**Previous months:**

2007 - 0703(2)

2008 - 0812(1)

2009 - 0907(1) - 0908(3) - 0909(1) - 0910(2)

2010 - 1001(3) - 1002(1) - 1003(1) - 1006(13) - 1007(2) - 1009(2) - 1010(3) - 1011(1) - 1012(5)

2011 - 1101(4) - 1102(4) - 1103(3) - 1104(1) - 1105(3) - 1106(2) - 1107(2) - 1108(4) - 1109(2) - 1110(1) - 1111(10) - 1112(2)

2012 - 1201(3) - 1202(2) - 1203(6) - 1204(3) - 1205(5) - 1206(8) - 1207(4) - 1208(4) - 1209(2) - 1210(2) - 1211(4) - 1212(7)

2013 - 1301(8) - 1302(7) - 1303(7) - 1304(5) - 1305(27) - 1306(6) - 1307(8) - 1308(7) - 1309(7) - 1310(9) - 1311(12) - 1312(2)

2014 - 1401(11) - 1402(8) - 1403(16) - 1404(12) - 1405(8) - 1406(6) - 1407(4) - 1408(9) - 1409(8) - 1410(6) - 1411(7) - 1412(8)

2015 - 1501(11) - 1502(11) - 1503(9) - 1504(10) - 1505(12) - 1506(8) - 1507(8) - 1508(10) - 1509(4) - 1510(19) - 1511(11) - 1512(8)

2016 - 1601(6) - 1602(9) - 1603(9) - 1604(6) - 1605(14) - 1606(11) - 1607(6) - 1608(13) - 1609(17) - 1610(18) - 1611(6) - 1612(23)

2017 - 1701(9) - 1702(9) - 1703(5) - 1704(11) - 1705(20) - 1706(8) - 1707(14)

Any replacements are listed further down

[652] **viXra:1707.0296 [pdf]**
*submitted on 2017-07-22 15:52:25*

**Authors:** Sayan Nag

**Comments:** 6 Pages.

“Art attracts us only by what it reveals of our most secret self.”- Alfred North Whitehead
The basic building blocks upon which the natural world is built are Fractals. Recognizing these patterns in Nature is essential-because of these patterns Nature is so aesthetically pleasing. We try to find these patterns everywhere instinctively. In our work we look forward to find the fractality in Abstract art-the paintings of the renowned artist Jackson Pollock using a novel approach of 2D-Multifractal Detrended Fluctuation Analysis in his paintings.

**Category:** Mathematical Physics

[651] **viXra:1707.0284 [pdf]**
*submitted on 2017-07-21 09:18:46*

**Authors:** Jean-Luc Paillet, Andrew Meulenberg

**Comments:** 12 Pages. Submitted to 12th Intern. Workshop on Anomalies in Hydrogen Loaded Metal.

In previous works, we analyzed and countered arguments against the deep orbits, as discussed in
published solutions. Moreover, we revealed the essential role of Special Relativity as source of electron deep orbits (EDOs). We also showed, from a well-known analytic method of solution of the Dirac equation, that the obtained EDOs have a positive energy. When including the magnetic interactions near the nucleus, we observed a
breakthrough in how to satisfy the Heisenberg Uncertainty Relation (HUR) for electrons confined near the nucleus, in a radial zone of only a few fm. Here we chose a different method, by directly facing the HUR for such confined electrons, from which we deduce the coefficient γ of these highly relativistic electrons. Then we show the effective Coulomb potential due to a relativistic correction, can maintain the electrons in containment. Next we resume and deepen our study of the effects of EM interactions near the nucleus. We first obtain computation
results: though approximate, we can effectively expect high-energy resonances near the nucleus. These results should be confirmed by using QFT-based methods.

**Category:** Mathematical Physics

[650] **viXra:1707.0266 [pdf]**
*submitted on 2017-07-20 05:11:07*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 4 Pages. This paper has not been submitted to a journal. Your comments are welcome

In recent years, there are several proposals of using MHD theory for clean power generators on top of coal plant. But the theory involved appears too complicated, so in this paper we will use a simpler approach using ideal MHD equations which then they can be reduced to a system of coupled quaternionic Riccati equations. Further numerical and experimental investigations are advisable.

**Category:** Mathematical Physics

[649] **viXra:1707.0216 [pdf]**
*submitted on 2017-07-15 19:08:22*

**Authors:** Tracy Klein

**Comments:** 9 Pages.

The following manuscript establishes the role of dialectical forces in our physical universe.
The dialectical relationship links opposing theories of quantum mechanics and bridges the gap
between quantum physics and general relativity.

**Category:** Mathematical Physics

[648] **viXra:1707.0214 [pdf]**
*submitted on 2017-07-15 12:13:56*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 3 Pages.

Advance superstrings are consider incalculable particles. With this in mind a more refine definition of the grand unification and metaspace is presented.

**Category:** Mathematical Physics

[647] **viXra:1707.0195 [pdf]**
*submitted on 2017-07-14 03:38:22*

**Authors:** Paris Samuel Miles-Brenden

**Comments:** 10 Pages. The laws of physics in their abstraction are blind to the world.

The laws of physics in their abstraction are blind to the world.

**Category:** Mathematical Physics

[646] **viXra:1707.0193 [pdf]**
*submitted on 2017-07-13 13:33:10*

**Authors:** William O. Straub

**Comments:** 3 Pages.

An intriguing connection between some work of Oswald Veblen with that of Hermann Weyl is presented.

**Category:** Mathematical Physics

[645] **viXra:1707.0144 [pdf]**
*submitted on 2017-07-11 03:13:02*

**Authors:** John Peel

**Comments:** 35 Pages. Part 1 of two files regarding information fields

The role of geometry in particle physics

**Category:** Mathematical Physics

[644] **viXra:1707.0129 [pdf]**
*submitted on 2017-07-09 21:31:05*

**Authors:** John Peel

**Comments:** 72 Pages. Perhaps important

This paper hopes to clarify the notion of Information Fields and the role of geometry in particle physics.

**Category:** Mathematical Physics

[643] **viXra:1707.0128 [pdf]**
*submitted on 2017-07-09 22:59:57*

**Authors:** Jack Bidnik

**Comments:** 13 Pages.

Abstract:
This paper explains my derivation of a number of equations to describe gravitational forces from the relativistic relative momentum of Albert Einstein's Special Relativity. One of these equations parallels Issac Newton's Gravitational Equation by replacing the Gravitational Constant, G, with a velocity dependent expression. The resulting equation is applied to the orbital parameters of the planets and a number of their moons, with very close results. The forces derived have applications in other areas of physics, including electromagnetic force, and have some surprising properties hitherto unknown in physics. I derive these results with no external forces assumed to be present, so that the only mechanical force here must be gravity.

**Category:** Mathematical Physics

[642] **viXra:1707.0109 [pdf]**
*submitted on 2017-07-07 10:28:47*

**Authors:** Ehsan Azadi

**Comments:** 28 pages

In this article, we give a general exact mathematical framework that all of the fundamental relations and conservation equations in continuum mechanics can be derived based on it. We consider a general integral equation contains the parameters that act on the volume and the surface of the integral's domain. The idea is to determine how many local relations can be derived from this general integral equation and what these local relations are? Thus, we first derive the general Cauchy lemma and then by a new general exact tetrahedron argument derive two other local relations. So, there are three local relations that can be derived from the general integral equation. Then we show that all of the fundamental laws in continuum mechanics, include the conservation of mass, linear momentum, angular momentum, energy, and the entropy law, can be shown and considered in this general framework. So, we derive the integral form of these fundamental laws in this framework and applying the general three local relations lead to exactly derivation of the mass flow, continuity equation, Cauchy lemma for traction vectors, existence of stress tensor, general equation of motion, symmetry of stress tensor, existence of heat flux vector, differential energy equation, and differential form of the Clausius-Duhem inequality for entropy law.
The general exact tetrahedron argument is an exact proof that removes all of the challenges on the derivation of fundamental relations in continuum mechanics. During this proof, there is no approximating or limiting process and the parameters are exact point-base functions. Also, it gives a new understanding and a deep insight into the origins and the physics and mathematics of the fundamental relations and conservation equations in continuum mechanics. This general mathematical framework can be used in many branches of continuum physics and the other sciences.

**Category:** Mathematical Physics

[641] **viXra:1707.0106 [pdf]**
*submitted on 2017-07-06 13:56:20*

**Authors:** Ehsan Azadi

**Comments:** 34 pages

Cauchy in 1822 presented the idea of traction vector that contains both the normal and tangential components of the internal surface forces per unit area and gave the tetrahedron argument to prove the existence of stress tensor. These great achievements form the main part of the foundation of continuum mechanics. During nearly two centuries, some versions of tetrahedron argument and a few other proofs for the existence of stress tensor are presented in every text in continuum mechanics, fluid mechanics, and the related subjects. In this article, we show the birth, importance, and location of these Cauchy's achievements, then by presenting the formal tetrahedron argument in detail, for the first time we extract some fundamental challenges. These conceptual challenges are related to the result of applying the conservation of linear momentum to any mass element and the order of its surface and volume terms, the definition of traction vectors on the surfaces that pass through the same point, the limiting and approximating processes in the derivation of stress tensor, and some others. In a comprehensive review, we present the different tetrahedron arguments and the proofs for the existence of stress tensor, consider the challenges in each one, and classify them in two general approaches. In the first approach that is followed in most texts, the traction vectors do not define exactly on the surfaces that pass through the same point so, most of the challenges hold. But in the second approach, the traction vectors are defined on the surfaces that pass exactly through the same point, so some of the related challenges are removed. We also represent the improved works of Hamel and Backus, and show that the original work of Backus removes most of the challenges. This article shows that the foundation of continuum mechanics is not a finished subject and there are still some fundamental challenges.

**Category:** Mathematical Physics

[640] **viXra:1707.0022 [pdf]**
*submitted on 2017-07-02 10:02:30*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 10 Pages. This paper has not been submitted to a journal

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details.

**Category:** Mathematical Physics

[639] **viXra:1706.0572 [pdf]**
*submitted on 2017-06-30 11:04:20*

**Authors:** Gary D. Simpson

**Comments:** 11 Pages.

This text continues the development of pentuples begun in Part – 2 of these works. Matrix formulations are presented that are easily inverted. The presentation of a pentuple is similar to the form of a quaternion. A functionality is presented in Equation 4.2 that mimics wave-function collapse. Octonion multiplication is shown to be very similar irrespective of whether the complex i commutes normally or anti-commutes.

**Category:** Mathematical Physics

[638] **viXra:1706.0456 [pdf]**
*submitted on 2017-06-23 18:05:12*

**Authors:** Mauro Bernardini

**Comments:** 44 Pages. Comment (Abstract) replacement

This is a brief summary of the Theory of Transcendent Reality (TTR), which describes the main postulates and mathematics used to describe and support the rationality of the Alef's model as unique and absolute being container of all the existences. This first issiue allow to describe the real physical composition of all the parallel universes contained in Alef's body. Universes that are logically and rationally constituted exclusively by Particles of Existence with a mass equal to that of a Proton and which generate an "apparent" existence since they are interpreted as existent only by the under-dimensional beings they generate in each single universe. Highlighting therefore that the Particles of Existence present in every universe are in fact 11 dimensional body slices of the Points of Alef, which, in turn, are the only real components of Alef's body: and, therefore, Particles of Existence that never really born nor died.

**Category:** Mathematical Physics

[637] **viXra:1706.0416 [pdf]**
*submitted on 2017-06-21 09:12:37*

**Authors:** Miroslav Josipović

**Comments:** 1 Page.

There is an erroneous formula in the article Functions of multivectors in 3D Euclidean geometric algebra via spectral decomposition (for physicists and engineers).

**Category:** Mathematical Physics

[636] **viXra:1706.0193 [pdf]**
*submitted on 2017-06-15 01:41:20*

**Authors:** A. A. Frempong

**Comments:** 19 Pages. Copyright © by A. A. Frempong

Coincidences. The US Supreme Court consists of nine members, one of whom is the Chief Justice of the Court. So also, a one-direction Navier-Stokes equation consists of nine members, one of which is the indispensable gravity term, without which there would be no incompressible fluid flow as shown by the solutions of the N-S equations (viXra:1512.0334). Another coincidence is that numerologically, the number, 9, is equivalent to the 1800's (1 + 8 + 0 + 0 = 9) time period during which the number of the members of the Supreme Court became fixed at 9, while the formulation of the nine-term N-S equations was completed. Another coincidence is that the solutions of the N-S equations were completed (viXra:1512.0334) by the author in the year, 2016 (2 + 0 +1+ 6 = 9). Using a new introductory approach, this paper covers the author's previous solutions of the N-S equations (viXra:1512.0334). In particular, the N-S solutions have been compared to the equations of motion and liquid pressure of elementary physics. The N-S solutions are (except for the constants involved) very similar or identical to the equations of motion and liquid pressure of elementary physics. The results of the comparative analysis show that the N--S equations have been properly solved. It could be stated that the solutions of the N-S equations have existed since the time the equations of motion and liquid pressure of elementary physics were derived. A one-direction Navier-Stokes equation has also been derived from the equations of motion and liquid pressure of elementary physics. Insights into the solutions include how the polynomial parabolas, the radical parabolas, and the hyperbolas interact to produce turbulent flow. It is argued that the solutions and methods of solving the N-S equations are unique, and that only the approach by the author will ever produce solutions to the N-S equations. By a solution, the equation must be properly integrated and the integration results must be tested in the original equation for identity before the integration results are claimed as solutions

**Category:** Mathematical Physics

[635] **viXra:1706.0189 [pdf]**
*submitted on 2017-06-15 03:48:11*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 6 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Normalized Similarity Measure considered to Exhaustion [1] (please see the addendum of [1] as well).

**Category:** Mathematical Physics

[634] **viXra:1706.0137 [pdf]**
*submitted on 2017-06-09 16:04:55*

**Authors:** Marcellin Nonti, Fernando Y. J. Kpomahou, Jean Akande, Damien K. K. Adjaï, Lucas H. Koudahoun, Marc D. Monsia

**Comments:** 3 pages

Hamiltonian dynamics and exact Gibbs statistical mechanics of a system of quadratic Liénard type oscillators have been investigated. The work has shown that the canonical ensemble for the harmonic oscillator is a particular case of the Gibbs ensemble theory developed in this paper.

**Category:** Mathematical Physics

[633] **viXra:1706.0123 [pdf]**
*submitted on 2017-06-09 01:36:02*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 8 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Normalized Similarity Measure considered to Exhaustion [1] (please see the addendum of [1] as well).

**Category:** Mathematical Physics

[632] **viXra:1706.0034 [pdf]**
*submitted on 2017-06-05 02:03:41*

**Authors:** Richard L Amoroso, Georges Lemaitre

**Comments:** 13 Pages. Lemaitre's 1948 paper translated from original French, ACTA, Vol. XII, No. 8, pp. 57-80

The author applies the notion of quaternions, as practiced by Klein in the Erlangen program, to determine the fundamental
properties of elliptical space.

**Category:** Mathematical Physics

[631] **viXra:1705.0470 [pdf]**
*submitted on 2017-05-31 08:41:13*

**Authors:** Renzun Lian

**Comments:** 20 Pages.

In the Part I of Line-Surface formulation of the ElectroMagnetic-Power-based Characteristic Mode Theory for Metal-Material combined objects (LS-MM-EMP-CMT), the relevant fundamental principle had been established, and some very valuable complements and improvements are done in this Part II.
In this Part II, the traditional surface equivalent principle for a homogeneous material body whose boundary is only constructed by a closed surface is generalized to the line-surface equivalent principle of a homogeneous material body whose boundary can include some lines and open surfaces besides a closed surface; a new line-surface formulation of the input/output power operator for metal-material combined objects is given, and the new formulation is more advantageous than the formulation given in Part I; some more detailed formulations for establishing LS-MM-EMP-CMT are explicitly provided here, such as the formulations corresponding to the decompositions for currents and their domains and the formulations corresponding to variable unification.
In addition, a new concept intrinsic resonance is introduced in this paper, and then a new Characteristic Mode (CM) set, intrinsic resonant CM set, is introduced into the EMP-CMT family.

**Category:** Mathematical Physics

[630] **viXra:1705.0374 [pdf]**
*submitted on 2017-05-25 20:55:10*

**Authors:** Zihao Song

**Comments:** 5 Pages. If one physical quantity can't find where it is originated, it's not a good physical quantity.

Physicists are proposing different mechanics to describe the nature, physical body is measured by intrinsic properties like electric charge, and extrinsic properties being related to space like generalized coordinates or velocities etc., with these properties we can predict what event will happen. We can naturally define the fact of the event and the cause of the event as information, the information grasped by physicist must be originated from something objective, information must have its object container. Intrinsic property information is contained by object itself, but container of extrinsic property information like position is ambiguous, position is a relation based on multiple objects, it's hard to define which one is the information container. With such ambiguity, no mechanics is a complete theory, errors hidden in assumptions are hard to find. Here we show a new theoretical framework with strict information container restriction, on which we can build complete determinism theories to approach grand unification.

