into 4-dimensional space-time. The Lorentz symmetry is a projection of particle-wave symmetry from 5-dimensional space-time into 4-dimensional space-time. The gravity is an additional projection force of Lorentz symmetry. The new gravity is an extension to Lorentz symmetry. The new gravity can be seen as some kind of symmetry. Gravity only exists in 4-dimensional space-time. In 5-dimensional space-time, there not have gravity. Equivalence principle is invalid in the new gravitation. In the new gravitation, there does not have gravitational acceleration. In the new gravitation, there only have inertial coordinates, not have non-inertial coordinates. In the new gravitation, the gravity source is only the rest mass, not energy. The particle can’t be the gravity source if the particle not has rest mass. The photon not has gravity. But any particle can be affected by gravity. The photon is affected by gravity also. The gravitational mass is only equivalent to the rest mass. Under approximate weak gravity and approximate circular orbit condition, the new gravitation is equivalent to the General Relativity. The four classic experimental tests, the deflection of light by the sun, the precession of mercury, the red shift of light by the sun, the radar echo delay, are experimental tests to the new gravitation also. But even under approximate weak gravity condition, if the orbit is not approximate circular, if the orbit has higher eccentricity, there exists obvious difference between the General Relativity and the new gravitation. This difference can be a experimental test to distinguish which one is more realistic. The space-time is flat in the new gravitation, not is curved. In the new gravitation, the energy is conserved. The new gravitation is simpler than the General Relativity. In the new gravitation, the photon’s equivalent gravitational acceleration is twice of the acceleration in Newton Gravitation. In the new gravitation, there not exists black hole, but exists empty hole, and not exists space-time singularity and energy singularity. The new gravity has obvious scale effect. The new gravity has the scale factor. In gravity field, the scale factor determines the quantization results of particle’s motion. The new gravity perhaps is a force that inhibits the uncertainty of macroscopic objects. The new gravitation can derive out the result of the Planck Energy.
]]> <![CDATA[Projection Gravitation, a Projection Force from 5-Dimensional Space-Time Into 4-Dimensional Space-Time]]>
http://viXra.org/abs/1710.0172
2017-10-17 05:55:47Quantum Gravity and String Theory reference: viXra:1710.0172v1 title: Projection Gravitation, a Projection Force from 5-Dimensional Space-Time Into 4-Dimensional Space-Time authors: XiaoLin Li category: Quantum Gravity and String Theory type: submission date: 2017-10-17 05:55:47 abstract:
A new gravity theory. Gravity is a projection force from 5-dimensional space-time into 4-dimensional space-time. The Lorentz symmetry is a projection of particle-wave symmetry from 5-dimensional space-time into 4-dimensional space-time. The gravity is an additional projection force of Lorentz symmetry. The new gravity is an extension to Lorentz symmetry. The new gravity can be seen as some kind of symmetry. Gravity only exists in 4-dimensional space-time. In 5-dimensional space-time, there not have gravity. Equivalence principle is invalid in the new gravitation. In the new gravitation, there does not have gravitational acceleration. In the new gravitation, there only have inertial coordinates, not have non-inertial coordinates. In the new gravitation, the gravity source is only the rest mass, not energy. The particle can’t be the gravity source if the particle not has rest mass. The photon not has gravity. But any particle can be affected by gravity. The photon is affected by gravity also. The gravitational mass is only equivalent to the rest mass. Under approximate weak gravity and approximate circular orbit condition, the new gravitation is equivalent to the General Relativity. The four classic experimental tests, the deflection of light by the sun, the precession of mercury, the red shift of light by the sun, the radar echo delay, are experimental tests to the new gravitation also. But even under approximate weak gravity condition, if the orbit is not approximate circular, if the orbit has higher eccentricity, there exists obvious difference between the General Relativity and the new gravitation. This difference can be a experimental test to distinguish which one is more realistic. The space-time is flat in the new gravitation, not is curved. In the new gravitation, the energy is conserved. The new gravitation is simpler than the General Relativity. In the new gravitation, the photon’s equivalent gravitational acceleration is twice of the acceleration in Newton Gravitation. In the new gravitation, there not exists black hole, but exists empty hole, and not exists space-time singularity and energy singularity. The new gravity has obvious scale effect. The new gravity has the scale factor. In gravity field, the scale factor determines the quantization results of particle’s motion. The new gravity perhaps is a force that inhibits the uncertainty of macroscopic objects.
