# Mathematical Physics

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## Recent submissions

Any replacements are listed further down

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

### Poly-Complex Clifford Algebra and Grand Unification

Authors: Robert G Wallace

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

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

### Additions to A Class of Position-Dependent Mass Liénard Differential Equations via a General Nonlocal Transformation

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

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

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

### Generalized Solutions of the Klein-Gordon Equation and Some Relativistic Equations in a Class of Tempered Distribotions (In Polish)

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

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

### Produit Tensoriel de Matrices en Théorie de Dirac

Authors: Christian Rakotonirina

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

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

### A Class of Position-Dependent Mass Liénard Differential Equations Via a General Nonlocal Transformation

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

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

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

### A Class of Integrable Mixed Liénard-Type Differential Equations

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

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

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

### A General Class of Exactly Solvable Inverted Quadratic Liénard Type Equations

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

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

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

### Quaternion Dynamics, Part 2 - Identities, Octonions, and Pentuples

Authors: Gary D. Simpson

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

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

### The Current Reversal Phenomenon of Brownian Particles in a Two-Dimensional Potential with L{\'{e}}vy Noise

Authors: Bing Wang

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

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

### Breakdown of Euler Equations – New Approach

Authors: Valdir Monteiro dos Santos Godoi

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

[504] viXra:1607.0384 [pdf] submitted on 2016-07-20 15:09:39

### Coordinate Systems Larger Than Four Dimensions

Authors: Jerry L. Decker
Comments: 5 Pages. Eliminating transformations space like and time like at high speed

A method was found for constructing coordinate systems larger than four dimensions. Velocity vectors and base units were used to define a reference frame by attaching a clock to each of the velocity components. Additional meters were also attached to velocity components. All of the resulting systems can be physically constructed and tested.
Category: Mathematical Physics

[503] viXra:1607.0374 [pdf] submitted on 2016-07-19 18:32:01

### Explanatory Theory of Physics: The Grand Unification Scheme

Authors: Miguel A. Sanchez-Rey

Why did unification work better with the Super-Yang Mills Gauge Analog than any other unification attempts?
Category: Mathematical Physics

[502] viXra:1607.0199 [pdf] submitted on 2016-07-17 15:09:37

### A Theory of Exactly Integrable Quadratic Liénard type Equations

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

The dynamics of quadratic Liénard type equations is usually investigated in the only context of periodic solutions. The problem of interest in this work is then to demonstrate the existence of a simple variable transformation generating a class of exactly integrable quadratic Liénard type equations that preserves the three distinct damped dynamical operating regimes of nonlinear oscillators. Specific examples of equation belonging to this class and their exact solutions in terms of the periodic solution to linear harmonic oscillator are provided for illustrating the developed theory.
Category: Mathematical Physics

[501] viXra:1607.0148 [pdf] submitted on 2016-07-12 13:43:28

### Metaspace

Authors: Miguel A. Sanchez-Rey

What is metaspace?
Category: Mathematical Physics

[500] viXra:1607.0123 [pdf] submitted on 2016-07-10 14:02:38

### Massive Scalar Field Theory on Discrete N-Scales

Authors: Furkan Semih Dundar

$N$-scales are a generalization of time-scales that has been put forward to unify continuous and discrete analyses to higher dimensions. In this paper we investigate massive scalar field theory on $n$-scales. In a specific case of a regular 2-scale, we find that the IR energy spectrum is almost unmodified when there are enough spatial points. This is regarded as a good sign because the model reproduces the known results in the continuum approximation. Then we give field equation on a general $n$-scale. It has been seen that the field equation can only be solved via computer simulations. Lastly, we propose that $n$-scales might be a good way to model singularities encountered in the general theory of relativity.
Category: Mathematical Physics

[499] viXra:1607.0096 [pdf] submitted on 2016-07-08 06:09:08

### Consideration of Some Generalizations of Riemann-Liouville Integral in Physics

Authors: Zoran B. Vosika

Generalization of fractal density on a fractals for spaces with positive and negative fractal dimensions. Fractal-fractional generalized physics (i.e. classical or quantum physics). Generalized Hausdorff measures. Numbers and generalized functions as generalized logical values. Beyond logics and numbers. Generalized concept of physical field, i.e generalized universes and multiverses. Fractional generalization of path integrals.
Category: Mathematical Physics

[498] viXra:1606.0294 [pdf] submitted on 2016-06-27 10:58:21

### A Note About The Resolution of Navier-Stokes Equations

This note represents an attempt of solving the Navier-Stokes equations under the assumptions (A) of the problem as described by the Clay Institute (C.L. Fefferman, 2006).
Category: Mathematical Physics