**Category:** Mathematical Physics

[629] **viXra:1705.0358 [pdf]**
*submitted on 2017-05-24 13:09:34*

**Authors:** Paul B. Slater

**Comments:** 35 pages, 26 figures

We investigate relationships between two forms of Hilbert-Schmidt two-re[al]bit and two-qubit "separability functions''--those recently advanced by Lovas and Andai (arXiv:1610.01410), and those earlier presented by Slater ({\it J. Phys. A} {\bf{40}} [2007] 14279). In the Lovas-Andai framework, the independent variable $\varepsilon \in [0,1]$ is the ratio $\sigma(V)$ of the singular values of the $2 \times 2$ matrix $V=D_2^{1/2} D_1^{-1/2}$ formed from the two $2 \times 2$ diagonal blocks ($D_1, D_2$) of a
randomly generated $4 \times 4$ density matrix $D$. In the Slater setting, the independent variable $\mu$ is the diagonal-entry ratio $\sqrt{\frac{d_ {11} d_ {44}}{d_ {22} d_ {33}}}$--with, importantly, $\mu=\varepsilon$ or $\mu=\frac{1}{\varepsilon}$ when both $D_1$ and $D_2$ are themselves diagonal. Lovas and Andai established that their two-rebit function $\tilde{\chi}_1 (\varepsilon )$ ($\approx \varepsilon$) yields the
previously conjectured Hilbert-Schmidt separability probability of $\frac{29}{64}$. We are able, in the Slater framework (using cylindrical algebraic decompositions [CAD] to enforce positivity constraints), to reproduce this result. Further, we similarly obtain its new (much simpler) two-qubit counterpart, $\tilde{\chi}_2(\varepsilon) =\frac{1}{3} \varepsilon ^2 \left(4-\varepsilon ^2\right)$. Verification of the companion conjecture of a Hilbert-Schmidt separability probability of $\frac{8}{33}$ immediately follows in the Lovas-Andai framework. We obtain the formulas for $\tilde{\chi}_1(\varepsilon)$ and $\tilde{\chi}_2(\varepsilon)$ by taking $D_1$ and $D_2$ to be diagonal, allowing us to proceed in lower (7 and 11), rather than the full (9 and 15) dimensions occupied by the convex sets of two-rebit and two-qubit states. The CAD's themselves involve 4 and 8 variables, in addition to $\mu=\varepsilon$. We also investigate extensions of these analyses to rebit-retrit and qubit-qutrit ($6 \times 6$) settings.

**Category:** Mathematical Physics

[628] **viXra:1705.0357 [pdf]**
*submitted on 2017-05-24 16:04:15*

**Authors:** Victor Christianto

**Comments:** 5 Pages. this paper has been submitted to MDPI - Mathematics

The problem of the formal connection between electrodynamics and wave mechanics has attracted the attention of a number of authors, especially there are some existing proofs on Maxwell-Dirac isomorphism. Here the author will review two derivations of Maxwell-Dirac isomorphism i.e. by Hans Sallhofer and Volodimir Simulik. A few plausible extensions will be discussed too.

**Category:** Mathematical Physics

[627] **viXra:1705.0347 [pdf]**
*submitted on 2017-05-24 01:33:15*

**Authors:** Preobrazhenskiy Andrey

**Comments:** 10 Pages.

ABSTRACT. This paper deals with the analysis of physically possible constructions of a viscous incompressible fluid model. Physical principles that allow to create the only possible construction of this model were found. The new model does not use new constants that characterize properties of the fluid and coincides with the Stokes model only in the plane case. Within the framework of this model, new equations for fluid motion were obtained. The new equations coincide with Navier-Stokes system in the plane case, but do not coincide in the three-dimensional one. The model makes it possible to see why the three-dimensional Navier-Stokes equations cannot physically adequately describe fluids motion, and obliquely confirms the finite time for the existence of its regular solutions.

**Category:** Mathematical Physics

[626] **viXra:1705.0330 [pdf]**
*submitted on 2017-05-22 05:15:16*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 11 Pages.

This article explores the nonlinear aspects underlying music , particularly focusing on melody. By using the concept of scale as the basis, the article explores ways to formulate and study the features and 'feature richness' of a given melody or Raga, and to do this, the Raga scale is represented as a 1-Dimensional array. The Signature graph of a Raga plotted as Interval as a function of Note position, established a graphic visualization of the Raga. The progression and trend of intervals was computed using the Second Level Interval Array. This trend graph reveals the complexity in a Raga structure, through looping, crowded and intricate curves in the graph. Next, the concept of chaos in the context of melody is explored, fundamentally by performing a sensitivity test, which analyzes that given a Raga, and a particular evolution path, how starting at two nearby Swaras results in two entirely different ending Swaras, when sampled after a certain period in time. As a measure of the complexity in a Raga, the entropy, a measure of uncertainty is proposed, and computed using the interval arrays as bases for an occurrence array yielding empirical probabilities. The entropy is seen as a measure of richness, a measure of variety of inter-Swara intervals that a given Raga possesses. One notes that Ragas with high entropy, on account of their interval richness, usually fall under the category of pleasant, appealing and melodious Ragas. These are also the Ragas one finds being employed in film music, clearly owing to their pleasant feel.

**Category:** Mathematical Physics

[625] **viXra:1705.0300 [pdf]**
*submitted on 2017-05-20 09:41:01*

**Authors:** Miroslav Josipović

**Comments:** 79 Pages.

This is translation of the article "Multiplication of Vectors and Structure of 3D Euclidean Space" to Croatian.

**Category:** Mathematical Physics

[624] **viXra:1705.0274 [pdf]**
*submitted on 2017-05-18 09:56:01*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 46 Pages.

Using the cogito ergo sum as a starting point, I introduce a methodology which allows non-trivial knowledge to be obtained without the formal introduction of axioms. Using this methodology which I formalize, I then obtain a theory of everything (ToE) in physics. This method allows me to avoid the self-referential problem of a ToE which I argue is the core difficulty of any ToE built upon formal axioms. The theory obtained has enough generality to recover both general relativity and quantum field theory. Some of the new physics derived herein include a hard arrow time, an explanation of the quantum mechanical measurement, and a thermodynamic proof that the speed of light is maximal.

**Category:** Mathematical Physics

[623] **viXra:1705.0262 [pdf]**
*submitted on 2017-05-18 03:29:30*

**Authors:** D. K. K. Adjaï, L. H. Koudahoun, J. Akande, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 11 Pages. 1-11

This paper slightly extends the theory of exact trigonometric periodic solutions to quadratic
Liénard type equations introduced earlier by the authors of the present contribution. The
extended theory is used to determine the general periodic solutions to the Duﬃng equation and to some Painlevé-Gambier equations as illustrative examples. Finally the mathematical equivalence between the Duﬃng equation and the Painlevé-Gambier XIX equation has been highlighted by means of the proposed extended theory.

**Category:** Mathematical Physics

[622] **viXra:1705.0261 [pdf]**
*submitted on 2017-05-18 03:29:03*

**Authors:** Zhi Cheng

**Comments:** 14 Pages. Include Chinese version

In this paper, we propose a concept of vector complex function to prove that the whole world can be reduced to a very simple function f(Z) = F + iG by introducing the knowledge of complex function theories. We can also derive Maxwell equations through the differential and integral analysis of the vector complex function.

**Category:** Mathematical Physics

[621] **viXra:1705.0251 [pdf]**
*submitted on 2017-05-16 19:11:11*

**Authors:** Victor Christianto

**Comments:** 39 Pages. This paper has not been submitted to a journal

The present book consists of 6 papers that I and some colleagues developed throughout the last 3-4 years. The subjects discussed cover wireless energy transmission, soliton model of DNA, cosmology, and also solutions of Navier-Stokes equations both in 2D and 3D.
Some additional graphical plots for solution of 3D Navier-Stokes equations are also given. Hopefully the readers will find these papers at least interesting to ponder.

**Category:** Mathematical Physics

[620] **viXra:1705.0212 [pdf]**
*submitted on 2017-05-14 02:26:57*

**Authors:** Sjaak Uitterdijk

**Comments:** 3 Pages.

Showing that the Special Theory of Relativity is an untenable theory, many times leads to the reaction that the GPS is so accurate thanks to the STR corrections. This article shows that the supposed relativity errors are by far negligible relative to the errors caused by atmospheric circumstances.

**Category:** Mathematical Physics

[619] **viXra:1705.0203 [pdf]**
*submitted on 2017-05-12 22:53:16*

**Authors:** ShengYu.Shu

**Comments:** 62 Pages.

I have mainly analyzed the mathematical meaning of non-classical mathematical theory for three fundamental physics equations - Maxwell’s equations, Dirac’s equations, Einstein’s equations from the quantized core theory of ancient China’s Taoism, and found they have some structures described in the core of the theory of ancient China’s Taoism, especially they all obviously own the yin-yang induction structure. This reveals the relations between the ancient China’s Taoism and modern mathematics and physics in a way, which may help us to understand some problems of the fundamental theory of physics.

**Category:** Mathematical Physics

[618] **viXra:1705.0133 [pdf]**
*submitted on 2017-05-08 07:55:21*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 2 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Similarity Measure considered to Exhaustion [1].

**Category:** Mathematical Physics

[617] **viXra:1705.0104 [pdf]**
*submitted on 2017-05-04 12:18:15*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 4 Pages.

In this research investigation, the author has presented a Recursive Past Equation based on the Ananda-Damyanthi Similarity Measure [1]. Also, in this research investigation, the author has presented a Recursive Future Equation based on the Ananda-Damyanthi Similarity Measure [1].

**Category:** Mathematical Physics

[616] **viXra:1705.0095 [pdf]**
*submitted on 2017-05-03 22:01:08*

**Authors:** John Peel

**Comments:** 6 Pages. The sets at the end are important

Calculating certain aspects of geometry has been difficult. They have defied analytics. Here I propose a
method of analysing shape and space in terms of two variables (n,m).

**Category:** Mathematical Physics

[615] **viXra:1705.0091 [pdf]**
*submitted on 2017-05-04 06:15:57*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 2 Pages.

The author has presented a Recursive Future Equation

**Category:** Mathematical Physics

[614] **viXra:1705.0035 [pdf]**
*submitted on 2017-05-03 09:46:41*

**Authors:** Victor Christianto, Sergey Ershkov

**Comments:** 7 Pages. This paper has not been submitted to a journal

In a recent paper, Ershkov derived a system of two coupled Riccati ODEs as solution of non-stationary incompressible 3D Navier-Stokes equations. Now in this paper, we solve these coupled Riccati ODEs using: a) Maxima and b) Mathematica 11 computer algebra packages. The result seems to deserve further investigation in particular in comparison with rigid body motion, which will be discussed elsewhere.

**Category:** Mathematical Physics

[613] **viXra:1705.0012 [pdf]**
*submitted on 2017-05-01 22:52:24*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 3 Pages.

In this research manuscript, the author has presented a Recursive Equation Connecting Future And Past

**Category:** Mathematical Physics

[612] **viXra:1705.0011 [pdf]**
*submitted on 2017-05-01 23:45:14*

**Authors:** Richard L. Amoroso

**Comments:** 14 Pages. Version to be published in 10th proceedings honoring mathematical physicist Jean-Pierre Vigier by World Scientific

Ontological-Phase Topological Field Theory (OPTFT) under seminal development to formally describe 3rd regime Unified Field Mechanics (UFM) (classical-Quantum-UFM) is extended to relate the duality of Newton-Einstein gravitation theory by added degrees of freedom in a semi-quantum limit enabling insight into topological Dirac-Majorana doublet fusion supervening the uncertainty principle.

**Category:** Mathematical Physics

[611] **viXra:1704.0396 [pdf]**
*submitted on 2017-04-30 05:48:03*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 1 Page.

In this research manuscript, the author has presented a Recursive Future Equation.

**Category:** Mathematical Physics

[610] **viXra:1704.0320 [pdf]**
*submitted on 2017-04-24 08:43:53*

**Authors:** Yakov A. Iosilevskii

**Comments:** 72 pages

This exposition has the following main objects in view. (1) All main depth-integrated time-dependent and time-averaged characteristics, – as the velocity potential, velocity, pressure, momentum flux density tensor, volumetric kinetic, potential, and total energies, Poynting (energy flux density) vector, radiation (wave) stress tensor, etc, – of the ideal (inviscid, incompressible, and irrotational) fluid flow in an imaginary wave-perturbed infinite water layer with an arbitrary shaped bed and with a free upper boundary surface, and also the pertinent depth-integrated time-dependent and time-averaged differential continuity equations, – as those of the mass density, energy density, and momentum flux density (Euler’s and Bernoulli’s equations), etc, – are rigorously deduced from the respective basic local (bulk and surface) characteristics and from the respective bulk continuity equations, with allowance for the corresponding exact kinematic boundary conditions at the upper (free) and bottom surfaces and also with allowance for the corresponding exact dynamic boundary condition at the free surface, which follows from the basic Bernoulli equation. (2) The recursive asymptotic perturbation method with respect to powers of ka that has been developed recently by the present author for the local characteristics and bulk continuity equations of the ideal fluid flow in the presence of a priming (seeding) progressive, or standing, monochromatic gravity water wave (PPPMGWW or PSPMGWW) of a wave number k>0 and of wave amplitude a>0 in an imaginary infinite water layer of a uniform depth d>0 is extended to flow’s momentary and time-averaged (TA), depth-integrated (DI) characteristics and to their continuity equations, particularly to the 3x3 radiation, or wave, stress tensor (RST). (3) The extended recursive method is applied to PPPMGWW’s and PSPMGWW’s with the purpose to obtain their main TADI characteristics in terms of elementary functions. (4) The first non-vanishing asymptotic approximation of a characteristic, particularly that of the 3x3-TADIRST, of a PPPMGWW or PSPMGWW is generalized to a priming progressive, or standing, quasi-pane (PPQP or PSQP) MGWW. (5) The longshore wave–induced sediment transport rate, expressed by the so-called CERC (Coastal Engineering Research Council) formula, is briefly discussed in its relation to the (x,y)-component of the 3x3-TADIRST of the pertinent PPQPMGWW. (6) The presently common 2x2-TADIRST’s of progressive and standing water waves, which have been deduced by various writers from intuitive considerations and have been canonized about 55 years ago, are revised in accordance with the 3x3 ones of the recursive asymptotic theory.

**Category:** Mathematical Physics

[609] **viXra:1704.0264 [pdf]**
*submitted on 2017-04-20 18:59:25*

**Authors:** Paul J. Werbos

**Comments:** 15 pages, 36 equations, 34 references

Today’s standard model of physics treats the physical masses of elementary particles as given, and assumes that they have a bare radius of zero, as in the older classical physics of Lorentz. Many physicists have studied the properties of the Yang-Mills-Higgs model of continuous fields in hopes that it might help to explain where elementary particles (and their masses) come from in the first place. This paper reviews some of the important prior work on Yang-Mills-Higgs and solitons in general, but it also shows that stable particles in that model cannot have intrinsic angular momentum (spin). It specifies four extensions of Yang-Mills Higgs, the Lagrangians L1 through L4, which are closer to the standard model of physics, and shows that one of the four (L3) does predict/explain spin from a purely neoclassical theory. The paper begins by summarizing the larger framework which has inspired this work, and ends by discussing two possibilities for further refinement.

**Category:** Mathematical Physics

[608] **viXra:1704.0223 [pdf]**
*submitted on 2017-04-17 17:50:17*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 2 Pages.

Define and explain Incalculability.

**Category:** Mathematical Physics

[607] **viXra:1704.0199 [pdf]**
*submitted on 2017-04-15 08:20:18*

**Authors:** J. Akande, D.K.K. Adjaï, L.H. Koudahoun, Y.J.F. Kpomahou, M.D. Monsia

**Comments:** 16 Pages. 1-16

The problem of finding exact trigonometric periodic solutions to non-linear differential equations is still an open mathematical research field. In this paper it is shown that the inverted Painlevé-Gambier XVIII equation and other quadratic Liénard type equations may exhibit trigonometric functions as exact periodic solutions but with amplitude-dependent frequency. Other inverted Painlevé-Gambier equations are shown to admit exact periodic solutions.

**Category:** Mathematical Physics

[606] **viXra:1704.0157 [pdf]**
*submitted on 2017-04-12 08:50:23*

**Authors:** Valery B. Smolensky

**Comments:** 3 Pages.

The article, according to the author, sheds new light on the nature of PI. The original output of PI as a function of States of nature.

**Category:** Mathematical Physics

[605] **viXra:1704.0135 [pdf]**
*submitted on 2017-04-11 08:21:43*

**Authors:** Yakov A. Iosilevskii

**Comments:** 137 pages

It is shown with complete logical and mathematical rigor that under the appropriate hypotheses of analytical extension and of asymptotic matching, which are stated in the article, the nonlinear problem of irrotational and incompressible gravity waves on an infinite water layer of a constant depth d reduces to an infinite recursive sequence of linear two-plane boundary value problems for a harmonic velocity potential with respect to powers of a dimensionless real-valued scaling parameter ‘ka’, where k>0 is the wave number and a>0 the amplitude of a priming (seeding) progressive, or standing, plane monochromatic gravity water wave (briefly PPPMGWW or PSPMGWW respectively). The method, by which the given nonlinear water wave problem is treated in the exposition from scratch, can be regarded as a peculiar instance of the general perturbation method, which is known as the Liouville-Green (LG) method in mathematics and as the Wentzel-Kramers-Brillouin (WKB) method in physics. In the framework of the recursive theory developed, the velocity potential and any bulk or surface measurable characteristic of the wave motion is represented by an infinite asymptotic power series with respect to ‘ka’, whose all coefficients are expressed in quadratures in accordance with a well-established an algorithm for their successive calculation. The theory developed applies particularly in the case where the depth d is taken to infinity. Besides the priming velocity potential of the first, linear asymptotic approximation in ka, the partial velocity potential and all relevant characteristics of wave motion of the second order with respect to ka are calculated in terms of elementary functions both in the case of a PPPMGWW and in the case of a PSPMGWW. Accordingly, the recursive theory incorporates the conventional Airy (linear) theory of water waves linear as its first non-vanishing approximation with the following proviso. In the Airy theory, the boundary condition at the perturbed free (upper) surface of a water layer is paradoxically stated at the equilibrium plane z=0, in spite of the fact that at any instant of time some part of the plane is necessarily located in air or in vacuum, and not in water. This and also a similar paradox arising in computing the time averages of bulk characteristics at spatial points close to the perturbed free surface are solved in the article.

