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Any replacements are listed further down

[516] **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

[515] **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

[514] **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

[513] **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

[512] **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

[511] **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

[510] **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

[509] **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

[508] **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

[507] **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

[506] **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

[505] **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

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

**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*

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

**Comments:** 3 Pages.

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*

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

**Comments:** 10 pages

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*

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

**Comments:** 4 Pages.

What is metaspace?

**Category:** Mathematical Physics

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

**Authors:** Furkan Semih Dundar

**Comments:** 4 Pages.

$N$-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*

**Authors:** Zoran B. Vosika

**Comments:** 17 Pages.

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*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 16 Pages.

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*

**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

**Category:** Mathematical Physics

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

**Authors:** Ramesh Chandra Bagadi

**Comments:** 18 Pages.

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*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 16 Pages.

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*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 14 Pages.

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*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 13 Pages.

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*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 12 Pages.

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*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 12 Pages.

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*

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

**Comments:** 3 Pages.

Is infrared divergence irrelevent to D-energy?

**Category:** Mathematical Physics

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

**Authors:** Ramesh Chandra Bagadi

**Comments:** 9 Pages.

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*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 8 Pages.

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*

**Authors:** Ricardo Gil

**Comments:** 3 Pages.

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*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 5 Pages.

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*

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

**Comments:** 3 Pages.

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*

**Authors:** I. V. Drozdov

**Comments:** 25 Pages.

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*

**Authors:** V. A. Budarin

**Comments:** 9 Pages. MSC 76D09

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*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 4 Pages.

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*

**Authors:** Dionysios G. Raftopoulos

**Comments:** 424 Pages.

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*

**Authors:** Frank H. Makinson

**Comments:** 3 Pages.

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*

**Authors:** Giuseppe Azzarello

**Comments:** 8 Pages.

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*

**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*

**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

**Category:** Mathematical Physics

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

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

**Comments:** 3 Pages.

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*

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

**Comments:** 3 Pages.

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*

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

**Comments:** 3 Pages.

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*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 4 Pages. In english.

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*

**Authors:** Ashes Mi

**Comments:** 113 Pages.

Solves Prime Numbers using PRIMES to Count With

**Category:** Mathematical Physics

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

**Authors:** Terubumi Honjou

**Comments:** 7 Pages.

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*

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

**Comments:** 3 Pages.

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*

**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*

**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*

**Authors:** Jonathan Tooker

**Comments:** 1 Page.

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*

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

**Comments:** 3 Pages.

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*

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

**Comments:** 3 Pages.

Conceptual definition of GRS and physics.

**Category:** Mathematical Physics

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

**Authors:** Victor Christianto, Yunita Umniyati

**Comments:** 8 Pages. This paper has been submitted to IJET (www.scipress.com). Your comments are welcome

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*

**Authors:** Wei Cen, Ning Gu

**Comments:** Pages.

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*

**Authors:** Claude Latourre

**Comments:** 8 Pages. en francais

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*

**Authors:** Robert G. Wallace

**Comments:** 26 Pages.

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*

**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

[459] **viXra:1602.0255 [pdf]**
*submitted on 2016-02-20 10:38:07*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 75 Pages. In French.

It is a traduction to French of the booklet of Prof. Torben Krarup " A Contribution on the Mathematical Foundation of Physical Geodesy " publication N°44 of the Institute of Geodesy of Danmark, 1969. It represents the foundation of physical geodesy after Molodensky and Hotine contributions.

**Category:** Mathematical Physics

[458] **viXra:1602.0254 [pdf]**
*submitted on 2016-02-20 10:55:25*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 16 Pages. In French.

The papier presents an essay of the resolution of Navier-Stokes equations under the hypothesis (A) of the open problem cited by Clay Institute (C.L. Fefferman, 2006).

**Category:** Mathematical Physics

[457] **viXra:1602.0167 [pdf]**
*submitted on 2016-02-14 13:07:31*

**Authors:** R E Watson

**Comments:** 39 Pages.

Kaluza's 1921 theory of gravity and electromagnetism using a fifth wrapped-up spatial dimension is inspiration for many modern attempts to develop new physical theories. The original theory has problems which may well be overcome, and thus Kaluza theory should be looked at again: it is a natural, if not necessary, geometric unification of gravity and electromagnetism. Here a general demonstration that the Lorentz force law can be derived from a range of Kaluza theories is presented. This is investigated via non-Maxwellian kinetic definitions of charge that are divergence-free and relate Maxwellian charge to 5D components of momentum. The possible role of torsion is considered as an extension. It is shown, however, that symmetric torsion components are likely not admissible in any prospective theory. As a result Kaluza's original theory is rehabilitated and a call for deeper analysis made.

**Category:** Mathematical Physics

[456] **viXra:1602.0122 [pdf]**
*submitted on 2016-02-10 15:47:26*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 4 Pages.

A simple mathematical proof reveals that time-inversion symmetry and reversibility are different concepts, which also resolves the
Loschmidt paradox.

**Category:** Mathematical Physics

[455] **viXra:1602.0114 [pdf]**
*submitted on 2016-02-09 13:34:59*

**Authors:** Robert B. Easter

**Comments:** 87 Pages.

This paper introduces the G(4,8) Double Conformal Space-Time Algebra (DCSTA). G(4,8) DCSTA is a straightforward extension of the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA). G(4,8) DCSTA extends G(8,2) DCGA with spacetime boost operations and differential operators for differentiation with respect to the time-like w=c t direction and time t. The spacetime boost operation can implement anisotropic dilation (directed non-uniform scaling) of quadric surface entities. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the length contraction effect of special relativity. To demonstrate G(4,8) DCSTA as concrete mathematics with possible applications, this paper includes sample code and example calculations using the symbolic computer algebra system SymPy.

**Category:** Mathematical Physics

[454] **viXra:1602.0095 [pdf]**
*submitted on 2016-02-08 12:08:17*

**Authors:** Branko Zivlak

**Comments:** 4 Pages. 12 formulas

After examining the relationships in the universe, is determined a hypothetical quantum temperature and then obtained temperature of cosmic microwave background radiation (CMB). It is rejected an explanation of that temperature as a result of the relic radiation from the Big Bang.

**Category:** Mathematical Physics

[453] **viXra:1602.0066 [pdf]**
*submitted on 2016-02-05 13:54:42*

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

**Comments:** 3 Pages.

Give formal definition of SUPREME and explain it's implications.

**Category:** Mathematical Physics

[452] **viXra:1602.0049 [pdf]**
*submitted on 2016-02-04 10:02:29*

**Authors:** Jean Claude Dutailly

**Comments:** 380 Pages. New on QM, RG, gravitation

This book proposes a review and, on some important points, a new interpretation of the main concepts of Theoretical Physics. Rather than offering an interpretation based on exotic physical assumptions (additional dimension, new particle, cosmological phenomenon,…) or a brand new abstract mathematical formalism, it proceeds to a systematic review of the main concepts of Physics, as Physicists have always understood them : space, time, material body, force fields, momentum, energy… and propose the right mathematical tools to deal with them, chosen among well known mathematical theories.
After a short introduction about the place of Mathematics in Physics, a new interpretation of the main axioms of Quantum Mechanics is proposed. It is proven that these axioms come actually from the way mathematical models are expressed, and this leads to theorems which validate most of the usual computations and provide safe and clear conditions for their use, as it is shown in the rest of the book.
Relativity is introduced through the construct of the Geometry of General Relativity, based on 5 propositions and the use of tetrads and fiber bundles, which provide tools to deal with practical problems, such as deformable solids.
A review of the concept of momenta leads to the introduction of spinors in the framework of Clifford algebras. It gives a clear understanding of spin and antiparticles.
The force fields are introduced through connections, in the, now well known, framework of gauge theories, which is here extended to the gravitational field. It shows that this field has actually a rotational and a transversal component, which are masked under the usual treatment by the metric and the Levy-Civita connection. A thorough attention is given to the topic of the propagation of fields with interesting results, notably to explore gravitation.
The general theory of lagrangians in the application of the Principle of Least Action is reviewed, and two general models, incorporating all particles and fields are explored, and used for the introduction of the concepts of currents and energy-momentum tensor. Precise guidelines are given to find operational solutions of the equations of the gravitational field in the most general case.
The last chapter shows that bosons can be understood as discontinuities in the fields.
In this 4th version of this book, changes have been made :
- in Relativist Geometry : the ideas are the same, but the chapter has been rewritten, notably to introduce the causal structure and explain the link with the practical measures of time and space;
- in Spinors : the relation with momenta has been introduced explicitly
- in Force fields : the section dedicated to the propagation of fields is new, and is an important addition.
- in Continuous Models : the section about currents and energy-momentum tensor are new.
- in Discontinuous Processes : the section about bosons has been rewritten and the model improved.

**Category:** Mathematical Physics

[451] **viXra:1602.0048 [pdf]**
*submitted on 2016-02-04 10:11:31*

**Authors:** Domenico Oricchio

**Comments:** 11 Pages.

I open a dusty old drawer, and I found this article, rejected by every journal, with a complete, total loss of time; a thing that I'll never make; and I change only the bibliography, that is to initially conceived .
The old idea sounds interesting, and here, on vixra, there is not rejection.
I don't remember the whole theory, and the whole programs, but it can be useful to others; so I share it with you.
It seem that without the complication of the least common divisor, the calculation is more simple, and elegant.

**Category:** Mathematical Physics

[450] **viXra:1601.0312 [pdf]**
*submitted on 2016-01-29 03:55:49*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 18 Pages. Need yet revision and complete translation for english.

A solution to the 6th millenium problem, respect to breakdown of Navier-Stokes solutions and the bounded energy. We have proved that there are initial velocities u^0 (x) and forces f(x,t) such that there is no physically reasonable solution to the Navier-Stokes equations for t>0, which corresponds to the case (C) of the problem relating to Navier-Stokes equations available on the website of the Clay Institute.

**Category:** Mathematical Physics

[449] **viXra:1601.0280 [pdf]**
*submitted on 2016-01-25 20:07:50*

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

**Comments:** 3 Pages.

Procedure will be stated.