[497] viXra:1606.0259 [pdf] submitted on 2016-06-24 10:04:44

### Relativity and Electron Deep Orbits of the Hydrogen Atom

Authors: Jean-Luc Paillet, Andrew Meulenberg
Comments: Pages. Presented to 1st Symp. on RNBE (LENR), March 18-20 2016, Avignon, France

This work continues our previous works on electron deep orbits of the hydrogen atom. An introduction shows the importance of the deep orbits of hydrogen (H or D) for research in the LENR domain, and gives some general considerations on the Electron Deep Orbits (EDOs). In a first part we quickly recall the known criticism against the EDO and how we face it. In particular, a solution to fix all problems is to consider a modified Coulomb potential with finite value inside the nucleus. For this reason, we deeply analyzed the specific work of Maly and Va’vra on deep orbits as solutions of the Dirac equation, with such a modified Coulomb potential without singular point. Then, by using a more complete ansatz, we made numerous computations on the wavefunctions of these EDOs, allowing to confirm the approximate size of the mean radii of orbits and to find further properties. Moreover, we observed that the essential element for obtaining deep orbits solutions is special relativity. At a first glance, this fact results from an obvious algebraic property of the expression of energy levels obtained by the relativistic equations. Now, a comparative analysis of the relativistic and of the non-relativistic Schrödinger equation allows us to affirm that Special Relativity leads to the existence of EDOs because of the non-linear form of the relativistic expression for the total energy, which implies a relativistic non-linear correction to the Coulomb potential
Category: Mathematical Physics

[496] viXra:1606.0185 [pdf] submitted on 2016-06-17 22:38:08

### 1. Universal Relative Metric That Generates A Field Super-Set To The Fields Generated By Some Number Of Distinct Relative Metrics 2. Universal Function Generation (MP)

In this research investigation, the author has presented a theory of ‘Universal Relative Metric That Generates A Field Super-Set To The Fields Generated By Various Distinct Relative Metrics’.
Category: Mathematical Physics

[495] viXra:1606.0174 [pdf] submitted on 2016-06-17 08:49:58

### 1. Universal Holistic Beauty Primality Tree Of Any Set 2. Universal Growth Of Any Given Set (MP)

In this research investigation, the author has presented a theory of ‘Universal Holistic Beauty Primality Tree Of Any Set, Universal Growth Of Any Given Set’.
Category: Mathematical Physics

[494] viXra:1606.0153 [pdf] submitted on 2016-06-15 07:32:26

### Universal Natural Memory Embedding - 2 MP

In this research investigation, the author has presented a theory of ‘The Universal Irreducible Any Field Generating Metric’.
Category: Mathematical Physics

[493] viXra:1606.0134 [pdf] submitted on 2016-06-14 00:59:43

### The Universal Any Field Generating Metric - I

In this research investigation, the author has presented a theory of ‘The Universal Irreducible Any Field Generating Metric’.
Category: Mathematical Physics

[492] viXra:1606.0089 [pdf] submitted on 2016-06-09 23:29:20

### 1.Complete Recursive Sub-Sets Found To Exhaustion Of A Set 2.The Example Of The Same Explaining The Quantization Scheme Of Any Universal Natural Manifestation In Holisticness (New)

In this research investigation, the author has presented the theory of ‘Complete Recursive Sub-Sets Found To Exhaustion Of A Set’ with ‘The Example Of The Same Explaining The Quantization Scheme Of Any Universal Natural Manifestation In Holisticness’.
Category: Mathematical Physics

[491] viXra:1606.0086 [pdf] submitted on 2016-06-09 06:42:55

### 1. Complete Recursive Sub-Sets Found To Exhaustion Of A Set 2.The Example Of The Same Explaining The Quantization Scheme Of Any Universal Natural Manifestation In Holisticness

In this research investigation, the author has presented the theory of ‘Complete Recursive Sub-Sets Found To Exhaustion Of A Set’ with ‘The Example Of The Same Explaining The Quantization Scheme Of Any Universal Natural Manifestation In Holisticness’.
Category: Mathematical Physics