**Category:** Mathematical Physics

[604] **viXra:1704.0108 [pdf]**
*submitted on 2017-04-08 14:03:01*

**Authors:** Frederick Ira Moxley III

**Comments:** 9 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture.

**Category:** Mathematical Physics

[603] **viXra:1704.0080 [pdf]**
*submitted on 2017-04-06 17:43:13*

**Authors:** Gregory Natanson

**Comments:** 48 Pages.

The paper presents the uniform technique for constructing SUSY ladders of rational canonical Sturm-Liouville equations (RCSLEs) conditionally exactly quantized by Gauss-seed (GS) Heine polynomials. Each ladder starts from the RCSLE exactly quantized by classical Jacobi, generalized Laguerre or Romanovski-Routh polynomials. We then use its nodeless almost everywhere holomorphic (AEH) solutions formed by the appropriate set of non-orthogonal polynomials to construct multi-step rational SUSY partners of the given Liouville potential on the line. It was proven that eigenfunctions of each RCSLE in the ladder have an AEH form, namely, each eigenfunction can be represented as a weighted polynomial fraction (PFrs), with both numerator and denominator remaining finite at the common singular points of all the RCSLEs in the given ladder. As a result both polynomials satisfy the second-order differential equations of Heine type.

**Category:** Mathematical Physics

[602] **viXra:1704.0064 [pdf]**
*submitted on 2017-04-05 11:34:03*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 6 Pages.

A brief draft respect to a problem found in the equations of Euler and Navier-Stokes, whose adequate treatment solves a centennial problem about the solution of these equations and a most correct modeling of fluid movement.

**Category:** Mathematical Physics

[601] **viXra:1704.0018 [pdf]**
*submitted on 2017-04-03 04:36:13*

**Authors:** Andrej Liptaj

**Comments:** 7 Pages.

Results of perturbative calculations in quantum physics have the form of truncated power series in a coupling constant. In order to evaluate the uncertainty of such results, the power series of the inverse function are constructed. These are inverted and the difference between the outcome of this procedure and the initial power series is taken as uncertainty.

**Category:** Mathematical Physics

[600] **viXra:1703.0282 [pdf]**
*submitted on 2017-03-29 15:51:34*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 10 Pages.

Given an adiabatic system of particles as defined in [4], the problem is whether and to what degree one can break it into its constituents and describe their mutual interaction.

**Category:** Mathematical Physics

[599] **viXra:1703.0274 [pdf]**
*submitted on 2017-03-28 13:29:37*

**Authors:** DT Froedge

**Comments:** 16 Pages. This work is based in Geometrical or Clifford Algebra

This paper will focus on a Geometric Algebra model of an electron illustrating the physical properties including the source of the charge. It will be shown that a particle such as an electron can be modeled as a pair of interaction photons bound in circular motion by their own interaction vectors, and having a Lorentz Scalar rest mass. This model is not QM, and does not have a probability interpretation, but rather it is defined in terms of an electromagnetic gauge. The notation used here is generally Feynman Slash [2] and the conventions are those of Doran, Lasenby [3].

**Category:** Mathematical Physics

[598] **viXra:1703.0259 [pdf]**
*submitted on 2017-03-27 07:52:41*

**Authors:** V.A.Budarin

**Comments:** 13 Pages. Incompressible viscous fluids, pdf

The object of research is obtaining general integrals and some particular solutions for two common flow conditions of incompressible liquid – laminar and averaged turbulent flow. Mathematical description is based on the system of equations of motion in stresses (Navier) and its special case for the Newtonian liquid. A condition of integrating the equations is the constancy of pressure drop and viscosity along the flow. The block schemes of obtaining the general integrals for flow in a pipe and turbulent flow on a plate are represented.
Are as a result, three new general integrals and four particular solutions, which are compared with the known equations, were found. It was shown that the integrals of the Navier equation describe the distribution of tangential stress for turbulent flow. An analysis of solutions for the distribution of velocity showed that the Poiseuille equation for laminar flow in a pipe and the Blasius curve for laminar flow on a plate are particular solutions of one general integral. An analysis of the particular solutions made it possible to estimate the thickness of the laminar sublayer under turbulent flow condition. The results of the work create prerequisites for a more detailed further analysis of laminar and turbulent flows.

**Category:** Mathematical Physics

[597] **viXra:1703.0117 [pdf]**
*submitted on 2017-03-13 07:56:34*

**Authors:** Mauro Bernardini

**Comments:** 5 Pages.

The final solutions of the equation (1), obtained starting from the postulates of the TTR Theory [1], show that the mass m of a Particle of Existence (PE) corresponds to the mass of the Proton. This result has been obtained by placing m as unknown factor in the equation (1) and time t = 80 years (corresponding to the average life time of a Human Being), also lets it to assume (analysis still in progress that will be provided with a later publication), that all the 6 types of possible PE within our 3d universe, really correspond to 6 types of Super-Hydrogens having a total mass approximately equivalent to that of a Super-Proton.

**Category:** Mathematical Physics

[596] **viXra:1703.0102 [pdf]**
*submitted on 2017-03-11 04:09:04*

**Authors:** Sergey G. Fedosin

**Comments:** 18 pages. Reports in Advances of Physical Sciences (2017).http://dx.doi.org/10.1142/S2424942417500025.25

The general field, containing all the macroscopic fields in it, is divided into the mass component, the source of which is the mass four-current, and the charge component, the source of which is the charge four-current. The mass component includes the gravitational field, acceleration field, pressure field, dissipation field, strong interaction and weak interaction fields, other vector fields. The charge component of the general field represents the electromagnetic field. With the help of the principle of least action we derived the field equations, the equation of the matter’s motion in the general field, the equation for the metric, the energy and momentum of the system of matter and its fields, and calibrated the cosmological constant. The general field components are related to the corresponding vacuum field components so that the vacuum field generates the general field at the macroscopic level.

**Category:** Mathematical Physics

[595] **viXra:1703.0101 [pdf]**
*submitted on 2017-03-11 05:42:37*

**Authors:** Damien K. K. Adjaï, Jean Akande, Lucas H. Koudahoun, Biswanath Rath, Pravanjan Mallick, Rati Ranjan Sahoo, Y. J. Fernando Kpomahou, Marc D. Monsia

**Comments:** 10 pages

The quantum mechanics of inverse square potentials in one dimension is usually studied through renormalization, self-adjoint extension and WKB approximation. This paper shows that such potentials may be investigated within the framework of the position-dependent mass quantum mechanics formalism under the usual boundary conditions. As a result, exact discrete bound state solutions are expressed in terms of associated Laguerre polynomials with negative energy spectrum using the Nikiforov-Uvarov method for the repulsive inverse square potential.

**Category:** Mathematical Physics

[594] **viXra:1702.0270 [pdf]**
*submitted on 2017-02-21 18:42:59*

**Authors:** Pairoaj Sungkung

**Comments:** 4 Pages. Very cool.

The simple case of Fiez identity for interacting four-fermion in four-dimensional space-time has been worked out explicitly.

**Category:** Mathematical Physics

[593] **viXra:1702.0249 [pdf]**
*submitted on 2017-02-19 15:20:15*

**Authors:** William O. Straub

**Comments:** 6 Pages.

The necessity of Weyl's vector field in his 1918 theory is examined.

**Category:** Mathematical Physics

[592] **viXra:1702.0244 [pdf]**
*submitted on 2017-02-19 10:43:43*

**Authors:** Victor Christianto, Sergey Ershkov

**Comments:** 3 Pages. This paper has not been submitted to any journal. Your comments are welcome.

In a recent paper, Ershkov derived a system of two coupled Riccati ODEs as solution of nonstationary 3D Navier-Stokes equations. Now in this paper, we will solve these coupled Riccati ODEs using Maxima computer algebra package. The result seems to deserve further investigation in particular for finding nonstationaryNavier-Stokes equations for real fluid.

**Category:** Mathematical Physics

[591] **viXra:1702.0242 [pdf]**
*submitted on 2017-02-19 12:24:40*

**Authors:** Jean Akande, Damien K. K. Adjaï, Lucas H. Koudahoun, Biswanath Rath, Pravanjan Mallick, Rati Ranjan Sahoo, Fernando Y. J. Kpomahou, Marc D. Monsia

**Comments:** 13 pages

The quantization of second order dissipative dynamical systems is well known to be a complicated Sturm-Liouville problem. This work is devoted to the exact quantization of a given quadratic Liénard type oscillator equation. The bound state solutions of the resulting Schrödinger equation in terms of associated Laguerre polynomials and the possibility to recover the energy spectrum of the quantum harmonic oscillator are discussed following the specific values of system parameters, using the Nikiforov-Uvarov method.

**Category:** Mathematical Physics

[590] **viXra:1702.0231 [pdf]**
*submitted on 2017-02-18 09:09:57*

**Authors:** Gary D. Simpson

**Comments:** 10 Pages.

This text demonstrates that the complex i can be combined with a Hamilton style quaternion to produce a 5-D mathematical structure. Essentially, the complex plane is combined with an arbitrary unit vector. The complex i is shown to anti-commute with the unit vectors i, j, and k. The resulting geometry is shown to be an extension of Hamilton’s quaternions based upon the complex plane rather than real numbers. This new geometric structure is presented in Figure 1 and Equations 3 through 3.3. This configuration makes it possible to calculate the diameter of the proton at rest with the estimated value being 1.668 x 10-15 meter. This is within the accepted measured range of the proton diameter at 1.755(102) x 10-15 meter as given by the NIST, and it is very close to the proton diameter at 1.68174(78) x 10-15 meter as measured at the Paul Scherrer Institute in 2010 by using muonic hydrogen.

**Category:** Mathematical Physics

[589] **viXra:1702.0210 [pdf]**
*submitted on 2017-02-17 02:05:51*

**Authors:** Viktor Strohm

**Comments:** 3 Pages.

. In this paper we consider some problems of the origin of body rotation under the influence of the thermal radiation

**Category:** Mathematical Physics

[588] **viXra:1702.0182 [pdf]**
*submitted on 2017-02-15 10:36:36*

**Authors:** Chang Li

**Comments:** 2 Pages.

This article proved two theorems and presented one conjecture about the real-zeros of Jones Polynomial of Torus. The distribution of zeros of Jones Polynomial is an interesting topic in knots theory of math and physics.

**Category:** Mathematical Physics

[587] **viXra:1702.0098 [pdf]**
*submitted on 2017-02-07 15:02:00*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 3 Pages.

From string theory to topstringy.

**Category:** Mathematical Physics

[586] **viXra:1702.0069 [pdf]**
*submitted on 2017-02-04 08:00:54*

**Authors:** M.W.Kalinowski

**Comments:** 37 Pages.

W pracy rozpatrujemy podstawy mechaniki kwantowej w języku logik kwantowych w zasto-
sowaniu do teorii parametrów ukrytych i możliwych uogólnień mechaniki kwantowej. Omawiamy
związek mechaniki kwantowej z logikami wielowartościowymi. Wprowadzamy system aksjoma-
tyczny Mackaya–Mączyńskiego ogólnego systemu mechanicznego. Badamy ogólne własności ob-
serwabli i ich reprezentacje boolowskie. Z aksjomatu QM mechaniki kwantowej wyprowadzamy
podstawowe postulaty tej mechaniki. Omawiamy hipotezę o parametrach ukrytych, dyskusję na
ich temat oraz paradoks EPR (Einsteina–Podolskiego–Rosena) wraz z nierównością Bella.

**Category:** Mathematical Physics

[585] **viXra:1701.0679 [pdf]**
*submitted on 2017-01-30 21:21:09*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 2 Pages.

Establish topological schemes in metamorphic space as A-scheme and B-scheme.

**Category:** Mathematical Physics

[584] **viXra:1701.0653 [pdf]**
*submitted on 2017-01-28 10:44:20*

**Authors:** J.L.Paillet, A.Meulenberg

**Comments:** 12 Pages.

In previous works, we discussed arguments for and against the deep orbits, as exemplified in published solutions. So we considered the works of Maly and Va’vra on the topic, the most complete solution available and one showing an infinite family of EDO solutions. In particular, we deeply analyzed their 2nd of these papers, where they consider a finite nucleus and look for solutions with a Coulomb potential modified inside the nucleus. In the present paper, we quickly recall our analysis, verification, and extension of their results. Moreover, we answer to a recent criticism that the EDOs would represent negative energy states and therefore would not qualify as an answer to the questions posed by Cold Fusion results. We can prove, by means of a simple algebraic argument based on the solution process, that, while at the transition region, the energy of the EDOs are positive. Next, we deepen the essential role of Special Relativity as source of the EDOs, which we discussed in previous papers. But the central topic of our present study is an initial analysis of the magnetic interactions near the nucleus, with the aim of solving important physical questions: do the EDOs satisfy the Heisenberg Uncertainty relation (HUR)? Are the orbits stable? So, we examine some works related to the Vigier-Barut Model, with potentials including magnetic coupling. We also carried out approximate computations to evaluate the strength of these interactions and the possibilities of their answering some of our questions. As a first result, we can expect the HUR to be respected by EDOs, due to the high energies of the magnetic interactions near the nucleus. Present computations for stability do not yet give a plain result; we need further studies and tools based on QED to face the complexity of the near-nuclear region. For the creation of EDOs, we outline a possibility based on magnetic coupling.

**Category:** Mathematical Physics

[583] **viXra:1701.0651 [pdf]**
*submitted on 2017-01-28 08:06:57*

**Authors:** Robert B. Easter, Eckhard Hitzer

**Comments:** 10 pages. In proceedings: S. Sivasundaram (ed.), International Conference in Nonlinear Problems in Aviation and Aerospace ICNPAA 2016, AIP Conf. Proc., Vol. 1798, 020066 (2017); doi: 10.1063/1.4972658. 4 color figures.

The Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra G(4,8) that extends the concepts introduced with the Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) G(8,2) with entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) in spacetime with a new boost operator. The base algebra in which spacetime geometry is modeled is the Space-Time Algebra (STA) G(1,3). Two Conformal Space-Time subalgebras (CSTA) G(2,4) provide spacetime entities for points, flats (incl. worldlines), and hyperbolics, and a complete set of versors for their spacetime transformations that includes rotation, translation, isotropic dilation, hyperbolic rotation (boost), planar reflection, and (pseudo)spherical inversion in rounds or hyperbolics. The DCSTA G(4,8) is a doubling product of two G(2,4) CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new bivector entities for (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime hyperbolics or other surface entities using the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in rounds or hyperbolics. An operation for the directed non-uniform scaling (anisotropic dilation) of the bivector general quadric entities is defined using the boost operator and a spatial projection. DCSTA allows general quadric surfaces to be transformed in spacetime by the same complete set of doubled CSTA versor (i.e., DCSTA versor) operations that are also valid on the doubled CSTA point entity (i.e., DCSTA point) and the other doubled CSTA entities. The new DCSTA bivector entities are formed by extracting values from the DCSTA point entity using specifically defined inner product extraction operators. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the length contraction effect of special relativity. DCSTA is an algebra for computing with quadrics and their cyclide inversions in spacetime. For applications or testing, DCSTA G(4,8) can be computed using various software packages, such as Gaalop, the Clifford Multivector Toolbox (for MATLAB), or the symbolic computer algebra system SymPy with the GAlgebra module.

**Category:** Mathematical Physics

[582] **viXra:1701.0540 [pdf]**
*submitted on 2017-01-18 19:08:15*

**Authors:** Michail Zak

**Comments:** 7 Pages.

New physical principle for simulations of PDE has been introduced. It is based upon replacing the PDE to be solved by the system of ODE for which the PDE represents the corresponding Liouville equation. The proposed approach has a polynomial (rather than exponential) algorithmic complexity, and it is applicable to nonlinear parabolic, hyperbolic, and elliptic PDE.

**Category:** Mathematical Physics

[581] **viXra:1701.0533 [pdf]**
*submitted on 2017-01-18 05:02:17*

**Authors:** J. Dunning-Davies, J. P. Dunning-Davies

**Comments:** 7 Pages.

Ever since Oliver Heaviside's suggestion of the possible existence of a set of equations, analogous to Maxwell's equations for the electromagnetic field, to describe the gravitational field, others have considered and built on the original notion. However, if such equations do exist and really are analogous to Maxwell's electromagnetic equations, new problems could arise related to presently accepted notions concerning special relativity. This note, as well as offering a translation of a highly relevant paper by Carstoiu, addresses these concerns in the same manner as similar concerns regarding Maxwell's equations were.

