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Any replacements are listed farther down

[762] **viXra:1805.0329 [pdf]**
*submitted on 2018-05-19 02:11:41*

**Authors:** Vu B Ho

**Comments:** 5 Pages.

In this work we discuss the possibility to classify geometric interactions with respect to the dimensions of the submanifolds which are decomposed and emitted from a differentiable manifold. The manifold, which is assumed to be an elementary particle, can be assumed to have the mathematical structure of a CW complex which is composed of n-cells. The decomposed n-cells will be identified with force carriers. In particular, for the case of differentiable manifolds of dimension three, there are four different types of geometric interactions associated with 0-cells, 1-cells, 2-cells and 3-cells. We discuss in more details the case of geometric interactions that are associated with the decomposition of 3-cells from a differentiable manifold and show that the physical interactions that are associated with the evolution of the geometric processes can be formulated in terms of general relativity.

**Category:** Mathematical Physics

[761] **viXra:1805.0170 [pdf]**
*submitted on 2018-05-08 08:04:23*

**Authors:** Sergey V. Ershkov

**Comments:** 10 pages, 7 figures; Keywords: Navier-Stokes equations, non-stationary flow, boundary layer

Solving the Navier-Stokes equations for 3D boundary layer of the incompressible flow of Newtonian fluids is the most unsolved problem in fluid mechanics. A lot of authors have been executing their researches to obtain the analytical and semi-analytic solutions for the boundary layer approximation of Navier-Stokes equations, even for example for 2D case of compressible gas flow. But there is an essential deficiency of 3D solutions for the boundary layer indeed.
In current research, an elegant ansatz is developed to obtain 3D solutions for the boundary layer approximation of Navier-Stokes equations of incompressible fluids (in the vicinity of the point of separating of boundary layer from surface to the outer ideal flow). The governing equation for such the process is proved to be the Poisson equation for each the component of velocity field of boundary layer flow, which could nevertheless be reduced to the Laplace equation in case of the uniform outer flow.

**Category:** Mathematical Physics

[760] **viXra:1805.0159 [pdf]**
*submitted on 2018-05-06 12:58:26*

**Authors:** Timoteo Briet Blanes, Ignacio Suarez Marcelo, Enrique Scalabroni

**Comments:** 56 Pages.

The performance of an F1 race car is greatly influenced by its aerodynamics. Race teams try to improve the vehicle performance by aiming for more levels of downforce. A huge amount of time is spent in wind tunnel and track testing. Typical wind tunnel testing is carried out in steady aerodynamic conditions and with car static configurations. However, the ride heights of a car are continuously changing in a race track because of many factors.
These are, for example, the roughness and undulations of the track, braking, accelerations, direction changes, aerodynamic load variations due to varying air speed and others. These factors may induce movements on suspensions components (sprung and unsprung masses) at different frequencies and may cause aerodynamic fluctuations that vary tires grip. When the frequency of the movement of a race car is high enough the steady aerodynamic condition and the car static configurations are not fulfilled. Then, transient effects appear and the dynamics of the system changes: heave, pitch and roll transient movements of the sprung mass affect both downforce and center of pressure position. The suspension system have to cope with them, but in order for the suspension to be effective, unsteady aerodynamics must be considered.The main objective is to model the effects of unsteady aerodynamics and know really the car dynamic, with the aim of optimizing the suspension performance, improving tire grip and finally reducing lap times.

**Category:** Mathematical Physics

[759] **viXra:1805.0111 [pdf]**
*submitted on 2018-05-05 08:45:51*

**Authors:** Timoteo Briet Blanes, Ignacio Suarez Marcelo, Enrique Scalabroni

**Comments:** 40 Pages.

Vehicles running at high speed are greatly influenced by their aerodynamic profile. Racing car teams strive to tune the setup seeking higher levels of downforce aerodynamic load. Wind tunnel tests or track data for specific vehicle positions are useful but incomplete and very expensive. Transient loads on the vehicle come from very different sources and, to date, there is no established methodology to take them into consideration. Computer simulation seems to be a good starting point to study the effect of transient aerodynamic loads in the design and optimization of the tuning of the suspension of a racing car.
This paper studies the effect of transient aerodynamic loads on the downforce of a vehicle. Heave vibrations on an aileron are analyzed on a simulation model. The data obtained in this simulation model are validated both in a steady and a transient state for different frequencies (1-800Hz). These results lead to the obtainment of a transfer function for the downforce on the aileron in question. Finally, a new quarter car model including aerodynamic effects from these studies is presented and some results on the influence of heave transient aerodynamics loads on a racing car are obtained.

**Category:** Mathematical Physics

[758] **viXra:1805.0073 [pdf]**
*submitted on 2018-05-02 23:58:53*

**Authors:** Rodney Bartlett

**Comments:** 14 Pages. Cite: https://doi.org/10.6084/m9.figshare.6214049.v1

What is the Dark Matter that holds together galaxies and galaxy clusters? Does causality (the law of cause and effect) really depend on the arrow of time only ever flying from the past to the present to the future? Or is that merely a way of thinking we've gotten used to - with the universe not caring about our temporal biases, and creating entanglement of all things in space-time through time going back and forth? In order to lay the groundwork for the relation between matter and antimatter and dark matter, I found it necessary to repeat earlier ideas about binary digits / Mobius strips / figure-8 Klein bottles / Wick rotation. I don't enjoy repeating myself – readers want new thoughts presented to them. But all these are required for the extra so called "imaginary" dimension to escape being a mathematical oddity, and to manifest as part of space-time. These ideas might seem to be going from strange to stranger, but they're validated by Werner Heisenberg's matrix version of quantum mechanics as well as the mathematics of matrix multiplication. The article ends with a few paragraphs summing up the relation between matter, antimatter, dark matter and extra dimensions. In the process, the Fixed Point Theorem is used logically to show that the cosmos must be infinite and eternal. This necessitates a Paradoxical PS attempting a rational explanation for an infinite, eternal universe (the Cosmic Microwave Background and redshift objections are addressed).

**Category:** Mathematical Physics

[757] **viXra:1805.0039 [pdf]**
*submitted on 2018-05-01 18:49:08*

**Authors:** Vu B Ho

**Comments:** 7 Pages.

In this work we discuss the possibility to identify physical interactions with geometric processes whose revolutions can be described by the Ricci flow. In particular, we show that it is possible to suggest that the charge of an elementary particle does not exist as a physical quantity possessed by the elementary particle itself but rather a collective dynamical effect that is associated with the intermediate particles, which are the force carriers. These force carrying particles have the geometric structures of two-dimensional spheres or n-tori. Furthermore, since the Ricci flow on two-dimensional manifolds does not give rise to neckpinches and if such geometric flows can be shown to not exist then it can be stated that the force carrying particles are the only particles that are truly fundamental.

**Category:** Mathematical Physics

[756] **viXra:1804.0475 [pdf]**
*submitted on 2018-04-28 14:20:02*

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

**Comments:** 5 pages

The Schrödinger eigenvalue problem with diverse potentials is investigated in this work. It is shown that exact and explicit discrete bound state solutions may be computed in terms of elementary functions.

**Category:** Mathematical Physics

[755] **viXra:1804.0303 [pdf]**
*submitted on 2018-04-22 02:13:16*

**Authors:** Rodney Bartlett

**Comments:** 20 Pages. Cite: https://doi.org/10.6084/m9.figshare.6169019.v1

Abstract -
"When we solve (19th-century Scottish physicist James Clerk) Maxwell's equations for light, we find not one but two solutions: a 'retarded' wave, which represents the standard motion of light from one point to another; but also an 'advanced' wave, where the light beam goes backward in time. Engineers have simply dismissed the advanced wave as a mathematical curiosity since the retarded waves so accurately predicted the behavior of radio, microwaves, TV, radar, and X-rays. But for physicists, the advanced wave has been a nagging problem for the past century." ("Physics of the Impossible" by Michio Kaku - Penguin Books, 2009: pp. 276-277)
Advanced waves are usually discarded because they are thought to violate the causality principle: advanced waves could be detected before their emission. On one level, I can appreciate that reasoning. But ultimately, I think it's an error that should be replaced by Isaac Newton's idea of gravity and the modern idea of quantum mechanics' entanglement. After writing a paragraph about entanglement and Newtonian gravity, several paragraphs are devoted to the motion of electromagnetism and gravitation, plus absorption and re-radiation. These are followed by (1) advanced waves and the dating of, among other things, dinosaur fossils, (2) existing technology that, unknown to everyone, detects the presence of advanced waves, (3) advanced waves plus disease and ageing, (4) partially overcoming ageing with technology based on noise-cancelling headphones, and (5) the role of Wick rotation and advanced waves in entanglement and evolution.
Just as advanced waves are usually discarded, very few physicists or mathematicians will venture to ascribe a physical meaning to imaginary numbers, which seem to have no correspondence with external reality. Here, it will be shown that imaginary time (which is described by such numbers) has two physical meanings - (1) it provides a way to unify space and time into one space-time, (2) it will allow construction of what may be called "imaginary computers".
Keywords
Wheeler-Feynman absorber theory; Transactional Interpretation of Quantum Mechanics; retarded waves; advanced waves; electromagnetism; gravitation; radioactive dating; noise-cancelling headphones; better health; longer life; nature of space and time; increasing Astronomical Unit; Pioneer anomaly; entanglement; evolution; imaginary computers; SUSY; supersymmetry
Table of Contents
ADVANCED WAVES AND DINOSAURS
CIRCLES, SPHERES, EVOLUTION AND DINOSAURS
WICK ROTATION, BITS, COSMIC TOPOLOGY
WICK ROTATION, SPACE-TIME AND SUSY
WICK ROTATION AND IMAGINARY COMPUTERS

**Category:** Mathematical Physics

[754] **viXra:1804.0222 [pdf]**
*submitted on 2018-04-16 10:45:14*

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

**Comments:** 9 pages

This paper shows that the solution of a class of Schrödinger equations may be performed in terms of the solution of the equation of constant coefficients.

**Category:** Mathematical Physics

[753] **viXra:1804.0202 [pdf]**
*submitted on 2018-04-15 06:29:29*

**Authors:** Spiros Konstantogiannis

**Comments:** 19 Pages.

Starting from a simple, one-parameter, symmetric wave function, we derive an attractive double Dirac delta potential with a centrifugal, angular-momentum-like tale, which has only one bound state, the energy of which can be set to zero.

**Category:** Mathematical Physics

[752] **viXra:1804.0160 [pdf]**
*submitted on 2018-04-11 15:44:00*

**Authors:** William O. Straub

**Comments:** 13 Pages.

A basic introduction to the calculus of differential forms for undergraduate physics students

**Category:** Mathematical Physics

[751] **viXra:1804.0159 [pdf]**
*submitted on 2018-04-11 16:36:41*

**Authors:** Dan Visser

**Comments:** 7 Pages.

This article discards the constant Planck-energy. This will be in service of a rotating vacuum-torus as a new building-stone in a variable vacuum for the benefit of a rotating hologram-universe. The new building-stone hosts all the sub-information for the quantum-information for each emerging not-fundamental Big Bang-universe. This leads to the presentation of a new formula for dimensional variable dark energy. Also a handwritten image shows the author’s velocity-tensor of rotating vacuum, which is combined with an energy of dark force emerged from a dark vacuum particle. He uses his tensor to explain the name of his theory, the Double Torus Theory (DTT) .

**Category:** Mathematical Physics

[750] **viXra:1804.0105 [pdf]**
*submitted on 2018-04-08 02:51:00*

**Authors:** Mikhail L. Sokolnikov

**Comments:** 2 Pages. https://youtu.be/rUI7Dmu62Uo

Logical continuation of the work of the Soviet aircraft designer, the Italian Earl of Croatian origin Roberto Oros di Bartini.
Логическое продолжение работы советского авиаконструктора, итальянского графа хорватского происхождения Roberto Oros di Bartini.
Time = x^4

**Category:** Mathematical Physics

[749] **viXra:1804.0097 [pdf]**
*submitted on 2018-04-08 12:12:33*

**Authors:** Alexander I.Dubinyansky, Pavel Churlyaev.

**Comments:** 10 Pages. dubinyansky@mail.ru

Development of the mathematical model of the elastic universe. The energy of the loks (3.0), (3.1), (3.2), and (3.3) is calculated. Assumptions are made regarding other loks. The first conclusions on the identification of elementary particles in a set of loks.

**Category:** Mathematical Physics

[748] **viXra:1804.0068 [pdf]**
*submitted on 2018-04-04 15:14:17*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 4 Pages.

Newton's mechanics is simple. His equivalence principle is simple, as is the inverse
square law of gravitational force. A simple theory should have simple solutions
to simple models. A system of n particles, given their initial speed and positions along
with their masses, is such a simple model. Yet, solving for n>2 is not simple.
This paper discusses, why that is a difficult problem and what could be done to get around that problem.

**Category:** Mathematical Physics

[747] **viXra:1803.0434 [pdf]**
*submitted on 2018-03-22 10:30:01*

**Authors:** Spiros Konstantogiannis

**Comments:** 40 Pages.

Starting with a general rational wave function, we search for potentials admitting it as a bound energy eigenfunction. We thus derive singular and regular potentials asymptotically decaying as the inverse of x squared, with the latter being simple or multiple volcanoes having a finite number of bound eigenstates. We present specific examples and examine the transition from singular to volcano potentials.

**Category:** Mathematical Physics

[746] **viXra:1803.0397 [pdf]**
*submitted on 2018-03-22 00:51:36*

**Authors:** Keaten Wood

**Comments:** 3 Pages.

It is popularly known that dark matter is responsible for the accelerating expansion of our universe, as well as many other phenomena. This could very well be the case. Through many mathematical steps, using mechanical laws and calculus, I have determined the amount of energy needed to expand the universe a certain distance quickly converges, meaning that all the universe needs is a sufficient amount of energy in order to expand infinitely, either given initially by the big bang or gradually by dark matter.

**Category:** Mathematical Physics

[745] **viXra:1803.0301 [pdf]**
*submitted on 2018-03-20 15:26:28*

**Authors:** R.T.Longo

**Comments:** 25 Pages.

In this paper, a general modeling principle is introduced that was found useful for modeling complex physical systems for engineering applications. The technique is a nonlinear asymptotic method (NLAM), constructed from simplified physical theories, i.e., physical theories that were developed from particular points of view, that can be used to construct a more global theory. Originally, the technique was envisioned primarily for engineering applications, but its success has led to a more general principle. Four examples are presented to discuss and illustrate this method.

**Category:** Mathematical Physics

[744] **viXra:1803.0300 [pdf]**
*submitted on 2018-03-20 18:24:51*

**Authors:** Dan Visser

**Comments:** 9 Pages.

This article describes the rotation and expansion of a fast rotating vacuum below the Planck-scale, with approximately 10-21 rad/s, which emerges an approximately 1018 Hertz frequency of x-rays above the Planck-scale. This high-frequent radiation is really observed by several observatory, with an energy of about 3,5 keV. In this respect I describe evidence for the existence of ‘light-holes’, which replaces the conservative Planck-scale seen from a distance in perspective of my new cosmological model, called the rotating hologram-universe. The new model therefore discards a single Big Bang-universe as not-fundamental. Due to the exercises given here a connection is presented with another (single) Big Bang-universe. Coming closer to these ‘light-holes’ high-frequent light becomes lower in frequency due to my formula Tdan , showing that vacuum expands by ‘crumbling the quantum-unit’. The closer to the ‘light-hole’, the more a parallel Big Bang-universe appears to be a part of the fundamental rotating hologram-universe.