[490] viXra:1606.0061 [pdf] submitted on 2016-06-06 15:38:04

### Relevance of Infrared Divergences to D-energy

Authors: Miguel A. Sanchez-Rey

Is infrared divergence irrelevent to D-energy?
Category: Mathematical Physics

[489] viXra:1606.0056 [pdf] submitted on 2016-06-06 06:37:02

### Relative Metric And Field Generation Based On The Same With An Example Of The Universal Field {Version Two}

In this research investigation, the author has presented the notion of ‘Relative Metric And Field Generation Based On The Same’.
Category: Mathematical Physics

[488] viXra:1606.0037 [pdf] submitted on 2016-06-03 23:03:41

### Relative Metric And Field Generation Based On The Same. An Example Of The Universal Field

In this research investigation, the author has presented the notion of ‘Relative Metric And Field Generation Based On The Same’.
Category: Mathematical Physics

[487] viXra:1605.0292 [pdf] submitted on 2016-05-29 10:43:19

### Frequential Spacetime

Authors: Ricardo Gil

Einstein merged Space with Time hence Spacetime. Tesla has a Unified Theory based on Fields and Electromagnetism. The logical progression is to merge the two and suggest Frequential Spacetime in which the frequency of matter dictates the shape and speed of entanglement of matter in Spacetime.
Category: Mathematical Physics

[486] viXra:1605.0270 [pdf] submitted on 2016-05-26 07:15:55

### Positve And Negative Time Scaling And Time Portal Engineering - II

In this research investigation, the author has presented a Scheme for ‘Positive And Negative Time Scaling And Time Portal Engineering’
Category: Mathematical Physics

[485] viXra:1605.0255 [pdf] submitted on 2016-05-24 15:15:40

### Candidacy and the Grand Unification Scheme

Authors: Miguel A. Sanchez-Rey

Does any unification candidate necessitate the grand unification scheme?
Category: Mathematical Physics

[484] viXra:1605.0240 [pdf] submitted on 2016-05-23 04:23:55

### The Second-order Local Formalism for Time Evolution of Dynamical Systems

Authors: I. V. Drozdov

The second-order approach to the entropy gradient maximization for systems with many degrees of freedom provides the dynamic equations of first order and light-like second order without additional ergodicity conditions like conservation laws. The first order dynamics lead to the definition of the conserved kinetic energy and potential energy. In terms of proper degrees of freedom the total energy conservation reproduces the Einstein's mass-energy relation. The newtonian interpretation of the second order dynamic equations suggests the definition for general inertial mass and for the interaction potential.
Category: Mathematical Physics

[483] viXra:1605.0199 [pdf] submitted on 2016-05-19 09:42:01

### The Method of Calculating the Velocity Field and Shear Stresses in Incomressible Fluid

Authors: V. A. Budarin

The velocity field culculation method is based on the use of two special cases of the Newtonian fluid motion equations, not including the Navier-Stokes equation. Two shear stress calculation ways are considered. The first way is the differentiation on the velocity field equation, and the second one requires the solution of the first-order differential equation. The second way provides the distribution of shear stresses for any continuous medium, including Newtonian fluid. Culculation equations for a laminar flow in a round pipe are found. It is shown that parabolic velocity distribution along the radius is a special case of more general equation. The factors affecting the shear stresses for the three flow models are found. Stresses are determined by the linear velocity gradients in the laminar flow. In the 3D vortex, they can be found by various equations, which include vorticity. Total stresses for the averaged turbulent flow are culculated by summing the previously found stresses. The equations of the method are incomplete and may be used for the accurate solution of simple problems.
Category: Mathematical Physics

[482] viXra:1605.0183 [pdf] submitted on 2016-05-17 08:17:14

### Positive And Negative Time Scaling And Time Portal Engineering

In this research investigation, the author has detailed a scheme for 'Positive And Negative Time Scaling And Time Portal Engineering'.
Category: Mathematical Physics

[481] viXra:1605.0167 [pdf] submitted on 2016-05-15 03:57:58

### The Theory of Harmonicity of the Field of Light (Book in English)

Authors: Dionysios G. Raftopoulos

The Theory of the Harmonicity of the Field of Light is an axiomatic theory motivated by the logical contradictions of Special Relativity Theory and based on two fundamental acceptances: 1. The adoption of the natural philosophy of Werner Heisenberg and the school of Copenhagen, according to which a consistent natural description of the Cosmos shouldn’t ignore the existence of the Observer or at least the instrument of observation and measurement and 2. The choice of the Projective Space as the Geometrical Space of its natural description. This choice is validated following the fundamental separation of the Perceptible Space, which is objective, and the Geometrical Space, that exists only in our minds. As all logically consistent Geometries are accepted in Mathematical Science, the adoption of a Geometrical Space by a Theory of Physics is free. Further on, this theory adopts as its first fundamental hypothesis the second hypothesis of the Special Relativity Theory, properly modified. Then, during the study of the kinematics of the material point, the property of harmonicity of the field of light emerges practically automatically. Via this theory Human Reason is restored.
Category: Mathematical Physics