**Category:** Mathematical Physics

[448] **viXra:1601.0134 [pdf]**
*submitted on 2016-01-12 21:34:25*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 27 Pages.

We have obtained an equivalent circuit that explains selfheating effects and have tested the presence of nonlinearity and IMD using simulation. The significance of the approach lies in successfully modeling thermal effects in interconnects in ICs using SOI technology with al conductors. Future work: proposing of circuits and techniques that can be used for compensation of selfheating effects.

**Category:** Mathematical Physics

[447] **viXra:1601.0075 [pdf]**
*submitted on 2016-01-08 13:26:02*

**Authors:** Rami Mehrem

**Comments:** 5 Pages.

The integral $\int_0^\infty r^{2-\lambda}\,
j_0(k_1r)\,j_0(k_2r)\,j_\lambda(k_3r)\,dr$ is evaluated for any real positive $k_1$, $k_2$, $k_3$ and $\lambda \ge 0$

**Category:** Mathematical Physics

[446] **viXra:1601.0045 [pdf]**
*submitted on 2016-01-06 09:49:26*

**Authors:** Carsten S.P. Spanheimer

**Comments:** 26 Pages. in german language

Die Einführung 'quaternionischer Differentialformen' auf einer Mannigfaltigkeit ergibt ein vielversprechendes mathematisches System zur Beschreibung unserer physikalischen (3+1)-Raumzeit schon mit einem Minimum von Grundannahmen.
Hier wird die Grundlage dieses Modells einer 'Quaternionischen Raumzeit' dargestellt.

**Category:** Mathematical Physics

[445] **viXra:1601.0007 [pdf]**
*submitted on 2016-01-01 13:31:01*

**Authors:** S.E. Grimm

**Comments:** 3 Pages.

The conservation of quanta transfer in our universe has consequences for the description of the
observable activities of well known phenomena like objects and forces. To keep it simple the
examination will start with the help of Newtonian mechanics

**Category:** Mathematical Physics

[444] **viXra:1512.0475 [pdf]**
*submitted on 2015-12-29 15:06:13*

**Authors:** S.E. Grimm

**Comments:** 3 Pages.

Have quanta a mass of their own? The question was subject of discussions between physicists in the
past. The answer shows to be positive: quanta have mass of their own. The result emerges from a
compare between the two most famous equations of Planck and Einstein.

**Category:** Mathematical Physics

[443] **viXra:1512.0458 [pdf]**
*submitted on 2015-12-28 10:27:37*

**Authors:** Markos Georgallides

**Comments:** 33 Pages. The Unsolved ancient-Greek Problems , The Unsolved Special E-Problems

The Special Problems of E-geometry consist the Quantization Moulds of Euclidean Geometry in it , to become → The Basic monad , through mould of Space –Anti-space in itself , which is the material dipole in inner monad Structure which is Identical with the Electromagnetic cycloidal field → Linearly , through mould of Parallel Theorem , which are the equal distances of common Line-meter between the points of parallel and line → In Plane , through mould of Squaring the circle , where the two equal and perpendicular monads consist a Plane acquiring the common Plane-meter ,pi,→ and in Space ,(volume) , through mould of the Duplication of the Cube , where any two Un-equal and perpendicular monads acquire the common Space-meter ³√2 ,to be twice each other , as this in analytical methods explained . The article consist a provocation to all scarce today Geometers and mathematicians in order to give an answer to these Old-age standing Unsolved Problems.
All Geometrical solutions are clearly Exposed and presented on Dr-Geo machine , and unveill the pass-over-faults of Relativity . E-Geometry is proved to be the base of all natural sciences and also the reflective logic from the objective reality , which is nature , to us

**Category:** Mathematical Physics

[442] **viXra:1512.0443 [pdf]**
*submitted on 2015-12-26 14:29:46*

**Authors:** Dan Visser

**Comments:** 11 Pages.

The formulation of the Einstein-field equations are changed: Herewith I present dynamical formulations for the multiplication of Big Bang-universes embedded in an eternal rotating holographic universe. This is beyond the current assumption the universe could be a hologram; that assumption was made without detailed knowledge of shape and deeper dynamics of a holographic universe. The new formulations introduce a dynamical process of deeper dynamics by which an object or subject could be transformed to another part of the holographic universe. This may happen by recalculation. But how? The recalculation described here is based on an amount of ‘duo-bits of dark matter’, which recalculate the quantum-dynamics. The recalculation-process emerges from a domain below the Planck-scale. The ‘duo-bit recalculation’ starts for a calculated lower-limit of Planck-areas. From my calculation follows, for example: 17 x 10^53 ‘duo-bits’ can recalculate 64 x 10^6 Planck-areas. This subquantum informational process is embedded in the modified Einstein-field-equations by a geometrical ratio of quantum-gravity and Planck-areas. This ratio is correlated to an additional energy-tensor of dark matter-energy. The geometrical ratio is more refined than the Einstein cosmological constant, which is only a number. The refined ratio replaces the cosmological constant. Therefore the main-issue in this paper is, that the accelerated space-expansion in the current Big Bang-universe is based on a ‘fake-dynamic’ due to one of many possible quasi Big Bang-universes that directly exist in physical reality. Or in other words: Directly existing parallel universes are part of the holographic dynamics. According to the new formulations parallel universes do not exist outside the conservative Big Bang-universe. In an appendix a description is added for the media written in Dutch.

**Category:** Mathematical Physics

[441] **viXra:1512.0401 [pdf]**
*submitted on 2015-12-22 11:25:45*

**Authors:** Sergey V. Ershkov

**Comments:** 10 Pages. Keywords: Arnold-Beltrami-Childress (ABC) flow, helical flow, stationary points

The existence of stationary points for the dynamical system of ABC-flow is considered.
The ABC-flow, a three-parameter velocity field that provides a simple stationary solution of Euler's equations in three dimensions for incompressible, inviscid fluid flows, is the prototype for the study of turbulence (it provides a simple example of dynamical chaos).
But, nevertheless, between the chaotic trajectories of the appropriate solutions of such a system we can reveal the stationary points, the deterministic basis among the chaotic behaviour of ABC-flow dynamical system. It has been proved the existence of 1 point for two partial cases of parameters {A, B, C}: 1) A = B = 1; 2) C = 1 (A² + B² = 1). Moreover, dynamical system of ABC-flow allows 3 points of such a type, depending on the meanings of parameters {A, B, C}.

**Category:** Mathematical Physics

[440] **viXra:1512.0341 [pdf]**
*submitted on 2015-12-16 14:56:32*

**Authors:** Branko Zivlak

**Comments:** 3 Pages. 1 Formula, 1 Table

The formula connecting fundamental physical constants has been verified based on the 2010 and 2014 recommended CODATA values of physical constants.

**Category:** Mathematical Physics

[439] **viXra:1512.0334 [pdf]**
*submitted on 2015-12-16 00:15:11*

**Authors:** A. A. Frempong

**Comments:** 46 Pages. Copyright © A. A. Frempong

Over nearly a year and half ago, the Navier-Stokes (N-S) equations in 3-D for incompressible fluid flow were analytically solved by the author. However, some of the solutions contained implicit terms. In this paper, the implicit terms have been expressed explicitly in terms of x, y, z and t. The author proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It was mathematically shown that without gravity forces on earth, there would be no incompressible fluid flow on earth as is known, and also, there would be no magnetohydrodynamics. In addition to the usual method of solving these equations, the N-S equations were also solved by a second method in which the three equations in the system were added to produce a single equation which was then integrated. The solutions by the two methods were identical, except for the constants involved. Ratios were used to split-up the equations; and the resulting sub-equations were readily integrable, and even, the nonlinear sub-equations were readily integrated. The examples in the preliminaries show everyday examples on using ratios to divide a quantity into parts, as well as possible applications of the solution method in mathematics, science, engineering, business, economics, finance, investment and personnel management decisions. The
x-direction Navier-Stokes equation was linearized, solved, and the solution analyzed. This solution was followed by the solution of the Euler equation of fluid flow. The Euler equation represents the nonlinear part of the Navier-Stokes equation. Following the Euler solution, the Navier-Stokes equation was solved essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion of fluids. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in the parabolic, periodic and decreasingly exponential motion. Periodicity increases with viscosity. The variable acceleration term is also involved in the periodic and decreasingly exponential motion.
The fluid flow in the Navier-Stokes solution may be characterized as follows. The x-direction solution consists of linear, parabolic, and hyperbolic terms. The first three terms characterize parabolas. If one assumes that in laminar flow, the axis of symmetry of the parabola for horizontal velocity flow profile is in the direction of fluid flow, then in turbulent flow, the axis of symmetry of the parabola would have been rotated 90 degrees from that for laminar flow. The characteristic curve for the x-nonlinear term is such a parabola whose axis of symmetry has been rotated 90 degrees from that of laminar flow. The y-nonlinear term is similar parabolically to the x-nonlinear term. The characteristic curve for the z-nonlinear term is a combination of two similar parabolas and a hyperbola. If the above x-direction flow is repeated simultaneously in the y-and z-directions, the flow is chaotic and consequently turbulent.
For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and thus prove the existence of smooth solutions of the Navier-Stokes equations.

**Category:** Mathematical Physics

[438] **viXra:1512.0333 [pdf]**
*submitted on 2015-12-16 00:24:04*

**Authors:** A. A. Frempong

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

The system of magnetohydrodynamic (MHD) equations have been solved analytically in this paper. The author applied the technique used in solving the Navier-Stokes equations and applied a new law, the law of definite ratio for MHD. This law states that in MHD, the other terms of the system of equations divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no magnetohydrodynamics on earth as is known. The equations in the system of equations were added to produce a single equation which was then integrated. Ratios were used to split-up this single equation into sub-equations which were readily integrated, and even, the non-linear sub-equations were readily integrated. Twenty-seven sub-equations were integrated. The linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions revealed the role of each term in magnetohydrodynamics. In particular, the gravity term is the indispensable term in magnetohydrodynamics. The solutions of the MHD equations were compared with the solutions of the N-S equations, and there were similarities and dissimilarities.