**Category:** Mathematical Physics

[743] **viXra:1803.0263 [pdf]**
*submitted on 2018-03-17 17:12:50*

**Authors:** R. G. Chester

**Comments:** 275-page book in English. Links to internet resources are included.

The purpose of this work is to present a more realistic model for a number of dynamic three–dimensional physical phenomena which are traditionally depicted statically in two dimensions and are therefore misleading. It is also to provide a model for phenomena which are regarded as conceivable only in abstract mathematical terms, and are therefore thought to be permanently inaccessible to the non–specialist. The use of the QSO model will reveal pattern and enable analysis in hitherto untouched areas.

**Category:** Mathematical Physics

[742] **viXra:1803.0212 [pdf]**
*submitted on 2018-03-15 12:19:50*

**Authors:** Markos Georgallides

**Comments:** 36 Pages.

Article [67] is a Summary of prior [64-65-66] and because of its energy value , I believe that a wider discussion of it is for the benefit both the scientific development of knowledge from misconceptions of science , the application to new sources of energy , and in which is referred ,
a.. The Material points are produced from the unclashed , Matter (+) and Anti-matter (-) , lying into Energy-Chaos and following the Glue-Bond-Principle and NOT the Forced-collision .
b.. The Spin of monads which is the Angular-Momentum vector ,B, due to the eternal rotation of (+) Space around the (-) Anti-space and the HOW and the WHY Spin is ½ or 1 .
c.. Part of the Total-Energy produced in Primary particles from a ,Circular-motion, is trapped into wavelength λ, of particles as a Stationary-wave with 1,2,3,,n, lobes and ,n, frequencies following the Stationary-Wave-Nodes-Principle and which consists the Energy-tanks of particles .
d.. Part of the Total-Energy produced in Primary particles from a ,Cycloidal-motion, is stored in Energy-tanks of cave ,λ, as the ,n, frequencies due to oscillations , and additionally because of the centrifugal acceleration is created the Skin-effect at Stress-common-curve and the Kinetic-energy as an Electromagnetic-wave moves Outward the cave . Electromagnetic-wave and others are following the Breakage-Principle which is [(+) Space as the Electric-field , (-) Anti-space as the Magnetic-field , and (0=λ) the Energy-loop as the Energy-tank of particle .
e.. In case of the Compound particles as the Bohr model of atoms Breakage-Principle is still existing , particularly on the three Constituents and on all Total structure (formation) as , the Nucleus = The Space = the matter and the equal in charge counterpart Electron = The Anti-space = the Anti-matter , and Orbitals = The Energy loop as the Energy-tanks of atom. All above were analytically presented in the three prior articles and the present is a general summary of forgoing.

**Category:** Mathematical Physics

[741] **viXra:1803.0196 [pdf]**
*submitted on 2018-03-14 10:15:19*

**Authors:** Spiros Konstantogiannis

**Comments:** 12 Pages.

For one-dimensional potentials having, at most, finite discontinuities and simple poles at which the wave functions have simple zeros, we give an algebraic – i.e. operator-based – proof that an eigenfunction having no other zeros is a minimum-energy eigenfunction, and thus it describes the ground state.

**Category:** Mathematical Physics

[740] **viXra:1803.0086 [pdf]**
*submitted on 2018-03-06 06:43:51*

**Authors:** Jaykov Foukzon, S.A.Podosenov, A.A.Potapov, E.Menkova

**Comments:** 135 Pages.

In present article the original proposition is a generalization of the Einstein's world tensor g ij by the introduction of pure inertial field tensor g ac ij such that R α μνλ (g ac ij )≠0 .Bimetric theory of gravitational-inertial field is considered for the case when the gravitational-Inertial field is governed by either a perfect magnetic fluid.In a series of papers published during the past decade with respect to Mössbauer experiments in a rotating system [71]-[75],it has been experimentally shown that the relative energy shift ΔE/E between the source of resonant radiation (situated at the center of the rotating system) and the resonant absorber (located on the rotor rim) is described by the relationship ΔE/E=−ku 2 /c 2 , where u is the tangential velocity of the absorber, c the velocity of light in vacuum, and k some coefficient, which -- contrary to what had been classically predicted equal 1/2 (see for example [35]) -- turns out to be substantially larger than 1/2. It cannot be stressed enough that the equality k=1/2 had been predicted by general theory of relativity (GTR) on account of the special relativistic time dilation effect delineated by the tangential displacement of the rotating absorber, where the "clock hypothesis" by Einstein (i.e., the non-reliance of the time rate of any clock on its acceleration [35]) was straightly adopted. Hence, the revealed inequality k>1/2 indicates the presence of some additional energy shift (next to the usual time dilation effect arising from tangential displacement alone) between the emitted and absorbed resonant radiation. By using Bimetric Theory of Gravitational-Inertial Field [76] we obtain k=0.625 in a good agreement with experimental result k=0.69 [75].

**Category:** Mathematical Physics

[739] **viXra:1803.0010 [pdf]**
*submitted on 2018-03-01 15:21:18*

**Authors:** Colin James III

**Comments:** 1 Page. © Copyright 2018 by Colin James III All rights reserved.

In the classical real Minkowski plane, we confirm the set of points as tautologous. However, we refute the set of cycles as being not tautologous and not contradictory.
This means that basing quantum theory on the set of cycles in the classical real Minkowski plane is suspicious.

**Category:** Mathematical Physics

[738] **viXra:1803.0009 [pdf]**
*submitted on 2018-03-01 16:17:11*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 24 Pages. Complexification of Maxwell’s equations with an extension of the gauge condition to non-Abelian algebras, yields a putative metrical unification of relativity, electromagnetism and quantum theory. This unique new approach also yields a universal nonlocali

Complexification of Maxwell’s equations with an extension of the gauge condition to non-Abelian algebras, yields a putative metrical unification of relativity, electromagnetism and quantum theory. This unique new approach also yields a universal nonlocality with implications for Bell’s Theorem and the possibility of instantaneous quantum connections because spatial separation can vanish by utilizing the complex space.

**Category:** Mathematical Physics

[737] **viXra:1802.0441 [pdf]**
*submitted on 2018-02-28 12:07:01*

**Authors:** Richard L Amoroso

**Comments:** 17 Pages. Preprint, to appear in IOP (2018) conference proceedings, PIRT, Moscow 2017

Newton claimed instantaneous G-influence; Einstein insisted no influence
propagated faster than c . Quantum Mechanics (QM) the so-called basement of reality, posits a
Quantum Gravity, for which no a priori science exists. We propose a paradigm shift with
duality between a semi-quantum Standard Model (SM) limit and Large-Scale Additional
Dimensionality (LSXD) in a modified M-Theoretic Unified Field (UF) brane arena as the
regime of integration described by an Ontological-Phase Topological Field Theory (OPTFT)
requiring fundamental changes in the concept of dimensionality and matter. OPTFT is
developed to formally describe 3rd regime Unified Field Mechanics (UFM) (classical-
Quantum-UFM) to relate Newton-Einstein duality by added degrees of freedom in a semiquantum
limit enabling topological Dirac-Majorana doublet fusion supervening the uncertainty
principle.

**Category:** Mathematical Physics

[736] **viXra:1802.0438 [pdf]**
*submitted on 2018-02-28 14:07:14*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 18 Pages. https://doi.org/10.1142/9789814324250_0011

Utilizing the spinor approach, electromagnetic and gravitational metrics are mapable to the twistor algebra, which corresponds to the complexified Minkowski space. Quaternion transformations relate to spin and rotation corresponding to the twistor analysis.

**Category:** Mathematical Physics

[735] **viXra:1802.0436 [pdf]**
*submitted on 2018-02-28 16:02:08*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 24 Pages. https://doi.org/10.1142/9789814324250_0012

In this paper we develop complex solutions to the Dirac equation and discuss various implications and applications.

**Category:** Mathematical Physics

[734] **viXra:1802.0424 [pdf]**
*submitted on 2018-02-28 10:01:12*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 17 Pages. https://doi.org/10.1142/9789814324250_0007

We outline the relativistic formalism which gives a more comprehensive explanation of the complexification scheme. Such issues as considering the Higgs Boson as a soliton depends on Lorentz invariance and relativistic causality constraints. We relate the complexification of Maxwell's equations to models of nonlocal micro and macro phenomena. In this chapter we relate the electromagnetic fields, F and A , the potentials to the gravitational field, G . We examine, for example, the manner in which advanced potentials may explain the remote connectedness which is indicated by the Clauser test of Bell's theorem. Similar arguments apply to Young's double slit experiment. The collective coherent phenomena of superconductivity is also explainable by considering the relativistic field theoretic approach in which wave equations are solved in the complex Minkowski space.

**Category:** Mathematical Physics

[733] **viXra:1802.0423 [pdf]**
*submitted on 2018-02-28 10:40:02*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 8 Pages. https://doi.org/10.1142/9789814324250_0008

In this work we analyze, calculate and extend modification of Maxwell’s equations in a complex Minkowski metric, M4 in a C2 complexified space using the SU2 gauge, SL(2,c) and other gauge groups, such as SUn for n > 2 expanding the U1 gauge theories of Weyl. Weyl identified the U1 gauge group for the standard Maxwell’s equations in its nonrelativistic form in M4 space. We expand the form of the elegant electromagnetic equations and express them in C4 space for the nonrelativistic formalism and for the relativistic formalism of the equations. The advanced and retarded formalisms are also examined. In the case where Maxwell’s equations are solved in C4 space, or the complex 8-space, we can extend the theory to considerations of other gauge groups such as SL(2,c), SUn for n > 2 and SU2 expanding the approach beyond U1 gauge conditions.

**Category:** Mathematical Physics

[732] **viXra:1802.0422 [pdf]**
*submitted on 2018-02-28 11:05:16*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 10 Pages. https://doi.org/10.1142/9789814324250_0009

We consider in this chapter the transformations of an oscillatory form of A mu in a complex 12D Minkowski space. The form of the transformation of A mu or (A , Phi) depends on whether such a transformation is a superluminal Lorentz transformation (SLT) or a subluminal Lorentz transformation.

**Category:** Mathematical Physics

[731] **viXra:1802.0419 [pdf]**
*submitted on 2018-02-28 11:55:59*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 17 Pages. https://doi.org/10.1142/9789814324250_0010

We develop a formalism for the Schrödinger equation in an eight dimensional (8D) complex Minkowski space and discuss its relation to the Dirac equation, properties of nonlocality, remote connectedness, Young’s double slit experiment, Bell’s Theorem, the EPR paradox and anticipatory parameters of spacetime; and also identify an imaginary temporal component as a small nonlinear term and find soliton or solitary wave solutions. These coherent solutions can carry information over long distances, are consistent with Lorentz invariance and appear to provide a fundamental methodology for describing the issue of quantum measurement and a new context for the basis of quantum theory. In the Copenhagen view models of reality are not desirable. However, our new approach may enable the redefinition of concepts of reality from a new nonlocal and anticipatory quantum theory. Certainly, the most desirable consequence of scientific discovery is the ability to refine our concepts of reality.

**Category:** Mathematical Physics

[730] **viXra:1802.0416 [pdf]**
*submitted on 2018-02-27 15:16:59*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 26 Pages. https://doi.org/10.1142/9789814324250_0002

We consider the properties and implications of three n > 4 multidimensional geometries. These are Descartes geometry [1], the properties and implications of which are enumerated in [2-6]. Both macroscopic and microscopic implications of these geometries are presented. We also develop several forms of complex Minkowski space in terms of a generalized metric containing terms derived from real and imaginary coordinates. The metric of the space is real and therefore physical [7-17]. This geometry is found to be one-to-one with Kaluza-Klein geometry [18-20] in which there has been much recent interest in developing M-Theory, in particular in the apparent relationship between the gravitational and electromagnetic fields often called Quantum Gravity. We have discussed the properties and implications of complex geometries in a number of works. The basic structure of the geometries is based on the construction of complexified dimensions, consisting of orthogonal real and imaginary parts. We examine the implication of a complex 8-space geometry in which we introduce imaginary components for each real spatial dimension, X = (x,y,z) and temporal dimension, t.

**Category:** Mathematical Physics

[729] **viXra:1802.0412 [pdf]**
*submitted on 2018-02-27 17:30:47*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 27 Pages. https://doi.org/10.1142/9789814324250_0005

In this work we demonstrate that complex electric and magnetic fields are consistent with a geometry consisting of complex spacetime. We thus demonstrate that complex spacetime coordinates are not inconsistent with electromagnetic phenomena and may point to a direction for its unification with gravitational phenomena, in the weak Weyl field limit. The particular case we examine in detail is for an electron in a field where we derive Coulomb's equation. We examine this unification using the Weyl geometry in the linear approximation of the gravitational field.

**Category:** Mathematical Physics

[728] **viXra:1802.0411 [pdf]**
*submitted on 2018-02-27 17:57:51*

**Authors:** Richard L Amoroso, Elizabeth A Rauscher

**Comments:** 8 Pages. https://doi.org/10.1142/9789814324250_0006

The issue of whether Bell's theorem and other remote connectedness phenomena, such as Young's double slit experiment, demands superluminal or space-like signals or prior generated luminal signals is an area of hot debate. This also relates to the existence of advanced vs. retarded potentials and annihilation creation operators which are of interest in this regard. Using the complex model of we will examine the issue of the nonlocality of Bell's theorem as quantum mechanical ‘transactions’ providing a microscopic communication path between detectors across space-like intervals, which violate the EPR locality postulate [1]. See Chap. 4. This picture appears consistent with the remote connectedness properties of complex Minkowski space. Also, there are implications for macroscopic communications channels; another area of debate. Detailed discussions of Bell's theorem are given in [2].

**Category:** Mathematical Physics

[727] **viXra:1802.0355 [pdf]**
*submitted on 2018-02-24 12:29:27*

**Authors:** Robert A. Herrmann

**Comments:** 32 Pages.

The methods of nonstandard analysis are applied to general language logic-systems. This allows the operators for the only known mathematical cosmology, the General Grand Unification Model (GGU-model), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and processes are predicted from certain observable entities, which are physical processes and mental procedures that we use to construct physical objects. It is shown that, for each of the four types of instruction paradigms, there exists an ultra-word-like object such that when an hyper-algorithm is applied to it an ultra-logic-system is *-deduced. Another application of an hyper-algorithm yields a hyperfinite instruction paradigm that is hyper-deduced in the in the required sequential order. It is shown that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the Patten and Wheeler participator universe requirements. In this version, the participator process portion of the GGU-model is significantly altered from the original process presented and a correction is made to an equation and its applications. A specific data-set is generalized and the set of all ultra-propertons is obtained and its properties examined. This set is shown to be sufficient for universe construction. GGU-model schemes are presented in diagram form. A process is introduced that leads, when applied, to the individual developmental of each universe-wide frozen-frame. An operator is shown to exist, which, via a substratum medium and processes, changes hyper-instruction information into substratum info-fields. From these info-fields, all physical-systems are produced. In this refinement, the page 11 statement, in the original version of this paper on quantum theory, is completely modified and the previous statement is now essentially incorrect.