**Category:** Mathematical Physics

[580] **viXra:1701.0523 [pdf]**
*submitted on 2017-01-17 04:41:39*

**Authors:** Grushka Ya.I.

**Comments:** 158 Pages. Mathematics Subject Classification: 03E75; 70A05; 83A05; 47B99

This work lays the foundations of the theory of kinematic changeable sets ("abstract kinematics"). Theory of kinematic changeable sets is based on the theory of changeable sets. From an intuitive point of view, changeable sets are sets of objects which, unlike elements of ordinary (static) sets, may be in the process of continuous transformations, and which may change properties depending on the point of view on them (that is depending on the reference frame). From the philosophical and imaginative point of view the changeable sets may look like as "worlds" in which evolution obeys arbitrary laws.
Kinematic changeable sets are the mathematical objects, consisting of changeable sets, equipped by different geometrical or topological structures (namely metric, topological, linear, Banach, Hilbert and other spaces). In author opinion, theories of changeable and kinematic changeable sets (in the process of their development and improvement), may become some tools of solving the sixth Hilbert problem at least for physics of macrocosm. Investigations in this direction may be interesting for astrophysics, because there exists the hypothesis, that in the large scale of Universe, physical laws (in particular, the laws of kinematics) may be different from the laws, acting in the neighborhood of our solar System. Also these investigations may be applied for the construction of mathematical foundations of tachyon kinematics.
We believe, that theories of changeable and kinematic changeable sets may be interesting not only for theoretical physics but also for other fields of science as some, new, mathematical apparatus for description of evolution of complex systems.

**Category:** Mathematical Physics

[579] **viXra:1701.0309 [pdf]**
*submitted on 2017-01-06 10:35:36*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages.

This paper is on the mathematical structure of space, time, and gravity.
It is shown that electrodynamics is neither charge inversion invariant, nor
is it time inversion invariant.

**Category:** Mathematical Physics

[578] **viXra:1701.0299 [pdf]**
*submitted on 2017-01-05 19:19:37*

**Authors:** William O. Straub

**Comments:** 9 Pages.

A very elementary overview of the spinor concept, intended as a guide for undergraduates.

**Category:** Mathematical Physics

[577] **viXra:1701.0166 [pdf]**
*submitted on 2017-01-03 13:20:03*

**Authors:** J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 6 pages

In quantum mechanics, the wave function and energy are required for the complete characterization of fundamental properties of a physical system subject to a potential energy. It is proved in this work, the existence of a Schrödinger equation with position-dependent mass having the prolate spheroidal wave function as exact solution, resulting from a classical quadratic Liénard-type oscillator equation. This fact may allow the extension of the current one-dimensional model to three dimensions and increase the understanding of analytical features of quantum systems.

**Category:** Mathematical Physics

[576] **viXra:1612.0415 [pdf]**
*submitted on 2016-12-31 21:01:16*

**Authors:** Richard A Jowsey

**Comments:** 13 Pages.

The fundamental fabric of spacetime is revealed by deep Dimensional Analysis of the Planck Units of mass, energy, and electromagnetism. Using a little-known expression derived by James Clerk Maxwell for the dimensional reduction of mass and charge into units of length and inverse-time (frequency), all of the physical quantities can be expressed in terms of metres and inverse-seconds (Hz). On arranging these quantities into a 2D log-log space/time matrix, simple (but compelling) patterns emerge in the mathematical relationship between fundamental units. The space/time matrix requires five spatial dimensions to accommodate the physical units, two of which are shown to be imaginary spatially-gauged wavelengths, i.e. unobservable dimensions of complex 5+1D spacetime, measured in metres, which exist (mathematically), but are not real.

**Category:** Mathematical Physics

[575] **viXra:1612.0409 [pdf]**
*submitted on 2016-12-31 06:11:07*

**Authors:** Wen Chen

**Comments:** 6 Pages.

This short note proposes a general time-space metric by an extension of the power-function based fractal concept to the structural-function fabric. The structural function can be an arbitrary-function to describe complex metric underlying physical systems. We call such a metric Structal, and the fractal is its special case. This work is inspired by our recent work on the structural derivative, in which the structural function takes into account the significant influence of time-space fabric of a complex system on its physical behaviors, in particular, the ultra-slow diffusion. Based on the structal concept, this communication suggests the structural time-space transformation and introduces the general diffusion model. In addition, the statistics implication of the structal and the structural derivative model is also briefly discussed.

**Category:** Mathematical Physics

[574] **viXra:1612.0357 [pdf]**
*submitted on 2016-12-27 07:30:29*

**Authors:** Renzun Lian

**Comments:** 10 Pages.

As a supplement to the previous Parts I and II, the Surface formulations of the ElectroMagnetic-Power-based Characteristic Mode Theory for the system constructed by Multiple Homogeneous Material bodies (Surf-MHM-EMP-CMT) are established in this Part III. The coupling phenomenon among different bodies is specifically studied, and then a new kind of power-based Characteristic Mode (CM) set, Coupling power CM (CoupCM) set, is developed for characterizing the coupling character.

**Category:** Mathematical Physics

[573] **viXra:1612.0353 [pdf]**
*submitted on 2016-12-27 03:13:34*

**Authors:** Victor L. Mironov

**Comments:** 9 Pages.

In the present paper we develop the description of electromagnetic field in an anisotropic medium using the sedeonic wave equations based on sedeonic potentials and space-time operators.

**Category:** Mathematical Physics

[572] **viXra:1612.0352 [pdf]**
*submitted on 2016-12-27 04:22:39*

**Authors:** Renzun Lian

**Comments:** 13 Pages.

Both the previous Part I and this Part II focus on the linear electromagnetic system constructed by a Single Homogeneous Material body (SHM), and the SHM can be electric and/or magnetic. The studies for the system constructed by Multiple Homogeneous Material bodies (MHM) will be finished in Part III.
It is indispensable for the Surface formulations of the ElectroMagnetic-Power-based SHM Characteristic Mode Theory (Surf-SHM-EMP-CMT) to relate the surface equivalent electric and magnetic currents, and a boundary condition based method for establishing the relation has been provided in the Part I. In this Part II, some further studies for the boundary condition based method are done (such as the revelation for physical essence, the numerical analysis, and the improvement), and a new conservation law based method is given.
As a supplement to the Part I, some new surface formulations for the output power of a SHM are developed in this Part II, and then some new surface formulations for constructing the Output power Characteristic Mode (OutCM) set and some new variational formulations for the scattering problem of a SHM are established.
In addition, the power relation contained in the PMCHWT formulation for a SHM is analyzed. Then, it is clearly revealed that the physical essence of the PMCHWT formulation for the SHM scattering problem is the conservation law of energy; the power character of the CM set derived from the PMCHWT-based CMT is not always identical to the OutCM set derived from the Surf-SHM-EMP-CMT; the PMCHWT-based CMT can be viewed as a special case of the object-oriented EMP-CMT.

**Category:** Mathematical Physics

[571] **viXra:1612.0299 [pdf]**
*submitted on 2016-12-19 12:57:58*

**Authors:** Markos Georgallides

**Comments:** 21 Pages.

Everything in this cosmos , is Done or Becomes , from a Mould where , in Geometry is the Monad , the discrete continuity AB , In Mechanics and Physics is the Recent Acquisition of Material-Geometry where , Material-point is the discrete continuity |{⊕+⊝}| = The Quantum , In Plane is Archimedes number ,π, which is becoming from the Squaring of the circle , In Space ,volume, is the number ³√2 which is becoming from the Duplication of the Cube . In article [STPL] Geometrical Mechanism produces and composite all opposite Spaces and Anti-spaces Points , to Material-points which are the three Breakages {[s²=±(w ̅.r)², [i]= 2(wr)²] of [MFMF] Gravity , under thrust v ̅= c ̅ } , where through it become the Fermions → [ ±v ̅.s²] and Bosons → [v ̅.I = [v ̅.2(w ̅.r)²] = [v ̅.2s²] , i.e. STPL is the Energy-Space Genesis Mechanism .
Big Bang and GR was a temporary solution to the weakness of what men-kind had to answer . Nature cannot be described through infinite concepts as this can happen in Algebra and values , and this because are devoid of any meaning in Objective -Reality , the Physical world which is the Nature . Material Geometry is the Science and the Quantization-Quality of this Cosmos which joints the , infinite dimensionless and meaningless Points , because these have only Position , with those of Nature which are Qualitative Positive - Negative - Zero Points and which have , Positions , Directions and Magnitudes with infinite meanings , which through the Physical laws are the language of them in itself . The Work , as Energy , is the essence of this deep connection of Material-Points , the Space , and through the Conservation-laws is making , Energy-Material-Geometry . Extension of Material-Geometry to Chemical-Sector gives the possibility for new materials in a drained way of thinking .

**Category:** Mathematical Physics

[570] **viXra:1612.0258 [pdf]**
*submitted on 2016-12-15 15:55:23*

**Authors:** M. D. Sheppeard

**Comments:** 15 Pages.

An introduction to Hopf algebras in quantum field theory from the perspective of category theory.

**Category:** Mathematical Physics

[569] **viXra:1612.0229 [pdf]**
*submitted on 2016-12-12 13:34:06*

**Authors:** Algirdas Antano Maknickas

**Comments:** 8 Pages.

It was proposed gravity propulsion method by using asymmetric conical capacitor charged by high voltage. It was used linear approximation of general relativity equations for derivation of gravity field potential of charged conical capacitor and was shown that negative gravity capabilities of conical capacitor depends only on ratio of electric energy and capacitor mass density, where electric energy density depends on applied voltage and geometric parameters of conical capacitor.

**Category:** Mathematical Physics

[568] **viXra:1612.0201 [pdf]**
*submitted on 2016-12-11 02:01:52*

**Authors:** Robert Deloin

**Comments:** 7 Pages.

Riemann's hypothesis (1859) is the conjecture stating that:
The real part of every non trivial zero of Riemann's zeta function is 1/2.
The main contribution of this paper is to achieve the proof of Riemann's hypothesis. The key idea is to provide an Hamiltonian operator whose
real eigenvalues correspond to the imaginary part of the non trivial zeros of Riemann's zeta function and whose existence, according to Hilbert and Polya, proves Riemann's hypothesis.

**Category:** Mathematical Physics

[567] **viXra:1612.0184 [pdf]**
*submitted on 2016-12-09 20:49:53*

**Authors:** Taha Sochi

**Comments:** 20 Pages.

In this article we present an analytical method for deriving the relationship between the pressure drop and flow rate in laminar flow regimes, and apply it to the flow of power-law fluids through axially-symmetric corrugated tubes. The method, which is general with regards to fluid and tube shape within certain restrictions, can also be used as a foundation for numerical integration where analytical expressions are hard to obtain due to mathematical or practical complexities. Five converging-diverging geometries are used as examples to illustrate the application of this method.

**Category:** Mathematical Physics

[566] **viXra:1612.0182 [pdf]**
*submitted on 2016-12-09 20:55:36*

**Authors:** Taha Sochi

**Comments:** 23 Pages.

The one-dimensional Navier-Stokes equations are used to derive analytical expressions for the relation between pressure and volumetric flow rate in capillaries of five different converging-diverging axisymmetric geometries for Newtonian fluids. The results are compared to previously-derived expressions for the same geometries using the lubrication approximation. The results of the one-dimensional Navier-Stokes are identical to those obtained from the lubrication approximation within a non-dimensional numerical factor. The derived flow expressions have also been validated by comparison to numerical solutions obtained from discretization with numerical integration. Moreover, they have been certified by testing the convergence of solutions as the converging-diverging geometries approach the limiting straight geometry.

**Category:** Mathematical Physics

[565] **viXra:1612.0180 [pdf]**
*submitted on 2016-12-09 21:00:49*

**Authors:** Taha Sochi

**Comments:** 29 Pages.

Euler-Lagrange variational principle is used to obtain analytical and numerical flow relations in cylindrical tubes. The method is based on minimizing the total stress in the flow duct using the fluid constitutive relation between stress and rate of strain. Newtonian and non-Newtonian fluid models; which include power law, Bingham, Herschel-Bulkley, Carreau and Cross; are used for demonstration.

**Category:** Mathematical Physics

[564] **viXra:1612.0178 [pdf]**
*submitted on 2016-12-09 21:11:29*

**Authors:** Taha Sochi

**Comments:** 15 Pages.

We use a method based on the lubrication approximation in conjunction with a residual-based mass-continuity iterative solution scheme to compute the flow rate and pressure field in distensible converging–diverging tubes for Navier–Stokes fluids. We employ an analytical formula derived from a one-dimensional version of the Navier–Stokes equations to describe the underlying flow model that provides the residual function. This formula correlates the flow rate to the boundary pressures in straight cylindrical elastic tubes with constant-radius. We validate our findings by the convergence toward a final solution with fine discretization as well as by comparison to the Poiseuille-type flow in its convergence toward analytic solutions found earlier in rigid converging–diverging tubes. We also tested the method on limiting special cases of cylindrical elastic tubes with constant-radius where the numerical solutions converged to the expected analytical solutions. The distensible model has also been endorsed by its convergence toward the rigid Poiseuille-type model with increasing the tube wall stiffness. Lubrication-based one-dimensional finite element method was also used for verification. In this investigation five converging–diverging geometries are used for demonstration, validation and as prototypes for modeling converging–diverging geometries in general.

**Category:** Mathematical Physics

[563] **viXra:1612.0160 [pdf]**
*submitted on 2016-12-09 05:07:35*

**Authors:** Taha Sochi

**Comments:** 22 Pages.

In this paper, we use a generic and general variational method to obtain solutions to the flow of generalized Newtonian fluids through circular pipes and plane slits. The new method is not based on the use of the Euler-Lagrange variational principle and hence it is totally independent of our previous approach which is based on this principle. Instead, the method applies a very generic and general optimization approach which can be justified by the Dirichlet principle although this is not the only possible theoretical justification. The results that were obtained from the new method using nine types of fluid are in total agreement, within certain restrictions, with the results obtained from the traditional methods of fluid mechanics as well as the results obtained from the previous variational approach. In addition to being a useful method in its own for resolving the flow field in circular pipes and plane slits, the new variational method lends more support to the old variational method as well as for the use of variational principles in general to resolve the flow of generalized Newtonian fluids and obtain all the quantities of the flow field which include shear stress, local viscosity, rate of strain, speed profile and volumetric flow rate. The theoretical basis of the new variational method, which rests on the use of the Dirichlet principle, also provides theoretical support to the former variational method.

**Category:** Mathematical Physics

[562] **viXra:1612.0157 [pdf]**
*submitted on 2016-12-09 05:12:34*

**Authors:** Taha Sochi

**Comments:** 31 Pages.

We continue our investigation to the use of the variational method to derive flow relations for generalized Newtonian fluids in confined geometries. While in the previous investigations we used the straight circular tube geometry with eight fluid rheological models to demonstrate and establish the variational method, the focus here is on the plane long thin slit geometry using those eight rheological models, namely: Newtonian, power law, Ree-Eyring, Carreau, Cross, Casson, Bingham and Herschel-Bulkley. We demonstrate how the variational principle based on minimizing the total stress in the flow conduit can be used to derive analytical expressions, which are previously derived by other methods, or used in conjunction with numerical procedures to obtain numerical solutions which are virtually identical to the solutions obtained previously from well established methods of fluid dynamics. In this regard, we use the method of Weissenberg-Rabinowitsch-Mooney-Schofield (WRMS), with our adaptation from the circular pipe geometry to the long thin slit geometry, to derive analytical formulae for the eight types of fluid where these derived formulae are used for comparison and validation of the variational formulae and numerical solutions. Although some examples may be of little value, the optimization principle which the variational method is based upon has a significant theoretical value as it reveals the tendency of the flow system to assume a configuration that minimizes the total stress. Our proposal also offers a new methodology to tackle common problems in fluid dynamics and rheology.

**Category:** Mathematical Physics

[561] **viXra:1612.0155 [pdf]**
*submitted on 2016-12-09 05:30:01*

**Authors:** Taha Sochi

**Comments:** 17 Pages.

This article deals with the flow of Newtonian fluids through axially-symmetric corrugated tubes. An analytical method to derive the relation between volumetric flow rate and pressure drop in laminar flow regimes is presented and applied to a number of simple tube geometries of converging-diverging nature. The method is general in terms of fluid and tube shape within the previous restrictions. Moreover, it can be used as a basis for numerical integration where analytical relations cannot be obtained due to mathematical difficulties.

**Category:** Mathematical Physics

[560] **viXra:1612.0154 [pdf]**
*submitted on 2016-12-09 05:32:16*

**Authors:** Taha Sochi

**Comments:** 15 Pages.

We derive analytical expressions for the flow of Newtonian and power law fluids in elastic circularly-symmetric tubes based on a lubrication approximation where the flow velocity profile at each cross section is assumed to have its axially-dependent characteristic shape for the given rheology and cross sectional size. Two pressure-area constitutive elastic relations for the tube elastic response are used in these derivations. We demonstrate the validity of the derived equations by observing qualitatively correct trends in general and quantitatively valid asymptotic convergence to limiting cases. The Newtonian formulae are compared to similar formulae derived previously from a one-dimensional version of the Navier-Stokes equations.

**Category:** Mathematical Physics

[559] **viXra:1612.0153 [pdf]**
*submitted on 2016-12-09 05:34:38*

**Authors:** Taha Sochi

**Comments:** 27 Pages.

In this paper, analytical expressions correlating the volumetric flow rate to the pressure drop are derived for the flow of Carreau and Cross fluids through straight rigid circular uniform pipes and long thin slits. The derivation is based on the application of Weissenberg-Rabinowitsch-Mooney-Schofield method to obtain flow solutions for generalized Newtonian fluids through pipes and our adaptation of this method to the flow through slits. The derived expressions are validated by comparing their solutions to the solutions obtained from direct numerical integration. They are also validated by comparison to the solutions obtained from the variational method which we proposed previously. In all the investigated cases, the three methods agree very well. The agreement with the variational method also lends more support to this method and to the variational principle which the method is based upon.