[480] viXra:1605.0163 [pdf] submitted on 2016-05-14 21:39:22

### Cosmic Units of Measure

Authors: Frank H. Makinson

The commonly used units of measure have changed over the centuries. The numeric value for the speed of light was measured before it was known that light was an electromagnetic wave and how electromagnetic waves were produced. The scientific community adopted a set of units of measures that were originally developed for joint commercial, scientific and common use. There is an on going effort by the various metrology organizations to update them. There is no need to change the generally accepted units of measure for commercial and common use, but scientific units of measure need major improvements.
Category: Mathematical Physics

[479] viXra:1605.0126 [pdf] submitted on 2016-05-12 07:50:50

### Symmetric Theory Planck’s Particle

Authors: Giuseppe Azzarello

You will be shown the symmetry properties of the Planck’s particle, and will be drawn to its magnetic charge. This will unify the gravitational, electrical and magnetic forces in a single force, now known as superforce. This is possible by introducing a new constant, symmetrical coupling factor call, which allows the transformation between forces.
Category: Mathematical Physics

[478] viXra:1605.0101 [pdf] submitted on 2016-05-10 15:26:40

### Merging Mathematical Technologies by Applying the Reverse Bra-Ket Method

Authors: J.A.J. van Leunen
Comments: 10 Pages. The .docx version is accessible via the author's website http://www.e-physics.eu

Quaternionic Hilbert spaces can store discrete quaternions and quaternionic continuums in the eigenspaces of operators that reside in these Hilbert spaces. The reverse bra-ket method is an extension of the bra-ket notation that was introduced by P.M. Dirac. The reverse bra-ket method can create natural parameter spaces from quaternionic number systems and can relate the combinations of functions and their parameter spaces with eigenspaces and eigenvectors of corresponding operators that reside in non-separable Hilbert spaces. This also works for separable Hilbert spaces. The defining functions relate the separable Hilbert space with its non-separable companion. In this way, the method links Hilbert space technology with function technology, differential technology and integral technology. Quaternionic number systems exist in several versions that differ in the way that they are ordered. This is applied by defining multiple types of parameter spaces in the same Hilbert space. The set of closed subspaces of a separable Hilbert space has the relational structure of an orthomodular lattice. This fact makes the Hilbert space suitable for modelling quantum physical systems. The reverse bra-ket method is a powerful tool for generating quaternionic models that help investigating quantum physical models.
Category: Mathematical Physics

[477] viXra:1605.0099 [pdf] submitted on 2016-05-10 12:41:46

### Electron Deep Orbits of the Hydrogen Atom

Authors: Jean-Luc Paillet, Andrew Meulenberg
Comments: 17 Pages. paper presented to the 11th Workshop on Anomalies in Hydrogen Loaded Metals, Airbus-Toulouse (Fr.), 15-16 Oct. 2015

This work continues our previous work [1] and in a more developed form [2]), on electron deep orbits of the hydrogen atom. An introduction shows the importance of the deep orbits of hydrogen (H or D) for research in the LENR domain, and gives some general considerations on the EDO (Electron Deep Orbits) and on other works about deep orbits. A first part recalls the known criticism against the EDO and how we face it. At this occasion we highlight the difference of resolution of these problems between the relativistic Schrödinger equation and the Dirac equation, which leads for this latter, to consider a modified Coulomb potential with finite value inside the nucleus. In the second part, we consider the specific work of Maly and Va’vra [3], [4]) on deep orbits as solutions of the Dirac equation, so-called Deep Dirac Levels (DDLs). As a result of some criticism about the matching conditions at the boundary, we verified their computation, but by using a more complete ansatz for the “inside” solution. We can confirm the approximate size of the mean radii of DDL orbits and that decreases when the Dirac angular quantum number k increases. This latter finding is a self-consistent result since (as distinct from the atomic-electron orbitals) the binding energy of the DDL electron increases (in absolute value) with k. We observe that the essential element for obtaining deep orbits solutions is special relativity.
Category: Mathematical Physics