**Category:** Mathematical Physics

[726] **viXra:1802.0310 [pdf]**
*submitted on 2018-02-21 18:46:48*

**Authors:** Yongsop Ri, Namhyok Ri, Jonggwang Pak, Iljin Kim, Zhihua Chen –Department of Mechanics Enineering, Kim Il Sung University, Pyongyang, DPR of Korea - School of Civil Engineering, Tianjin University, Tianjin 300072, PR of Chi

**Comments:** 21 Pages.

The topology optimization using the homogenization method is to find optimal layout of microstructures which satisfies design demand in the neighborhood of an arbitrary point in a given design domain. The homogenization approach is to compute proper mechanical properties of those microstructures in terms of integral averaging by accepting the periodicity assumption and characteristic function.
In this paper, we described a stiffness homogenization theory that is able to avoid the complication of the homogenization approach and reduce the computation cost by considering the topology optimization process in consistence with the finite element analysis. The method can be applied more flexibly to individual or simultaneous optimization of the topology, shape, size and material layout. We discussed a stiffness homogenization during meshing the space structure with different kinds of elements in detail. An optimal criterion for the minimum weight design problem, as one of typical optimization design problems, was derived and the computational algorithm was presented. Numerical results of an example were compared with previous methods, which show the validation of the method.

**Category:** Mathematical Physics

[725] **viXra:1802.0239 [pdf]**
*submitted on 2018-02-18 13:58:51*

**Authors:** Alexander I.Dubinyansky, Pavel Churlyaev.

**Comments:** 6 Pages. dubinyansky@mail.ru http://universe100.narod.ru/ http://universe100.narod.ru/002-Oglavlenie-angl-jpg.html (English)

Development of the mathematical model of the elastic universe. The spins of the loks (0,0), (1,0) and (1,1) are calculated. Assumptions are made regarding other loks. Further conclusions were drawn on the identification of elementary particles in a set of loks.

**Category:** Mathematical Physics

[724] **viXra:1802.0231 [pdf]**
*submitted on 2018-02-19 00:43:55*

**Authors:** Jack Bidnik

**Comments:** 6 Pages.

Electrostatics, Gravity, and Galactic Force © US 2015
by Jack Bidnik
This paper is a continuation of my paper entitled Gravitational Forces Revisited (GFR), http://vixra.org/abs/1707.0128 and may be considered as Chapter 2 of the concepts developed in that paper.
Two corollaries of the derivation of Gs in GFR are elaborated here to show that the formula can be extended to include both the smallest and the largest masses and spaces. The same formula can give both the electrostatic force of the Hydrogen atom and also the force which counteracts the centrifugal force of large galaxies. I believe this development nullifies the most basic motive for postulating dark matter, which is that the gravitational force at such high speeds could not hold the galaxy together. Examples are given for galaxies of various size.
The paper starts with continuing analysis of the mathematical conclusion in GFR that the derived force Ft is equivalent to the centripetal force of the orbit vo2/r. This analysis is perhaps superfluous since there is no other acceleration present radially than the one derived for Ft , but I present various looks at the math to dispel any nagging doubts.
Another set of doubts to be dispelled involves the idea of frames of motion. It suffices to point out that when one uses the reduced mass, it is the equivalent of the motion of either mass in the frame of the other, since it is the equivalent of one mass being stationary.

**Category:** Mathematical Physics

[723] **viXra:1802.0207 [pdf]**
*submitted on 2018-02-16 06:19:14*

**Authors:** Alexander I. Dubinyansky, Pavel Churlyaev.

**Comments:** 7 Pages. dubinyansky@mail.ru http://universe100.narod.ru/ http://universe100.narod.ru/002-Oglavlenie-angl-jpg.html (English)

Development of the mathematical model of the elastic universe. The energy of the loks (0,0), (1,0) and (1,1) are calculated. Assumptions are made regarding other loks. The first conclusions on the identification of elementary particles in a set of loks are made.

**Category:** Mathematical Physics

[722] **viXra:1802.0183 [pdf]**
*submitted on 2018-02-15 07:40:11*

**Authors:** Renzun Lian

**Comments:** 5 Pages.

Traditionally, all working modes of a perfect electric conductor are classified into resonant modes, inductive modes, and capacitive modes, and the resonant modes are further classified into internal resonant modes and external resonant modes. In this paper, the resonant modes are alternatively classified into intrinsically resonant modes and non-intrinsically resonant modes, and the intrinsically resonant modes are further classified into non-radiative intrinsically resonant modes and radiative intrinsically resonant modes. Based on the modal expansion corresponding to this new modal classification, an alternative modal decomposition method is proposed. In addition, it is also proved that: all intrinsically resonant modes and all non-radiative intrinsically resonant modes constitute linear spaces respectively, but all resonant modes and all radiative intrinsically resonant modes cannot constitute spaces respectively.

**Category:** Mathematical Physics

[721] **viXra:1802.0114 [pdf]**
*submitted on 2018-02-11 01:51:57*

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

**Comments:** 2 Pages.

A no-brainer.

**Category:** Mathematical Physics

[720] **viXra:1802.0109 [pdf]**
*submitted on 2018-02-10 02:51:25*

**Authors:** Antoine Balan

**Comments:** 2 pages, written in french

The KdV equations are generalized over differentiable manifolds. The equations are integrable.

**Category:** Mathematical Physics

[719] **viXra:1802.0055 [pdf]**
*submitted on 2018-02-05 20:46:50*

**Authors:** Vu B Ho

**Comments:** 9 Pages.

In this work we show that, as in the case of Dirac equation, it is possible to formulate Maxwell field equations of electromagnetism from a general system of linear first order partial differential equations. A prominent feature that emerges from formulating Dirac and Maxwell field equations from a general system of linear first order partial differential equations is that the field equations must be formed in such a way that the functions that represent the system also obey a wave equation. This type of mathematical duality may be related to the wave-particle duality in quantum physics.

**Category:** Mathematical Physics

[718] **viXra:1802.0016 [pdf]**
*submitted on 2018-02-02 23:39:32*

**Authors:** Durgadas Datta.

**Comments:** 7 Pages. A paper for CERN .

The meaning of fine tuning and emergent gravitation.

**Category:** Mathematical Physics

[717] **viXra:1801.0417 [pdf]**
*submitted on 2018-01-30 09:07:40*

**Authors:** Peter Bissonnet

**Comments:** 11 Pages.

The author used to think that the only representation of prime numbers, etc. was the prime number double helix
representation. However, in 2011, the author published a paper which puzzled him and it eventually dawned upon him that
there was more than one representation of prime numbers. The second representation will be referred to as the hyperbolic
representation. The third representation will be called the parabolic representation and is related to the hyperbolic
representation. The fourth representation is the triangular representation and is related to the hyperbolic representation.
Both of the primary representations, the double helix and the hyperbolic both reject that 2 and 3 are prime numbers. The
hyperbolic representation is shown to be related to Lorentz-like transformations.

**Category:** Mathematical Physics

[716] **viXra:1801.0287 [pdf]**
*submitted on 2018-01-23 04:40:36*

**Authors:** Renzun Lian

**Comments:** 15 Pages.

In this paper, we generalize Huygens' principle (HP), extinction theorem (ET), and Franz-Harrington formulation (FHF) in two parts. In Part I, the traditional HP, ET, and FHF in homogeneous isotropic environment are generalized to inhomogeneous anisotropic lossy environment; the traditional FHF of homogeneous isotropic material system is generalized to inhomogeneous anisotropic lossy material system and then to piecewise inhomogeneous anisotropic lossy material system; the traditional HP, ET, and FHF of simply connected material system are generalized to multiply connected system and then to non-connected system; the traditional FHF of external scattering field and internal total field are generalized to internal scattering field and internal incident field. In Part I, it is proved that the generalized HP (GHP) and generalized ET (GET) are equivalent to each other; the GHP, GET, and generalized FHF (GFHF) satisfy so-called topological additivity, i.e., the GHP/GET/GFHF of whole electromagnetic (EM) system equals to the superposition of the GHP/GET/GFHF corresponding to all sub-systems. In this Part II, the above results obtained in previous Part I, which focuses on the EM system constructed by material bodies, are further generalized to the metal-material combined EM system in inhomogeneous anisotropic lossy environment, and traditional surface equivalence principle is generalized to line-surface equivalence principle.

**Category:** Mathematical Physics

[715] **viXra:1801.0268 [pdf]**
*submitted on 2018-01-22 00:27:33*

**Authors:** Miroslav Súkeník, Jozef Šima

**Comments:** 3 Pages. No comment

The paper covers applicability areas of the Euler – Mascheroni constant in General Theory of Relativity and Quantum Theory.

**Category:** Mathematical Physics

[714] **viXra:1801.0267 [pdf]**
*submitted on 2018-01-22 01:55:25*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 4 Pages. dubinyansky@mail.ru

A formula is obtained that relates the mass (energy) of a lok (1,0) with the parameters of the elasticity of a Gukuum.

**Category:** Mathematical Physics

[713] **viXra:1801.0266 [pdf]**
*submitted on 2018-01-21 04:53:30*

**Authors:** Renzun Lian

**Comments:** 19 Pages.

Huygens' principle (HP), extinction theorem (ET), and Franz's / Franz-Harrington formulation (FHF, which is a mathematical expression of surface equivalence principle) are the important components of electromagnetic (EM) theory, and they are generalized from the following aspects.
1) Traditional HP, ET, and FHF in homogeneous isotropic environment are generalized to inhomogeneous anisotropic lossy environment. 2) Traditional FHF for homogeneous isotropic material system is generalized to inhomogeneous anisotropic lossy material system in this Part I, and will be further generalized to metal-material combined system in future Part II. 3) The Huygens' surface in traditional HP and ET is a single closed surface. In Part I, it is generalized to the "Huygens' surface" which is constructed by multiple closed surfaces. In Part II, it will be further generalized to the "Huygens' boundary" which includes some lines and open surfaces. 4) For a material body, traditional FHF has only ability to express the external scattering field and the internal total field (the summation of scattering and incident fields) in terms of the equivalent sources on material boundary, and it is generalized to formulating the internal scattering and incident fields in this paper.
In addition, the relationships among HP, ET, and FHF are studied, and it is proved that HP and ET are equivalent to each other.

**Category:** Mathematical Physics

[712] **viXra:1801.0258 [pdf]**
*submitted on 2018-01-20 09:33:26*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 6 Pages. dubinyansky@mail.ru

A theoretical calculation is made of the total energy of the wave vortex in a vacuum, for the general case.

**Category:** Mathematical Physics

[711] **viXra:1801.0240 [pdf]**
*submitted on 2018-01-19 10:26:34*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 9 Pages. dubinyansky@mail.ru

Some solutions of the wave equation in gukuum, possibly creating the whole variety of matter.

**Category:** Mathematical Physics

[710] **viXra:1801.0232 [pdf]**
*submitted on 2018-01-18 05:29:53*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 8 Pages. Details on the site http://universe100.narod.ru/

The beginning of a more rigorous exposition of the theory of the elastic universe.

**Category:** Mathematical Physics

[709] **viXra:1801.0197 [pdf]**
*submitted on 2018-01-16 05:17:24*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 5 Pages. Russian: http://universe100.narod.ru/ English: http://universe100.narod.ru/002-Oglavlenie-angl-jpg.html dubinyansky@mail.ru

In the wave vortices, the energy is capable of winding itself onto itself and at the same time being redistributed.

**Category:** Mathematical Physics

[708] **viXra:1801.0163 [pdf]**
*submitted on 2018-01-15 04:26:21*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 7 Pages. site http://universe100.narod.ru/index.html

The hypothesis is stated that the whole variety of the material world, the whole variety of elementary particles, the whole variety of physics, can be explained by localized solutions of the three-dimensional wave equation in the elastic continuum.

**Category:** Mathematical Physics

[707] **viXra:1801.0162 [pdf]**
*submitted on 2018-01-14 05:28:47*

**Authors:** Alexander Dubinyansky, Pavel Churlyaev.

**Comments:** 1 Page. Details on the site http://universe100.narod.ru/

The universe is a solid elastic continuum - gukuum. This continuum does not contain any numerical parameters or constraints.
All visible and invisible objects of the universe, from large to small, are wave objects in this continuum.
All the wave objects in the gukuum are described by the letter specification of the elasticity parameters of the solid body and the three-dimensional wave equation.
The nonlinearity that exists in the universe is explained by the law of "winding the linear solution on itself." As a result of such winding, or layering, the linear solution becomes non-linear and creates the entire variety of the material world.

**Category:** Mathematical Physics

[706] **viXra:1801.0079 [pdf]**
*submitted on 2018-01-07 05:41:04*

**Authors:** Ricardo Gil

**Comments:** 1 Page. All these items are off the shelf items. Try them and upload a comment with results.

The objective of this paper is to suggest that bullet with a watch battery on it(superglue them on) will have reduced mass and travel more efficiently. Place them in a conventional revolver and in a conventional shot gun.(single or double barrel)

**Category:** Mathematical Physics

[705] **viXra:1801.0066 [pdf]**
*submitted on 2018-01-06 10:25:14*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages.

This paper is an appendix to the article "From Bernoulli to Laplace and Beyond"
(refenced below), and discusses different aspects of it: electromagnetism, field tensors,
general relativity, and probability.

**Category:** Mathematical Physics

[704] **viXra:1801.0047 [pdf]**
*submitted on 2018-01-04 20:41:10*

**Authors:** YiMing Xia

**Comments:** 17 Pages. 1.A new split-full node notion is presented and a novel technique is proposed to construct a simple and clear basic full node shape function for a triangular plate-bending element.

A triangular plate-bending element with a new multi-resolution analysis (MRA) is proposed and a novel multiresolution element method is hence presented. The MRA framework is formulated out of a displacement subspace sequence whose basis functions are built out of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by means of extending the shape function triangle domain for a split node at the zero coordinates to the hexagon area enclosing the zero coordinates. As a result, a new split-full node notion is presented and a novel rational MRA concept together with the resolution level (RL) is constituted for the element. Via practical examples, it is found that the traditional triangular plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated. The continuous full node shape function unveils secrets behind assembling artificially of node-related items in global matrix formation by the conventional FEM.

**Category:** Mathematical Physics

[703] **viXra:1801.0036 [pdf]**
*submitted on 2018-01-03 16:51:21*

**Authors:** Ricardo Gil

**Comments:** 3 Pages. MIT unknowingly has a dark matter quantum computer. This is the topological computer Krysta Svore is working on at Microsoft but Peter Shor at MIT has unknowingly achieved the dark matter quantum computer that has time reversal. Ref: Hooft,Wilzek.MIT.

The purpose of these 5 papers(paragraphs) is to share my thoughts on Dark Matter, Dark Energy and my observation on Light Theory with respect to different gravities.

**Category:** Mathematical Physics

[702] **viXra:1801.0025 [pdf]**
*submitted on 2018-01-03 09:38:11*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages. Retracted & now republished: Fixed forgotten factor i.