**Category:** Mathematical Physics

[437] **viXra:1512.0332 [pdf]**
*submitted on 2015-12-16 00:45:22*

**Authors:** A. A. Frempong

**Comments:** 12 Pages. Copyright © A. A. Frempong

This paper covers the solutions of the Euler equations in 3-D and 4-D for incompressible fluid flow. The solutions are the spin-offs of the author's previous analytic solutions of the Navier-Stokes equations (vixra:1405.0251 of 2014). However, some of the solutions contained implicit terms. In this paper, the implicit terms have been expressed explicitly in terms of x, y, z and t.
The author applied a new law, the law of definite ratio for fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. This law evolved from the author's earlier solutions of the Navier-Stokes equations. In addition to the usual approach of solving these equations, the Euler equations have also been solved by a second method in which the three equations in the system are added to produce a single equation which is then integrated. The solutions by the two approaches are identical, except for the constants involved. From the experience gained in solving the linearized Navier-Stokes equations, only the equation with the gravity term as the subject of the equation was integrated. The experience was that when each of the terms of the Navier-Stokes equation was used as the subject of the equation, only the equation with the gravity term as the subject of the equation produced a solution. Ratios were used to split-up the x-direction Euler equation with the gravity term as the subject of the equation. The resulting five sub-equations were readily integrable, and even, the non-linear sub-equations were readily integrated. The integration results were combined. The combined results satisfied the corresponding equation. This equation which satisfied its corresponding equation would be defined as the driver equation; and each of the other equations which would not satisfy its corresponding equation would be called a supporter equation. A supporter equation does not satisfy its corresponding equation completely, but provides useful information which is not apparent in the solution of the driver equation. The solutions and relations revealed the role of each term of the Euler equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the forward motion of fluids. The pressure gradient term is also involved in the forward motion. The variable acceleration term is also involved in the forward motion. The fluid flow behavior in the Euler solution may be characterized as follows. The x-direction solution consists of linear, parabolic, and hyperbolic terms. If one assumes that in laminar flow, the axis of symmetry of the parabola for horizontal velocity flow profile is in the direction of fluid flow, then in turbulent flow, the axis of symmetry of the parabola would have been rotated 90 degrees from that for laminar flow. The characteristic curve for the x-nonlinear term is such a parabola whose axis of symmetry has been rotated 90 degrees from that of laminar flow. The y-nonlinear term is similar parabolically to the x-nonlinear term. The characteristic curve for the z-nonlinear term is a combination of two similar parabolas and a hyperbola. If the above x-direction flow is repeated simultaneously in the y-and z-directions, the flow is chaotic and consequently turbulent.

**Category:** Mathematical Physics

[436] **viXra:1512.0261 [pdf]**
*submitted on 2015-12-07 21:43:24*

**Authors:** Rodney Bartlett

**Comments:** 6 Pages.

The Fields Medal is an award established in 1924 by the ICM (International Congress of Mathematicians) and is restricted to mathematicians up to the age of 40. It recognizes both existing work and future promise, and is equivalent to the Nobel Prize.
A trick is shown in this article that proves 1=2. However, during the steps division by zero is used. Since this is not allowed, the conclusion is false. Or it would be unless zero could be shown not to be nothing. Zeros are something because they're paired with ones to compose the binary digits essential to the formation of everything in space-time. This means zero has been misunderstood throughout history, division by zero is indeed permitted and the conclusion that 1=2 is correct. In turn, this means that while 1+1=2, 1+1 must also equal 1. This mathematically validates the centuries-long march of physics towards unification of everything in this cosmos. Unification occurs not just in the present but the entire past and future are naturally part of this one entity/event.
The article then explores possible consequences for 1) Einstein being correct to divide by zero, 2) Hidden Variables and Determinism, 3) that zero is not nothing but actually something, 4) that zero redefines the term infinity, 5) that there really is another explanation for the origin of the universe besides the Big Bang, 6) and another explanation for black holes, 7) possibilities regarding life after death and life before conception.

**Category:** Mathematical Physics

[435] **viXra:1511.0288 [pdf]**
*submitted on 2015-11-29 16:42:41*

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

**Comments:** 3 Pages.

Are certain variants that do not meet the EOC Guideline be included in the grand unification scheme? Can these certain variants have applications to the physical sciences even if they are not important to GRS?

**Category:** Mathematical Physics

[434] **viXra:1511.0272 [pdf]**
*submitted on 2015-11-28 11:46:57*

**Authors:** S.E. Grimm

**Comments:** 47 Pages.

The document describes the foundations of physics. The basic description is a concept about the structure of space and time and – because of that – the structure of physic phenomena like particles and force fields. The hypothesis elucidates reality at the lowest level – including quantum reality – owing to the bottom up approach.

**Category:** Mathematical Physics

[433] **viXra:1511.0173 [pdf]**
*submitted on 2015-11-20 03:23:37*

**Authors:** Richard L. Amoroso, Elizabeth A. Rauscher, Peter Rowlands

**Comments:** 23 Pages.

space-antispace quaternionic form and discuss various implications and applications. We note unique solutions in complex spin space. Tachyonic/tardonic signaling also appears to arise from this formalism as well as extensions to micro and macro nonlocality. Complex 8-space Dirac equation solutions exhibit additional nonlinear terms which may yield extension of the formalism from Special to General Relativity.

**Category:** Mathematical Physics

[432] **viXra:1511.0154 [pdf]**
*submitted on 2015-11-18 04:16:45*

**Authors:** Rodney Bartlett

**Comments:** 3 Pages.

This rebuttal of the multiverse hypothesis, the idea that other universes exist alongside ours, draws on mathematics' topology, or rubber-sheet geometry. The topology takes the form of electronics' binary digits (1's and 0's) composing 2 Möbius strips which are united into a figure-8 Klein bottle constituting a "sub"universe. The encoding of infinitely-long irrational and transcendental numbers like pi, e, √2 by the digits produces an infinite series of sub-universes (an infinite universe). And other subs can naturally affect our own 13.8 billion-year-old subcosmos. (“Our Mathematical Universe” by cosmologist Max Tegmark – Random House/Knopf, January 2014 believes the universe has a mathematical foundation).

**Category:** Mathematical Physics

[431] **viXra:1511.0152 [pdf]**
*submitted on 2015-11-17 16:07:44*

**Authors:** Seamus McCelt

**Comments:** 3 Pages.

This is a new type of math based on string particle lengths.

It doesn't mean everything else is incorrect, it means this can also be correct.

**Category:** Mathematical Physics

[430] **viXra:1511.0141 [pdf]**
*submitted on 2015-11-16 21:09:05*

**Authors:** Seamus McCelt

**Comments:** 2 Pages.

If you have an equation for a sphere, it is mapping out a solid sphere...

Nothing is Solid (except something like a neutron star, protons and neutrons are supposedly solid but they might just have a very loose string pack)

A "reality" math would be based on strings and commandeering sections of space.

**Category:** Mathematical Physics

[429] **viXra:1511.0094 [pdf]**
*submitted on 2015-11-11 15:23:28*

**Authors:** Sergey V. Ershkov

**Comments:** 6 Pages. Keywords: Navier-Stokes equations, non-stationary helical flow, Arnold-Beltrami-Childress (ABC) flow

In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations, even for 3D case of compressible gas flow. But there is an essential deficiency of non-stationary solutions indeed.
In our derivation, we explore the case of non-stationary helical flow of the Navier-Stokes equations for incompressible fluids at any given initial conditions for velocity fields (it means an open choice for the space part of a solution).

**Category:** Mathematical Physics

[428] **viXra:1511.0088 [pdf]**
*submitted on 2015-11-11 08:41:59*

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

**Comments:** 4 Pages.

How do variants bond?

**Category:** Mathematical Physics

[427] **viXra:1511.0083 [pdf]**
*submitted on 2015-11-10 16:59:41*

**Authors:** C. A. Brannen

**Comments:** 20 Pages.

We present a new decomposition of unitary matrices particularly useful for mixing matrices. The decomposition separates the complex phase information from the mixing angle information of the matrices and leads to a new type of parameterization. We show that the mixing angle part of U(n) is equivalent to U(n-1). We give closed form parameterizations for 3x3 unitary mixing matrices (such as the CKM and MNS matrices) that treat the mixing angles equally.
We show the relationship between Berry-Pancharatnam or quantum phase and the Jarlskog invariant Jcp that gives the CP-violation in the standard model.
We established the likely existence of the new decomposition by computer simulation in 2008. Philip Gibbs proved the n=3 case in 2009 and in 2011, Samuel Lisi proved the general case using Floer theory in symplectic geometry. We give an accessible version of Lisi's proof.

**Category:** Mathematical Physics

[426] **viXra:1511.0073 [pdf]**
*submitted on 2015-11-09 23:13:27*

**Authors:** E. V. Rothstein Chan

**Comments:** 5 Pages.

The exchange integrals occur in solving for the quantum mechanical wave function using
the Schroedinger equation. r12STOmolecular deals with interelectronic distances and
STOs ( Slater type orbitals), centered at various molecular origins. STOs have a radially
dependent exponential term (multiplied by radial distance term to the power of principal
quantum number n minus one) multiplied by a spherical harmonic with quantum
numbers l and m. The small and large radial behavior differ from Gaussians. Ipython
notebook with arbitrary precision for evaluation from analytic formula is presented. This
work was undertaken to make accurate molecular computation more readily available to
other researchers.

