**Previous months:**

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2017 - 1701(9) - 1702(7)

Any replacements are listed further down

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

**Authors:** Victor Christianto, Sergey Ershkov

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

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

**Category:** Mathematical Physics

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

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

**Comments:** 13 pages

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

**Category:** Mathematical Physics

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

**Authors:** Gary D. Simpson

**Comments:** 10 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Viktor Strohm

**Comments:** 3 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Chang Li

**Comments:** 2 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 3 Pages.

From string theory to topstringy.

**Category:** Mathematical Physics

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

**Authors:** M.W.Kalinowski

**Comments:** 37 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 2 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 12 Pages.

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

**Category:** Mathematical Physics

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

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

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

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

**Category:** Mathematical Physics

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

**Authors:** Michail Zak

**Comments:** 7 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 7 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Grushka Ya.I.

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

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

**Category:** Mathematical Physics

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

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** William O. Straub

**Comments:** 9 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 6 pages

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

**Category:** Mathematical Physics

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

**Authors:** Richard A Jowsey

**Comments:** 13 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Wen Chen

**Comments:** 6 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Renzun Lian

**Comments:** 10 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Victor L. Mironov

**Comments:** 9 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Renzun Lian

**Comments:** 13 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Markos Georgallides

**Comments:** 21 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** M. D. Sheppeard

**Comments:** 15 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Algirdas Antano Maknickas

**Comments:** 8 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Robert Deloin

**Comments:** 7 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 20 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 23 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 29 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 15 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 22 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 31 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 17 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 15 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 27 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 20 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 31 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Harry Watson

**Comments:** 5 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 1 Page.

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

**Category:** Mathematical Physics

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

**Authors:** Nicolas Poupart

**Comments:** 6 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 15 Pages.

A Guide Through Metaspace.

**Category:** Mathematical Physics

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

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

**Comments:** 11 pages

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

**Category:** Mathematical Physics

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

**Authors:** M.E. Hassani

**Comments:** 8 Pages;8 References

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

**Category:** Mathematical Physics

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

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

**Comments:** 11 pages

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

**Category:** Mathematical Physics

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

**Authors:** Biswanath Rath

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

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

**Category:** Mathematical Physics

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

**Authors:** Renzun Lian

**Comments:** 12 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Renzun Lian

**Comments:** 8 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Renzun Lian

**Comments:** 13 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Renzun Lian

**Comments:** 15 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Nicolas Poupart

**Comments:** 6 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Renzun Lian

**Comments:** 17 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** M.E.Hassani

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

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

**Category:** Mathematical Physics

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

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

**Comments:** 83 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 8 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 15 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 16 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 9 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 43 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Taha Sochi