Reviewing Laplace's equation of gravitation from the perspective of D. Bernoulli, known as Poisson-equation, it will be shown that Laplace's equation tacitly assumes the temperature T of the mass system to be approximately 0 degrees of Kelvin.
For temperatures greater zero, the gravitational field will have to be given an additive correctional field.
Now, temperature is intimately related to the heat, and heat is known to be radiated as an electromagnetic field.
It is shown to take two things in order to get at the gravitational field in the low temperature limit:
the total square energy density of the source in space-time and a (massless) field, which expresses the equivalence of inert and gravitational mass/energy in a quadratic, Lorentz-invariant form.
This field not only necessarily must include electromagnetic interaction, it also will be seen to behave like it.

**Category:** Mathematical Physics

[701] **viXra:1712.0663 [pdf]**
*submitted on 2017-12-29 15:54:44*

**Authors:** Vu B Ho

**Comments:** 7 Pages.

In this work we discuss the possibility to formulate gravity as a coupling of two electromagnetic fields of equal magnitude but opposite direction.

**Category:** Mathematical Physics

[700] **viXra:1712.0598 [pdf]**
*submitted on 2017-12-25 14:56:26*

**Authors:** Jonathan Tooker

**Comments:** 284 Pages. The Persian Stitch is one thing and Chaos Monkey typesetter malware is quite another.

In lieu of an abstract each chapter in this book has a description of its contents.

**Category:** Mathematical Physics

[699] **viXra:1712.0594 [pdf]**
*submitted on 2017-12-24 19:34:26*

**Authors:** Harry Watson

**Comments:** 2 Pages.

We make the following Ansatz for the mass ratio of the neutron to the electron:
m_n /m_e is approx (4pi)(4pi-1/pi)(4pi-2/pi) +ln(4pi) = 1838.682763
where m_n is the neutron rest mass and m_e is the electron rest mass. The CODATA value is 1838.68366158. The neutron decays into a proton and an electron. If ln(4pi) is the neutron-proton mass difference, then m_p/m_e is (4pi)(4pi-1/pi)(4pi-2/pi), where m_p is the proton rest mass.
harry.watson@att.net

**Category:** Mathematical Physics

[698] **viXra:1712.0419 [pdf]**
*submitted on 2017-12-12 13:58:40*

**Authors:** Nikola Samardzija

**Comments:** 16 Pages. This review paper was written in 2014, and since has raised quite a few eyebrows in academia. The simplicity of the globotoroid model is far reaching, and alters some central themes in mathematics and sciences - Namely, the singularity based theories.

Mathematical models can give us invaluable insights into natural phenomena, and as such play an important role in science. The intent of this paper is to give a high-level overview of a simple continuous dynamical model that offers an insight into a qualitative behavior seldom reported or discussed. This model has no equilibrium or singular points, yet its phase space unveils four distinct topological features: a limit cycle, a torus, a sphere and a wormhole. Each of these features results from model solutions that can be periodic, quasi-periodic and chaotic, which collectively form a space-time structure referred to as the globotoroid. The model generalizes the energy behavior of many processes of interest, and consequently is reshaping contemporary systems theory to fit more completely with different natural phenomena. Specifically, the globotoroid is the simplest 3-dimensional dynamic model that exposes the concept of the wormhole, which embodies an important energy behavior throughout our universe. The fields of science that may benefit from this modeling approach are many, including physics, cosmology, biology, chemistry, engineering, cognitive sciences, economics, politics, and business and finance. This is demonstrated by reviewing some well-known phenomena in natural and social sciences.

**Category:** Mathematical Physics

[697] **viXra:1712.0404 [pdf]**
*submitted on 2017-12-13 03:42:44*

**Authors:** Vu B Ho

**Comments:** 12 Pages.

In this work, we discuss a method to derive Dirac equation and other equations, such as the Cauchy-Riemann equations, from a general system of linear first order partial differential equations, with the hope that when studied more thoroughly the general system may provide deeper insights into geometrical and topological structures of quantum particles and fields.

**Category:** Mathematical Physics

[696] **viXra:1712.0399 [pdf]**
*submitted on 2017-12-12 03:53:52*

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

**Comments:** 3 pages

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear two-point boundary value problem may be computed in a direct and straightforward fashion from the general solution obtained by a generalized Sundman transformation for the related differential equation, which appeared to be a special case of a more general equation. As a result, various initial and boundary value problems may be solved explicitly and exactly.

**Category:** Mathematical Physics

[695] **viXra:1712.0364 [pdf]**
*submitted on 2017-12-10 07:52:18*

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

**Comments:** 3 pages

This paper shows, for the first time, that the mathematical pendulum and generalized mathematical pendulum initial and boundary value problems may be computed from the explicit and exact general solution to the corresponding differential equation in a straightforward fashion by a direct method.

**Category:** Mathematical Physics

[694] **viXra:1712.0149 [pdf]**
*submitted on 2017-12-06 10:01:43*

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

**Comments:** 13 pages

A generalized Bratu equation is established in the framework of Sundman transformation. The well-known exact solution to the Bratu boundary value problem is deduced from the obtained explicit and exact general solution which may be also used to compute the exact solution to Bratu type initial and boundary value problems.

**Category:** Mathematical Physics

[693] **viXra:1711.0468 [pdf]**
*submitted on 2017-11-28 12:24:15*

**Authors:** Richard L Amoroso, Peter Rowlands, Louis H Kauffman

**Comments:** 11 Pages. Paper from VIII international symposium honoring mathematical physicist Jean-Pierre Vigier

We make a preliminary exploratory study of higher dimensional (HD) orthogonal forms of the quaternion algebra in order to explore
putative novel Nilpotent/Idempotent/Dirac symmetry properties. Stage-1 transforms the dual quaternion algebra in a manner that
extends the standard anticommutative 3-form, i, j, k into a 5D/6D triplet. Each is a copy of the others and each is self-commutative
and believed to represent spin or different orientations of a 3-cube. The triplet represents a copy of the original that contains no new
information other than rotational perspective and maps back to the original quaternion vertex or to a second point in a line element. In
Stage-2 we attempt to break the inherent quaternionic property of algebraic closure by stereographic projection of the Argand plane
onto rotating Riemann 4-spheres. Finally, we explore the properties of various topological symmetries in order to study
anticommutative - commutative cycles in the periodic rotational motions of the quaternion algebra in additional HD dualities.

**Category:** Mathematical Physics

[692] **viXra:1711.0459 [pdf]**
*submitted on 2017-11-29 03:16:37*

**Authors:** Christopher Goddard

**Comments:** 21 Pages.

I sketch roughly how an Alcubierre drive could work, by examining exotic geometries consisting of soliton solutions to the dynamics of space filling curves. I also briefly consider how remote sensing might work for obstacle avoidance concerning a craft travelling through space via a 'wormhole wave'. Finally I look into how one might adopt remote sensing ideas to build intrasolar wormhole networks, as well as extrasolar jump gates.

**Category:** Mathematical Physics

[691] **viXra:1711.0446 [pdf]**
*submitted on 2017-11-28 03:18:52*

**Authors:** Vu B Ho

**Comments:** 18 Pages.

In this work, we will investigate possible spacetime structures of massless particles by formulating Dirac equation in a six-dimensional spatial-temporal continuum in both pseudo-Euclidean and Euclidean metrics. We show that the state of a massless particle flows as an irrotational and incompressible fluid in steady fluid dynamics in the sense that all spatial and temporal components of the wavefunction of a massless particle can be described by Laplace equation. Furthermore, we also show that the six components of the wavefunction are coupled in pairs to form two-dimensional subspaces and this result may suggest why quantum particles possess an intrinsic spin angular momentum that takes half-integral values.

**Category:** Mathematical Physics

[690] **viXra:1711.0435 [pdf]**
*submitted on 2017-11-26 15:20:30*

**Authors:** Dan Visser

**Comments:** 23 Pages.

This article breaks with the inviolability of the quantum-unit. It ‘crumbles’ (or cuts up, or refines) the quantum-vacuum. That also crumbles the constant vacuum-energy-density, or dark energy. It offers a new definition for dark energy. New dark energy does no longer belong to the Big Bang-universe: New dark energy is part of a rotating-hologram universe. Such a universe has the shape of a Double Torus, which has an inner-torus that rotates while an outer-torus represents the ‘crumble of the vacuum’ with time below the Planck-scale. The ‘vacuum-crumbling’ implies a ‘new ‘building-stone’ for vacuum:Tdan . This is a new (rotating) energy-tensor, which has two states , one for above and one for below the Planck-scale. The ‘beauty’ is the dimension of the tensor remains unchanged in those two states! Hence, the quantum-Planck-unit is transparent for migration. That makes the Big Bang-universe no longer a fundamental universe. The Big Bang-universe is emerged (or induced) by rotation of the hologram-universe. This means the Big Bang-universe will exist in every place of the rotating hologram-universe implying: parallel universes ‘outside’ a Big Bang-universe are a nonissue. Parallel universes exist embedded in the rotating hologram-universe. Thereby the origin of the ‘old Big Bang-universe’ is no longer relevant. A new definition of age of the universe lies in the cycle-duration of one cycle, although rotation goes on eternally. Continuously the origin is recalculated. Seemingly the Big Bang-universe is materialized above the Planck-scale and dé-materializes below the Planck-scale, however, such a perspective is reciprocal facing the transparent frontier. Against all expectations my formulas show that one can migrate from one to the other parallel-universe. Locally that is interpreted as ‘change’, but on larger scales it is called traveling through time without space. Because there is extra time (or refined time in the crumble of vacuum), which affects relativistic time that can make traveling faster than traveling through space with the speed of light. There is no horizon between the physics of the ‘soul’ and the physics of ‘materialization’ including the other way around.

**Category:** Mathematical Physics

[689] **viXra:1711.0395 [pdf]**
*submitted on 2017-11-24 05:57:12*

**Authors:** Spiros Konstantogiannis

**Comments:** 33 Pages.

Making an intuitive assumption, and using the completeness of the position and momentum eigenstates, along with the postulates of quantum mechanics, we provide a geometric presentation of the position and momentum representations in quantum mechanics, in the hope of offering a perspective complementary to those given in standard textbooks.

**Category:** Mathematical Physics

[688] **viXra:1711.0365 [pdf]**
*submitted on 2017-11-21 01:59:25*

**Authors:** Giuliano Bettini

**Comments:** 19 Pages. in Italian

Starting from the 32 crystal classes, we find a complete classification scheme of the same with only 5 bits, and at least in part the meaning of the various bits.
There is no inverse demonstration, ie only 5 bits must generate all 32 crystalline classes in nature.
However, the proposed classification seems to invoke a logical process of formation of the various classes, doing this way:
the matter first aggregates without any symmetry, then it adopts various rotation symmetries (no symmetry, binary, ternary, etc., simple or composite) and then adds to each symmetry of rotation the additional symmetries c (center), m (planes) or c + m together

**Category:** Mathematical Physics

[687] **viXra:1711.0348 [pdf]**
*submitted on 2017-11-17 14:12:41*

**Authors:** Gary D. Simpson

**Comments:** 9 Pages.

This essay discusses the meaning and role of the term “fundamental” as it applies to Math and Physics. The importance of Lagrange’s Four Squares Theorem is also discussed. It is argued that the vacuum is a 5-D Quantum-Space-Time and that the vacuum is fundamental.

**Category:** Mathematical Physics

[686] **viXra:1711.0272 [pdf]**
*submitted on 2017-11-10 13:59:02*

**Authors:** Dmitri Martila

**Comments:** 4 Pages.

Do Stokes and Gauss's theorems from Vector Analyses hold also in curved spacetime (or in the curved coordinates of a flat manifold)? These theorems (especially the Gauss's or the "Divergence" theorem) are ones of the utmost importance, especially for theoretical astrophysics. My opinion is in the file. Can you tell me what journal will accept this "nonsense"?

**Category:** Mathematical Physics

[685] **viXra:1711.0270 [pdf]**
*submitted on 2017-11-10 17:28:55*

**Authors:** David Njeru kathuri

**Comments:** 62 Pages.

This publication is about a theory that tries to scientifically prove that under certain conditions, fire is a portal that can be used in teleportation of matter.
The document also tries to give an alternative to General Relativity in the most scientifically precise way that leaves no room for doubt. This is done by giving a testable alternative theory of what the past & future is and its relation to gravity.

**Category:** Mathematical Physics

[684] **viXra:1711.0260 [pdf]**
*submitted on 2017-11-09 07:17:38*

**Authors:** Spiros Konstantogiannis

**Comments:** 42 Pages.

Quasi-exactly solvable symmetrized sextic oscillators have been proposed and studied by Quesne, who categorized them based on the parity – natural or unnatural – of their known eigenfunction [2]. Herein, we examine the quasi-exact solvability of symmetrized sextic oscillators using a quotient-polynomial approach [3, 4, 5], which, in this case, opens up the possibility to construct non-analytic sextic oscillators from analytic quotient polynomials, and thus to distinguish the oscillators resulting from analytic quotient polynomials from those resulting from non-analytic quotient polynomials. We analyze the cases n=0 and n=1, and we show that the results are in agreement with those of Quesne [2]. In the case n=2, we construct sextic oscillators using only analytic quotient polynomials, and focusing on the non-analytic oscillators whose known eigenfunction is of unnatural parity, we register a relation between the coefficients of the two non-analytic terms of the exponential polynomial, which then we generalize to the higher cases n=3 and n=4, to construct new non-analytic sextic oscillators whose known eigenfunction is of unnatural parity.

**Category:** Mathematical Physics

[683] **viXra:1711.0201 [pdf]**
*submitted on 2017-11-06 03:26:57*

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

**Comments:** 5 Pages.

The occurrence of infinite values in physical equations, such as singularity in the description of black holes, is a painstaking problem that causes many theories to break down and/or being incapable of describing extreme events. Different methods, such as re-normalization, have been used in the assessment of physical observables in order to erase the undesirable infinity. Here we propose a novel technique, based on geometrical considerations, that allows removal of infinity and achievement of physical theories void of such a problem. We compare finite quantities to curved lines endowed in positive-curvature manifolds, and intractable infinity to a straight line. In order to restore the equations and erase the straight line of infinity, we project the quantities onto curved lines endowed in negative-curvature manifolds.

**Category:** Mathematical Physics

[682] **viXra:1710.0346 [pdf]**
*submitted on 2017-10-31 09:40:52*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 13 Pages. This paper has not been submitted to a journal. Your comments are welcome

Borges has a rare ability to put wild ideas into detective stories with reporting style. At least that is the impression that we got on his short stories. In particular, one of his short story is worthnoting: Tlon, Uqbar, Orbis Tertius. The story told us about a mysterious country called Uqbar, in apparently an unofficial reprint of Encyclopedia Britannica. It also tells about Tlon, a mysterious planet, created purely by imaginative minds. While this story clearly criticizes Berkeley view and may be not related to our daily reality, a reinterpretation of this story leads us to a long standing discourse in the philosophy of science: to how extent the entire modern physics follow such a Berkeley-antirealism tendency? This paper is intended to bring this subject into our attention. We will also discuss shortly on the antirealism in certain trends in theoretical physics and cosmology.