**Category:** Mathematical Physics

[558] **viXra:1612.0147 [pdf]**
*submitted on 2016-12-09 01:26:02*

**Authors:** Taha Sochi

**Comments:** 20 Pages.

In this paper we investigate the yield condition in the mobilization of yield-stress materials in distensible tubes. We discuss the two possibilities for modeling the yield-stress materials prior to yield: solid-like materials and highly-viscous fluids and identify the logical consequences of these two approaches on the yield condition. As part of this investigation we derive an analytical expression for the pressure field inside a distensible tube with a Newtonian flow using a one-dimensional Navier-Stokes flow model in conjunction with a pressure-area constitutive relation based on elastic tube wall characteristics.

**Category:** Mathematical Physics

[557] **viXra:1612.0143 [pdf]**
*submitted on 2016-12-09 01:42:02*

**Authors:** Taha Sochi

**Comments:** 31 Pages.

A residual-based lubrication method is used in this paper to find the flow rate and pressure field in converging-diverging rigid tubes for the flow of time-independent category of non-Newtonian fluids. Five converging-diverging prototype geometries were used in this investigation in conjunction with two fluid models: Ellis and Herschel-Bulkley. The method was validated by convergence behavior sensibility tests, convergence to analytical solutions for the straight tubes as special cases for the converging-diverging tubes, convergence to analytical solutions found earlier for the flow in converging-diverging tubes of Newtonian fluids as special cases for non-Newtonian, and convergence to analytical solutions found earlier for the flow of power-law fluids in converging-diverging tubes. A brief investigation was also conducted on a sample of diverging-converging geometries. The method can in principle be extended to the flow of viscoelastic and thixotropic/rheopectic fluid categories. The method can also be extended to geometries varying in size and shape in the flow direction, other than the perfect cylindrically-symmetric converging-diverging ones, as long as characteristic flow relations correlating the flow rate to the pressure drop on the discretized elements of the lubrication approximation can be found. These relations can be analytical, empirical and even numerical and hence the method has a wide applicability range.

**Category:** Mathematical Physics

[556] **viXra:1612.0124 [pdf]**
*submitted on 2016-12-07 14:49:20*

**Authors:** Harry Watson

**Comments:** 5 Pages.

A Geometric Model
A family of models in Euclidean space is developed from the following
approximation.
m_p/m_e = 4pi(4pi- 1\pi)(4pi-2/pi) = 1836.15 (1)
where (m_p) and (m_e) are the numeric values for the mass of the proton and the mass of electron, respectively. In particular, we will develop models (1) that agree with the recommended value of the mass ratio of the proton to the electron to six significant figures, (2) that explain the “shape-shifting” behavior of the proton, and (3) that are formed concisely from the sole transcendental number pi. This model is solely geometric, relying on volume as the measure of mass. Claim that inclusion of quantum/relativistic properties enhance the accuracy of the model. The goal is to express the ratio of the proton mass to the electron mass in terms of (1) pure mathematical constants and (2) a quantum corrective factor.
harry.watson@att.net

**Category:** Mathematical Physics

[555] **viXra:1612.0071 [pdf]**
*submitted on 2016-12-06 13:59:21*

**Authors:** Ulrich E. Bruchholz, Horst Eckardt

**Comments:** Pages.

It is demonstrated how to unify all physics on the basis of general relativity. Electrodynamics is revealed to be part of general relativity,
as already seen by Rainich. The properties of elementary particles follow from the equations of the unified theory. The way of calculating these properties is indicated, and successful applications of this method are referenced.
These insights and results have inevitably to be joined with a criticism of contemporary physics.

**Category:** Mathematical Physics

[554] **viXra:1612.0070 [pdf]**
*submitted on 2016-12-06 07:24:24*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 1 Page.

Demonstration of SUSY [super-symmetry]-like electrostatic backgrounds fields of quantum differential topological K-theory.

**Category:** Mathematical Physics

[553] **viXra:1611.0293 [pdf]**
*submitted on 2016-11-20 13:15:56*

**Authors:** Nicolas Poupart

**Comments:** 6 Pages.

It will be demonstrated in this paper that dark mass is a necessary consequence of the relativistic mechanics. This demonstration disregards the forces of physics and is therefore a purely mechanical explanation. The Tully-Fisher relation will be deduced naturally, without appealing to any new physics, and it is therefore possible to derive this law without modifying the Newtonian gravity or general relativity. In addition, a theoretical prediction on a new form of frequency shift will be carried out which makes it possible to refute or confirm this theory.

**Category:** Mathematical Physics

[552] **viXra:1611.0253 [pdf]**
*submitted on 2016-11-16 18:03:50*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 15 Pages.

A Guide Through Metaspace.

**Category:** Mathematical Physics

[551] **viXra:1611.0214 [pdf]**
*submitted on 2016-11-14 10:00:31*

**Authors:** L. H. Koudahoun, Y. J. F. Kpomahou, D. K. K. Adjaï, J. Akande, B. Rath, P. Mallick, M. D. Monsia

**Comments:** 11 pages

A mathematical model describing the nonlinear oscillations in elastic structures is proposed. The Energy Balance Method (EBM) is applied to solve the generalized nonlinear Duffing equation obtained in absence of excitation. The numerical results show an excellent agreement with the periodic solutions obtained through the Energy Balance Method. Finally the effects of different parameters on the system behavior are studied.

**Category:** Mathematical Physics

[550] **viXra:1611.0163 [pdf]**
*submitted on 2016-11-11 08:42:21*

**Authors:** M.E. Hassani

**Comments:** 8 Pages;8 References

In 1916, Johannes Droste independently found an exact (vacuum) solution to the Einstein's (gravitational) field equations in empty space. Droste's solution is quasi-comparable to Schwarzschild's one . Droste published his paper entitled “The field of a single centre in Einstein's theory of gravitation, and the motion of a particle in that fieldˮ. The paper communicated (in the meeting of May 27, 1916) by Prof. H.A. Lorentz, and published in ʻProceedings of the Royal Netherlands Academy of Arts and Science. 19 (1): 197-215 (1917)ʼ. In the present article, the Droste's solution is scrutinized and proven to be invalid purely and simply because the procedure used by Droste is mathematically questionable since he had systematically, deliberately, and without any justification ‒removed the constant coefficient ʻ2ʼ from the differential term (v'w') in Eq.(6) and added the differential term (wv'') to the same Eq.(6) in order to obtain Eq.(7) which was and is his principal objective, that is, the desired solution. Consequently, Eqs.(6,7) had clearly been falsified.

**Category:** Mathematical Physics

[549] **viXra:1611.0162 [pdf]**
*submitted on 2016-11-11 08:59:33*

**Authors:** Biswanath Rath, P. Mallick, Jean Akande, Damien K.K. Adjaï, Lucas H. Koudahoun, Y.J. Fernando Kpomahou, Marc D. Monsia

**Comments:** 11 pages

We generate a general model of Liénard type of second order differential
equation and study its classical solution. We also generate Hamiltonian
from the differential equation and study its stable eigenvalues.

**Category:** Mathematical Physics

[548] **viXra:1611.0146 [pdf]**
*submitted on 2016-11-11 00:07:25*

**Authors:** Biswanath Rath

**Comments:** 07 Pages. A new Eigenvalue mathod sing fractional matrix has been introduced .

A new member in Matrix representation has been introduced under
the name Fractional − Matrix and defined properly. Further we show
how one can address spectral analysis using this Fractional − Matrix.
Interesting examples have been considerd .

**Category:** Mathematical Physics

[547] **viXra:1610.0386 [pdf]**
*submitted on 2016-10-31 23:23:00*

**Authors:** Renzun Lian

**Comments:** 12 Pages.

An ElectroMagnetic-Power-based Characteristic Mode Theory (CMT) for Metal-Material combined objects (MM-EMP-CMT) was built by expressing the various electromagnetic powers as the functions of the line current on metal line, the surface current on metal surface, the surface current on the boundary of metal volume, and the total field in material volume, so it can be simply called as the Line-Surface-Volume formulation for the MM-EMP-CMT (LSV-MM-EMP-CMT). As a companion to the LSV-MM-EMP-CMT, a Line-Surface formulation for the MM-EMP-CMT (LS-MM-EMP-CMT) is established in this paper by expressing the various powers as the functions of the line and surface currents on metal part and the surface equivalent current on the boundary of material part.
The physical essence of LS-MM-EMP-CMT is the same as LSV-MM-EMP-CMT, i.e., to construct the various power-based Characteristic Mode (CM) sets for metal-material combined objects, but the LS-MM-EMP-CMT is more advantageous than the LSV-MM-EMP-CMT in some aspects. For example, the former saves computational resources; the former avoids to calculate the modal scattering field in source region; the field-based definitions for the impedance and admittance of metal-material combined electromagnetic systems can be easily introduced into the former.

**Category:** Mathematical Physics

[546] **viXra:1610.0354 [pdf]**
*submitted on 2016-10-29 07:32:58*

**Authors:** Renzun Lian

**Comments:** 8 Pages.

As a companion to the ElectroMagnetic-Power-based Characteristic Mode Theory (EMP-CMT) for PEC systems (PEC-EMP-CMT) and the EMP-CMT for Material bodies (Mat-EMP-CMT), an EMP-CMT for Metal-Material combined objects (MM-EMP-CMT) is established in this paper, and then some power-based Characteristic Mode (CM) sets are constructed for depicting the inherent power characteristics of metal-material combined objects. The MM-EMP-CMT is valuable for analyzing and designing the metal-material combined electromagnetic structures, such as the microstrip antennas and the Dielectric Resonant Antennas (DRAs) mounted on metal platforms etc. In addition, a variational formulation for the scattering problem of metal-material combined objects is provided based on the conservation law of energy.

**Category:** Mathematical Physics

[545] **viXra:1610.0345 [pdf]**
*submitted on 2016-10-28 22:26:32*

**Authors:** Renzun Lian

**Comments:** 13 Pages.

Recently, a volume formulation of the ElectroMagnetic-Power-based Characteristic Mode Theory (CMT) for Material bodies (Mat-EMP-CMT) is built by expressing various electromagnetic powers as the functions of the total fields in material bodies, so it can be simply called as Vol-Mat-EMP-CMT. As a companion to the Vol-Mat-EMP-CMT, several Surface formulations of the Mat-EMP-CMT (Surf-Mat-EMP-CMT) are established in this paper by expressing various electromagnetic powers as the functions of the surface equivalent sources on the boundaries of material bodies.
The physical essence of Surf-Mat-EMP-CMT is the same as the Vol-Mat-EMP-CMT, i.e., to construct the various power-based Characteristic Mode (CM) sets for material bodies, but the former is more advantageous than the latter in some aspects. For example, the former saves computational resources; the former avoids to compute the modal scattering field in source region; the field-based definitions for the impedance and admittance of material bodies can be easily introduced into the former.

**Category:** Mathematical Physics

[544] **viXra:1610.0340 [pdf]**
*submitted on 2016-10-28 05:21:45*

**Authors:** Renzun Lian

**Comments:** 15 Pages.

In this paper, an ElectroMagnetic-Power-based Characteristic Mode Theory (CMT) for Material bodies (Mat-EMP-CMT) is provided. The Mat-EMP-CMT is valid for the inhomogeneous and lossy material bodies, and it is applicable to the bodies which are placed in complex electromagnetic environments.
Under the Mat-EMP-CMT framework, a series of power-based Characteristic Mode (CM) sets are constructed, and they have abilities to depict the inherent power characteristics of material bodies from different aspects. All power-based CM sets are independent of the external electromagnetic environment and excitation.
Among the various power-based CM sets constructed in Mat-EMP-CMT, only the Input power CM (InpCM) set has the same physical essence as the CM set constructed in Mat-VIE-CMT (the Volume Integral Equation based CMT for Material bodies), and the other CM sets are completely new. However, the power characteristic of the InpCM set is more physically reasonable than the CM set derived from Mat-VIE-CMT.
In addition, not only radiative CMs and real characteristic currents but also non-radiative CMs and complex characteristic currents can be constructed under the Mat-EMP-CMT framework; the traditional characteristic quantity, Modal Significance (MS), is generalized, and some new characteristic and non-characteristic quantities are introduced to depict the modal characteristics from different aspects; a variational formulation for the scattering problem of material scatterer is established based on the conservation law of energy.

**Category:** Mathematical Physics

[543] **viXra:1610.0337 [pdf]**
*submitted on 2016-10-27 20:25:31*

**Authors:** Nicolas Poupart

**Comments:** 6 Pages.

Nous démontrerons dans cet article que la masse noire est une conséquence nécessaire de la mécanique relativiste soit de la combinaison de la mécanique classique et de la relativité restreinte. Ainsi, il faudra soit accepter ce résultat soit mettre en doute la consistance de la mécanique relativiste.

**Category:** Mathematical Physics

[542] **viXra:1610.0332 [pdf]**
*submitted on 2016-10-28 04:20:20*

**Authors:** Renzun Lian

**Comments:** 17 Pages.

In this paper, an ElectroMagnetic-Power-based Characteristic Mode Theory (CMT) for PEC systems (PEC-EMP-CMT) is built. The PEC-EMP-CMT is valid for the PEC systems which are surrounded by any electromagnetic environment, and it can construct the complex characteristic currents and non-radiative Characteristic Modes (CMs).
In this paper, some traditional concepts, such as the system input impedance and modal input impedance etc., are redefined; the traditional characteristic quantity, Modal Significance (MS), is generalized; a series of new power-based CM sets are introduced.
It is proven in this paper that various power-based CM sets of a certain objective PEC structure are independent of the external environment and excitation; the non-radiative space constituted by all non-radiative modes is identical to the interior resonance space constituted by all interior resonant modes of closed PEC structures, and the non-radiative CMs constitute a basis of the space. Based on above these, the normal Eigen-Mode Theory (EMT) for closed PEC structures is classified into the PEC-EMP-CMT framework.
In addition, a variational formulation for the external scattering problem of PEC structures is provided in this paper, based on the conservation law of energy.

**Category:** Mathematical Physics

[541] **viXra:1610.0315 [pdf]**
*submitted on 2016-10-26 08:43:06*

**Authors:** M.E.Hassani

**Comments:** 6 Pages; 4 References.

In the present paper, the Schwarzschild’s original solution (1916) is scrutinized and proven to be logically, mathematically and physically not only wrong but basically meaningless because the ʻeasy trickʼ used by Schwarzschild violated the fundamental concepts of analytic geometry (rectangular coordinates), trigonometry (triangles) and dimensional analysis (consistency and homogeneity). It seems that Schwarzschild had systematically and deliberately violated these fundamental concepts in order to avoid/break an unavoidable/unbreakable impasse (the determinant ≠ 1). Then he had mathematically cheated to have the determinant =1 in an anti-mathematical manner since he was not attached to his initial claim, viz., ‒ x1, x2, x3 and x, y, z are rectangular coordinates ‒ Thus, as scientists we should not forget one very important thing, namely, mathematics is not only an exact science, but it is the language of Science itself.

**Category:** Mathematical Physics

[540] **viXra:1610.0231 [pdf]**
*submitted on 2016-10-19 15:07:45*

**Authors:** Arturo Tozzi, James F Peters

**Comments:** 83 Pages.

This manuscript encompasses our published and unpublished topological results in physics. Topology, the mathematical branch that assesses objects and their properties preserved through deformations, stretching and twisting, allows the investigation of the most general physical systems features. In particular, the Borsuk-Ulam Theorem (BUT) states that, if a single point projects to a higher spatial dimension, it gives rise to two antipodal points with matching description. Physical counterparts of BUT and its variants allow an inquiry of physical problems. The opportunity to treat systems as topological structures makes BUT a universal principle underlying natural phenomena.

**Category:** Mathematical Physics

[539] **viXra:1610.0221 [pdf]**
*submitted on 2016-10-19 03:43:29*

**Authors:** Arturo Tozzi, James F Peters

**Comments:** 8 Pages.

The Borsuk-Ulam Theorem (BUT) states that a single point, if embedded in one spatial dimension higher, gives rise to two antipodal points with matching descriptions and similar features. Novel BUT variants allow the assessment of countless physical systems, from entropies to quantum entanglement. We argue that BUT, cast in a quantitative fashion which has the potential of being operationalized, is a universal principle underlying a number of natural phenomena.

**Category:** Mathematical Physics

[538] **viXra:1610.0198 [pdf]**
*submitted on 2016-10-17 11:30:45*

**Authors:** Taha Sochi

**Comments:** 15 Pages.

We use a generic and general numerical method to obtain solutions for the flow of generalized Newtonian fluids through circular pipes and plane slits. The method, which is simple and robust can produce highly accurate solutions which virtually match any analytical solutions. The method is based on employing the stress, as a function of the pipe radius or slit thickness dimension, combined with the rate of strain function as represented by the fluid rheological constitutive relation that correlates the rate of strain to stress. Nine types of generalized Newtonian fluids are tested in this investigation and the solutions obtained from the generic method are compared to the analytical solutions which are obtained from the Weissenberg-Rabinowitsch-Mooney-Schofield method. Very good agreement was obtained in all the investigated cases. All the required quantities of the flow which include local viscosity, rate of strain, flow velocity profile and volumetric flow rate, as well as shear stress, can be obtained from the generic method. This is an advantage as compared to some traditional methods which only produce some of these quantities. The method is also superior to the numerical meshing techniques which may be used for resolving the flow in these systems. The method is particularly useful when analytical solutions are not available or when the available analytical solutions do not yield all the flow parameters.