**Category:** Mathematical Physics

[425] **viXra:1511.0050 [pdf]**
*submitted on 2015-11-06 03:59:09*

**Authors:** Fu Yuhua

**Comments:** 16 Pages.

The strict "unified theory" cannot be existed. Applying least square method, "partial and temporary unified theory of natural science so far" including all the equations of natural science so far can be established. In this way, the theory of everything to express all of natural laws, described by Hawking that a single equation could be written on a T-shirt, is partially and temporarily realized in the form of "partial and temporary unified variational principle of natural science so far". With the help of "partial and temporary unified theory of natural science so far", this paper successfully deals with some faster-than-light (FTL) problems. From a ray of light to observe another ray of light, the variation range of the speed of another light equals 0 to 2c (c=300,000 km/s). When the speed of an object is close or equal to the speed of light, for breaking the light barrier, the speed of this object could be faster than light as it passes through the Sun’s gravitational field. According to Hubble's law, the value of far away speed of a galaxy is the exponential function of time, and therefore it can be faster-than-light.
Key words: Unified theory, partial and temporary unified theory of natural science so far, partial and temporary unified variational principle of natural science so far, Hawking, T-shirt, Hubble's law, faster-than-light (FTL)

**Category:** Mathematical Physics

[424] **viXra:1511.0026 [pdf]**
*submitted on 2015-11-03 12:13:23*

**Authors:** Florentin Smarandache

**Comments:** 130 Pages.

This book is a collection of articles, notes, reviews, blogs and abstracts on Physics. Some are published for the first time here, some were previously published in journals, and revised here.
We approach a novel form of plasma, Unmatter Plasma. The electron-positron beam plasma was generated in the laboratory in the beginning of 2015. This experimental fact shows that unmatter, a new form of matter that is formed by matter and antimatter bind together (mathematically predicted a decade ago) really exists.
Further, we generalize the Lorentz Contraction Factor for the case when the lengths are moving at an oblique angle with respect to the motion direction, and show that the angles of the moving relativistic objects are distorted.
Then, using the Oblique-Length Contraction Factor, we show several trigonometric relations between distorted and original angles of moving object lengths in the Special Theory of Relativity.
We also discuss some paradoxes which we call “neutrosophic” since they are based on indeterminacy (or neutrality, i.e. neither true nor false), which is the third component in neutrosophic logic. We generalize the Venn diagram to a Neutrosophic Diagram, which deals with vague, inexact, ambiguous, ill-defined ideas, statements, notions, entities with unclear borders. We define the neutrosophic truth table, then we introduce two neutrosophic operators (neuterization and antonymization operators), and give many classes of neutrosophic paradoxes.
Other topics addressed in this book are: neutrosophic physics as a new field of research, neutrosophic numbers in physics, neutrosophic degree of paradoxicity, unparticle and unmatter, multispace and multistructure, nucleon clusters, and others.

**Category:** Mathematical Physics

[423] **viXra:1510.0482 [pdf]**
*submitted on 2015-10-28 20:31:46*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 12 Pages.

The generation of Chaos in Electronics has largely been implemented using the Chua circuits, where the initial conditions are described by system parameters such as resistors and capacitors. The present work provides a radical shift in approach by proposing signal based chaos generators. The essential design here is the coupling of two sinusoidal signal sources to a CMOS inverter circuit, which is seen to exhibit nonlinear behavior thanks to its transfer characteristics and non-quasi static behavior. The Standard Circle Map, ideally suited to describing nonlinear coupling of oscillations with competing frequencies is studied and a ‘frequency map’ is derived from it. The latter is studied using bifurcation and cobweb plots. A second perspective, the amplitude map is created by forming a difference equation using the CMOS inverter transfer function. This map is explored using the bifurcation plots and phase portraits. Finally, the proposed design is implemented experimentally and the generated chaotic output is validated using phase portraits and Fourier spectra. The effect of driving frequency on the output is characterized using Kolmogorov Entropy and Lyapunov Exponents, giving rise to the term ‘Frequency Dependent Chaos’. The fresh perspectives of a signal oriented chaos discussed in the present work exhibits the advantages of simple circuitry and easy tunability, and this forms the novelty of the present work.

**Category:** Mathematical Physics

[422] **viXra:1510.0479 [pdf]**
*submitted on 2015-10-28 20:35:13*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 8 Pages.

The fluctuations accompanying the DC offset in a photovoltaic cell open circuit voltage waveform are studied. Nonlinear analyses performed on these waveforms ascertain the presence of a highly unstable chaotic behavior. The results are validated using various parameters such as Kolmogorov Entropy, Fractal Dimension and Lyapunov Exponent. It is observed that the chaotic behavior responds to atmospheric and cosmic disturbances and hence can be used to study such effects. The information and inferences about the chaotic behavior coupled with proper synchronization techniques could potentially lead to cost effective means of enhancing the solar cell output.

**Category:** Mathematical Physics

[421] **viXra:1510.0468 [pdf]**
*submitted on 2015-10-28 08:01:16*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 6 Pages.

The present work pertains to the generation of a chaotic signal by taking the inverse Fourier Transform of a Fractal Spectral Profile. The presence of chaos is ascertained and characterized using phase portraits, recurrence plots, Lyapunov exponents and Kolmogorov entropies. This signal is modulated by a hyperbolic secant solitary pulse to formulate the “Fractal Chaotic Solitary Wavelet” (FCSW), the analysis of which reveals vanishing higher moments, translating to efficient capabilities of burst and discontinuity detection, apart from the advantage of security owing to the induced unpredictability of chaos. This results in the proposed Fractal Chaotic Solitary Wavelets having potential applications in secure communications and encryption.

**Category:** Mathematical Physics

[420] **viXra:1510.0467 [pdf]**
*submitted on 2015-10-28 08:02:21*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 4 Pages.

Chaotic signals serve as ideal candidates as carriers in secure communication systems. The present work proposes the generation of a ‘digital’ chaotic signal using a frequency dependent iterative map. The proposed design is implemented using Field Programmable Gate Array and nonlinear characterization using Lyapunov exponent confirms the presence of chaos. A proof-of-concept communication system is then numerically designed and evaluated using the Mean Square Error, which reveals the sensitivity of the system to perfect decryption. The simplicity of the design, coupled with the high level of security obtained form the highlights of the present work.

**Category:** Mathematical Physics

[419] **viXra:1510.0466 [pdf]**
*submitted on 2015-10-28 08:03:01*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 4 Pages.

The present work pertains to the exploration of signal based chaos generation in the Microwave X-Band frequency range. Specifically, two reflex klystrons are used as sources to two ports of the magic tee, while a third port is terminated. By taking the output from the fourth port, the envelope waveforms and phase portraits are seen to exhibit reasonable degree of richness and complexity. The presence of chaos is quantitatively ascertained using Lyapunov Exponents and Kolmogorov Entropies. The results outlined in the present work offer a far simpler alternative to generate easy-to-tune signal dependent chaos, suitable for telecommunication applications.

**Category:** Mathematical Physics

[418] **viXra:1510.0459 [pdf]**
*submitted on 2015-10-28 09:19:22*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 4 Pages.

The basic components for most secure computing and communication systems of today are random number generators. The present work purports to a radically novel approach to the design and implementation of random number generators. Firstly, a nonlinear analysis of the photovoltaic cell open circuit voltage is performed, and the presence of chaos is ascertained using standard measures such as Lyapunov Exponents. Following this, the chaotic output is adapted into a bit stream and randomness tests from the NIST Suite are performed. It is seen that the chaotic output indeed passes all the randomness tests. The histogram of the output reveals similarities with Gaussian Normal Distributions, confirming the stochastic nature. Thus, the photovoltaic cell output is a potential power generating random number generator, drastically differing from the conventional power dissipative random number generators.

**Category:** Mathematical Physics

[417] **viXra:1510.0452 [pdf]**
*submitted on 2015-10-28 09:29:42*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 7 Pages.

A two-dimensional photonic crystal based on a lattice of silicon rods in air with a photonic bandgap in the visible and near-ultraviolet spectra is proposed, by removing some of the silicon rods or resizing their radius, to create a monotonically varying tapered line defect, thereby pertaining to a case of structure-based nonlinearity and making it possible to operate with low input powers. By properly manipulating the length of the line defect, pulse compression and consequent adiabatic amplification is seen, along with bunching/anti-bunching of pulses. For certain modes of operation, field confinement is observed, and this leads to the formation of discrete pulses, or light bullets. Following this, by appropriate use of cavity defects, the localization of discrete pulses is obtained, with the ‘gate’-output transfer curve resembling optical bistability. Such a structure can be used as a multi-functional device, with some of the functionalities being optical non-pumped amplification, frequency upconversion, memory writing, matched termination and slow wave guiding, that form the major conclusions of the work.

**Category:** Mathematical Physics

[416] **viXra:1510.0451 [pdf]**
*submitted on 2015-10-28 09:30:32*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 6 Pages.

A simplified photonic crystal design for an all-optical NAND gate operating in the visible spectrum is proposed and validated with numerical experiments using Finite Difference Time Domain method. Considering the NAND gate as a optical four-port network, the scattering matrix is determined. Also, two-dimensional autocorrelation-based leakage analysis is done and temporal analysis of the output pulse is performed. From the above mentioned valuations, one can obtain the optimal performance of the NAND gate structure with minimal loss and distortion, which forms the novelty of the present work.

**Category:** Mathematical Physics

[415] **viXra:1510.0450 [pdf]**
*submitted on 2015-10-28 09:31:42*

**Authors:** Sai Venkatesh Balasubramanian, Ganapathy R, Porsezian K

**Comments:** 3 Pages.

A ‘T-shaped’ defect is introduced in a two-dimensional photonic crystal lattice made of silicon, and for a small-signal optical input, this structure thus acts as an optical amplifier. A detailed analysis yields optimal linear and nonlinear performance of the optical amplifier operating in the visible region with minimal leakage and distortion.

**Category:** Mathematical Physics

[414] **viXra:1510.0355 [pdf]**
*submitted on 2015-10-22 09:44:59*

**Authors:** Sai Venkatesh Balasubramanian

**Comments:** 13 Pages.

A frequency dependant chaos generator offering the twin advantages of simplicity of implementation and easy control and tunability is proposed using an iterative map based on the circle map and characterized using bifurcation diagrams. The nonlinearity of a single MOS transistor is effectively harnessed and is used to design a frequency dependant chaos generator using ring oscillators for the driving signals. The proposed design is implemented at the deep submicron VLSI level at 180nm CMOS Technology using SPICE Simulation. The generated chaos is characterized qualitatively using waveforms, spectra and phase portrait. Quantitative characterization using Lyapunov Exponent, Kolmogorov Entropy and Fractal Dimension ascertain the chaotic nature. Finally, the dependance of the nature of chaos generated on the power supply and on the driving signal frequency is characterized. The simplicity of circuitry coupled with the frequency dependence and low power dissipation form the key highlights of the present work. The chaotic signal generated in the present work serve as a potential candidate as a carrier in secure communication systems and encryption techniques.