**Category:** Mathematical Physics

[681] **viXra:1710.0233 [pdf]**
*submitted on 2017-10-20 23:29:29*

**Authors:** Paris S. Miles-Brenden

**Comments:** 60 Pages. Grand Unified Theory of Electromagnetism Updated

The proposal of this thesis formulation is that of the development, design, and creation of a `Light Gyroscope' which is the formulation of a method to bal- ance light on a point with all such other light in existence; as an emanation of di erence between light and darkness; for which there is a balance between complete physical form and nonphysical formlessness; from that of a non-dual relation of physical electrical component design of general form of an in nite cascade of quarter wave re ectors of nite dimension and volume; of the nature for which an in nite cascade non related to that of the quadrature condition of elliptic function is met with a dual to an in nite cascade of ordinary elliptic operator solutions as their dual sine wave harmonic functions of free extension in space, time, and quanti able moment of temporal singular event structure; for which there exists an in nitely encompassed volumetric space of in nite dimension by co-parallelism of electricity and magnetism of no form other than topological nature; with in nite depth of four fold relation.

**Category:** Mathematical Physics

[680] **viXra:1710.0219 [pdf]**
*submitted on 2017-10-17 19:41:10*

**Authors:** Huai-Yi Xie

**Comments:** 115 Pages.

In this paper, we have derived planar multilayer dyadic Green’s functions by Fourier expansion method and have checked its correctness by comparing results for reflected electric fields from dipole emissions near such structures available in previous literature. Furthermore, we show how these dyadic Green’s functions can be applied to calculate reflected fields from a dipole source with arbitrary orientations. We believe our formulation will be powerful in the modeling of molecular fluorescence near these structures.

**Category:** Mathematical Physics

[679] **viXra:1710.0198 [pdf]**
*submitted on 2017-10-15 23:37:12*

**Authors:** Hongbing Zhang

**Comments:** 30 Pages.

The geometric significance of complex numbers is well known, such as the meaning of imaginary unit i is to rotate a vector with pi/2, etc. In this article, we will try to find some intuitive geometric significances of Pauli matrices, split-complex numbers, SU(2), SO(3), and their relations, and some other operators often used in quantum physics, including a new method to lead to the spinor-space and Dirac equation.

**Category:** Mathematical Physics

[678] **viXra:1710.0197 [pdf]**
*submitted on 2017-10-15 23:42:10*

**Authors:** Hongbing Zhang

**Comments:** 7 Pages.

In history, the problem of Johann Bernoulli's Brachistochrone Curve (BBC) was assumed the case that the force of gravity on the falling body is constant, for example, the case of near the surface of the Earth. In this article, we will propose and solve a new problem of the General Brachistochrone Curve (GBC), in case of the body falling in a large space of Newton gravity field, or in stronger Newton gravity field, in which the force of gravity is inversely proportional to the square of the height above the center of the star or planet.

**Category:** Mathematical Physics

[677] **viXra:1710.0196 [pdf]**
*submitted on 2017-10-15 23:46:11*

**Authors:** Hongbing Zhang

**Comments:** 6 Pages.

The metric tensor of Minkowski space-time, the electromagnetic field tensor, etc., are usually represented by 4x4 matrices in many textbooks, but in this paper we will demonstrate that this form of matrix-representation is unreasonable. We will introduce more reasonable rules of matrix-form for representing any (p,q)-type tensor.

**Category:** Mathematical Physics

[676] **viXra:1710.0155 [pdf]**
*submitted on 2017-10-13 16:20:37*

**Authors:** Antoine Balan

**Comments:** 2 pages, written in french

Here are introduced KdV type equations following the stationary solution which is the Weierstrass fonction of an elliptic curve.

**Category:** Mathematical Physics

[675] **viXra:1710.0119 [pdf]**
*submitted on 2017-10-10 20:58:30*

**Authors:** Harry Watson

**Comments:** 2 Pages.

Let Q denote a function from the nonnegative integers into the real numbers, such that: Q(0) = 1.000000509157;
Q(1) = Q(0) * (4pi));
Q(2) = Q(0) * (4pi) * (4pi-1/pi);
Q(3) = Q(0) * (4pi) * (4pi-1/pi) * (4pi-2/pi);
Q(4) = Q(0) * (4pi) * (4pi-1/pi) * (4pi-2/pi) * (4pi-3/pi);
Q(5) = Q(0) * (4pi) * (4pi-1/pi) * (4pi-2/pi) * (4pi-3/pi) * (4pi-4/pi).
Consider Q(3) = 1836.15267389 and Q(5)=240773.8273. Q(3) is the CODATA value for the ratio of the proton mass to the electron mass. Q(5) approximates the mass ratio of the Higgs Boson to the electron. (The value of Q(5)/Q(3) is 131.1295246. If the CODATA value for the mass ratio of the proton to the electron is revised, it will only have to be changed in Q(0). The approximation Q(5)/Q(3) is compared with changing values of the mass ratio of the Higgs Boson to the proton.
harry.watson@att.net

**Category:** Mathematical Physics

[674] **viXra:1710.0106 [pdf]**
*submitted on 2017-10-09 08:46:09*

**Authors:** Markos Georgallides

**Comments:** 89 Pages.

The Geometrical Inversion Mechanism .
In article is presented the Algebraic and Geometric Solution , and the Geometrical
Construction of all the n-Regular Polygons . The Method , is the Geometrical - Inversion on three circles , of the Alternate Interior angles of the Mechanism , where Extrema ( maximum or minimum Magnitude between two Positions which are the vertices of any two Sequent-Regular-Even-Polygons ) is expressed in this closed and bounded - interval , as the Inflection or Deflection of Coupler curves , and as the local maximum or minimum between the two Points , and which is their critical point .

**Category:** Mathematical Physics

[673] **viXra:1710.0102 [pdf]**
*submitted on 2017-10-09 13:58:58*

**Authors:** Louai Hassan Elzein Bashier

**Comments:** 22 Pages.

This paper is prepared to show the synthesis of the Newtonian mechanical
force and its counter part the inertial force. It is shows that the Newtonian
mechanical force splits into two counter forces when it is act upon a rigid
body. The paper is also shows the derivation of the momentum and the
kinetic energy that occur due to the presence of the inertial force.

**Category:** Mathematical Physics

[672] **viXra:1710.0084 [pdf]**
*submitted on 2017-10-08 01:22:16*

**Authors:** Moises Dominguez-Espinosa

**Comments:** 5 Pages.

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

[671] **viXra:1710.0076 [pdf]**
*submitted on 2017-10-07 09:38:09*

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

**Comments:** 3 Pages.

From a mathematical perspective, the key to the universe lies at the central tenet of Pythagorean thought - that the universe can be explained by pure numbers, i.e. dimensionless ratios. A Planck constants hierarchy is created that postulates an undiscovered Planck constant - the Planck circumference, symbol (P). The Planck constants hierarchy produces dimensionless ratios, that allow for the first time the theoretical calculation of constants, e.g. the Planck momentum, Planck mass and Planck energy constants.

**Category:** Mathematical Physics

[670] **viXra:1710.0074 [pdf]**
*submitted on 2017-10-07 13:09:06*

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

**Comments:** 16 pages

This work exhibits a generalized Painlevé-Gambier XVII equation and its applications in physics.

**Category:** Mathematical Physics

[669] **viXra:1710.0061 [pdf]**
*submitted on 2017-10-05 10:26:57*

**Authors:** Andrei P. Kirilyuk

**Comments:** 10 pages, 15 eqs, 15 refs; Paper presented at the FQXi essay contest 2016-2017, http://fqxi.org/community/forum/topic/2774

Based on the unreduced, non-perturbative solution to arbitrary interaction problem, we show that any interaction process underlying real system dynamics and object properties gives rise to irreversible time flow, universally specified evolution purpose and meaningful intentions at higher levels of universally defined dynamic complexity. The new mathematics of real-world complexity contains thus well-specified intrinsic teleology due to its rigorously derived extension with respect to usual, “goal-free” and “mindless” theory. We outline major aspects and applications of that extended, naturally teleological and causally complete science framework, including critically important problem solutions.

**Category:** Mathematical Physics

[668] **viXra:1710.0014 [pdf]**
*submitted on 2017-10-01 11:18:40*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 20 Pages.

We describe a fluid motion in three dimensions with rectangular, cylindrical and spherical coordinates.

**Category:** Mathematical Physics

[667] **viXra:1710.0011 [pdf]**
*submitted on 2017-10-01 07:55:47*

**Authors:** Spiros Konstantogiannis

**Comments:** 28 Pages.

The quasi-exact solvability of symmetrized quartic anharmonic oscillators has been studied first by Znojil [2] and then by Quesne [3]. In this work, we examine the solvability of these models using, as basic parameter, the energy-dependent, constant (i.e. position-independent) term of a quotient polynomial. We examine the cases n=0 and n=1, and we show that our results are in agreement with those of Quesne. For n=2, following a different path from that of Znojil, we derive the cubic equation that our parameter satisfies and for the case it has a root at zero, we follow the zero root to obtain an even-parity, ground-state wave function and an odd-parity, third-excited-state wave function. As in the case of the sextic anharmonic oscillator [6], the straightforwardness and transparency of the analysis demonstrates the eligibility of the quotient polynomial as a solvability tool of polynomial oscillators.

**Category:** Mathematical Physics

[666] **viXra:1709.0356 [pdf]**
*submitted on 2017-09-23 12:39:53*

**Authors:** Paris Samuel Miles-Brenden

**Comments:** 10 Pages. relativity, time, theory, everything, equivalence, wave, equation

Be ready for a 10 page compendium of the principles by which time operates with that of the relativistic theory in duplicity of reconcilation between either end of the wave equation. This theory incorporates the ideal of time and space transformation in very general form under entirely compatible principles and only two general equations for that of the theory of everything together. There is a rough synthesis of what is required then to understand the transformations of time; that of a theory second only to Albert Einstein's theory of special and general relativity; without contradiction.

**Category:** Mathematical Physics

[665] **viXra:1709.0332 [pdf]**
*submitted on 2017-09-23 11:15:52*

**Authors:** Christopher L. Andreadis

**Comments:** 15 Pages. A though experiment rooted in non-linear time.

This is a calibration procedure that is prefaced by a set of premises that led up to said procedure. It deals with the possibility that "cause preceded by effect" is greater than null at the macroscopic scale.

**Category:** Mathematical Physics

[664] **viXra:1709.0330 [pdf]**
*submitted on 2017-09-22 15:05:15*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages.

Usually, physics students don't like thermodynamics: it is incomprehensible.
They commonly get told to get used to it. Later on, as an expert, they'll find that the thermodynamic calculations come with surprises: sometimes evil, sometimes good. That can mean only
one thing: The theory is inconsistent. In here, it will be shown where that is.

**Category:** Mathematical Physics

[663] **viXra:1709.0329 [pdf]**
*submitted on 2017-09-22 23:43:46*

**Authors:** Vu B Ho

**Comments:** 10 Pages.

In this work, we discuss the possibility to formulate a temporal electromagnetic field that can be produced by a temporal system, such as a temporal hydrogen atom in the temporal continuum. We also show that a temporal electromagnetic field can manifest itself not only in the temporal continuum but also in the spatial space.

**Category:** Mathematical Physics

[662] **viXra:1709.0321 [pdf]**
*submitted on 2017-09-21 06:08:47*

**Authors:** Vu B Ho

**Comments:** 12 Pages.

In our previous works on possible relationship between Schrödinger wavefunctions and spacetime structures of quantum particles we suggested that a Ricci scalar curvature for a particular quantum state of a quantum system could be constructed using the Schrödinger wavefunctions as mathematical objects. In this work we will extend our discussions by suggesting possible line elements that can be used to construct relativistic spacetime structures of a hydrogen atom. We also discuss the possibility to use a covariant Ricci flow as evolution equations to describe the dynamics of the hydrogen atom geometric structures.

**Category:** Mathematical Physics

[661] **viXra:1709.0029 [pdf]**
*submitted on 2017-09-03 04:28:49*

**Authors:** Spiros Konstantogiannis

**Comments:** 33 Pages.

Among the one-dimensional, smooth and real polynomial potentials, the sextic anharmonic oscillator is the only one than can be quasi-exactly solved [6, 7], in the sense that it is expressed in terms of a non-negative integer n and for every value of n, we can find n+1 energies and the respective eigenfunctions in closed form. In this work, we use, as basic parameter, the constant term of a quotient polynomial [3], to quasi-exactly solve the sextic anharmonic oscillator and demonstrate that the new parameter is a preferential one to study the system, as it makes the analysis straightforward and transparent.

**Category:** Mathematical Physics

[660] **viXra:1708.0445 [pdf]**
*submitted on 2017-08-29 05:42:34*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 5 Pages. This paper has not been submitted to a journal. Your comments are welcome

While it is known that Euclid’s five axioms include a proposition that a line consists at
least of two points, modern geometry avoid consistently any discussion on the precise
definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean
geometry: how many points are there in a line segment? – from discrete space viewpoint.
In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete
gravitational theories.

**Category:** Mathematical Physics

[659] **viXra:1708.0424 [pdf]**
*submitted on 2017-08-29 02:39:21*

**Authors:** Vu B Ho

**Comments:** 5 Pages.

In this work, we discuss the possibility to formulate a covariant Ricci flow so that it satisfies the principle of relativity and therefore can be applied to all coordinate systems defined on a Riemannian manifold. Since the investigation may be considered to be in the domain of pure mathematics, which is outside our field of physical investigations, therefore there may be errors in mathematical arguments that we are unable to foresee.

**Category:** Mathematical Physics

[658] **viXra:1708.0406 [pdf]**
*submitted on 2017-08-28 04:39:26*

**Authors:** Abdelmajid Ben Hadj Salem

**Comments:** 6 Pages. In French.

From the equations of the problem of $n$ body, we consider that $t$ is a function of the variables $(x_k,y_k,z_k)_{k=1,n}$. We write a new formulation of the equations of the $n$ body problem.

**Category:** Mathematical Physics

[657] **viXra:1708.0328 [pdf]**
*submitted on 2017-08-24 06:50:21*

**Authors:** Spiros Konstantogiannis

**Comments:** 17 Pages.

Making use of the Bethe ansatz, we introduce a quotient polynomial and we show that the presence of intermediate terms in the quotient polynomial, i.e. terms other than the constant and the leading one, constitutes a non-solvability condition for the respective potential. In this context, both the exact solvability of the quantum harmonic oscillator and the quasi-exact solvability of the sextic anharmonic oscillator stem naturally from the quotient polynomial, as in the first case, it is an energy-dependent constant, while in the second case, it is a second-degree binomial with no linear term. In all other cases, the quotient polynomial has at least one intermediate term, the presence of which makes the respective potentials non-solvable.

**Category:** Mathematical Physics

[656] **viXra:1708.0254 [pdf]**
*submitted on 2017-08-21 21:54:53*

**Authors:** Robert B. Easter

**Comments:** 24 pages. Written as an invited extended paper, extending the 10-page conference paper Double Conformal Geometric Algebra (ICNPAA 2016), for possible later submission to the journal Mathematics in Engineering, Science and Aerospace (MESA).

The G(4,8) Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra that extends the concepts introduced with the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) 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 G(1,3) Space-Time Algebra (STA). Two G(2,4) Conformal Space-Time subalgebras (CSTA) provide spacetime entities for points, hypercones, hyperplanes, hyperpseudospheres (and their intersections) 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. G(4,8) DCSTA is a doubling product of two orthogonal G(2,4) CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new 2-vector entities for general (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime surface entities that use the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in hyperpseudospheres. An operation for the directed non-uniform scaling (anisotropic dilation) of the 2-vector general quadric entities is defined using the boost operator and a spatial projection. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the Thomas-Wigner rotation and length contraction of special relativity. DCSTA is an algebra for computing with general quadrics and their inversive geometry in spacetime. For applications or testing, G(4,8) DCSTA can be computed using various software packages, such as the symbolic computer algebra system SymPy with the GAlgebra module.