[476] viXra:1605.0083 [pdf] submitted on 2016-05-09 00:20:00

### C2R and Anomalies

Authors: Miguel A. Sanchez-Rey

Given a unification candidate which is both inefficient and non-optimal will the experimental physics have validity with all such candidates?
Category: Mathematical Physics

[475] viXra:1605.0025 [pdf] submitted on 2016-05-02 18:29:22

### Induce Bonding Between D-variants

Authors: Miguel A. Sanchez-Rey

What to do when there is a lack of bonding between D-variants?
Category: Mathematical Physics

[474] viXra:1604.0284 [pdf] submitted on 2016-04-19 10:21:38

### Suitablity or Non-Suitability of Certain Unification Schemes for the Grand Unification Scheme

Authors: Miguel A. Sanchez-Rey

We aim to discuss some earlier unification candidates and whether such unification candidates are suitable or non-suitable for the grand unification scheme?
Category: Mathematical Physics

[473] viXra:1604.0283 [pdf] submitted on 2016-04-19 08:58:26

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[472] viXra:1604.0266 [pdf] submitted on 2016-04-18 08:44:03

### Prime Itteration

Authors: Ashes Mi

Solves Prime Numbers using PRIMES to Count With
Category: Mathematical Physics

[471] viXra:1604.0202 [pdf] submitted on 2016-04-12 12:51:08

### The Prime Number is Connected to the Quantum-Mechanical Basic Equation.

Authors: Terubumi Honjou

The prime number is connected to the quantum-mechanical basic equation. Mathematician Euler discovered a prime number and a connection with π (Japanese yen) for the first time. The left side of a go board of the following equation that I had only with a prime number is equal to π2/6. I transformed the following equation and had the equation of the area of Japanese yen. Then it became the equation that the prime number equation (zeta function) of the oiler assumed a prime number a radius. Here, a prime number and the correlation with what I set were provided on the top of the pulsation wave pattern of the figure of prime number, physics fusion as if I showed it to a figure of of the Lehman expectation proof that I contributed from an association between Schrodinger equation and circular motion of the elementary particle pulsation principle correlation chart in the online posting before last time. The prime number has a quantum-mechanical basic equation, the connection that are close to Schrodinger equation.
Category: Mathematical Physics

[470] viXra:1604.0159 [pdf] submitted on 2016-04-10 02:14:06

### Infrared Divergences in the Grand Unification Scheme

Authors: Miguel A. Sanchez-Rey

Infrared divergences are prominent in the process toward grand unification. Where do we see infrared divergences in the grand unification scheme?
Category: Mathematical Physics

[469] viXra:1604.0021 [pdf] submitted on 2016-04-03 15:39:27

### Universality of Causality Principle

Authors: M.E. Hassani
Comments: 18 Pages; 2 Tables; 13 References.

The causality principle is physically investigated in the framework of special relativity theory (SRT) and it is proven to be absolutely valid for subluminal, luminal and superluminal signals under any natural and/or artificial circumstances; also Einstein's thought experiment (1907), Tolman's paradox (1917), tachyonic antitelephone (1970) and Moller's thought experiment (1952) are re-examined in order to show more conclusively that the so-called causality paradoxes are in fact a pure mental construction resulted from some too-common misconceptions which mainly spring from the confusion between the concepts of (relative) velocity and (relative) speed. Thus, in light of the present work, the old and semi-persistent concern about causality violation by superluminal signals and its consequences at micro and macrophysical levels may be conceptually ruled out if one approaches the physico-mathematical formalism of SRT in an open-minded way.
Category: Mathematical Physics

[468] viXra:1603.0377 [pdf] submitted on 2016-03-27 23:47:52

### A Simple Model of Quantization: an Approach from Chaos

Authors: Moises Dominguez-Espinosa, Jaime Melendez-Martinez
Comments: 4 Pages. 3 figures, dynamical systems, quatum mechanics.

There is a paradigm in Quantum Mechanics that explains quantization through normal vibration modes called Eigenstates that arise from Schrodinger wave equation. In this contribution we propose an alternative methodology of quantization by using basic concepts of mechanics and chaos from which a Toy Model is built.
Category: Mathematical Physics

[467] viXra:1603.0371 [pdf] submitted on 2016-03-27 10:37:50

### On Wick Rotation

Authors: Jonathan Tooker

Wick rotation produces numbers that agree with experiment and yet the method is mathematically wrong and not allowed by any self-consistent rule. We explore a small slice of wiggle room in complex analysis and show that it may be possible to use QFT without reliance Wick rotations.
Category: Mathematical Physics