**Category:** Mathematical Physics

[413] **viXra:1510.0346 [pdf]**
*submitted on 2015-10-21 07:23:12*

**Authors:** Nicolae Mazilu; Maricel Agop

**Comments:** 23 Pages.

The extended matter should be first characterized by a surface of separation from the empty space. This surface cannot be neatly, i.e. purely geometrically, defined. When it comes to extended particles, which are the fundamental structural units of the matter, the physical evidence is that they are not even stable: they are in a continuous transformation, and so are their limits of separation from space. The present work describes a concept of extended particle with special emphasis on this limit of separation. It turns out that the properties of inertia, as classically understood, are intrinsically related to the spin properties of quantum origin. Thus, the extended particle model cannot be but “holographic” when it comes to imbedding it in a physical structure. The spin properties turn out to be essential, inasmuch as they decide the forces of interaction issuing from the particle.

**Category:** Mathematical Physics

[412] **viXra:1510.0340 [pdf]**
*submitted on 2015-10-20 18:28:10*

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

**Comments:** 4 Pages.

Will the physics of GRS look similar or different from current physics [primarily strings]?

**Category:** Mathematical Physics

[411] **viXra:1510.0322 [pdf]**
*submitted on 2015-10-18 19:04:59*

**Authors:** Andrew Nassif

**Comments:** 5 Pages.

We will be taking a look at analyzing different papers from the Cambridge University Press on Computational Mathematics, Theoretical Physics, and Mathematical Physics. We will be reviewing them through a literary, rhetorical, and ofcourse scientific perspective.

**Category:** Mathematical Physics

[410] **viXra:1510.0145 [pdf]**
*submitted on 2015-10-17 07:58:06*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 7 Pages.

Merriam-Webster's Collegiate Dictionary, Eleventh Edition, gives a technical definition of curvature, "the rate of change of the angle through which the tangent to a curve turns in moving along the curve and which for a circle is equal to the reciprocal of the radius". That precisely describes a curve's intuitive curvature, but the Riemann "curvature" tensor is zero for all curves! We work out the natural extension of intuitive curvature to hypersurfaces, based on the rates that their tangents develop components which are orthogonal to the local tangent hyperplane. Intuitive curvature is seen to have the form of a second-rank symmetric tensor which cannot be algebraically expressed in terms of the metric tensor and a finite number of its partial derivatives. The Riemann "curvature" tensor contrariwise is a fourth-rank tensor with both
antisymmetric and symmetric properties that famously is algebraically expressed in terms of the metric tensor and its first and second partial derivatives. Thus use of the word "curvature" in connection with the Riemann tensor is quite misleading. Likewise, use of the words "differential geometry" in connection
with the drastic Gauss-Riemann restriction of that geometry is misleading; the restriction permits only algebraic functions of the metric and its partial derivatives, namely the possible ingredients of field theories of the metric.

**Category:** Mathematical Physics

[409] **viXra:1510.0130 [pdf]**
*submitted on 2015-10-15 04:14:17*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 13 Pages.

A novel kind of classical bracket of classical observables is proposed. This bracket is used directly as a derivation* of the commutator of the quantum mechanical observables that are simply obtained by Dirac quantization of the classical observables. Light bending in the presence of a massive object in Schwarzschild’s metric is considered and the above bracket is used to obtain a second quantized equation of the wave function of the photon in this situation via the Dirac quantization.

**Category:** Mathematical Physics

[408] **viXra:1510.0111 [pdf]**
*submitted on 2015-10-13 11:04:50*

**Authors:** V.A.Budarin

**Comments:** 7 Pages. MSC 76D09, doi:10.15587/1729-4061.2015.39886

The paper considers transformation of the equation of motion in stresses for an incompressible Newtonian fluid. The aim of the transformation is to obtain more detailed equations that account for the impact of vortex (rotational) and linear (forward) flows on the process of viscous friction. The transformation method is based on adding zero to the expressions for shear stresses with subsequent distinguishing of rotor velocity function and derivatives characterizing the linear flow. This approach as a form of recording the original equation does not require any additional restrictions. The transformation has resulted in new systems of equations for viscous vortex and vortex-free flows as well as three-dimensional vortex. The obtained equations allow obtaining the known exact solution for the laminar flow (Poiseuille’s formula) and Euler’s differential equation for an ideal fluid. We have shown that the Navier-Stokes equation is a separate case of a more general equation for Newtonian fluid motion. The obtained equations and connections between them allow improvement of the mathematical description of the incompressible fluid flow.

**Category:** Mathematical Physics

[407] **viXra:1510.0104 [pdf]**
*submitted on 2015-10-13 03:03:32*

**Authors:** Algirdas Antano Maknickas

**Comments:** 2 Pages.

It was shown that using spatial transform obtained by applying the difference to spatial global coordinates and time integral of velocities non linear Navier-Stokes equation transforms into parabolic equations.

**Category:** Mathematical Physics

[406] **viXra:1510.0084 [pdf]**
*submitted on 2015-10-10 10:19:08*

**Authors:** Peter Cameron

**Comments:** 6 Pages.

The eight geometric objects of the impedance model of the electron, as fortuitous
happenstance would have it, are those of the 3D Pauli subalgebra of the geometric interpretation
of Clifford algebra. Given that impedance is a measure of the amplitude and phase of opposition
to the flow of energy, and that quantum phase is the gauge parameter in quantum mechanics, one
might consider an approach in which the elements of a gauge group of the electron would be
impedances of interactions between these geometric objects. The resulting 4D Dirac subalgebra
is examined in relation to the E8 exceptional Lie group.

**Category:** Mathematical Physics

[405] **viXra:1510.0063 [pdf]**
*submitted on 2015-10-06 18:28:56*

**Authors:** Harry Watson

**Comments:** 4 Pages.

Let B denote a ball centered at the origin with radius R=(4pi-1/pi). Gravitational forces from a singularity generate rotation about an axis. Internal rotational forces form a vacuous prolate ellipsoid, with major axis (4pi-1/pi) and minor axes {1/pi, 1/pi}. The ball B ejects a volume (4pi/3)(pi^(-2))(4pi-1/pi). This is the volume of the circumscribed prolate ellipsoid. It is also the volume of an elliptical wedge with curved surface area 4/pi and the elliptical sector with curved surface area 4/pi. It is not unreasonable to suppose that the electron is a ball of unit radius. The volume of the electron is V_e = (4pi/3). The ratio of the volume of ball B to the volume of the electron is given by V_B/V_e = (4pi-1/pi)^3 = 1837.392727.... Let V_w be the volume of the wedge of ejecta.
(V_B-V_w)/(V_e) = (4pi-1/pi)^3-(pi^(-2)(4pi-1/pi) = 1836.15
Look at V_w. V_w/V_e = (pi^(-2))(4pi-1/pi) = 1.24098801$. This ejecta easily supports a charged unit ball, whereas the original ball only had the property of gravitational attraction. At this point we have the basic two stable particles, namely the proton and the electron. We then look at the mass ratio of the proton to the electron.
V_p/V_e = (V_B-V_w)/(V_e) = 1836.15
There are several expressions that yield the same numerical value as the previous equation. First among equals is
(4pi)(4pi-1/pi)(4pi-2/pi) = 1836.15
Moreover,
64pi^3-48pi+8/pi = 1836.15
The above equation is the original estimate.
harry.watson@att.net

**Category:** Mathematical Physics

[404] **viXra:1510.0028 [pdf]**
*submitted on 2015-10-03 13:57:55*

**Authors:** Evgeny A. Novikov

**Comments:** 9 Pages.

This work is based on modification of the general relativity, which includes effects of production /absorption of matter by the vacuum. The theory (without fitting parameters) is in good quantitative agreement with cosmological observations (SnIa, SDSS-BAO and reduction of acceleration of the expanding universe). In this theory, there is no Big Bang at the beginning, but some local bangs during the evolution are probable. Also, there is no critical density of the universe and, therefore, no dark energy. Based on exact Gaussian solution for the scale factor, it is shown that an effective age of the universe is about 327 billion years. Production of primary dark matter particles have started 43 billion years later. It is shown that characteristic distance between particles is 30 times smaller than the thermal de Brogle wavelength, so that quantum effects, including formation of the Bose-Einstein condensate, can dominate. "Ordinary" matter was synthesized from dark matter in galaxies. Supplementary exact solutions are obtained for various ranges of parameters. From the theory we get an interface between dark and ordinary matter (IDOM), which very likely exist not only in cosmos, but everywhere, including our body and our brain.
Key words: cosmology; age of the universe; dark matter; interface between dark and ordinary matter.

**Category:** Mathematical Physics

[403] **viXra:1510.0010 [pdf]**
*submitted on 2015-10-01 18:03:19*

**Authors:** Eun Ji Jang, Jihun Cha, Young Kyu Lee, Won Sang Chung

**Comments:** 12 Pages.

In this paper we extend the so-called dual or mirror image
formalism and Caldirola's- Kanai's formalism for damped harmonic oscillator to the case that both frictional coefficient and time-dependent frequency depend on time explicitly.
As an solvable example, we consider the case that frictional coefficient $ \ga (t) = \frac{ \ga_0}{1 + q t} , (q > 0 )$ and angular frequency function $ w(t) = \frac{ w_0}{ 1 + q t } $. For this choice, we construct the quantum harmonic Hamiltonian and express it in terms of $su(2)$ algebra generators. Using the exact invariant for the Hamiltonian and its unitary transform, we solve the time-dependent Schro\"dinger equation with time-dependent frictional coefficient and time-dependent frequency.

**Category:** Mathematical Physics

[402] **viXra:1509.0135 [pdf]**
*submitted on 2015-09-15 13:45:00*

**Authors:** Branko Zivlak

**Comments:** 6 Pages. 16 formulas, 2 tables

Koide formula has improved on the result 2/3 in the formula (14). The tau lepton mass is also calculated. This is third version of the article.