**Category:** Mathematical Physics

[655] **viXra:1708.0226 [pdf]**
*submitted on 2017-08-18 17:46:16*

**Authors:** Vu B Ho

**Comments:** 10 Pages.

Investigations into the nature of the principle of least action have shown that there is an intrinsic relationship between geometrical and topological methods and the variational principle in classical mechanics. In this work, we follow and extend this kind of mathematical analysis into the domain of quantum mechanics. First, we show that the identification of the momentum of a quantum particle with the de Broglie wavelength in 2-dimensional space would lead to an interesting feature; namely the action principle δS=0 would be satisfied not only by the stationary path, corresponding to the classical motion, but also by any path. Thereupon the Bohr quantum condition possesses a topological character in the sense that the principal quantum number n is identified with the winding number, which is used to represent the fundamental group of paths. We extend our discussions into 3-dimensional space and show that the charge of a particle also possesses a topological character and is quantised and classified by the homotopy group of closed surfaces. We then discuss the possibility to extend our discussions into spaces with higher dimensions and show that there exist physical quantities that can be quantised by the higher homotopy groups. Finally we note that if Einstein’s field equations of general relativity are derived from Hilbert’s action through the principle of least action then for the case of n=2 the field equations are satisfied by any metric if the energy-momentum tensor is identified with the metric tensor, similar to the case when the momentum of a particle is identified with the curvature of the particle’s path.

**Category:** Mathematical Physics

[654] **viXra:1708.0198 [pdf]**
*submitted on 2017-08-17 01:42:13*

**Authors:** Vu B Ho

**Comments:** 24 Pages.

In this work we discuss the possibility of reconciling quantum mechanics with classical mechanics by formulating a temporal dynamics, which is a dynamics caused by the rate of change of time with respect to distance. First, we show that a temporal dynamics can be derived from the time dilation formula in Einstein’s theory of special relativity. Then we show that a short-lived time-dependent force derived from a dynamical equation that is obtained from the temporal dynamics in a 1-dimensional temporal manifold can be used to describe Bohr’s postulates of quantum radiation and quantum transition between stable orbits in terms of classical dynamics and differential geometry. We extend our discussions on formulating a temporal dynamics to a 3-dimensional temporal manifold. With this generalisation we are able to demonstrate that a sub-quantum dynamics is a classical dynamics.

**Category:** Mathematical Physics

[653] **viXra:1708.0197 [pdf]**
*submitted on 2017-08-17 01:50:44*

**Authors:** Vu B Ho

**Comments:** 10 Pages.

In this work we discuss the possibility of combining the Coulomb potential with the Yukawa’s potential to form a mixed potential and then investigate whether this combination can be used to explain why the electron does not radiate when it manifests in the form of circular motions around the nucleus. We show that the mixed Coulomb-Yukawa potential can yield stationary orbits with zero net force, therefore if the electron moves around the nucleus in these orbits it will not radiate according to classical electrodynamics. We also show that in these stationary orbits, the kinetic energy of the electron is converted into potential energy, therefore the radiation process of a hydrogen-like atom does not related to the transition of the electron as a classical particle between the energy levels. The radial distribution functions of the wave equation determine the energy density rather than the electron density at a distance r along a given direction from the nucleus. It is shown in the appendix that the mixed potential used in this work can be derived from Einstein’s general theory of relativity by choosing a suitable energy-momentum tensor. Even though such derivation is not essential in our discussions, it shows that there is a possible connection between general relativity and quantum physics at the quantum level.

**Category:** Mathematical Physics

[652] **viXra:1708.0196 [pdf]**
*submitted on 2017-08-17 01:54:09*

**Authors:** Vu B Ho

**Comments:** 15 Pages.

In this work we develop a theory of temporal relativity, which includes a temporal special relativity and a temporal general relativity, on the basis of a generalised Newtonian temporal dynamics. We then show that a temporal relativity can be used to study the dynamics of quantum radiation of an elementary particle from a quantum system.

**Category:** Mathematical Physics

[651] **viXra:1708.0192 [pdf]**
*submitted on 2017-08-17 03:51:07*

**Authors:** Vu B Ho

**Comments:** 18 Pages.

In this work we propose a covariant formulation for the gravitational field and derive equations that can be used to construct the spacetime structures for short-lived and stable quantum particles. We also show that Schrödinger wavefunctions can be used to construct spacetime structures for the quantum states of a quantum system, such as the hydrogen atom. Even though our discussions in this work are focused on the microscopic objects, the results obtained can be applied equally to the macroscopic phenomena.

**Category:** Mathematical Physics

[650] **viXra:1708.0184 [pdf]**
*submitted on 2017-08-16 10:47:23*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 10 Pages.

In a previous work I have derived the theory of everything (ToE) in a 74 pages paper. To make the theory more accessible, in this work, I derive the equation for the ToE on one page. I then follow the derivation with a few pages of discussion.

**Category:** Mathematical Physics

[649] **viXra:1708.0166 [pdf]**
*submitted on 2017-08-15 06:49:15*

**Authors:** Spiros Konstantogiannis

**Comments:** 50 Pages.

Exactly solvable rational extensions of the harmonic oscillator have been constructed as supersymmetric partner potentials of the harmonic oscillator [1] as well as using the so-called prepotential approach [2]. In this work, we use the factorization property of the energy eigenfunctions of the harmonic oscillator and a simple integrability condition to construct and examine series of regular and singular rational extensions of the harmonic oscillator with two known eigenstates, one of which is the ground state. Special emphasis is given to the interrelation between the special zeros of the wave function, the poles of the potential, and the excitation of the non-ground state. In the last section, we analyze specific examples.

**Category:** Mathematical Physics

[648] **viXra:1708.0147 [pdf]**
*submitted on 2017-08-13 21:51:40*

**Authors:** Harry Watson

**Comments:** 1 Page.

Abstract: Consider the product
(4pi)(4pi-1/pi)(4pi-2/pi)(pi-2/pi)(4pi-4/pi).
The product of the first three terms is 1836.15.
The product of the last two terms is 134.72. The mass ratio of the proton to the electron is 1836.15.
We may sharpen the result by letting the last two terms be (4pi-3/pi)(4pi-4/pi) = 131.13$.

**Category:** Mathematical Physics

[647] **viXra:1708.0031 [pdf]**
*submitted on 2017-08-03 09:30:29*

**Authors:** Hideki Mutoh

**Comments:** 5 Pages.

Dirac equation includes the 4 x 4 complex differential operator matrix, which is one of square roots of d' Alembertian with spin. We found another 4 x 4 complex differential matrix as a spinless square root of d' Alembertian, which we call diamond operator. The extended Maxwell's equations including charge creation-annihilation field and the linear gravitational field equations including energy creation-annihilation field can be simply written by using the diamond operator. It is shown that the linear gravitational field equations derive Klein-Gordon equation, time independent Schrödinger equation, and the principle of quantum mechanics.

**Category:** Mathematical Physics

[646] **viXra:1708.0011 [pdf]**
*submitted on 2017-08-02 04:28:15*

**Authors:** Hong Lai Zhu

**Comments:** 53 Pages.

In this paper, using proposed three new transformation methods we have solved general solutions and exact solutions of the problems of definite solutions of the Laplace equation, Poisson equation, Schrödinger equation, the homogeneous and non-homogeneous wave equations, Helmholtz equation and heat equation. In the process of solving, we find that in the more general case, general solutions of partial differential equations have various forms such as basic general solution, series general solution, transformational general solution, generalized series general solution and so on.

**Category:** Mathematical Physics

[569] **viXra:1805.0073 [pdf]**
*replaced on 2018-05-11 01:09:25*

**Authors:** Rodney Bartlett

**Comments:** 23 Pages. Cite: https://doi.org/10.6084/m9.figshare.6214049.v3

When his paper regarding mathematical formulas creating reality was submitted to a scientific journal and rejected as being too speculative, U.S. cosmologist Max Tegmark showed the rejection letter to his friend John Wheeler (1911-2008), a Princeton theoretical physicist. Wheeler said, “Extremely speculative? Bah!” Then he reminded Tegmark that some of the original papers on quantum mechanics were also considered extremely speculative. After Wheeler sent the journal his objection to their objection, Tegmark's paper was published.
This paper of mine can also be seen as a "too speculative" extension of Werner Heisenberg's matrix version of quantum mechanics. In particular, the part equating the Mobius strip to a,b,c,d,e and being a relation of matrix mathematics – and the part which says Brouwer's Fixed Point Theorem shows the universe must be infinite and eternal (the universe may seem unrelated to the quantum world, but the former is composed of the latter and this article's cosmology is a direct outgrowth of matrix mechanics).
What is the Dark Matter that holds together galaxies and galaxy clusters? Nobody knows. Some say it's gravitational, and requires modification of Einstein's General Relativity. Some say it's a form of matter, consisting of dark particles. Those ideas are combined here with 20th-century physicist Richard Feynman's interpretation of advanced and retarded waves. (Feynman found that adding the contributions of advanced and retarded waves creates a consistent quantum theory called QED - Quantum Electrodynamics - in which the terms that might violate causality cancel precisely.) I believe LIGO (the Laser Interferometer Gravitational-wave Observatory) will build on Richard Feynman's QED and his love of "advanced" waves that travel backwards in time. There should be several applications of this extension of QED:
(1) Radioactive dating of dinosaur fossils, ancient rocks, and Earth itself should all result in readings that are many times less - at least a thousand (for dinosaurs), to nearly a million (for Earth).
(2) Health might be dramatically improved and lifespan dramatically increased.
(3) United with electronic binary digits, cosmic topology and mathematical Wick rotation; extra large-scale dimensions could be discovered - and these dimensions joined with matter and mass, space and time into one physical space-time unification.
(4) Matter, antimatter and dark matter should become viewed as different aspects of one thing when combined with advanced waves, Wick rotation and the mathematical Matrix.
(5) Maths like Brouwer's Fixed Point Theorem and so called "imaginary" time agree that space-time can be seen as one literally infinite and eternal "block" universe containing all the past as well as the entire future (the Cosmic Microwave Background and redshift objections are addressed).
(6) The new maths in this article tells us that our present maths is incomplete within a unified universe, is therefore relied upon too much, and is incapable of producing a successful theory of Quantum Gravity (unification of quantum mechanics and Einstein's theory of gravity, general relativity). Paradoxically, "new maths" also says ∞= 0 (the infinity of the universe's size equals the zero-ness of space-time/gravity) and points to a new physics. Science seems to avoid infinity at all costs – equating it with zero will give scientists many more headaches. Maybe they could accept infinity if ∞= 0 was viewed as the ultimate form of renormalization – a renormalization that, thanks to E=mc2, doesn't reduce the infinite size of the universe but reduces the distances in space and between times to zero.

**Category:** Mathematical Physics

[568] **viXra:1805.0073 [pdf]**
*replaced on 2018-05-05 02:57:07*

**Authors:** Rodney Bartlett

**Comments:** 18 Pages. Cite: https://doi.org/10.6084/m9.figshare.6214049.v2

When his paper regarding mathematical formulas creating reality was submitted to a scientific journal and rejected as being too speculative, U.S. cosmologist Max Tegmark showed the rejection letter to his friend John Wheeler (1911-2008), a Princeton theoretical physicist. Wheeler said, “Extremely speculative? Bah!” Then he reminded Tegmark that some of the original papers on quantum mechanics were also considered extremely speculative. After Wheeler sent the journal his objection to their objection, Tegmark's paper was published.
This paper of mine can also be seen as a "too speculative" extension of Werner Heisenberg's matrix version of quantum mechanics. In particular, the part equating the Mobius strip to a,b,c,d,e and being a relation of matrix mathematics – and the part which says Brouwer's Fixed Point Theorem shows the universe must be infinite and eternal (the universe may seem unrelated to the quantum world, but the former is composed of the latter and this article's cosmology is a direct outgrowth of matrix mechanics).
What is the Dark Matter that holds together galaxies and galaxy clusters? Nobody knows. Some say it's gravitational, and requires modification of Einstein's General Relativity. Some say it's a form of matter, consisting of dark particles. Those ideas are combined here with 20th-century physicist Richard Feynman's interpretation of advanced and retarded waves. (Feynman found that adding the contributions of advanced and retarded waves creates a consistent quantum theory called QED - Quantum Electrodynamics - in which the terms that might violate causality cancel precisely.) I believe LIGO (the Laser Interferometer Gravitational-wave Observatory) will build on Richard Feynman's QED and his love of "advanced" waves that travel backwards in time. There should be several applications of this extension of QED:
(1) Radioactive dating of dinosaur fossils, ancient rocks, and Earth itself should all result in readings that are many times less - at least a thousand (for dinosaurs), to nearly a million (for Earth).
(2) Health might be dramatically improved and lifespan dramatically increased.
(3) United with electronic binary digits, cosmic topology and mathematical Wick rotation; extra large-scale dimensions could be discovered - and these dimensions joined with matter and mass, space and time into one physical space-time unification.
(4) Matter, antimatter and dark matter should become viewed as different aspects of one thing when combined with advanced waves, Wick rotation and the mathematical Matrix.
(5) Maths like Brouwer's Fixed Point Theorem and so called "imaginary" time could enable space-time to be seen as one literally infinite and eternal "block" universe containing all the past as well as the entire future (the Cosmic Microwave Background and redshift objections are addressed).

**Category:** Mathematical Physics

[567] **viXra:1804.0160 [pdf]**
*replaced on 2018-04-13 06:30:08*

**Authors:** William O. Straub

**Comments:** 13 Pages. One typo fixed

An introduction to the calculus of differential forms for undergraduate physics students

**Category:** Mathematical Physics

[566] **viXra:1804.0160 [pdf]**
*replaced on 2018-04-12 09:12:44*

**Authors:** William O. Straub

**Comments:** 13 Pages.

A basic introduction to the calculus of differential forms for undergraduate physics students

**Category:** Mathematical Physics

[565] **viXra:1804.0105 [pdf]**
*replaced on 2018-04-21 22:46:12*

**Authors:** Mikhail L. Sokolnikov

**Comments:** 2 Pages. https://youtu.be/rUI7Dmu62Uo

Logical continuation of the work of the Soviet aircraft designer, the Italian Earl of Croatian origin Roberto Oros di Bartini.
Логическое продолжение работы советского авиаконструктора, итальянского графа хорватского происхождения Roberto Oros di Bartini.
Time = x^4

**Category:** Mathematical Physics

[564] **viXra:1804.0068 [pdf]**
*replaced on 2018-04-23 01:40:32*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 4 Pages. Enhanced version: The previous version was vague about the potential energy..

Newton's mechanics is simple. His equivalence principle is simple, as is the inverse square law of gravitational force. A simple theory should have simple solutions to simple models. A system of n particles, given their initial speed and positions along with their masses, is such a simple model. Yet, solving for n>2 is not simple. This paper discusses, why that is a difficult problem and what could be done to get around that problem.

**Category:** Mathematical Physics

[563] **viXra:1804.0068 [pdf]**
*replaced on 2018-04-21 08:08:34*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 4 Pages. Enhanced version: The previous version was vague about the potential energy..