**Category:** Mathematical Physics

[537] **viXra:1610.0196 [pdf]**
*submitted on 2016-10-17 11:34:00*

**Authors:** Taha Sochi

**Comments:** 16 Pages.

We investigate the possibility that the spatial dependency of stress in generalized Newtonian flow systems is a function of the applied pressure field and the conduit geometry but not of the fluid rheology. This possibility is well established for the case of a one-dimensional flow through simply connected regions, specifically tubes of circular uniform cross sections and plane thin slits. If it can also be established for the more general case of generalized Newtonian flow through non-circular or multiply connected geometries, such as the two-dimensional flow through conduits of rectangular or elliptical cross sections or the flow through annular circular pipes, then analytical or semi-analytical or highly accurate numerical solutions; regarding stress, rate of strain, velocity profile and volumetric flow rate; for these geometries can be obtained from the stress function, which can be easily obtained from the Newtonian case, in combination with the constitutive rheological relation for the particular non-Newtonian fluid, as done previously for the case of the one-dimensional flow through simply connected regions.

**Category:** Mathematical Physics

[536] **viXra:1610.0195 [pdf]**
*submitted on 2016-10-17 11:36:50*

**Authors:** Taha Sochi

**Comments:** 9 Pages.

In this article we challenge the claim that the previously proposed variational method to obtain flow solutions for generalized Newtonian fluids in circular tubes and plane slits is exact only for power law fluids. We also defend the theoretical foundation and formalism of the method which is based on minimizing the total stress through the application of the Euler-Lagrange principle.

**Category:** Mathematical Physics

[535] **viXra:1610.0194 [pdf]**
*submitted on 2016-10-17 11:51:12*

**Authors:** Taha Sochi

**Comments:** 43 Pages.

In this article, the extensional flow and viscosity and the converging-diverging geometry were examined as the basis of the peculiar viscoelastic behavior in porous media. The modified Bautista-Manero model, which successfully describes shearthinning, elasticity and thixotropic time-dependency, was used for modeling the flow of viscoelastic materials which also show thixotropic attributes. An algorithm, originally proposed by Philippe Tardy, that employs this model to simulate steadystate time-dependent flow was implemented in a non-Newtonian flow simulation code using pore-scale modeling and the initial results were analyzed. The findings are encouraging for further future development.

**Category:** Mathematical Physics

[534] **viXra:1610.0193 [pdf]**
*submitted on 2016-10-17 11:53:33*

**Authors:** Taha Sochi

**Comments:** 27 Pages.

Yield-stress is a problematic and controversial non-Newtonian flow phenomenon. In this article, we investigate the flow of yield-stress substances through porous media within the framework of pore-scale network modeling. We also investigate the validity of the Minimum Threshold Path (MTP) algorithms to predict the pressure yield point of a network depicting random or regular porous media. Percolation theory as a basis for predicting the yield point of a network is briefly presented and assessed. In the course of this study, a yield-stress flow simulation model alongside several numerical algorithms related to yield-stress in porous media were developed, implemented and assessed. The general conclusion is that modeling the flow of yield-stress fluids in porous media is too difficult and problematic. More fundamental modeling strategies are required to tackle this problem in the future.

**Category:** Mathematical Physics

[533] **viXra:1610.0150 [pdf]**
*submitted on 2016-10-14 01:23:44*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 31 Pages.

A 100 year task of minimal duration and of limitless measure

**Category:** Mathematical Physics

[532] **viXra:1610.0078 [pdf]**
*submitted on 2016-10-06 18:16:19*

**Authors:** Vito R. D'Angelo

**Comments:** 2 Pages.

In the spirit of the Pythagorean school of thought, that everything in the universe can be reduced to pure numbers; utilizing the Rydberg constant, arguably the most precise value in physics, an attempt is made to bring to fruition the aforementioned tenet. The relationships of seven well known constants are utilized within the context of four equations.

**Category:** Mathematical Physics

[531] **viXra:1610.0059 [pdf]**
*submitted on 2016-10-05 01:38:20*

**Authors:** Claude Michael Cassano

**Comments:** 9 Pages.

Elementary Linear Algebra theory handles transformations between sets of n-square matrix vector bases of M-dimensions well. Considering n-square & m-square matrices of M-dimensions, further theory and techniques, shown here, may be applied to yield results; including relationships between spin matrices and components.

**Category:** Mathematical Physics

[530] **viXra:1610.0027 [pdf]**
*submitted on 2016-10-03 07:39:34*

**Authors:** Ricardo Gil

**Comments:** 1 Page.

In quantum field theory, the mass gap is the difference in energy between the vacuum and the next lowest energy state. The energy of the vacuum is zero by definition, and assuming that all energy states can be thought of as particles in plane-waves, the mass gap is the mass of the lightest particle. The purpose of this paper is to suggest that the lowest state in a system is the entanglement which’s gravity for the Entanglement State is calculated by 2.99E12 x 1G / 9.8 m/s2 = 305102040846 G= 1/30510204086 G = 3.277592E-12 G X 1E-32m= 3.277 E-44 at 1/8.96 E20 Joules /Kg=1.11E-21 Joules/Kg energy state.

**Category:** Mathematical Physics

[529] **viXra:1609.0364 [pdf]**
*submitted on 2016-09-25 21:12:02*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 3 Pages.

At a certain point computation will initiate catastrophe. One must then impose computational factorization of variants [of stringy] in metaspace.

**Category:** Mathematical Physics

[528] **viXra:1609.0332 [pdf]**
*submitted on 2016-09-23 06:00:56*

**Authors:** Prado, Pf et al

**Comments:** 1 Page.

Addendum to hypothesis

**Category:** Mathematical Physics

[527] **viXra:1609.0302 [pdf]**
*submitted on 2016-09-20 22:49:31*

**Authors:** Lamont Williams

**Comments:** 2 Pages.

When thinking about the origin of the fine-structure constant, renowned physicist Richard Feynman speculated that it might be related to pi or the base of the natural logarithm. However, he could not envision how pi or the natural logarithm’s base could be associated with the constant. This article presents an equation that helps to address Feynman's question.

**Category:** Mathematical Physics

[526] **viXra:1609.0287 [pdf]**
*submitted on 2016-09-19 14:39:03*

**Authors:** Prado, PF et al

**Comments:** 1 Page.

Temprtive Math exploration

**Category:** Mathematical Physics

[525] **viXra:1609.0267 [pdf]**
*submitted on 2016-09-18 09:09:58*

**Authors:** J. Akande, L. H. Koudahoun, D. K. K. Adjaï, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 2 pages

The problem to solve consists of finding explicit solutions for the classical equation of motion of a particle subject to an exponential-type potential and for the quantum version.

**Category:** Mathematical Physics

[524] **viXra:1609.0261 [pdf]**
*submitted on 2016-09-17 12:07:14*

**Authors:** Vito R. D'Angelo

**Comments:** 7 Pages.

The Hertz-kilogram relationship constant, although obscure, is nonetheless a bona fide constant listed in the National Institute of Standards and Technology's (CODATA values) fundamental constants list[pg.6]. The Hertz-kilogram relationship constant is being used due to its value of (7.372497201 x10^-51 (91)) being very close to the Democritean indivisible unit, Y' (8.134865168 10^-54) It is shown that the 13/12 schematic of U-theory [2] theoretically calculates the fundamental constants within the uncertainty limits of (NIST) CODATA values [1]; utilizing twelve dimensionless constants.

**Category:** Mathematical Physics

[523] **viXra:1609.0260 [pdf]**
*submitted on 2016-09-17 08:51:16*

**Authors:** J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 5 pages

The generalized modified Emden equation also known as the generalized second order Riccati equation, is exactly solved in terms of the periodic solution of the linear harmonic oscillator. The solutions for specific values of parameters are discussed. The conditions for isochronous oscillations are also investigated.

**Category:** Mathematical Physics

[522] **viXra:1609.0247 [pdf]**
*submitted on 2016-09-16 13:54:39*

**Authors:** Prado, PF et al

**Comments:** 4 Pages.

Offers a math framework to the Perspective: Is there a structural resonant ruler in Nature? An exploratory framework to neuroscience and fundamental physics studies. Addition to Nextex set of conjectures: Version 1.0. Concluding that the resonant phenomenon probably is just the best signaling mark to the Principal phenomenon underlayered in Nature:the physical (realistic) implementation of the Fundamental theorem of Calculus or the called Theorem of Stokes.

**Category:** Mathematical Physics

[521] **viXra:1609.0239 [pdf]**
*submitted on 2016-09-15 16:32:52*

**Authors:** D. K. K. Adjaï, Y. J. F. Kpomahou, J. Akande, L. H. Koudahoun, M. D. Monsia

**Comments:** 4 pages

In this paper the qualitative properties of a family of an anharmonic oscillator equations of motion were carried out with phase portraits.

**Category:** Mathematical Physics

[520] **viXra:1609.0211 [pdf]**
*submitted on 2016-09-13 14:54:33*

**Authors:** Prado, Pf

**Comments:** 3 Pages.

Discussion on ressonance considerations about fundamental physics

**Category:** Mathematical Physics

[519] **viXra:1609.0142 [pdf]**
*submitted on 2016-09-11 12:00:21*

**Authors:** J. Akande, L. H. Koudahoun, D. K. K. Adjaï, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 3 pages

In this paper the Schrödinger equation is derived for a dynamical system with exponential-type restoring force function.

**Category:** Mathematical Physics

[518] **viXra:1609.0055 [pdf]**
*submitted on 2016-09-05 08:44:45*

**Authors:** J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 5 pages

This research work proposes a Lagrangian and Hamiltonian analysis for a class of exactly integrable quadratic Liénard-type harmonic nonlinear oscillator equations and its inverted version admitting a position-dependent mass dynamics.

**Category:** Mathematical Physics

[517] **viXra:1609.0037 [pdf]**
*submitted on 2016-09-04 06:28:30*

**Authors:** Y.F.J. Kpomahou, L.H. Koudahoun, D.K.K. Adjaï, J. Akande, M.D. Monsia

**Comments:** 3 pages

The main objective of this paper is to propose two simple analytical linearizing transformation for determining the exact analytical harmonic periodic solution of a class of Liénard-type position-dependent mass oscillator equations. The performed exact analysis shows that both employed analytical methods are efficient to solve this class of equations.

**Category:** Mathematical Physics

[516] **viXra:1609.0036 [pdf]**
*submitted on 2016-09-03 12:10:32*

**Authors:** M. D. Monsia, J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou

**Comments:** 3 pages

This paper purposes to show the existence of exact analytical solutions to a class of generalized Duffing-van der Pol and modified Emden type oscillator equations using nonlocal transformation.

**Category:** Mathematical Physics

[515] **viXra:1609.0029 [pdf]**
*submitted on 2016-09-02 15:17:50*

**Authors:** M. D. Monsia, J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou

**Comments:** 3 pages

The objective in this paper is to show that the generalized Duffing-van der Pol and modified Emden type equations consist of limiting cases of the exactly integrable Monsia et al.[2] nonlinear oscillator equation by expanding the exponential-type damping and restoring forces in a Taylor series.

**Category:** Mathematical Physics

[514] **viXra:1609.0024 [pdf]**
*submitted on 2016-09-02 07:47:41*

**Authors:** Miroslav Josipovic

**Comments:** 70 Pages.

Text is intended as some motivational surway of geometric algebra in 3D. This is just first (condensed) version.

**Category:** Mathematical Physics

[513] **viXra:1609.0003 [pdf]**
*submitted on 2016-09-01 08:27:12*

**Authors:** M. D. Monsia, J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou

**Comments:** 2 pages

This communication consists of additions to a previous work [1]. It presents certain Liénard-type and Duffing-type nonlinear oscillators equations with exponential-type restoring force, according to the recent theory of nonlinear differential equations of position-dependent mass oscillators formulated by Monsia et al. [1].

**Category:** Mathematical Physics

[512] **viXra:1608.0422 [pdf]**
*submitted on 2016-08-31 13:04:28*

**Authors:** Dan Visser

**Comments:** 17 Pages.

Dan Visser (DAN) creates Art from a way of thinking involving another universe. He is retired and has written down his way of thinking in articles through bypassing the institutions. “I know what dark matter is, and I know the institutions still don’t know”. I calculate the percentages of dark matter, dark energy and visible matter close to the measured Planck-satellite values. I also calculated the energy for a dark matter-force (a few years ago), which now appears to fit the experimental values performed by the decay of Berilium-8 showing a value of 16,7 MeV at the atom-scale of 10^-10 meter and a time-scale of about 10^-14 seconds. I also show dark matter co-operates with quantum-gravity in a new formula. The force of dark matter is also showing-up in an experiment revealing the proton-radius becomes 4% smaller due to a muon in orbit instead of an electron. This effect can be calculated by my new dark matter-topology and dark matter–dimensions. Both the experiments (berilium-8 decay and smaller proton-radius), as well as the used dark matter-topology and dark matter–dimensions, gave me the idea to posit a principle for an UFO-motor. Such a motor can be tuned to overcome a gravitational field like earth, or any other planet. Such motor enables to move within the hologram universe, instead of in the Big Bang space-time universe.

**Category:** Mathematical Physics

[511] **viXra:1608.0398 [pdf]**
*submitted on 2016-08-29 08:11:19*

**Authors:** M. D. Monsia, J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou

**Comments:** 2 pages

The present letter adds to the paper ’’ A Class of Position-Dependent Mass Liénard Differential Equations via a General Nonlocal Transformation’’. The purpose is to emphasize the fact that the mathematical theory of position-dependent mass nonlinear oscillator differential equations previously developed [1] provides exact analytical trigonometric periodic solutions to inverted quadratic Mathews-Lakshmanan oscillator equations.

**Category:** Mathematical Physics

[510] **viXra:1608.0368 [pdf]**
*submitted on 2016-08-26 19:09:34*

**Authors:** M. D. Monsia, J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou

**Comments:** 3 pages

This letter consists of additions to the paper ’’ A Class of Position-Dependent Mass Liénard Differential Equations via a General Nonlocal Transformation’’. The objective is to highlight the fact that the general second-order nonlinear differential equation theory of position-dependent mass oscillators developed previously has the ability to provide exact analytical periodic solutions with sinusoidal form to the class of quadratic Liénard-type equations, like the motion of a particle on a rotating parabola and Morse- type oscillator equation, under question.

**Category:** Mathematical Physics

[509] **viXra:1608.0317 [pdf]**
*submitted on 2016-08-25 03:50:33*

**Authors:** Robert G Wallace

**Comments:** 8 Pages.

An algebra for unit multivector components for a manifold of five poly-complex dimensions is presented. The algebra has many properties that suggest it may provide a basis for a grand unification theory.

**Category:** Mathematical Physics

[508] **viXra:1608.0266 [pdf]**
*submitted on 2016-08-23 09:05:27*

**Authors:** M. D. Monsia, J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou

**Comments:** 3 pages

This work aims to present some specific examples of the generalized mixed Liénard differential equation and position-dependent mass Liénard equation depicted in A Class of Position-Dependent Mass Liénard Differential Equations via a General Nonlocal Transformation.

**Category:** Mathematical Physics

[507] **viXra:1608.0244 [pdf]**
*submitted on 2016-08-22 11:03:47*

**Authors:** M.W.Kalinowski

**Comments:** 178 Pages. the paper is written in polish

The Cauchy initial value problem for the Klein-Gordon equation has been considered in a class of
tempered distributions using a notion of a section
of a distribution with a hyperplane. We consider also different linear PDE derivable from Klein-Gordon equation as Dirac, Proca ,Weyl and all the most important wave equations of relativistic quantum mechanics and quantum field theory. We consider also Maxwell equations.We consider also
classical Cauchy initial value problem for those
equations using obtained generalized results e.g.
for Maxwell equations.

**Category:** Mathematical Physics

[506] **viXra:1608.0232 [pdf]**
*submitted on 2016-08-21 14:31:45*

**Authors:** Christian Rakotonirina

**Comments:** 94 Pages. in French

Properties of tensor product of matrices have been constructed. These properties are used to study factorization by tensor product of matrices of some real Clifford algebras of square matrices. Applying these factorizations, we have found a way to get , from the Pauli matrices, twelve systems and only twelve. Each of them is formed of four matrices coefficients of a Dirac equation. We have looked for solutions of these twelve equations for free fundamental fermions. These twelve equations can be constructed by quantification of the relativistic energy-momentum relation. We have introduced a notion that we call ‘’equivalence of particles’’. Then, the equivalence between free fundamental fermions have been studied. Finally, we have proved equivalence between the Dirac equation and the Hestenes equation.

**Category:** Mathematical Physics

[505] **viXra:1608.0226 [pdf]**
*submitted on 2016-08-20 18:47:15*

**Authors:** M. D. Monsia, J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou

**Comments:** 2 pages

The objective, in this paper, consists of mapping the damped linear harmonic oscillator equation onto a class of Liénard nonlinear differential equations that incorporates the well known position dependent mass Mathews-Lakshmanan oscillator equations as specific examples through a general nonlocal transformation.