**Category:** Mathematical Physics

[401] **viXra:1509.0093 [pdf]**
*submitted on 2015-09-08 12:00:58*

**Authors:** Simon A. Okojokwu

**Comments:** 32 Pages.

A motive power generator having a magnetic potential energy of magnitude "Limk−>∞(τ * 2kπ)" Joules, where τ is the torque and "2kπ" is the angular displacement, the generator converting the magnetic potential energy into kinetic energy at the rate of (τ2 * σρ-1r-2)1/2 Joules per second, where r, ρ, and σ are respectively the average radius, the density, and the maximum tensile strength of the generator-rotor. The generator includes three concentric ring magnets positioned so that there are magnetic interactions among them, one of the ring magnets being pivoted to rotate about its axis of symmetry. First and second pluralities of oblique magnets are positioned in gaps between the ring magnets to incline the magnetic fields therein. The oblique magnets interact magnetically with the ring magnets, making them to exert magnetic shear forces on one another; the moment of the shear forces causes the pivoted ring magnet to rotate continuously.

**Category:** Mathematical Physics

[397] **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

[396] **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

[395] **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

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

**Category:** Mathematical Physics

[393] **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

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

**Category:** Mathematical Physics

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

**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

[386] **viXra:1604.0283 [pdf]**
*replaced on 2016-08-25 21:21:42*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

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

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 8 Pages.

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*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 7 Pages.

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*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 7 Pages.

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*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 7 Pages.

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*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 7 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 6 Pages.

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*

**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*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 6 Pages. Sorry, this paper yet is not good.

**Category:** Mathematical Physics

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

**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.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 6 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 5 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 5 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 4 Pages. ERRATA: x,y,z in equation (7) are in Lagrangian description

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 4 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 4 Pages. In english.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 4 Pages. Sorry. Unfortunately, x, y, z are not so free.

**Category:** Mathematical Physics

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

**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*

**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*

**Authors:** Jonathan Tooker

**Comments:** 1 Page. nice paper

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*

**Authors:** Doug Jensen

**Comments:** 2 Pages.

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*

**Authors:** CLaude Latourre

**Comments:** 8 Pages. en français

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*

**Authors:** Robert G Wallace

**Comments:** 48 pages

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*

**Authors:** Rob Wallace

**Comments:** 25 Pages.

The direct product of a right and left handed quaternion algebras generates an algebra isomorphic to the Clifford algebra Cl(3,1) which describes space-time with signature (+++-). Once a higher dimensional background is proposed as an underlying basis for reality, it becomes logical to seek an equivalent product for octonions. However, the non-associativity of octonions means that a direct product is not defined for them. In this paper, a modified Moufang loop construction is used to generate an algebra based on products of octonions which differs from that of the octo-octonions, labelled the kaotic algebra. Subalgebras of the kaotic algebra can be found that correspond to several models of particle physics proposed by others.

**Category:** Mathematical Physics

[362] **viXra:1603.0115 [pdf]**
*replaced on 2016-04-18 01:48:40*

**Authors:** Rob Wallace

**Comments:** 25 Pages.

The direct product of a right and left handed quaternion algebras generates an algebra isomorphic to the Clifford algebra Cl(3,1) which describes space-time with signature (+++-). Once a higher dimensional background is proposed as an underlying basis for reality, it becomes logical to seek an equivalent product for octonions. However, the non-associativity of octonions means that a direct product is not defined for them. In this paper, a modified Moufang loop construction is used to generate an algebra based on products of octonions which differs from that of the octo-octonions, labelled the kaotic algebra. Subalgebras of the kaotic algebra can be found that correspond to several models of particle physics proposed by others.

**Category:** Mathematical Physics

[361] **viXra:1602.0167 [pdf]**
*replaced on 2016-05-28 11:19:59*

**Authors:** Robert Watson

**Comments:** 39 Pages. Some important corrections made in v2 using dimensional analysis

Kaluza's 1921 theory of gravity and electromagnetism using a fifth wrapped-up spatial dimension is inspiration for many modern attempts to develop new physical theories. The original theory has problems which may well be overcome, and thus Kaluza theory should be looked at again: it is a natural, if not necessary, geometric unification of gravity and electromagnetism. Here a general demonstration that the Lorentz force law can be derived from a range of Kaluza theories is presented. This is investigated via non-Maxwellian kinetic definitions of charge that are divergence-free and relate Maxwellian charge to 5D components of momentum. The possible role of torsion is considered as an extension. It is shown, however, that symmetric torsion components are likely not admissible in any prospective theory. As a result Kaluza's original theory is rehabilitated and a call for deeper analysis made.

**Category:** Mathematical Physics

[360] **viXra:1602.0122 [pdf]**
*replaced on 2016-07-19 15:17:16*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 4 Pages.

A simple mathematical proof reveals that time-inversion symmetry and reversibility are different concepts, which also resolves the Loschmidt paradox.

**Category:** Mathematical Physics

[359] **viXra:1602.0122 [pdf]**
*replaced on 2016-02-12 14:46:47*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 4 Pages.

A simple mathematical proof reveals that time inversion symmetry and reversibility are different concepts, which also resolves the Loschmidt paradox.

**Category:** Mathematical Physics

[358] **viXra:1602.0114 [pdf]**
*replaced on 2016-07-28 13:07:54*

**Authors:** Robert B. Easter

**Comments:** 185 Pages.

This paper introduces the G(4,8) Double Conformal Space-Time Algebra (DCSTA). G(4,8) DCSTA is a straightforward extension of the G(2,8) Double Conformal Space Algebra (DCSA), which is a different form of the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA). G(4,8) DCSTA extends G(2,8) DCSA with spacetime boost operations and differential operators for differentiation with respect to the pseudospatial time w=ct direction and time t. The spacetime boost operation can implement anisotropic dilation (directed non-uniform scaling) of quadric surface entities. DCSTA is a high-dimensional 12D embedding of the G(1,3) Space-Time Algebra (STA) and is a doubling of the G(2,4) Conformal Space-Time Algebra (CSTA). The 2-vector quadric surface entities of the DCSA subalgebra appear in DCSTA as quadric surfaces at zero velocity that can be boosted into moving surfaces with constant velocities that display the length contraction effect of special relativity. DCSTA inherits doubled forms of all CSTA entities and versors. The doubled CSTA entities (standard DCSTA entities) include points, hypercones, hyperplanes, hyperpseudospheres, and other entities formed as their intersections, such as planes, lines, spatial spheres and circles, and spacetime hyperboloids (pseudospheres) and hyperbolas (pseudocircles). The doubled CSTA versors (DCSTA versors) include rotor, hyperbolic rotor (boost), translator, dilator, and their compositions such as the translated-rotor, translated-boost, and translated-dilator. The DCSTA versors provide a complete set of spacetime transformation operators on all DCSTA entities. DCSTA inherits the DCSA 2-vector spatial entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) and gains Darboux pseudocyclides formed in spacetime with the pseudospatial time dimension. All DCSTA entities can be reflected in, and intersected with, the standard DCSTA entities. To demonstrate G(4,8) DCSTA as concrete mathematics with possible applications, this paper includes sample code and example calculations using the symbolic computer algebra system SymPy.

**Category:** Mathematical Physics

[357] **viXra:1602.0114 [pdf]**
*replaced on 2016-07-06 17:36:15*

**Authors:** Robert B. Easter

**Comments:** 111 Pages.

This paper introduces the G(4,8) Double Conformal Space-Time Algebra (DCSTA). G(4,8) DCSTA is a straightforward extension of the G(2,8) Double Conformal Space Algebra (DCSA), which is a different form of the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA). G(4,8) DCSTA extends G(2,8) DCSA with spacetime boost operations and differential operators for differentiation with respect to the pseudospatial time w=ct direction and time t. The spacetime boost operation can implement anisotropic dilation (directed non-uniform scaling) of quadric surface entities. DCSTA is a high-dimensional 12D embedding of the G(1,3) Space-Time Algebra (STA) and is a doubling of the G(2,4) Conformal Space-Time Algebra (CSTA). The 2-vector quadric surface entities of the DCSA subalgebra appear in DCSTA as quadric surfaces at zero velocity that can be boosted into moving surfaces with constant velocities that display the length contraction effect of special relativity. DCSTA inherits doubled forms of all CSTA entities and versors. The doubled CSTA entities (standard DCSTA entities) include points, hypercones, hyperplanes, hyperpseudospheres, and other entities formed as their intersections, such as planes, lines, spatial spheres and circles, and spacetime hyperboloids (pseudospheres) and hyperbolas (pseudocircles). The doubled CSTA versors (DCSTA versors) include rotor, hyperbolic rotor (boost), translator, dilator, and their compositions such as the translated-rotor, translated-boost, and translated-dilator. The DCSTA versors provide a complete set of spacetime transformation operators on all DCSTA entities. DCSTA inherits the DCSA 2-vector spatial entities for Darboux cyclides (incl. parabolic and Dupin cyclides, general quadrics, and ring torus) and gains Darboux pseudocyclides formed in spacetime with the pseudospatial time dimension. All DCSTA entities can be reflected in, and intersected with, the standard DCSTA entities. To demonstrate G(4,8) DCSTA as concrete mathematics with possible applications, this paper includes sample code and example calculations using the symbolic computer algebra system SymPy.

**Category:** Mathematical Physics

[356] **viXra:1602.0114 [pdf]**
*replaced on 2016-02-24 01:21:52*

**Authors:** Robert B. Easter

**Comments:** 88 Pages.

This paper introduces the G(4,8) Double Conformal Space-Time Algebra (DCSTA). G(4,8) DCSTA is a straightforward extension of the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA). G(4,8) DCSTA extends G(8,2) DCGA with spacetime boost operations and differential operators for differentiation with respect to the time-like w=ct direction and time t. The spacetime boost operation can implement anisotropic dilation (directed non-uniform scaling) of quadric surface entities. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the length contraction effect of special relativity. To demonstrate G(4,8) DCSTA as concrete mathematics with possible applications, this paper includes sample code and example calculations using the symbolic computer algebra system SymPy.