[466] viXra:1603.0363 [pdf] submitted on 2016-03-25 18:33:06

### Meta-space Energy in the Grand Unification Scheme

Authors: Miguel A. Sanchez-Rey

What is required and restricted by the grand unification scheme when it comes to energy for any variant?
Category: Mathematical Physics

[465] viXra:1603.0245 [pdf] submitted on 2016-03-16 14:29:28

### Physics in the Grand Unification Scheme

Authors: Miguel A. Sanchez-Rey

Conceptual definition of GRS and physics.
Category: Mathematical Physics

[464] viXra:1603.0229 [pdf] submitted on 2016-03-15 22:31:38

### Four Possible Methods to Extend Lehnert’s Screw-Shaped Photon: Towards Soliton Orbital Angular Momentum Radio (Soamr)

Authors: Victor Christianto, Yunita Umniyati

This paper was at-least-partially inspired by the problem of relatively slow internet connection in our country. We believe that the same common problem has plagued other developing countries like ours, so it seems that we need a new technology to increase the internet capacity, especially the wireless network capacity. One way to do that is to look at the photon electrodynamics theory. In a series of papers, Bo Lehnert has suggested screw-shaped model of photon, inspired by his Revised Quantum Electrodynamics (RQED). Therefore in this paper we will review 4 possible methods to extend his screw-shaped photon model. In the mean time, there is recent debate concerning theoretical basis and utilization of photon orbital angular momentum (OAM), in particular as a means to increase wireless internet capacity. Promising results have been reported from laboratory experiments carried out by Bo Thide group and others too. But considering Vigier’s proposal to consider photon as soliton, in this paper we will discuss not the usual photon OAM as suggested by Thide group, instead we will consider soliton orbital angular momentum. If the proposed concept holds true, then it is possible to develop soliton radio wave based on OAM, which we call here as SOAmR (Soliton Orbital Angular Momentum Radio).
Category: Mathematical Physics

[463] viXra:1603.0223 [pdf] submitted on 2016-03-15 14:34:15

### Comment on 5 Papers by Gandhi and Colleagues

Authors: Wei Cen, Ning Gu

The bio-heat transfer equation for homogeneous material model can be easily calculated by using second order finite difference approximation to discretize the spatial derivatives and explicit finite-difference time-domain (FDTD) scheme for time domain discretization. Mr. Gandhi and colleagues solved the bio-heat equation for inhomogeneous models utilizing implicit finite-difference method. Whereas we appreciate their research, we would like to address a few issues that may help further clarify or confirm the research.
Category: Mathematical Physics

[462] viXra:1603.0121 [pdf] submitted on 2016-03-07 21:09:17

### Reformuled General Relativity

Authors: Claude Latourre

For more than a century, the equations of general relativity have evolved according to the observations of the universe. These changes are expressed through the cosmological constant (Λ), which was first added on the space-time part to account for a stationary universe, then removed when observed the evolution of it. More recently, the constant reappeared on the energy-momentum part to describe an accelerated expansion of the universe. Let's see now, how the contraction of the equations of general relativity can express exactly the value of the cosmological constant: Λ = -1/4 (R + κ T) and also to deduce an equivalent reformulation the equations of general relativity: (Rµ√ -1/4 gµ√ R) = κ (Tµ√ -1/4 gµ√ T). All this, without using any physical concept: Dark energy, Quintessence…
Category: Mathematical Physics

[461] viXra:1603.0115 [pdf] submitted on 2016-03-07 15:34:26

### Kaos, Reality and the Kaotic Algebra

Authors: Robert G. Wallace

Philosophical considerations suggest a dimensional structure of reality based on infinite subdivision of singularity via Cayley Dickson doubling. An algebra, labelled the Kaotic algebra, is constructed based on algebras obtained by Cayley-Dickson doubling. It provides a natural basis for a non-associative geometry with links to the associative geometry of Cl(1,10). Subalgebras of the kaotic algebra have a phenomenology corresponding to that of the fermions of the standard model.
Category: Mathematical Physics

[460] viXra:1603.0052 [pdf] submitted on 2016-03-04 04:38:37

### High-Order Spectral Volume Scheme for Multi-Component Flows Using Non-Oscillatory Kinetic Flux

Authors: Na Liu, Xihua Xu, Yibing Chen
Comments: 24 Pages. numerical method in CFD