**Comments:** 27 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 31 Pages.

A 100 year task of minimal duration and of limitless measure

**Category:** Mathematical Physics

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

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

**Comments:** 2 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Claude Michael Cassano

**Comments:** 9 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Ricardo Gil

**Comments:** 1 Page.

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

**Category:** Mathematical Physics

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

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

**Comments:** 3 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Prado, Pf et al

**Comments:** 1 Page.

Addendum to hypothesis

**Category:** Mathematical Physics

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

**Authors:** Lamont Williams

**Comments:** 2 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Prado, PF et al

**Comments:** 1 Page.

Temprtive Math exploration

**Category:** Mathematical Physics

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

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

**Comments:** 2 pages

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

**Category:** Mathematical Physics

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

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

**Comments:** 7 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 5 pages

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

**Category:** Mathematical Physics

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

**Authors:** Prado, PF et al

**Comments:** 4 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 4 pages

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

**Category:** Mathematical Physics

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

**Authors:** Prado, Pf

**Comments:** 3 Pages.

Discussion on ressonance considerations about fundamental physics

**Category:** Mathematical Physics

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

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

**Comments:** 3 pages

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

**Category:** Mathematical Physics

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

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

**Comments:** 5 pages

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

**Category:** Mathematical Physics

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

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

**Comments:** 3 pages

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

**Category:** Mathematical Physics

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

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

**Comments:** 3 pages

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

**Category:** Mathematical Physics

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

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

**Comments:** 3 pages

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

**Category:** Mathematical Physics

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

**Authors:** Miroslav Josipovic

**Comments:** 70 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 2 pages

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

**Category:** Mathematical Physics

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

**Authors:** Dan Visser

**Comments:** 17 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 2 pages

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

**Category:** Mathematical Physics

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

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

**Comments:** 3 pages

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

**Category:** Mathematical Physics

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

**Authors:** Robert G Wallace

**Comments:** 8 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 3 pages

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

**Category:** Mathematical Physics

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

**Authors:** M.W.Kalinowski

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

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

**Category:** Mathematical Physics

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

**Authors:** Christian Rakotonirina

**Comments:** 94 Pages. in French

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

**Category:** Mathematical Physics

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

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

**Comments:** 2 pages

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

**Category:** Mathematical Physics

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

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

**Comments:** 2 pages

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

**Category:** Mathematical Physics

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

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

**Comments:** 7 pages

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

**Category:** Mathematical Physics

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

**Authors:** Gary D. Simpson

**Comments:** 39 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Bing Wang

**Comments:** 10 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 8 Pages.

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

**Category:** Mathematical Physics

[499] **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

[498] **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

[497] **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

[496] **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

[495] **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

[494] **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

[493] **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

[492] **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

[491] **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

[490] **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

[489] **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

[488] **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

[487] **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

[486] **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

[485] **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

[484] **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

[483] **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

[482] **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

[481] **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

[480] **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

[479] **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

[478] **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

[477] **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

[476] **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

[475] **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

[474] **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

[473] **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

[472] **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

[471] **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

[470] **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

[469] **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

[468] **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

[467] **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

[466] **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

[465] **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

[464] **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

[463] **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

[462] **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

[461] **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

[460] **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

[459] **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

[458] **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

[457] **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

[456] **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

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

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

**Comments:** 3 Pages.

From string theory to topstringy.

**Category:** Mathematical Physics

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

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Hans Detlef Hüttenbach

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

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

**Category:** Mathematical Physics

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

**Authors:** Hans Detlef Hüttenbach

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

**Category:** Mathematical Physics

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

**Authors:** William O. Straub

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

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

**Category:** Mathematical Physics

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

**Authors:** William O. Straub

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

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

**Category:** Mathematical Physics

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

**Authors:** Robert Deloin

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

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

**Category:** Mathematical Physics

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

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

**Comments:** 18 pages

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

**Category:** Mathematical Physics

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

**Authors:** Nicolas Poupart

**Comments:** 6 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 5 pages

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

**Category:** Mathematical Physics

[407] **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

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

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

**Comments:** 4 pages

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

**Category:** Mathematical Physics

[405] **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

[404] **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

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

**Category:** Mathematical Physics

[402] **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

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 10 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 9 Pages.

**Category:** Mathematical Physics

[396] **viXra:1605.0192 [pdf]**
*replaced on 2016-09-14 11:29:59*

**Authors:** Bernd Ganter

**Comments:** 8 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 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

[395] **viXra:1605.0101 [pdf]**
*replaced on 2016-09-28 04:34:35*

**Authors:** J.A.J. van Leunen

**Comments:** 13 Pages.

Hilbert spaces can store discrete members of division rings and continuums that are formed by members of division rings in the eigenspaces of operators that reside in these Hilbert spaces. Only three suitable division rings exist. These are the real numbers, the complex numbers and the quaternions.
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 number systems that are division rings 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

[394] **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

[393] **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

[392] **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

[391] **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

[390] **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

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 7 Pages.

**Category:** Mathematical Physics

[388] **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

[387] **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

[386] **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

[385] **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

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 6 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 5 Pages.

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 5 Pages.

**Category:** Mathematical Physics

[381] **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

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 4 Pages.

**Category:** Mathematical Physics

[379] **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

[378] **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

[377] **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

[376] **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

[375] **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

[374] **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

[373] **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

[372] **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

[371] **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

[370] **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