**Category:** Mathematical Physics

[355] **viXra:1602.0010 [pdf]**
*replaced on 2016-02-05 04:29:56*

**Authors:** Zhang Yunfan

**Comments:** 36 Pages.

The theory of idealiscience is an accurate theoretical model, by the model we can deduce most important laws of Physics, explain a lot of physical mysteries, even a lot of basic and important philosophical questions. we can also get the theoretical values of a lot of physical constants, even some of the constants can not be deduced by traditional physical theories, such as neutron mass and magnetic moment,Avogadro constant and so on.

**Category:** Mathematical Physics

[354] **viXra:1601.0312 [pdf]**
*replaced on 2016-02-11 04:12:01*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 16 Pages. English and portuguese versions.

A solution to the 6th millenium problem, respect to breakdown of Navier-Stokes solutions and the bounded energy. We have proved that there are initial velocities u^0 (x) and forces f(x,t) such that there is no physically reasonable solution to the Navier-Stokes equations for t>0, which corresponds to the case (C) of the problem relating to Navier-Stokes equations available on the website of the Clay Institute.

**Category:** Mathematical Physics

[353] **viXra:1601.0312 [pdf]**
*replaced on 2016-02-05 04:43:59*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 16 Pages. English translation still incomplete.

A solution to the 6th millenium problem, respect to breakdown of Navier-Stokes solutions and the bounded energy. We have proved that there are initial velocities u^0 (x) and forces f(x,t) such that there is no physically reasonable solution to the Navier-Stokes equations for t>0, which corresponds to the case (C) of the problem relating to Navier-Stokes equations available on the website of the Clay Institute.

**Category:** Mathematical Physics

[352] **viXra:1601.0312 [pdf]**
*replaced on 2016-02-03 12:12:20*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 22 Pages. Sorry... example 2 wrong again.

**Category:** Mathematical Physics

[351] **viXra:1601.0312 [pdf]**
*replaced on 2016-02-02 08:17:02*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 20 Pages. Almost done (in portuguese).

**Category:** Mathematical Physics

[350] **viXra:1601.0312 [pdf]**
*replaced on 2016-01-31 15:05:53*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 20 Pages. Need yet revision and complete translation for english.

**Category:** Mathematical Physics

[349] **viXra:1601.0045 [pdf]**
*replaced on 2016-04-17 08:36:40*

**Authors:** Carsten S.P. Spanheimer

**Comments:** 26 Pages. In german language.

Die Einführung 'quaternionischer Differentialformen' auf dem Tangentialraum einer vierdimensionalen Mannigfaltigkeit ergibt ein vielversprechendes mathematisches System zur Beschreibung unserer physikalischen (3+1)-Raumzeit
schon mit einem Minimum von Grundannahmen.
Hier wird die Grundlage dieses Modells einer 'Quaternionischen Raumzeit' dargestellt.

**Category:** Mathematical Physics

[348] **viXra:1512.0334 [pdf]**
*replaced on 2016-02-26 01:37:13*

**Authors:** A. A. Frempong

**Comments:** 47 Pages. Copyright © by A. A. Frempong

Over nearly a year and half ago, the Navier-Stokes (N-S) equations in 3-D for incompressible fluid flow were analytically solved by the author. However, some of the solutions contained implicit terms. In this paper, the implicit terms have been expressed explicitly in terms of x, y, z and t. The author proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It was mathematically shown that without gravity forces on earth, there would be no incompressible fluid flow on earth as is known, and also, there would be no magnetohydrodynamics. In addition to the usual method of solving these equations, the N-S equations were also solved by a second method in which the three equations in the system were added to produce a single
equation which was then integrated. The solutions by the two methods were identical, except for the constants involved. Ratios were used to split-up the equations; and the resulting sub-equations were readily integrable; and even, the nonlinear sub-equations were readily integrated. The examples in the preliminaries show everyday examples on using ratios to divide a quantity into parts, as well as possible applications of the solution method in mathematics, science, engineering, business, economics, finance, investment and personnel management decisions. The x-direction Navier-Stokes equation was linearized, solved, and the solution analyzed. This solution was followed by the solution of the Euler equation of fluid flow. The Euler equation represents the nonlinear part of the Navier-Stokes equation. Following the Euler solution, the Navier-Stokes equation was solved essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equati
on, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion of fluids. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in the parabolic, periodic and decreasingly exponential motion. Periodicity increases with viscosity. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The fluid flow in the Navier-Stokes solution may be characterized as follows. The x-direction solution consists of linear, parabolic, and hyperbolic terms. The first three terms characterize parabolas. If one ass
umes that in laminar flow, the axis of symmetry of each parabola for horizontal velocity flow profile is in the direction of fluid flow, then in turbulent flow, the axes of symmetry of some of the parabolas would be at right angles to that for laminar flow. The characteristic curve for the integral of the x-nonlinear term is such a parabola whose axis of symmetry is at right angles that of laminar flow. The integral of the y-nonlinear term is similar, parabolically, to that of the x-nonlinear term. The characteristic curve for the integral of the z-nonlinear term is a combination of two similar parabolas and a hyperbola. If the above x-direction flow is repeated simultaneously in the y-and z-directions, the flow is chaotic and consequently turbulent.
For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and thus prove the existence of smooth solutions of the Navier-Stokes equations.

**Category:** Mathematical Physics

[347] **viXra:1512.0334 [pdf]**
*replaced on 2016-02-22 03:06:28*

**Authors:** A. A. Frempong

**Comments:** 47 Pages. Copyright © A. A. Frempong

Over nearly a year and half ago, the Navier-Stokes (N-S) equations in 3-D for incompressible fluid flow were analytically solved by the author. However, some of the solutions contained implicit terms. In this paper, the implicit terms have been expressed explicitly in terms of x, y, z and t. The author proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It was mathematically shown that without gravity forces on earth, there would be no incompressible fluid flow on earth as is known, and also, there would be no magnetohydrodynamics. In addition to the usual method of solving these equations, the N-S equations were also solved by a second method in which the three equations in the system were added to produce a single equation which was then integrated. The solutions by the two methods were identical, except for the constants involved. Ratios were used to split-up the equations; and the resulting sub-equations were readily integrable; and even, the nonlinear sub-equations were readily integrated. The examples in the preliminaries show everyday examples on using ratios to divide a quantity into parts, as well as possible applications of the solution method in mathematics, science, engineering, business, economics, finance, investment and personnel management decisions. The x-direction Navier-Stokes equation was linearized, solved, and the solution analyzed. This solution was followed by the solution of the Euler equation of fluid flow. The Euler equation represents the nonlinear part of the Navier-Stokes equation. Following the Euler solution, the Navier-Stokes equation was solved essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion of fluids. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in the parabolic, periodic and decreasingly exponential motion. Periodicity increases with viscosity. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The fluid flow in the Navier-Stokes solution may be characterized as follows. The x-direction solution consists of linear, parabolic, and hyperbolic terms. The first three terms characterize parabolas. If one assumes that in laminar flow, the axis of symmetry of each parabola for horizontal velocity flow profile is in the direction of fluid flow, then in turbulent flow, the axes of symmetry of some of the parabolas would be at right angles to that for laminar flow. The characteristic curve for the integral of the x-nonlinear term is such a parabola whose axis of symmetry is at right angles that of laminar flow. The integral of the y-nonlinear term is similar, parabolically, to that of the x-nonlinear term. The characteristic curve for the integral of the z-nonlinear term is a combination of two similar parabolas and a hyperbola. If the above x-direction flow is repeated simultaneously in the y-and z-directions, the flow is chaotic and consequently turbulent.
For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and thus prove the existence of smooth solutions of the Navier-Stokes equations.

**Category:** Mathematical Physics

[346] **viXra:1512.0334 [pdf]**
*replaced on 2015-12-16 22:28:55*

**Authors:** A. A. Frempong

**Comments:** 46 Pages. Copyright © A. A. Frempong

Over nearly a year and half ago, the Navier-Stokes (N-S) equations in 3-D for incompressible fluid flow were analytically solved by the author. However, some of the solutions contained implicit terms. In this paper, the implicit terms have been expressed explicitly in terms of x, y, z and t. The author proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It was mathematically shown that without gravity forces on earth, there would be no incompressible fluid flow on earth as is known, and also, there would be no magnetohydrodynamics. In addition to the usual method of solving these equations, the N-S equations were also solved by a second method in which the three equations in the system were added to produce a single equation which was then integrated. The solutions by the two methods were identical, except for the constants involved. Ratios were used to split-up the equations; and the resulting sub-equations were readily integrable, and even, the nonlinear sub-equations were readily integrated. The examples in the preliminaries show everyday examples on using ratios to divide a quantity into parts, as well as possible applications of the solution method in mathematics, science, engineering, business, economics, finance, investment and personnel management decisions. The x-direction Navier-Stokes equation was linearized, solved, and the solution analyzed. This solution was followed by the solution of the Euler equation of fluid flow. The Euler equation represents the nonlinear part of the Navier-Stokes equation. Following the Euler solution, the Navier-Stokes equation was solved essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion of fluids. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in the parabolic, periodic and decreasingly exponential motion. Periodicity increases with viscosity. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The fluid flow in the Navier-Stokes solution may be characterized as follows. The x-direction solution consists of linear, parabolic, and hyperbolic terms. The first three terms characterize parabolas. If one assumes that in laminar flow, the axis of symmetry of the parabola for horizontal velocity flow profile is in the direction of fluid flow, then in turbulent flow, the axis of symmetry of the parabola would have been rotated 90 degrees from that for laminar flow. The characteristic curve for the x-nonlinear term is such a parabola whose axis of symmetry has been rotated 90 degrees from that of laminar flow. The y-nonlinear term is similar parabolically to the x-nonlinear term. The characteristic curve for the z-nonlinear term is a combination of two similar parabolas and a hyperbola. If the above x-direction flow is repeated simultaneously in the y-and z-directions, the flow is chaotic and consequently turbulent.
For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and thus prove the existence of smooth solutions of the Navier-Stokes equations.