In this paper, an arbitrary high-order compact method is developed for compressible multi-component flows with a stiffened gas equations of state(EOS). The main contribution is combining the high-order, conservative, compact spectral volume scheme(SV) with the non-oscillatory kinetic scheme(NOK) to solve the quasi-conservative extended Euler equations of compressible multi-component flows. The new scheme consists of two parts: the conservative part and the non-conservative part. The original high order compact SV scheme is used to discretize the conservative part directly. In order to treat the equation of state of the stiffened gas, the NOK scheme is utilized to compute the numerical flux. Then, careful analysis is made to satisfy the necessary condition to avoid unphysical oscillation near the material interfaces. After that, a high-order compact scheme for the non-conservative part is obtained. This new scheme has the following advantages for numerical simulations of compressible multi-component stiffened gas: high order accuracy with compact stencil and oscillation-free near the material interfaces. Numerical tests demonstrate the good performance and the efficiency of the new scheme for multi-component flow simulations.
Category: Mathematical Physics

## Replacements of recent Submissions

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

### Breakdown of Euler Equations – New Approach

Authors: Valdir Monteiro dos Santos Godoi

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

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

### Breakdown of Euler Equations – New Approach

Authors: Valdir Monteiro dos Santos Godoi

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

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

### Breakdown of Euler Equations – New Approach

Authors: Valdir Monteiro dos Santos Godoi

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

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

### Breakdown of Euler Equations – New Approach

Authors: Valdir Monteiro dos Santos Godoi

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

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

### Breakdown of Euler Equations – New Approach

Authors: Valdir Monteiro dos Santos Godoi

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

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

### Breakdown of Euler Equations – New Approach

Authors: Valdir Monteiro dos Santos Godoi

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

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

### Breakdown of Euler Equations – New Approach

Authors: Valdir Monteiro dos Santos Godoi

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

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

### Breakdown of Euler Equations – New Approach

Authors: Valdir Monteiro dos Santos Godoi

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

[386] viXra:1605.0192 [pdf] replaced on 2016-07-06 00:19:28

### Deciphering the Fine Structure Constant

Authors: Bernd Ganter
Comments: 9 pages. The paper is the condensed version in English translation of the German parent document viXra:1408.0018. Comments please to bernd.ganter.fsk@gmx.de

In order to explain the strongly differing forces of the fundamental interactions, we use the hyper-operator of tetration in the form of optimal consecutive exponentiation (power towers) as mathematical instrument for the optimization of volumes or densities, and thus for information storage in the universe. From this approach it is possible to derive and calculate the value of the fine structure constant, the value of which has remained unexplained for 100 years now, as 137.035999100.
Category: Mathematical Physics

[385] viXra:1604.0283 [pdf] replaced on 2016-07-14 12:34:15

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations, supposing that there is some solution, following the Eulerian and Lagrangian descriptions, for spatial dimension n = 3. As we had seen in other previous articles, it is possible that there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[384] viXra:1604.0283 [pdf] replaced on 2016-07-07 12:37:12

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations following the Eulerian and Lagrangian descriptions, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[383] viXra:1604.0283 [pdf] replaced on 2016-06-24 12:16:36

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations following the Eulerian and Lagrangian descriptions, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[382] viXra:1604.0283 [pdf] replaced on 2016-06-23 12:07:43

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations following the Eulerian and Lagrangian descriptions, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[381] viXra:1604.0283 [pdf] replaced on 2016-06-20 07:03:31

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations following the Eulerian and Lagrangian descriptions, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[380] viXra:1604.0283 [pdf] replaced on 2016-06-16 12:20:05

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[379] viXra:1604.0283 [pdf] replaced on 2016-06-15 09:26:06

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi
Comments: 6 Pages. Sorry, this paper yet is not good.

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[378] viXra:1604.0283 [pdf] replaced on 2016-06-12 22:09:03

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi
Comments: 6 Pages. Sorry, this paper yet is not good.

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[377] viXra:1604.0283 [pdf] replaced on 2016-06-09 12:51:35

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi
Comments: ERRATA: Page 4, between equations (12) and (13) include the word "square" before the word "module": square module.

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[376] viXra:1604.0283 [pdf] replaced on 2016-06-04 16:06:11

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[375] viXra:1604.0283 [pdf] replaced on 2016-06-02 09:30:27

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[374] viXra:1604.0283 [pdf] replaced on 2016-05-31 07:59:27

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[373] viXra:1604.0283 [pdf] replaced on 2016-05-09 08:25:53

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi
Comments: 4 Pages. ERRATA: x,y,z in equation (7) are in Lagrangian description

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[372] viXra:1604.0283 [pdf] replaced on 2016-04-27 08:02:57

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[371] viXra:1604.0283 [pdf] replaced on 2016-04-23 20:37:16

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[370] viXra:1604.0283 [pdf] replaced on 2016-04-22 19:03:20

### Solution for Euler Equations – Lagrangian and Eulerian Descriptions

Authors: Valdir Monteiro dos Santos Godoi
Comments: 4 Pages. Sorry. Unfortunately, x, y, z are not so free.