**Category:** Mathematical Physics

[504] **viXra:1608.0181 [pdf]**
*submitted on 2016-08-17 14:44:03*

**Authors:** J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 2 pages

This letter is devoted to show the existence of a general class of integrable mixed Liénard-type equations that includes some physically important nonlinear differential equations like the generalized modified Emden-type equation (MEE) through the first integral under differentiation approach.

**Category:** Mathematical Physics

[503] **viXra:1608.0124 [pdf]**
*submitted on 2016-08-12 08:02:59*

**Authors:** J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 7 pages

The inverted quadratic Liénard type equation is very useful in various branches of classical and quantum theories, since it admits a position dependent mass dynamics. The objective of the present work is to show that some interesting inverted nonlinear oscillator equations like the inverted version of Mathews-Lakshmanan oscillator belong to a general class of exactly solvable inverted quadratic Liénard equations. This class of equations is generated from a first integral formulated as an integro-differential equation. The obtained results may be used for the identification and integrability of a family of dynamical systems equations.

**Category:** Mathematical Physics

[502] **viXra:1608.0096 [pdf]**
*submitted on 2016-08-08 16:47:42*

**Authors:** Gary D. Simpson

**Comments:** 39 Pages.

This text develops various identities for Hamilton's quaternions. The results are presented in order of difficulty. Results are organized as Axioms, Vectors, Quaternions, and Matrices. There are also sections for Octonions and Pentuples. Axioms are presented first and are largely without rigorous proof. Subsequent identities are constructed from prior identities. When complex conjugates are discussed, the author's thinking is biased towards the original quaternion having a positive vector portion and the conjugate having a negative vector portion. To genuinely understand what is presented, it is recommended that the reader should visualize the concepts in addition to manipulating them algebraically. The algebra is certainly true, but the visual understanding is more elegant and intuitive. This text will likely be updated occasionally.

**Category:** Mathematical Physics

[501] **viXra:1608.0095 [pdf]**
*submitted on 2016-08-08 17:38:43*

**Authors:** Bing Wang

**Comments:** 10 Pages.

Effects of L{\'{e}}vy noise on self-propelled particles in a two-dimensional potential is investigated. The current reversal phenomenon appear in the system. $V$($x$ direction average velocity) changes from negative to positive with increasing asymmetry parameter $\beta$, and changes from positive to negative with increasing self-propelled velocity $v_0$. The $x$ direction average velocity $V$ has a maximum with increasing modulation constant $\lambda$.

**Category:** Mathematical Physics

[500] **viXra:1608.0059 [pdf]**
*submitted on 2016-08-05 12:30:18*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 8 Pages.

The solution for the problem of Breakdown of Euler Equations, like the Millenium Problem for Navier-Stokes equations.

**Category:** Mathematical Physics

[476] **viXra:1707.0214 [pdf]**
*replaced on 2017-07-15 15:09:05*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 3 Pages.

Advance superstrings are consider incalculable particles. With this in mind a more refine definition of the grand unification scheme and metaspace is presented.

**Category:** Mathematical Physics

[475] **viXra:1707.0056 [pdf]**
*replaced on 2017-07-05 15:43:42*

**Authors:** Ehsan Azadi

**Comments:** 19 pages

The birth of modern continuum mechanics was the Cauchy's idea for traction vectors and his achievements of the existence of stress tensor and derivation of the general equation of motion. He gave a proof for the existence of stress tensor that is called Cauchy tetrahedron argument. But there are some challenges on the different versions of tetrahedron argument and the proofs for the existence of stress tensor. We give a new proof for the existence of stress tensor and derivation of the general equation of motion. The exact tetrahedron argument for the first time gives us a clear and deep insight into the origins and the nature of these fundamental concepts and equations in continuum mechanics. This new approach leads to the exact point-base definition and derivation of these fundamental parameters and relations in continuum mechanics. By the exact tetrahedron argument we derived the relation for the existence of stress tensor and the general equation of motion, simultaneously. In this new proof, there is no approximating or limiting process and all of the effective parameters are exact values not average values. Also, we show that in this proof, all the challenges on the previous tetrahedron arguments and the proofs for the existence of stress tensor are removed.

**Category:** Mathematical Physics

[474] **viXra:1707.0022 [pdf]**
*replaced on 2017-07-03 00:54:24*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 8 Pages. This paper has not been submitted to a journal. Your comments are welcome

It has been long known that a year after Schrödinger published his equation, Madelung also published a hydrodynamics version of Schrödinger equation. Quantum diffusion is studied via dissipative Madelung hydrodynamics. Initially the wave packet spreads ballistically, than passes for an instant through normal diffusion and later tends asymptotically to a sub‐diffusive law. In this paper we will review two different approaches, including Madelung hydrodynamics and also Bohm potential. Madelung formulation leads to diffusion interpretation, which after a generalization yields to Ermakov equation. Since Ermakov equation cannot be solved analytically, then we try to find out its solution with Mathematica package. It is our hope that these methods can be verified and compared with experimental data. But we admit that more researches are needed to fill all the missing details.

**Category:** Mathematical Physics

[473] **viXra:1706.0193 [pdf]**
*replaced on 2017-07-15 21:47:18*

**Authors:** A. A. Frempong

**Comments:** 19 Pages. Copyright © by A. A. Frempong

Coincidences. The US Supreme Court consists of nine members, one of whom is the Chief Justice of the Court. So also, a one-direction Navier-Stokes equation consists of nine members, one of which is the indispensable gravity term, without which there would be no incompressible fluid flow as shown by the solutions of the N-S equations (viXra:1512.0334). Another coincidence is that numerologically, the number, 9, is equivalent to the 1800's (1 + 8 + 0 + 0 = 9) time period during which the number of the members of the Supreme Court became fixed at 9, while the formulation of the nine-term N-S equations was completed. Also, another coincidence is that the solutions of the N-S equations were completed (viXra:1512.0334) by the author in the year, 2016 (2 + 0 +1+ 6 = 9). Using a new introductory approach, this paper covers the author's previous solutions of the N-S equations (viXra:1512.0334). In particular, the N-S solutions have been compared to the equations of motion and liquid pressure of elementary physics. The N-S solutions are (except for the constants involved) very similar or identical to the equations of motion and liquid pressure of elementary physics. The results of the comparative analysis show that the N--S equations have been properly solved. It could be stated that the solutions of the N-S equations have existed since the time the equations of motion and liquid pressure of elementary physics were derived. A one-direction Navier-Stokes equation has also been derived from the equations of motion and liquid pressure of elementary physics. Insights into the solutions include how the polynomial parabolas, the radical parabolas, and the hyperbolas interact to produce turbulent flow. It is argued that the solutions and methods of solving the N-S equations are unique, and that only the approach by the author will ever produce solutions to the N-S equations. By a solution, the equation must be properly integrated and the integration results must be tested in the original equation for identity before the integration results are claimed as solutions

**Category:** Mathematical Physics

[472] **viXra:1706.0193 [pdf]**
*replaced on 2017-07-03 01:18:21*

**Authors:** A. A. Frempong

**Comments:** 19 Pages. Copyright © by A. A. Frempong

Coincidences. The US Supreme Court consists of nine members, one of whom is the Chief Justice of the Court. So also, a one-direction Navier-Stokes equation consists of nine members, one of which is the indispensable gravity term, without which there would be no incompressible fluid flow as shown by the solutions of the N-S equations (viXra:1512.0334). Another coincidence is that numerologically, the number, 9, is equivalent to the 1800's (1 + 8 + 0 + 0 = 9) time period during which the number of the members of the Supreme Court became fixed at 9, while the formulation of the nine-term N-S equations was completed. Also, another coincidence is that the solutions of the N-S equations were completed (viXra:1512.0334) by the author in the year, 2016 (2 + 0 +1+ 6 = 9). Using a new introductory approach, this paper covers the author's previous solutions of the N-S equations (viXra:1512.0334). In particular, the N-S solutions have been compared to the equations of motion and liquid pressure of elementary physics. The N-S solutions are (except for the constants involved) very similar or identical to the equations of motion and liquid pressure of elementary physics. The results of the comparative analysis show that the N--S equations have been properly solved. It could be stated that the solutions of the N-S equations have existed since the time the equations of motion and liquid pressure of elementary physics were derived. A one-direction Navier-Stokes equation has also been derived from the equations of motion and liquid pressure of elementary physics. Insights into the solutions include how the polynomial parabolas, the radical parabolas, and the hyperbolas interact to produce turbulent flow. It is argued that the solutions and methods of solving the N-S equations are unique, and that only the approach by the author will ever produce solutions to the N-S equations. By a solution, the equation must be properly integrated and the integration results must be tested in the original equation for identity before the integration results are claimed as solutions

**Category:** Mathematical Physics

[471] **viXra:1706.0137 [pdf]**
*replaced on 2017-06-14 12:16:22*

**Authors:** Marcellin Nonti, Fernando Y. J. Kpomahou, Jean Akande, Damien K. K. Adjaï, Lucas H. Koudahoun, Marc D. Monsia

**Comments:** 4 pages

Hamiltonian dynamics and exact Gibbs statistical mechanics of a system of quadratic Liénard type oscillators have been investigated. The work has shown that the canonical ensemble for the harmonic oscillator is a particular case of the Gibbs ensemble theory developed in this paper.

**Category:** Mathematical Physics

[470] **viXra:1705.0374 [pdf]**
*replaced on 2017-06-12 02:09:24*

**Authors:** Zihao Song

**Comments:** 6 Pages. If one physical quantity can't find where it is originated, it's not a good physical quantity.

Physicists are proposing different mechanics to describe the nature, physical body is measured by intrinsic properties like electric charge, and extrinsic properties being related to space like generalized coordinates or velocities etc., with these properties we can predict what event will happen. We can naturally define the fact of the event and the cause of the event as information, the information grasped by physicist must be originated from something objective, information must have its object container. Intrinsic property information is contained by object itself, but container of extrinsic property information like position is ambiguous, position is a relation based on multiple objects, it's hard to define which one is the information container. With such ambiguity, no mechanics is a complete theory, errors hidden in assumptions are hard to find. Here we show a new theoretical framework with strict information container restriction, on which we can build complete determinism theories to approach grand unification.

**Category:** Mathematical Physics

[469] **viXra:1705.0347 [pdf]**
*replaced on 2017-06-19 04:02:19*

**Authors:** Preobrazhenskiy Andrey

**Comments:** 13 Pages.

ABSTRACT. This paper deals with the analysis of physically possible constructions of a viscous incompressible fluid model. Physical principles that allow to create the only possible construction of this model were found. The new model does not use new constants that characterize properties of the fluid and coincides with the Stokes model only in the plane case. Within the framework of this model, new equations for fluid motion were obtained. The new equations coincide with Navier-Stokes system in the plane case, but do not coincide in the three-dimensional one. The model makes it possible to see why the three-dimensional Navier-Stokes equations cannot physically adequately describe fluids motion, and obliquely confirms the finite time for the existence of its regular solutions.

**Category:** Mathematical Physics

[468] **viXra:1705.0347 [pdf]**
*replaced on 2017-05-27 09:01:13*

**Authors:** Preobrazhenskiy Andrey

**Comments:** 11 Pages.

ABSTRACT. This paper deals with the analysis of physically possible constructions of a viscous incompressible fluid model. Physical principles that allow to create the only possible construction of this model were found. The new model does not use new constants that characterize properties of the fluid and coincides with the Stokes model only in the plane case. Within the framework of this model, new equations for fluid motion were obtained. The new equations coincide with Navier-Stokes system in the plane case, but do not coincide in the three-dimensional one. The model makes it possible to see why the three-dimensional Navier-Stokes equations cannot physically adequately describe fluids motion, and obliquely confirms the finite time for the existence of its regular solutions.

**Category:** Mathematical Physics

[467] **viXra:1705.0300 [pdf]**
*replaced on 2017-05-23 08:56:56*

**Authors:** Miroslav Josipović

**Comments:** 80 Pages. geometric algebra

This is the translation of the article "Multiplication of Vectors and Structure of 3D Euclidean Space" to Croatian.

**Category:** Mathematical Physics

[466] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-22 05:29:56*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 72 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to a candidate for the theory of everything in physics (ToE). Part I is the axiomless derivation of the ToE-candidate. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy. Part III is the thesis that this master equation is indeed a credible ToE-candiate. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GR). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GR from this equation is considered strong evidence that they are unified in it. Using this unification, we also propose a quantum mechanical description of black holes, and derive laws specific to it.

**Category:** Mathematical Physics

[465] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-21 13:53:03*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 71 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to a candidate for the theory of everything in physics (ToE).
Part I is the axiomless derivation of the ToE-candidate. From this derivation I obtain, in part II, a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy.
Part III is the thesis that this master equation is indeed a credible ToE-candiate. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics (QM), special and general relativity (GM). These equations are derived entirely from pure reason with no appeal to physical observations. Deriving both QM and GM from this equation is considered strong evidence that they are unified in it. Using this unification, we also propose a quantum mechanical description of black holes, and derive laws specific to it.

**Category:** Mathematical Physics

[464] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-12 07:20:57*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 66 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE).
Part I is the axiomless derivation of the ToE. From this derivation I obtain a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy.
Part III is the thesis that this master equation is indeed the ToE. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics, special and general relativity. These equations are derived entirely from pure reason with no appeal to physical observations.
\end{abstract}

**Category:** Mathematical Physics

[463] **viXra:1705.0274 [pdf]**
*replaced on 2017-07-11 20:36:09*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 66 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE).
Part I is the axiomless derivation of the ToE. From this derivation I obtain a master equation formulated as a Gibb's ensemble and relating the algorithmic notions of program-observables to that of entropy.
Part III is the thesis that this master equation is indeed the ToE. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics, special and general relativity. These equations are derived entirely from pure reason with no appeal to physical observations.

**Category:** Mathematical Physics

[462] **viXra:1705.0274 [pdf]**
*replaced on 2017-05-26 07:05:40*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 48 Pages.

In this work, I present a formal construction of the axiomless position. This construction ultimately leads to the theory of everything in physics (ToE).
Part I of this work is the axiomless derivation of the ToE. From this derivation I obtain a master equation relating the notions of truth, knowledge and information to that of entropy.
Part II is the thesis that this master equation is indeed the ToE. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics, special and general relativity. These equations are derived entirely from pure reason with no appeal to physical observations.
The work here can also be interpreted as a constructive proof of René Descartes' cogito ergo sum. Where-as he proved the existence of the thinking self by contradiction, it is here proven by construction.

**Category:** Mathematical Physics

[461] **viXra:1705.0274 [pdf]**
*replaced on 2017-05-23 14:09:54*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 48 Pages.

Plato recognized that most of the disagreement in philosophy is ultimately linked to the choice of axioms made by the parties involved. He believed that by grinding away at the assumptions made for any argument, one could recover a kind universal truth. He believed that this universal truth, comprised of whatever survives the grinding process, could ultimately be used to build a logical framework in a manner that is entirely irrefutable. This is the axiomless position.
In this work, I present such a derivation.
Part I of this work is the axiomless derivation of the theory of everything in physics. From this derivation I obtain a master equation relating the notions of truth, knowledge and information to that of entropy.
Part II is the thesis that this master equation is indeed the theory of everything in physics. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics, special and general relativity. These equations are entirely derived from pure reason with no appeal to physical observations.
The work here can also be interpreted as a constructive proof of René Descartes' cogito ergo sum. Where-as he proved the existence of the thinking self by contradiction, it is here proven by construction.

**Category:** Mathematical Physics

[460] **viXra:1705.0274 [pdf]**
*replaced on 2017-05-18 12:57:31*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 46 Pages.

Using the cogito ergo sum as a starting point, I introduce a methodology which allows non-trivial knowledge to be obtained without the formal introduction of axioms. Using this methodology which I formalize, I then obtain a theory of everything (ToE) in physics. This method allows me to avoid the self-referential problem of a ToE which I argue is the core difficulty of any ToE built upon formal axioms. The theory obtained has enough generality to recover both general relativity and quantum field theory. Some of the new physics derived herein include a hard arrow time, an explanation of the quantum mechanical measurement, and a thermodynamic proof that the speed of light is maximal.

**Category:** Mathematical Physics

[459] **viXra:1705.0035 [pdf]**
*replaced on 2017-05-04 02:31:50*

**Authors:** Victor Christianto, Sergey Ershkov

**Comments:** 11 Pages. This paper is to be submitted to Royal Society Open Access journal. Your comments are welcome.

In a recent paper, Ershkov derived a system of two coupled Riccati ODEs as solution of non-stationary incompressible 3D Navier-Stokes equations. Now in this paper, we solve these coupled Riccati ODEs using: a) Maxima and b) Mathematica 11 computer algebra packages. The result seems to deserve further investigation in particular in comparison with rigid body motion, which will be discussed elsewhere.

**Category:** Mathematical Physics

[458] **viXra:1704.0264 [pdf]**
*replaced on 2017-06-06 07:20:18*

**Authors:** Paul Werbos

**Comments:** 15 Pages. 15p, 36 eq. typos corrected -- eq 7, refs to eqs 26 and 27.

Today’s standard model of physics treats the physical masses of elementary particles as given, and assumes that they have a bare radius of zero, as in the older classical physics of Lorentz. Many physicists have studied the properties of the Yang-Mills-Higgs model of continuous fields in hopes that it might help to explain where elementary particles (and their masses) come from in the first place. This paper reviews some of the important prior work on Yang-Mills-Higgs and solitons in general, but it also shows that stable particles in that model cannot have intrinsic angular momentum (spin). It specifies four extensions of Yang-Mills Higgs, the Lagrangians L1 through L4, which are closer to the standard model of physics, and shows that one of the four (L3) does predict/explain spin from a purely neoclassical theory. The paper begins by summarizing the larger framework which has inspired this work, and ends by discussing two possibilities for further refinement.