**Category:** Mathematical Physics

[345] **viXra:1512.0333 [pdf]**
*replaced on 2015-12-16 22:38:15*

**Authors:** A. A. Frempong

**Comments:** 10 Pages. Copyright © A. A. Frempong

The system of magnetohydrodynamic (MHD) equations has been solved analytically in this paper. The author applied the technique used in solving the Navier-Stokes equations and applied a new law, the law of definite ratio for MHD. This law states that in MHD, the other terms of the system of equations divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no magnetohydrodynamics on earth as is known. The equations in the system of equations were added to produce a single equation which was then integrated. Ratios were used to split-up this single equation into sub-equations which were readily integrated, and even, the non-linear sub-equations were readily integrated. Twenty-seven sub-equations were integrated. The linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions revealed the role of each term in magnetohydrodynamics. In particular, the gravity term is the indispensable term in magnetohydrodynamics. The solutions of the MHD equations were compared with the solutions of the N-S equations, and there were similarities and dissimilarities.

**Category:** Mathematical Physics

[344] **viXra:1512.0332 [pdf]**
*replaced on 2016-04-18 01:01:43*

**Authors:** A. A. Frempong

**Comments:** 12 Pages. Copyright © A. A. Frempong

This paper covers the solutions of the Euler equations in 3-D and 4-D for incompressible fluid flow. The solutions are the spin-offs of the author's previous analytic solutions of the Navier-Stokes equations (vixra:1405.0251 of 2014). However, some of the solutions contained implicit terms. In this paper, the implicit terms have been expressed explicitly in terms of x, y, z and t.
The author applied a new law, the law of definite ratio for fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. This law evolved from the author's earlier solutions of the Navier-Stokes equations. In addition to the usual approach of solving these equations, the Euler equations have also been solved by a second method in which the three equations in the system are added to produce a single equation which is then integrated. The solutions by the two approaches are identical, except for the constants involved. From the experience gained in solving the linearized Navier-Stokes equations, only the equation with the gravity term as the subject of the equation was integrated. The experience was that when each of the terms of the Navier-Stokes equation was used as the subject of the equation, only the equation with the gravity term as the subject of the equation produced a solution. Ratios were used to split-up the x-direction Euler equation with the gravity term as the subject of the equation. The resulting five sub-equations were readily integrable, and even, the non-linear sub-equations were readily integrated. The integration results were combined. The combined results satisfied the corresponding equation. This equation which satisfied its corresponding equation would be defined as the driver equation; and each of the other equations which would not satisfy its corresponding equation would be called a supporter equation. A supporter equation does not satisfy its corresponding equation completely, but provides useful information which is not apparent in the solution of the driver equation. The solutions and relations revealed the role of each term of the Euler equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the forward motion of fluids. The pressure gradient term is also involved in the forward motion. The variable acceleration term is also involved in the forward motion. The fluid flow behavior in the Euler solution may be characterized as follows. The x-direction solution consists of linear, parabolic, and hyperbolic terms. If one assumes that in laminar flow, the axis of symmetry of the parabola for horizontal velocity flow profile is in the direction of fluid flow, then in turbulent flow, the axis of symmetry of the parabola would have been rotated 90 degrees from that for laminar flow. The characteristic curve for the x-nonlinear term is such a parabola whose axis of symmetry has been rotated 90 degrees from that of laminar flow. The y-nonlinear term is similar parabolically to the x-nonlinear term. The characteristic curve for the z-nonlinear term is a combination of two similar parabolas and a hyperbola. If the above x-direction flow is repeated simultaneously in the y-and z-directions, the flow is chaotic and consequently turbulent.

**Category:** Mathematical Physics

[343] **viXra:1511.0094 [pdf]**
*replaced on 2015-12-04 16:30:58*

**Authors:** Sergey V. Ershkov

**Comments:** 9 Pages. Keywords: Navier-Stokes equations, non-stationary helical flow, Arnold-Beltrami-Childress (ABC) flow

In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations, even for 3D case of compressible gas flow. But there is an essential deficiency of non-stationary solutions indeed.
In our derivation, we explore the case of non-stationary helical flow of the Navier-Stokes equations for incompressible fluids at any given initial conditions for velocity fields (it means an open choice for the space part of a solution).
Such a non-stationary helical flow is proved to be decreasing exponentially in regard to the time-parameter, the extent of time-dependent exponential component is given by the coefficient of kinematic viscosity, multiplied by the square of the coefficient of proportionality between the vorticity and velocity field.

**Category:** Mathematical Physics

[342] **viXra:1511.0094 [pdf]**
*replaced on 2015-11-11 16:51:09*

**Authors:** Sergey V. Ershkov

**Comments:** 5 Pages. Keywords: Navier-Stokes equations, non-stationary helical flow, Arnold-Beltrami-Childress (ABC) flow

In fluid mechanics, a lot of authors have been executing their researches to obtain the analytical solutions of Navier-Stokes equations, even for 3D case of compressible gas flow. But there is an essential deficiency of non-stationary solutions indeed. In our derivation, we explore the case of non-stationary helical flow of the Navier-Stokes equations for incompressible fluids at any given initial conditions for velocity fields (it means an open choice for the space part of a solution).

**Category:** Mathematical Physics

[341] **viXra:1510.0322 [pdf]**
*replaced on 2015-10-30 16:32:53*

**Authors:** Andrew Nassif

**Comments:** 6 Pages.

We will be taking a look at analyzing different papers from the Cambridge University Press on Computational Mathematics, Theoretical Physics, and Mathematical Physics. We will be reviewing them through a literary, rhetorical, and ofcourse scientific perspective. Overall we will do this through an Annotated Bibliography.

**Category:** Mathematical Physics

[340] **viXra:1510.0322 [pdf]**
*replaced on 2015-10-30 12:05:17*

**Authors:** Andrew Nassif

**Comments:** 6 Pages.

We will be taking a look at analyzing different papers from the Cambridge University Press on Computational Mathematics, Theoretical Physics, and Mathematical Physics. We will be reviewing them through a literary, rhetorical, and ofcourse scientific perspective.

**Category:** Mathematical Physics

[339] **viXra:1510.0145 [pdf]**
*replaced on 2015-10-20 20:14:59*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 7 Pages.

Merriam-Webster's Collegiate Dictionary, Eleventh Edition, gives a technical definition of curvature, "the rate of change of the angle through which the tangent to a curve turns in moving along the curve and which for a circle is equal to the reciprocal of the radius". That precisely describes a curve's intuitive curvature, but the Riemann "curvature" tensor is zero for all curves! We work out the natural extension of intuitive curvature to hypersurfaces, based on the rates that their tangents develop components which are orthogonal to the local tangent hyperplane. Intuitive curvature is seen to have the form of a second-rank symmetric tensor which cannot be algebraically expressed in terms of the metric tensor and a finite number of its partial derivatives. The Riemann "curvature" tensor contrariwise is a fourth-rank tensor with both antisymmetric and symmetric properties that famously is algebraically expressed in terms of the metric tensor and its first and second partial derivatives. Thus use of the word "curvature" with regard to the Riemann tensor is misleading, and since it can't encompass intuitive curvature, Gauss-Riemann "geometry" oughtn't be termed differential geometry either. That "geometry" is no more than the class of the algebraic functions of the metric and any finite number of the metric's partial derivatives, which it is convenient to organize into generally covariant entities such as the Riemann tensor because those potentially play a role in generally-covariant metric-based field theories.

**Category:** Mathematical Physics

[338] **viXra:1510.0104 [pdf]**
*replaced on 2015-10-18 15:08:59*

**Authors:** Algirdas Antano Maknickas

**Comments:** 2 Pages.

It was shown that using spatial transform obtained by applying the difference to spatial global coordinates and time integral of velocities non linear Navier-Stokes equation transforms into parabolic equations

**Category:** Mathematical Physics

[337] **viXra:1510.0063 [pdf]**
*replaced on 2015-12-19 12:19:26*

**Authors:** Harry Watson

**Comments:** 6 Pages.

Let B denote a ball centered at the origin with radius R=(4pi-1/pi). Gravitational forces from a singularity generate rotation about an axis. Internal rotational forces form a vacuous prolate ellipsoid, with major axis (4pi-1/pi) and minor axes {1/pi, 1/pi}. The ball B ejects a volume (4pi/3)(pi^(-2))(4pi-1/pi). This is the volume of the circumscribed prolate ellipsoid. It is also the volume of an elliptical wedge with curved surface area 4/pi and the elliptical sector with curved surface area 4/pi. It is not unreasonable to suppose that the electron is a ball of unit radius. The volume of the electron is V_e = (4pi/3). The ratio of the volume of ball B to the volume of the electron is given by V_B/V_e = (4pi-1/pi)^3 = 1837.392727.... Let V_w be the volume of the wedge of ejecta.
(V_B-V_w)/(V_e) = (4pi-1/pi)^3-(pi^(-2)(4pi-1/pi) = 1836.15
Look at V_w. V_w/V_e = (pi^(-2))(4pi-1/pi) = 1.24098801$. This ejecta easily supports a charged unit ball, whereas the original ball only had the property of gravitational attraction. At this point we have the basic two stable particles, namely the proton and the electron. We then look at the mass ratio of the proton to the electron.
V_p/V_e = (V_B-V_w)/(V_e) = 1836.15
There are several expressions that yield the same numerical value as the previous equation. First among equals is
(4pi)(4pi-1/pi)(4pi-2/pi) = 1836.15
Moreover,
64pi^3-48pi+8/pi = 1836.15
The above equation is the original estimate.
harry.watson@att.net

**Category:** Mathematical Physics

[336] **viXra:1509.0093 [pdf]**
*replaced on 2015-09-09 08:48:56*

**Authors:** Simon A. Okojokwu

**Comments:** 32 Pages.

A motive power generator having a magnetic potential energy of magnitude "Limk−>∞(τ * 2kπ)" Joules, where τ is the torque and "2kπ" is the angular displacement, the generator converting the magnetic potential energy into kinetic energy at the rate of (τ^2 * σ * ρ^-1 * r^-2)^1/2 Joules per second, where r, ρ, and σ are respectively the average radius, the density, and the maximum tensile strength of the generator-rotor.

**Category:** Mathematical Physics