We find an exact solution for the system of Euler equations, following the description of the Lagrangian movement of an element of fluid, for spatial dimension n = 3. As we had seen in other previous articles, there are infinite solutions for pressure and velocity, given only the condition of initial velocity.
Category: Mathematical Physics

[369] viXra:1603.0377 [pdf] replaced on 2016-03-30 20:22:38

### A Simple Model of Quantization: an Approach from Chaos

Authors: Moises Dominguez-Espinosa, Jaime Melendez-Martinez
Comments: 4 Pages. 3 Figures, Dynamical Systems, Quantum Mechanics.

There is a paradigm in Quantum Mechanics that explains quantization through normal vibration modes called Eigenstates that arise from Schrodinger wave equation. In this contribution we propose an alternative methodology of quantization by using basic concepts of mechanics and chaos from which a Toy Model is built.
Category: Mathematical Physics

[368] viXra:1603.0377 [pdf] replaced on 2016-03-29 08:02:39

### A Simple Model of Quantization: an Approach from Chaos

Authors: Moises Dominguez-Espinosa, Jaime Melendez-Martinez
Comments: 4 Pages. 3 Figures, Dynamical Systems, Quantum Mechanics

There is a paradigm in Quantum Mechanics that explains quantization through normal vibration modes called Eigenstates that arise from Schrödinger wave equation. In this contribution we propose an alternative methodology of quantization by using basic concepts of mechanics and chaos from which a Toy Model is built.
Category: Mathematical Physics

[367] viXra:1603.0371 [pdf] replaced on 2016-04-15 17:31:25

### On Wick Rotation

Authors: Jonathan Tooker

Wick rotation produces numbers that agree with experiment and yet the method is mathematically wrong and not allowed by any self-consistent rule. We explore a small slice of wiggle room in complex analysis and show that it may be possible to use QFT without reliance on Wick rotations.
Category: Mathematical Physics

[366] viXra:1603.0213 [pdf] replaced on 2016-05-15 22:47:47

### Why Now is the Time to Replace Pi with Tau

Authors: Doug Jensen

There are many good reasons why we should replace pi with tau, this paper focuses on one definitive reason.
Category: Mathematical Physics

[365] viXra:1603.0121 [pdf] replaced on 2016-03-30 20:17:57

### Formal Expression of the Cosmological Constant and Formulation of General Relativity Resulting

Authors: CLaude Latourre

For more than a century, the equations of general relativity have evolved according to the observations of the universe. These changes are expressed through the cosmological constant (Λ), which was first added on the space-time part to account for a stationary universe, then removed when observed the evolution of it. More recently, the constant reappeared on the energy-momentum part to describe an accelerated expansion of the universe. Let's see now, how the contraction of the equations of general relativity can express exactly the value of the cosmological constant: Λ = -1/4 (R + κ T) and also to deduce an equivalent reformulation the equations of General Relativity: (Rµ√ -1/4 gµ√ R) = κ (Tµ√ -1/4 gµ√ T). All this, without using any physical concept: dark energy, Quintessence…
Category: Mathematical Physics

[364] viXra:1603.0115 [pdf] replaced on 2016-05-13 02:57:59

### Kaotic Algebras

Authors: Robert G Wallace

Manifolds of any dimension and signature have an associated Clifford algebra. Division algebras can be generated by repeated application of the Cayley-Dickson construction, which can be further extended to power associative algebras such as the sedenions. It is possible to apply the Cayley-Dickson construction to Clifford algebras. The series of algebras generated this procedure are referred to in this paper as kaotic algebras, and the notation Ka^n(p,q) is proposed to designate particular kaotic algebra obtained by $n$ applications of the Cayley-Dickson construction to a matrix group isomorphic to a Clifford algebra Cl(p,q). The Cayley table for Ka^3(1,4) is generated. This table has aspects suggesting that this algebra may have applications in physics.
Category: Mathematical Physics

[363] viXra:1603.0115 [pdf] replaced on 2016-04-19 20:36:50

### Kaotic Algebra

Authors: Rob Wallace