**Category:** Mathematical Physics

[457] **viXra:1704.0199 [pdf]**
*replaced on 2017-04-28 10:55:41*

**Authors:** J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 16 pages

The problem of finding exact trigonometric periodic solutions to non-linear differential equations is still an open mathematical research field. In this paper it is shown that the Painlevé-Gambier XVIII equation and its inverted version may exhibit exact trigonometric periodic solutions as well as other quadratic Liénard type equations but with amplitude-dependent frequency. Other inverted Painlevé-Gambier equations are also shown to admit exact periodic solutions.

**Category:** Mathematical Physics

[456] **viXra:1704.0199 [pdf]**
*replaced on 2017-04-17 09:28:29*

**Authors:** J. Akande, D.K.K. Adjaï, L.H. Koudahoun, Y.J.F. Kpomahou, M.D. Monsia

**Comments:** 16 pages

The problem of finding exact trigonometric periodic solutions to non-linear differential equations is still an open mathematical research field. In this paper it is shown that the Painlevé-Gambier XVIII equation and its inverted version may exhibit exact trigonometric periodic solutions as well as other quadratic Liénard type equations but with amplitude-dependent frequency. Other inverted Painlevé-Gambier equations are also shown to admit exact periodic solutions.

**Category:** Mathematical Physics

[455] **viXra:1704.0108 [pdf]**
*replaced on 2017-05-06 15:26:07*

**Authors:** Frederick Moxley

**Comments:** 14 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained. Finally, it is shown that all of the nontrivial zeros are located at $\Re(z)=1/2$.

**Category:** Mathematical Physics

[454] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-25 23:28:28*

**Authors:** Frederick Moxley

**Comments:** 15 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained. Finally, it is shown that all of the nontrivial zeros are located at $\Re(z)=1/2$.

**Category:** Mathematical Physics

[453] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-12 02:44:54*

**Authors:** Frederick Moxley

**Comments:** 12 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained.

**Category:** Mathematical Physics

[452] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-11 09:55:38*

**Authors:** Frederick Moxley

**Comments:** 12 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained.

**Category:** Mathematical Physics

[451] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-10 10:53:56*

**Authors:** Frederick Moxley

**Comments:** 11 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture. Moreover, a second quantization of the BBM Schr\"odinger equation is performed, and a closed-form solution for the nontrivial zeros of the Riemann zeta function is obtained.

**Category:** Mathematical Physics

[450] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-10 02:23:55*

**Authors:** Frederick Moxley

**Comments:** 11 Pages.

**Category:** Mathematical Physics

[449] **viXra:1704.0108 [pdf]**
*replaced on 2017-04-09 09:26:07*

**Authors:** Frederick I Moxley

**Comments:** 11 Pages.

In the year 2017 it was formally conjectured that if the Bender-Brody-M\"uller (BBM) Hamiltonian can be shown to be self-adjoint, then the Riemann hypothesis holds true. Herein we discuss the domain and eigenvalues of the Bender-Brody-M\"uller conjecture.

**Category:** Mathematical Physics

[448] **viXra:1704.0064 [pdf]**
*replaced on 2017-06-09 07:25:29*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 7 Pages. My next paper will be "On a Problem in Euler and Navier-Stokes Equations", complementing this one.

A brief draft respect to a problem found in the equations of Euler and Navier-Stokes, whose adequate treatment solves a centennial problem about the solution of these equations and a most correct modeling of fluid movement.

**Category:** Mathematical Physics

[447] **viXra:1704.0064 [pdf]**
*replaced on 2017-06-03 13:32:33*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 7 Pages.

A brief draft respect to a problem found in the equations of Euler and Navier-Stokes, whose adequate treatment solves a centennial problem about the solution of these equations and a most correct modeling of fluid movement.

**Category:** Mathematical Physics

[446] **viXra:1704.0064 [pdf]**
*replaced on 2017-04-29 20:24:09*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** page 6, change parabolic type by elliptic type. Sorry.

**Category:** Mathematical Physics

[445] **viXra:1704.0064 [pdf]**
*replaced on 2017-04-12 13:08:28*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 6 Pages.

**Category:** Mathematical Physics

[444] **viXra:1704.0064 [pdf]**
*replaced on 2017-04-09 10:06:32*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 6 Pages.

**Category:** Mathematical Physics

[443] **viXra:1703.0282 [pdf]**
*replaced on 2017-06-05 11:58:12*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 11 Pages.

Given an adiabatic system of particles as defined in [4], the problem is whether and to what degree one can break it into its constituents and describe their mutual interaction.

**Category:** Mathematical Physics

[442] **viXra:1703.0282 [pdf]**
*replaced on 2017-05-19 15:20:23*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 11 Pages.

Given an adiabatic system of particles as defined in [4], the problem is whether and to what degree one can break it into its constituents and describe their mutual interaction.

**Category:** Mathematical Physics

[441] **viXra:1703.0282 [pdf]**
*replaced on 2017-04-16 12:35:39*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 10 Pages.

**Category:** Mathematical Physics

[440] **viXra:1703.0282 [pdf]**
*replaced on 2017-04-04 11:14:46*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 10 Pages.

**Category:** Mathematical Physics

[439] **viXra:1703.0282 [pdf]**
*replaced on 2017-04-01 02:37:45*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 10 Pages.

**Category:** Mathematical Physics

[438] **viXra:1702.0244 [pdf]**
*replaced on 2017-02-26 21:01:18*

**Authors:** Victor Christianto

**Comments:** 4 Pages. This paper has been submitted to Prespacetime Journal

In a recent paper, Ershkov derived a system of two coupled Riccati ODEs as solution of non-stationary 3D Navier-Stokes equations. Now in this paper, we will solve these coupled Riccati ODEs using Maxima computer algebra package. The result seems to deserve further investigation in particular for finding non-stationary 3D Navier-Stokes equations for real fluid.

**Category:** Mathematical Physics

[437] **viXra:1702.0098 [pdf]**
*replaced on 2017-02-10 03:21:43*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 3 Pages.

From string theory to topstringy.

**Category:** Mathematical Physics

[436] **viXra:1701.0523 [pdf]**
*replaced on 2017-04-26 09:09:52*

**Authors:** Grushka Ya.I.

**Comments:** 208 Pages. Mathematics Subject Classification: 03E75; 70A05; 83A05; 47B99. DOI: 10.13140/RG.2.2.24968.62720

This work lays the foundations of the theory of kinematic changeable sets ("abstract kinematics"). Theory of kinematic changeable sets is based on the theory of changeable sets. From an intuitive point of view, changeable sets are sets of objects which, unlike elements of ordinary (static) sets, may be in the process of continuous transformations, and which may change properties depending on the point of view on them (that is depending on the reference frame). From the philosophical and imaginative point of view the changeable sets may look like as "worlds" in which evolution obeys arbitrary laws.
Kinematic changeable sets are the mathematical objects, consisting of changeable sets, equipped by different geometrical or topological structures (namely metric, topological, linear, Banach, Hilbert and other spaces). In author opinion, theories of changeable and kinematic changeable sets (in the process of their development and improvement), may become some tools of solving the sixth Hilbert problem at least for physics of macrocosm. Investigations in this direction may be interesting for astrophysics, because there exists the hypothesis, that in the large scale of Universe, physical laws (in particular, the laws of kinematics) may be different from the laws, acting in the neighborhood of our solar System. Also these investigations may be applied for the construction of mathematical foundations of tachyon kinematics.
We believe, that theories of changeable and kinematic changeable sets may be interesting not only for theoretical physics but also for other fields of science as some, new, mathematical apparatus for description of evolution of complex systems.

**Category:** Mathematical Physics

[435] **viXra:1701.0309 [pdf]**
*replaced on 2017-02-04 13:13:24*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages.

This paper is on the mathematical structure of space, time, and gravity. It is shown that electrodynamics is neither charge inversion invariant, nor is it time inversion invariant.

**Category:** Mathematical Physics

[434] **viXra:1701.0309 [pdf]**
*replaced on 2017-01-22 10:51:37*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages. added comment on mass gap + corrected function=>functional.

This paper is on the mathematical structure of space, time, and gravity. It is shown that electrodynamics is neither charge inversion invariant, nor is it time inversion invariant.

**Category:** Mathematical Physics

[433] **viXra:1701.0309 [pdf]**
*replaced on 2017-01-08 17:30:17*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages. added comment on mass gap.

**Category:** Mathematical Physics

[432] **viXra:1701.0299 [pdf]**
*replaced on 2017-01-15 11:21:14*

**Authors:** William O. Straub

**Comments:** 13 Pages. Finalized, with typos fixed in Equations (6.2.2) and (6.3.2)

A very elementary overview of the spinor concept, intended as a guide for undergraduates.

**Category:** Mathematical Physics

[431] **viXra:1701.0299 [pdf]**
*replaced on 2017-01-11 00:10:53*

**Authors:** William O. Straub

**Comments:** 13 Pages. Expanded and slightly revised in v2

A very elementary overview of the spinor concept, intended as a guide for undergraduates.

**Category:** Mathematical Physics

[430] **viXra:1612.0201 [pdf]**
*replaced on 2017-01-02 09:09:11*

**Authors:** Robert Deloin

**Comments:** 7 Pages. Version 2.

Riemann's hypothesis (1859) is the conjecture stating that:
The real part of every non trivial zero of Riemann's zeta function is 1/2.
The main contribution of this paper is to achieve the proof of Riemann's hypothesis. The key idea is to provide an Hamiltonian operator whose real eigenvalues correspond to the imaginary part of the non trivial zeros of Riemann's zeta function and whose existence, according to Hilbert and Polya, proves Riemann's hypothesis.

**Category:** Mathematical Physics

[429] **viXra:1611.0162 [pdf]**
*replaced on 2017-01-13 07:30:24*

**Authors:** Biswanath Rath, Pravanjan Mallick, Jean Akande, D.K.K. Adjay, L.H. Koudahoun, Y.J.F Kpomahou, Marc D. Monsia

**Comments:** 18 pages

We generate a general model of Liénard type of second order differential equation and study
its classical solution. We also generate Hamiltonian from the differential equation and study
its stable eigenvalues.

**Category:** Mathematical Physics

[428] **viXra:1610.0337 [pdf]**
*replaced on 2016-11-20 13:13:40*

**Authors:** Nicolas Poupart

**Comments:** 6 Pages.

Il sera démontré dans cet article que la masse noire est une conséquence nécessaire de la mécanique relativiste. Cette démonstration fait abstraction des forces de la physique et est donc une explication purement mécanique. La relation de Tully-Fisher sera déduite naturellement, sans appel à une quelconque nouvelle physique, et il est par conséquent possible de dériver cette loi sans modifier la gravitation de Newton ou la relativité générale. De plus, une prédiction théorique sur une nouvelle forme de décalage de fréquence sera effectuée permettant de réfuter ou de confirmer cette théorie.

**Category:** Mathematical Physics

[427] **viXra:1609.0055 [pdf]**
*replaced on 2016-10-05 08:35:53*

**Authors:** J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 5 pages

This research work proposes a Lagrangian and Hamiltonian analysis for the unique class of position-dependent mass oscillator characterized by a harmonic periodic solution and parabolic potential energy and its inverted version admitting a position-dependent mass dynamics.

**Category:** Mathematical Physics

[426] **viXra:1609.0024 [pdf]**
*replaced on 2017-05-23 08:59:11*

**Authors:** Miroslav Josipović

**Comments:** 82 Pages. geometric algebra

The text is intended as some motivational survey of geometric algebra in 3D. Proofs are short and original. Multiplication of vectors is discussed in general, then basics of geometric algebra are founded. Among others, the special relativity, quantum mechanics and electromagnetic theories are discussed, operations on subspaces, dual, hyperbolic and complex numbers, linear transformations, idempotents, nilpotents, rotations, functions on multivectors, conformal model, calculus in geometric algebra, etc. Some problems are left to reader to solve. This is a new version with extended literature, software and list of names. Some typos are corrected.

**Category:** Mathematical Physics

[425] **viXra:1609.0024 [pdf]**
*replaced on 2017-05-20 09:37:11*

**Authors:** Miroslav Josipović

**Comments:** 81 Pages.

The text is intended as some motivational survey of geometric algebra in 3D. Proofs are short and original. Multiplication of vectors is discussed in general, then basics of geometric algebra are founded. Among others, the special relativity, quantum mechanics and electromagnetic theories are discussed, operations on subspaces, dual, hyperbolic and complex numbers, linear transformations, idempotents, nilpotents, rotations, functions on multivectors, conformal model, calculus in geometric algebra, etc. Some problems are left to reader to solve.
This is a new version with extended literature, software and list of names. Some typos are corrected. Final version.

**Category:** Mathematical Physics

[424] **viXra:1609.0024 [pdf]**
*replaced on 2017-03-11 12:26:41*

**Authors:** Miroslav Josipović

**Comments:** 82 Pages. Please, give me a feedback! Thank you!

The text is intended as some motivational survey of geometric algebra in 3D. Proofs are
short and original. Multiplication of vectors is discussed in general, then basics of
geometric algebra are founded. Among others, the special relativity, quantum mechanics and
electromagnetic theories are discussed, operations on subspaces, dual, hyperbolic and
complex numbers, linear transformations, idempotents, nilpotents, rotations, functions on
multivectors, conformal model, calculus in geometric algebra, etc. Some problems are left
to reader to solve.
This is a new version with extended literature, software and list of names. Some typos are
corrected.

**Category:** Mathematical Physics

[423] **viXra:1609.0024 [pdf]**
*replaced on 2017-02-21 13:39:36*

**Authors:** Miroslav Josipović

**Comments:** 78 Pages. Please, give me a feedback! Thank you!

The text is intended as some motivational survey of geometric algebra in 3D. Proofs are short and original. Multiplication of vectors is discussed in general, then basics of geometric algebra are founded. Among others, the special relativity, quantum mechanics and electromagnetic theories are discussed, operations on subspaces, dual, hyperbolic and complex numbers, linear transformations, idempotents, nilpotents, rotations, functions on multivectors, conformal model, calculus in geometric algebra, etc. Some problems are left to reader to solve.

**Category:** Mathematical Physics

[422] **viXra:1608.0317 [pdf]**
*replaced on 2016-08-25 22:30:14*

**Authors:** Robert G Wallace

**Comments:** 9 Pages.

An algebra for unit multivector components for a manifold of five poly-complex dimensions is presented. The algebra has many properties that suggest it may provide a basis for a grand unification theory.

**Category:** Mathematical Physics

[421] **viXra:1608.0181 [pdf]**
*replaced on 2016-09-15 07:53:55*

**Authors:** J. Akande, D. K. K. Adjaï, L. H. Koudahoun, Y. J. F. Kpomahou, M. D. Monsia

**Comments:** 4 pages

The Lagrangian description of a dynamical system from the equation of motion consists of an inverse problem in mechanics. This problem is solved for a class of exactly integrable mixed and quadratic Liénard type oscillator equations from a given first integral of motion. The dynamics of this class of equations, which contains the generalized modified Emden equation, also known as the second-order Riccati equation, and the inverted versions of the Mathews-Lakshmanan equations, is then investigated from Hamiltonian and Lagrangian points of view.

**Category:** Mathematical Physics

[420] **viXra:1608.0059 [pdf]**
*replaced on 2016-08-27 13:33:54*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 11 Pages.

The solution for the problem of Breakdown of Euler Equations, like the Millenium Problem for Navier-Stokes equations.

**Category:** Mathematical Physics

[419] **viXra:1608.0059 [pdf]**
*replaced on 2016-08-19 06:48:23*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 11 Pages.

The solution for the problem of Breakdown of Euler Equations, like the Millenium Problem for Navier-Stokes equations.

**Category:** Mathematical Physics

[418] **viXra:1608.0059 [pdf]**
*replaced on 2016-08-15 18:59:23*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

**Category:** Mathematical Physics

[417] **viXra:1608.0059 [pdf]**
*replaced on 2016-08-15 06:56:32*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 4 Pages.

First date: remembering the need of impose the boundary condition u(x,t)=0 at infinity to ensure uniqueness solutions to the Navier-Stokes equations. Second date: verifying that for potential and incompressible flows there is no uniqueness solutions when the velocity is equal to zero at infinity. More than this, when the velocity is equal to zero at infinity for all t≥0 there is no uniqueness solutions, in general case. Exceptions when u^0=0. The first date is historical only. Last date: non-uniqueness in time for incompressible and potential flows, if u≠0.

**Category:** Mathematical Physics

[416] **viXra:1608.0059 [pdf]**
*replaced on 2016-08-13 16:24:12*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

**Category:** Mathematical Physics

[415] **viXra:1608.0059 [pdf]**
*replaced on 2016-08-12 13:12:29*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

**Category:** Mathematical Physics

[414] **viXra:1608.0059 [pdf]**
*replaced on 2016-08-08 12:48:47*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

**Category:** Mathematical Physics

[413] **viXra:1608.0059 [pdf]**
*replaced on 2016-08-08 03:21:24*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

**Category:** Mathematical Physics

[412] **viXra:1608.0059 [pdf]**
*replaced on 2016-08-06 11:13:40*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

**Category:** Mathematical Physics