]]> <![CDATA[Quantum Simulator of Plant Metabolism]]>
http://viXra.org/abs/1710.0171
2017-10-17 09:09:35Quantum Physics reference: viXra:1710.0171v1 title: Quantum Simulator of Plant Metabolism authors: George Rajna category: Quantum Physics type: submission date: 2017-10-17 09:09:35 abstract:
A quantum simulator is the preliminary stage of a quantum computer. [25] By finding materials that act in ways similar to the mechanisms that biology uses to retain and process information, scientists hope to find clues to help us build smarter computers. [25] Scientists have made a crucial step towards unlocking the "holy grail" of computing-microchips that mimic the way the human brain works to store and process information. [24] Considerable interest in new single-photon detector technologies has been scaling in this past decade. [23] Engineers develop key mathematical formula for driving quantum experiments. [22] Physicists are developing quantum simulators, to help solve problems that are beyond the reach of conventional computers. [21] Engineers at Australia's University of New South Wales have invented a radical new architecture for quantum computing, based on novel 'flip-flop qubits', that promises to make the large-scale manufacture of quantum chips dramatically cheaper-and easier-than thought possible. [20] A team of researchers from the U.S. and Italy has built a quantum memory device that is approximately 1000 times smaller than similar devices— small enough to install on a chip. [19] The cutting edge of data storage research is working at the level of individual atoms and molecules, representing the ultimate limit of technological miniaturisation. [18] This is an important clue for our theoretical understanding of optically controlled magnetic data storage media. [17] A crystalline material that changes shape in response to light could form the heart of novel light-activated devices. [16]
]]> <![CDATA[A Solution of the Fermat Conjecture]]>
http://viXra.org/abs/1710.0170
2017-10-17 09:12:45Number Theory reference: viXra:1710.0170v1 title: A Solution of the Fermat Conjecture authors: José Francisco García Juliá category: Number Theory type: submission date: 2017-10-17 09:12:45 abstract:
It is obtained a solution of the Fermat conjecture.
]]> <![CDATA[Prime Set Representation]]>
http://viXra.org/abs/1710.0169
2017-10-17 09:44:37Number Theory reference: viXra:1710.0169v1 title: Prime Set Representation authors: Steven Shawcross category: Number Theory type: submission date: 2017-10-17 09:44:37 abstract:
The integer 2 satisfies the divisibility definition of a prime number: it is only divisible by itself and 1. The integer 1 also satisfies this definition, and yet, mathematicians generally do not consider 1 a prime. Rather 1 merits a class of its own, belonging neither to the prime nor composite class. In divisibility theory, 2 does occupy a special subclass within the class of prime numbers: it is the only even prime. This paper introduces a theory of numbers called the Prime Set Representation Theory. This theory utilizes the odd primes and does not rely on the primeness of 2. In Prime Set Representation Theory, the odd primes are building blocks of the theory; all integers, including 2, have representations in terms of them. The import of the theory is not to dislodge the integer 2 from its solitary, even-prime status. The theory's efficacy is a better understanding of the distribution of primes, twin primes, and primes of the form x^2 + 1. A natural extension of the theory yields valid and strikingly direct approximation formulas for these prime classifications. The same theory furnishes a new and improved approximation to the number of Goldbach pairs associated with general even number 2n (the improvement is relative to Sylvester's formula for Goldbach pairs, but the formula performs well vis-à-vis the Hardy-Littlewood formulas in the ranges tested).
]]>