Newton's mechanics is simple. His equivalence principle is simple, as is the inverse square law of gravitational force. A simple theory should have simple solutions to simple models. A system of n particles, given their initial speed and positions along with their masses, is such a simple model. Yet, solving for n>2 is not simple. This paper discusses, why that is a difficult problem and what could be done to get around that problem.

**Category:** Mathematical Physics

[562] **viXra:1804.0068 [pdf]**
*replaced on 2018-04-07 09:51:55*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 4 Pages. Slight polishing of English.

**Category:** Mathematical Physics

[561] **viXra:1803.0300 [pdf]**
*replaced on 2018-03-25 12:58:26*

**Authors:** Dan Visser

**Comments:** 9 Pages.

A new cosmology-theory presents a spectacular statement: By this article the rotation and expansion of a fast rotating vacuum below the Planck-scale is described with approximately 10^21 rad/s. This subquantum vacuum-rotation emerges approximately 10^18 Hertz x-rays above the Planck-scale. Meanwhile it is a fact that x-ray-radiation is observed by several observatory with an energy of about 3,5 keV in accordance to the possible existence of sterile neutrinos. However, the energy here mentioned is used for direct evidence for the existence of ‘light-holes’, which seen from a distance replaces the Planck-scale in rotating vacuum and in perspective of my new cosmological model, the rotating hologram-universe. The new model discards the single modern-classic Big Bang-universe as not-fundamental. It means coming closer to ‘light-holes’ high-frequent x-rays become lower in frequency due to an also earlier published formula Tdan , which shows vacuum expands by ‘the crumbling of the vacuum-quantum-unit’. Hence, closer to the ‘light-hole’, a parallel Big Bang-universe will appear to be a part of the fundamental rotating hologram-universe. Let it be noticed the exercises given here are obviously ahead of media-pre-announced Hawking-Hertog publications about how to measure the existence of other Big Bangs, because I already carry on the evidence for this in this article.

**Category:** Mathematical Physics

[560] **viXra:1802.0355 [pdf]**
*replaced on 2018-02-25 07:26:12*

**Authors:** Robert A. Herrmann

**Comments:** 32 Pages.

The methods of nonstandard analysis are applied to general language logic-systems. This allows the
operators for the only known mathematical cosmogony, the General Grand Unification Model (GGUmodel), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and
processes are predicted from certain observable entities, which are physical processes and mental
procedures that we use to construct physical objects. It is shown that, for each of the four types of
instruction paradigms, there exists an ultra-word-like object such that when an hyper-algorithm is
applied to it an ultra-logic-system is *-deduced. Another application of an hyper-algorithm yields a
hyperfinite instruction paradigm that is hyper-deduced in the in the required sequential order. It is
shown that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the
Patten and Wheeler participator universe requirements. In this version, the participator process portion
of the GGU-model is significantly altered from the original process presented and a correction is
made to an equation and its applications. A specific data-set is generalized and the set of all ultrapropertons is obtained and its properties examined. This set is shown to be sufficient for universe
construction. GGU-model schemes are presented in diagram form. A process is introduced that leads,
when applied, to the individual developmental of each universe-wide frozen-frame. An operator is
shown to exist, which, via a substratum medium and processes, changes hyper-instruction information
into substratum info-fields. From these info-fields, all physical-systems are produced. In this
refinement, the page 11 statement, in the original version of this paper on quantum theory, is
completely modified and the previous statement is now essentially incorrect.

**Category:** Mathematical Physics

[559] **viXra:1802.0109 [pdf]**
*replaced on 2018-02-27 11:00:13*

**Authors:** Antoine Balan

**Comments:** 3 pages, written in french

The KdV equations are defined over manifolds. The system is integrable and we show that it is reduced to usual KdV equations.

**Category:** Mathematical Physics

[558] **viXra:1802.0109 [pdf]**
*replaced on 2018-02-23 10:57:19*

**Authors:** Antoine Balan

**Comments:** 3 pages, written in french

The KdV equations are defined over manifolds. The system is integrable and we show that it is reduced to usual KdV equations.

**Category:** Mathematical Physics

[557] **viXra:1801.0287 [pdf]**
*replaced on 2018-05-01 12:35:58*

**Authors:** Renzun Lian

**Comments:** 15 Pages.

In this paper, we generalize Huygens' principle (HP), extinction theorem (ET), and Franz-Harrington formulation (FHF) in two parts. In Part I, the traditional HP, ET, and FHF in homogeneous isotropic environment are generalized to inhomogeneous anisotropic lossy environment; the traditional FHF of homogeneous isotropic material system is generalized to inhomogeneous anisotropic lossy material system and then to piecewise inhomogeneous anisotropic lossy material system; the traditional HP, ET, and FHF of simply connected material system are generalized to multiply connected system and then to non-connected system; the traditional FHF of external scattering field and internal total field are generalized to internal scattering field and internal incident field. In Part I, it is proved that the generalized HP (GHP) and generalized ET (GET) are equivalent to each other; the GHP, GET, and generalized FHF (GFHF) satisfy so-called topological additivity, i.e., the GHP/GET/GFHF of whole electromagnetic (EM) system equals to the superposition of the GHP/GET/GFHF corresponding to all sub-systems. In this Part II, the above results obtained in previous Part I, which focuses on the EM system constructed by material bodies, are further generalized to the metal-material combined EM system in inhomogeneous anisotropic lossy environment, and traditional surface equivalence principle is generalized to line-surface equivalence principle.

**Category:** Mathematical Physics

[556] **viXra:1801.0266 [pdf]**
*replaced on 2018-04-30 10:04:14*

**Authors:** Renzun Lian

**Comments:** 21 Pages.

Huygens' principle (HP), extinction theorem (ET), and Franz's / Franz-Harrington formulation (FHF, which is a mathematical expression of surface equivalence principle) are the important components of electromagnetic (EM) theory, and they are generalized from the following aspects.
1) Traditional HP, ET, and FHF in homogeneous isotropic environment are generalized to inhomogeneous anisotropic lossy environment. 2) Traditional FHF for homogeneous isotropic material system is generalized to inhomogeneous anisotropic lossy material system in this Part I, and will be further generalized to metal-material combined system in future Part II. 3) The Huygens' surface in traditional HP and ET is a single closed surface. In Part I, it is generalized to the "Huygens' surface" which is constructed by multiple closed surfaces. In Part II, it will be further generalized to the "Huygens' boundary" which includes some lines and open surfaces. 4) For a material body, traditional FHF has only ability to express the external scattering field and the internal total field (the summation of scattering and incident fields) in terms of the equivalent sources on material boundary, and it is generalized to formulating the internal scattering and incident fields in this paper.
In addition, the relationships among HP, ET, and FHF are studied, and it is proved that HP and ET are equivalent to each other.

**Category:** Mathematical Physics

[555] **viXra:1801.0110 [pdf]**
*replaced on 2018-02-11 05:07:04*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 307 Pages. This book will be published by Pons Publisher, Brussels. Your comments are welcome

This book is a compilation of some rather old papers and some new papers, by myself and also Prof. Florentin Smarandache. In some papers, we also join working with other colleagues, e.g. Dr. Volodymyr Krasnoholovets from IOP Ukraine, and Dr. Yunita Umniyati. This compilation is inspired from a series of prophetic seminars by Rev. Jan Friso from Kingdom Impact , and also a discussion with Minister Dr. Robby Chandra. All in all, we are also grateful to a number of colleagues, including Prof. Thee Houw Liong, Prof. Liek Wilardjo, Prof. Atmonobudi Soebagyo, Dr. David Widihandojo, Sujarwo Silas & Linda, Dr. Wonsuk Ma, Minister Gatut Budiyono, Minister Gani Wiyono, Dr. Yonky Karman, Dr. Joas Adiprasetya, Dr. Paskalis Edwin Nyoman Paska, Minister Yulia Oeniyati, Prof. Akira Kanda, Dr. Carmen Wrede, Mrs. Hiroko Morioka, Prof. Jose Carlos Tiago Oliveira and Prof. Gusto Gadama, and many others, who often encouraged and reminded us to keep on being faithful Christians in this darkness time. As a last note, we also thank to Holy Spirit who always guide us in our way, especially whenever we were lost of our path to find the truth. That is why this book with title: Let The Wind blows is dedicated to Holy Spirit. Let us pray that the Holy Spirit will be poured once again in our time, as prophesied by Joel, one of OT prophets.

**Category:** Mathematical Physics

[554] **viXra:1801.0066 [pdf]**
*replaced on 2018-01-06 13:41:52*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages. minor correction - as always..

This paper is an appendix to the article "From Bernoulli to Laplace and Beyond"
(refenced below), and discusses different aspects of it: electromagnetism, field tensors,
general relativity, and probability.

**Category:** Mathematical Physics

[553] **viXra:1801.0047 [pdf]**
*replaced on 2018-05-07 23:52:44*

**Authors:** YiMing Xia

**Comments:** 21 Pages. Spit-Full node innovative notion is presented;The tradditional discretized model is repaced by the integrated; The rational MRA concept togather with the RL is constructed;The RL defines a uniform node distribution pattern over a structural domain.

A triangular plate-bending element with a new multi-resolution analysis (MRA) is proposed and a novel multiresolution element method is hence presented. The MRA framework is formulated out of a displacement subspace sequence whose basis functions are built out of scaling and shifting on the element domain of basic full node shape function. The basic full node shape function is constructed by means of extending the shape function triangle domain for a split node at the zero coordinates to the hexagon area enclosing the zero coordinates. As a result, a new split-full node notion is presented and a novel rational MRA concept together with the resolution level (RL) is constituted for the element. Via practical examples, it is found that the traditional triangular plate element and method is a mono-resolution one and also a special case of the proposed element and method. The meshing for the monoresolution plate element model is based on the empiricism while the RL adjusting for the multiresolution is laid on the rigorous mathematical basis. The analysis clarity of a plate structure is actually determined by the RL, not by the mesh. Thus, the accuracy of a structural analysis is replaced by the clarity, the irrational MRA by the rational and the mesh model by the RL that is the discretized model by the integrated. The continuous full node shape function unveils secrets behind assembling artificially of node-related items in global matrix formation by the conventional FEM.

**Category:** Mathematical Physics

[552] **viXra:1801.0025 [pdf]**
*replaced on 2018-02-28 10:47:53*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages. Left out background information, tried to increase focus on gravity itself. Corrected misprints.

Reviewing Laplace's equation of gravitation from the perspective of D. Bernoulli, known as Poisson-equation, it will be shown that Laplace's equation tacitly assumes the temperature T of the mass system to be approximately 0 degrees of Kelvin. For temperatures greater zero, the gravitational field will have to be given an additive correctional field. Now, temperature is intimately related to the heat, and heat is known to be radiated as an electromagnetic field. It is shown to take two things in order to get at the gravitational field in the low temperature limit: the total square energy density of the source in space-time and a (massless) field, which expresses the equivalence of inert and gravitational mass/energy in a quadratic, Lorentz-invariant form. This field not only necessarily must include electromagnetic interaction, it also will be seen to behave like it.

**Category:** Mathematical Physics

[551] **viXra:1801.0025 [pdf]**
*replaced on 2018-02-25 06:22:41*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages. Left out background information, tried to increase focus on gravity itself. Corrected misprints.

Reviewing Laplace's equation of gravitation from the perspective of D. Bernoulli, known as Poisson-equation, it will be shown that Laplace's equation tacitly assumes the temperature T of the mass system to be approximately 0 degrees of Kelvin. For temperatures greater zero, the gravitational field will have to be given an additive correctional field. Now, temperature is intimately related to the heat, and heat is known to be radiated as an electromagnetic field. It is shown to take two things in order to get at the gravitational field in the low temperature limit: the total square energy density of the source in space-time and a (massless) field, which expresses the equivalence of inert and gravitational mass/energy in a quadratic, Lorentz-invariant form. This field not only necessarily must include electromagnetic interaction, it also will be seen to behave like it.

**Category:** Mathematical Physics

[550] **viXra:1801.0025 [pdf]**
*replaced on 2018-02-24 05:17:35*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages. Left out background information, tried to increase focus on gravity itself.

**Category:** Mathematical Physics

[549] **viXra:1712.0399 [pdf]**
*replaced on 2017-12-19 15:09:52*

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

**Comments:** 4 pages

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear two-point boundary value problem may be computed in a direct and straightforward fashion from the general solution obtained by a generalized Sundman transformation for the related differential equation, which appeared with the sinh-Poisson and Poisson-Boltzmann equations to be special cases of a more general equation. As a result, various initial and boundary value problems for these equations may be solved explicitly and exactly.

**Category:** Mathematical Physics

[548] **viXra:1712.0149 [pdf]**
*replaced on 2018-03-29 08:35:17*

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

**Comments:** 8 pages

This work shows that the Bratu equation belongs to a general class of Liénard-type equations for which the general solution may be exactly and explicitly computed within the framework of the generalized Sundman transformation. In this perspective the exact solution of the Bratu nonlinear two-point boundary value problem as well as of some well-known Bratu-type problems have been determined.

**Category:** Mathematical Physics

[547] **viXra:1711.0446 [pdf]**
*replaced on 2017-11-29 23:58:35*

**Authors:** Vu B Ho

**Comments:** 15 Pages.

In this work, we will investigate possible spacetime structures of massless particles by formulating Dirac equation in a six-dimensional spatial-temporal continuum in both pseudo-Euclidean and Euclidean metrics. We show that the state of a massless particle flows as an irrotational and incompressible fluid in steady fluid dynamics in the sense that all spatial and temporal components of the wavefunction of a massless particle can be described by Laplace equation. Furthermore, we also show that the six components of the wavefunction are coupled in pairs to form two-dimensional subspaces and this result may suggest why quantum particles possess an intrinsic spin angular momentum that takes half-integral values.

**Category:** Mathematical Physics

[546] **viXra:1711.0435 [pdf]**
*replaced on 2017-12-10 17:42:53*

**Authors:** Dan Visser

**Comments:** 26 Pages.

This article breaks with the inviolability of the quantum-unit. It ‘crumbles’ (or cuts up, or refines) the quantum-vacuum. That also crumbles the constant vacuum-energy-density, or dark energy. It offers a new definition for dark energy. New dark energy does no longer belong to the Big Bang-universe: New dark energy is part of a rotating-hologram universe. Such a universe has the shape of a Double Torus, which has an inner-torus that rotates while an outer-torus represents the ‘crumble of the vacuum’ with time below the Planck-scale. The ‘vacuum-crumbling’ implies a ‘new ‘building-stone’ for vacuum: Tdan. This is a new (rotating) energy-tensor, which has two states , one for above and one for below the Planck-scale. The ‘beauty’ is the dimension of the tensor remains unchanged in those two states! Hence, the quantum-Planck-unit is transparent for migration. That makes the Big Bang-universe no longer a fundamental universe. The Big Bang-universe is emerged (or induced) by rotation of the hologram-universe. This means the Big Bang-universe will exist in every place of the rotating hologram-universe implying: parallel universes ‘outside’ a Big Bang-universe are a nonissue. Parallel universes exist embedded in the rotating hologram-universe. Thereby the origin of the ‘old Big Bang-universe’ is no longer relevant. A new definition of age of the universe lies in the cycle-duration of one cycle, although rotation goes on eternally. Continuously the origin is recalculated. Seemingly the Big Bang-universe is materialized above the Planck-scale and dé-materializes below the Planck-scale, however, such a perspective is reciprocal facing the transparent frontier. Against all expectations my formulas show that one can migrate from one to the other parallel-universe. Locally that is interpreted as ‘change’, but on larger scales it is called traveling through time without space. Because there is extra time (or refined time in the crumble of vacuum), which affects relativistic time that can make traveling faster than traveling through space with the speed of light. There is no horizon between the physics of the ‘soul’ and the physics of ‘materialization’ including the other way around. At last two physics-problems are solved: firstly a more fundamental cause for the origin of hurricanes wherein the building stone of vacuum is involved and secondly the hierarchy problem, the explanation why there is a large emptiness between the Planck-scale and the scale-existence of the smallest particles.

**Category:** Mathematical Physics

[545] **viXra:1711.0435 [pdf]**
*replaced on 2017-12-06 09:10:16*

**Authors:** Dan Visser

**Comments:** 23 Pages.

This article breaks with the inviolability of the quantum-unit. It ‘crumbles’ (or cuts up, or refines) the quantum-vacuum. That also crumbles the constant vacuum-energy-density, or dark energy. It offers a new definition for dark energy. New dark energy does no longer belong to the Big Bang-universe: New dark energy is part of a rotating-hologram universe. Such a universe has the shape of a Double Torus, which has an inner-torus that rotates while an outer-torus represents the ‘crumble of the vacuum’ with time below the Planck-scale. The ‘vacuum-crumbling’ implies a ‘new ‘building-stone’ for vacuum: Tdan. This is a new (rotating) energy-tensor, which has two states, one for above and one for below the Planck-scale. The ‘beauty’ is the dimension of the tensor remains unchanged in those two states! Hence, the quantum-Planck-unit is transparent for migration. That makes the Big Bang-universe no longer a fundamental universe. The Big Bang-universe is emerged (or induced) by rotation of the hologram-universe. This means the Big Bang-universe will exist in every place of the rotating hologram-universe implying: parallel universes ‘outside’ a Big Bang-universe are a nonissue. Parallel universes exist embedded in the rotating hologram-universe. Thereby the origin of the ‘old Big Bang-universe’ is no longer relevant. A new definition of age of the universe lies in the cycle-duration of one cycle, although rotation goes on eternally. Continuously the origin is recalculated. Seemingly the Big Bang-universe is materialized above the Planck-scale and dé-materializes below the Planck-scale, however, such a perspective is reciprocal facing the transparent frontier. Against all expectations my formulas show that one can migrate from one to the other parallel-universe. Locally that is interpreted as ‘change’, but on larger scales it is called traveling through time without space. Because there is extra time (or refined time in the crumble of vacuum), which affects relativistic time that can make traveling faster than traveling through space with the speed of light. There is no horizon between the physics of the ‘soul’ and the physics of ‘materialization’ including the other way around.

**Category:** Mathematical Physics

[544] **viXra:1711.0395 [pdf]**
*replaced on 2017-11-29 07:41:26*

**Authors:** Spiros Konstantogiannis

**Comments:** 33 Pages.

Making an intuitive assumption, and using the completeness of the position and momentum eigenstates, along with the postulates of quantum mechanics, we provide a geometric presentation of the position and momentum representations in quantum mechanics, in the hope of offering a perspective complementary to those given in standard textbooks.

**Category:** Mathematical Physics

[543] **viXra:1711.0365 [pdf]**
*replaced on 2017-12-05 14:08:19*

**Authors:** Giuliano Bettini

**Comments:** 24 Pages. In English. Updated. Some minor corrections.

Starting from the 32 crystal classes, we find a complete classification scheme of the same with only 5 bits, and at least in part the meaning of the various bits.
There is no inverse demonstration, ie only 5 bits must generate all 32 crystalline classes in nature.
However, the proposed classification seems to invoke a logical process of formation of the various classes, doing this way:
the matter first aggregates without any symmetry, then it adopts various rotation symmetries (no symmetry, binary, ternary, etc., simple or composite) and then adds to each symmetry of rotation the additional symmetries c (center), m (planes) or c + m together

**Category:** Mathematical Physics

[542] **viXra:1711.0365 [pdf]**
*replaced on 2017-11-30 10:23:23*

**Authors:** Giuliano Bettini

**Comments:** 20 Pages. In Italian. This is the update to the Italian version v1.

Starting from the 32 crystal classes, we find a complete classification scheme of the same with only 5 bits, and at least in part the meaning of the various bits.
There is no inverse demonstration, ie only 5 bits must generate all 32 crystalline classes in nature.
However, the proposed classification seems to invoke a logical process of formation of the various classes, doing this way:
the matter first aggregates without any symmetry, then it adopts various rotation symmetries (no symmetry, binary, ternary, etc., simple or composite) and then adds to each symmetry of rotation the additional symmetries c (center), m (planes) or c + m together

**Category:** Mathematical Physics

[541] **viXra:1710.0219 [pdf]**
*replaced on 2017-10-19 20:09:02*

**Authors:** Huai-Yi Xie

**Comments:** 115 Pages.

In this paper, we have derived planar multilayer dyadic Green’s functions by Fourier expansion method and have checked its correctness by comparing results for reflected electric fields from dipole emissions near such structures available in previous literature. Furthermore, we show how these dyadic Green’s functions can be applied to calculate reflected fields from a dipole source with arbitrary orientations. We believe our formulation will be powerful in the modeling of molecular fluorescence near these structures.

**Category:** Mathematical Physics

[540] **viXra:1710.0074 [pdf]**
*replaced on 2018-02-04 05:58:23*

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

**Comments:** 14 pages

Authors introduce a generalized singular differential equation of quadratic Liénard
type for study of exact classical and quantum mechanical solutions. The equation
is shown to exhibit periodic solutions and to include the linear harmonic
oscillator equation and the Painlevé-Gambier XVII equation as special cases.
It is also shown that the equation may exhibit discrete eigenstates as quantum
behavior under Nikiforov-Uvarov approach after several point transformations.

**Category:** Mathematical Physics

[539] **viXra:1710.0014 [pdf]**
*replaced on 2017-12-28 11:39:44*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 20 Pages.

We describe a fluid motion in three dimensions with rectangular, cylindrical and spherical coordinates.

**Category:** Mathematical Physics

[538] **viXra:1710.0011 [pdf]**
*replaced on 2017-10-30 08:47:52*

**Authors:** Spiros Konstantogiannis

**Comments:** 28 Pages.

The quasi-exact solvability of symmetrized quartic anharmonic oscillators has been studied first by Znojil [2] and then by Quesne [3]. In this work, we examine the solvability of these models using, as basic parameter, the energy-dependent, constant (i.e. position-independent) term of a quotient polynomial. We examine the cases n=0 and n=1, and we show that our results are in agreement with those of Quesne. For n=2, following a different path from that of Znojil, we derive the cubic equation that our parameter satisfies and for the case it has a root at zero, we follow the zero root to obtain an even-parity, ground-state wave function and an odd-parity, third-excited-state wave function. As in the case of the sextic anharmonic oscillator [6], the straightforwardness and transparency of the analysis demonstrates the eligibility of the quotient polynomial as a solvability tool of polynomial oscillators.

**Category:** Mathematical Physics

[537] **viXra:1709.0332 [pdf]**
*replaced on 2017-11-15 02:12:05*

**Authors:** Christopher Andreadis

**Comments:** 15 Pages.

Pondering existence is a journey of the mind that has no boundaries. In contrast to this lofty mesa, however, we must also accept the fact that our own existence is, regrettably, quite finite. This concern invariably encompasses the desire to foresee events that may adversely affect our lives. Thus, fundamental to our existence is the innate ability to understand how the choices we make today shape all our future tomorrows (τι μέλλει γενέσθαι;) as inexorably driven by cause and effect. Yet there may be undiscovered phenomena not strictly bound by causal reality that can never be completely observed or understood, and that may in some way forge our destinies. It is suggested that such phenomena are rooted in nonlinear time, specifically, they may not consistently flow from past to future, or from cause to effect.
Section [13] of this paper states the core hypothesis of how a prognostic system, based on a network of identical NRCL devices (section [1]), may be affected by unusual or extraordinary phenomena. Additionally, section [10] describes the basic configuration of such a network. If the core hypothesis is true, and each NRCL device can be optimally adjusted to collectively forecast events yet to come, then we may discover that our existence is not completely founded on causal reality, but may also be influenced by processes of “cause preceded by effect” that propagate at the macroscopic scale. Section [2] states proposals A through E of how existence may be more than what any casual observer can discern.

**Category:** Mathematical Physics

[536] **viXra:1709.0332 [pdf]**
*replaced on 2017-10-24 14:20:29*

**Authors:** Chris L. Andreadis

**Comments:** 15 Pages.

Pondering existence is a journey of the mind that has no boundaries. In contrast to this lofty mesa, however, we must also accept the fact that our own existence is, regrettably, quite finite. This concern invariably encompasses the desire to foresee events that may adversely affect our lives. Thus, fundamental to our existence is the innate ability to understand how the choices we make today shape all our future tomorrows (τι μέλλει γενέσθαι;) as inexorably driven by cause and effect. Yet there may be undiscovered phenomena not strictly bound by causal reality that can never be completely observed or understood, and that may in some way forge
our destinies. It is suggested that such phenomena are rooted in nonlinear time, specifically, they may not consistently flow from past to future, or from cause to effect.

**Category:** Mathematical Physics

[535] **viXra:1709.0332 [pdf]**
*replaced on 2017-10-19 08:48:27*

**Authors:** Chris L. Andreadis

**Comments:** 15 Pages.

The updated NRCL Low Entropy Calibration procedure radically alters the function of the NRCL prototype from an enhanced true random number generator (TRNG) to a network component that may have significant ramifications with respect to forecasting schemes.

**Category:** Mathematical Physics

[534] **viXra:1709.0332 [pdf]**
*replaced on 2017-10-05 14:12:26*

**Authors:** Christopher L. Andreadis

**Comments:** 16 Pages.

Exploring the mutability of "cause and effect" at the macroscopic scale.

**Category:** Mathematical Physics

[533] **viXra:1709.0330 [pdf]**
*replaced on 2017-09-24 09:06:33*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 8 Pages. misspelling corrected.

Usually, physics students don't like thermodynamics: it is incomprehensible. They commonly get told to get used to it. Later on, as an expert, they'll find that the thermodynamic calculations come with surprises: sometimes evil, sometimes good. That can mean only one thing: The theory is inconsistent. In here, it will be shown where that is.

**Category:** Mathematical Physics

[532] **viXra:1709.0029 [pdf]**
*replaced on 2017-09-05 06:02:43*

**Authors:** Spiros Konstantogiannis

**Comments:** 33 Pages.

Among the one-dimensional, smooth and real polynomial potentials, the sextic anharmonic oscillator is the only one that can be quasi-exactly solved [6, 7], in the sense that it is expressed in terms of a non-negative integer n and for every value of n, we can find n+1 energies and the respective eigenfunctions in closed form. In this work, we use, as basic parameter, the constant term of a quotient polynomial [3], to quasi-exactly solve the sextic anharmonic oscillator and demonstrate that the new parameter is a preferential one to study the system, as it makes the analysis straightforward and transparent.

**Category:** Mathematical Physics

[531] **viXra:1708.0445 [pdf]**
*replaced on 2018-01-29 09:35:59*

**Authors:** Victor Christianto, Florentin Smarandache

**Comments:** 15 Pages. This paper has been submitted to JOURNAL OF PURE AND APPLIED MATHEMATICS. Your comments are welcome

While it is known that Euclid’s five axioms include a proposition that a line consists at least of two points, modern geometry avoid consistently any discussion on the precise definition of point, line, etc. It is our aim to clarify one of notorious question in Euclidean geometry: how many points are there in a line segment? – from discrete-cellular space (DCS) viewpoint. In retrospect, it may offer an alternative of quantum gravity, i.e. by exploring discrete gravitational theories. To elucidate our propositions, in the last section we will discuss some implications of discrete cellular-space model in several areas of interest: (a) cell biology, (b) cellular computing, (c) Maxwell equations, (d) low energy fusion, and (e) cosmology modelling.

**Category:** Mathematical Physics

[530] **viXra:1708.0328 [pdf]**
*replaced on 2017-10-29 11:13:19*

**Authors:** Spiros Konstantogiannis

**Comments:** 17 Pages.

Making use of the Bethe ansatz, we introduce a quotient polynomial and we show that the presence of intermediate terms in it, i.e. terms other than the constant and the leading one, constitutes a non-solvability condition of the respective potential. In this context, both the exact solvability of the quantum harmonic oscillator and the quasi-exact solvability of the sextic anharmonic oscillator stem naturally from the quotient polynomial, as in the first case, it is an energy-dependent constant, while in the second case, it is a second-degree binomial with no linear term. In all other cases, the quotient polynomial has at least one intermediate term, the presence of which makes the respective potential non-solvable.

**Category:** Mathematical Physics

[529] **viXra:1708.0254 [pdf]**
*replaced on 2017-12-21 07:37:10*

**Authors:** Robert B. Easter

**Comments:** 26 pages. Extended paper, extending the 10-page conference paper Double Conformal Space-Time Algebra (ICNPAA 2016; DOI:10.1063/1.4972658).

The G(4,8) Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra that extends the concepts introduced with the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) 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 G(1,3) Space-Time Algebra (STA). Two G(2,4) Conformal Space-Time subalgebras (CSTA) provide spacetime entities for points, hypercones, hyperplanes, hyperpseudospheres (and their intersections) 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. G(4,8) DCSTA is a doubling product of two orthogonal G(2,4) CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new 2-vector entities for general (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime surface entities that use the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in hyperpseudospheres. An operation for the directed non-uniform scaling (anisotropic dilation) of the 2-vector general quadric entities is defined using the boost operator and a spatial projection. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the Thomas-Wigner rotation and length contraction of special relativity. DCSTA is an algebra for computing with general quadrics and their inversive geometry in spacetime. For applications or testing, G(4,8) DCSTA can be computed using various software packages, such as the symbolic computer algebra system SymPy with the GAlgebra module.

**Category:** Mathematical Physics

[528] **viXra:1708.0254 [pdf]**
*replaced on 2017-12-03 03:13:32*

**Authors:** Robert B. Easter

**Comments:** 25 pages. Extended paper, extending the 10-page conference paper Double Conformal Geometric Algebra (ICNPAA 2016).

The G(4,8) Double Conformal Space-Time Algebra (DCSTA) is a high-dimensional 12D Geometric Algebra that extends the concepts introduced with the G(8,2) Double Conformal / Darboux Cyclide Geometric Algebra (DCGA) 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 G(1,3) Space-Time Algebra (STA). Two G(2,4) Conformal Space-Time subalgebras (CSTA) provide spacetime entities for points, hypercones, hyperplanes, hyperpseudospheres (and their intersections) 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. G(4,8) DCSTA is a doubling product of two orthogonal G(2,4) CSTA subalgebras that inherits doubled CSTA entities and versors from CSTA and adds new 2-vector entities for general (pseudo)quadrics and Darboux (pseudo)cyclides in spacetime that are also transformed by the doubled versors. The "pseudo" surface entities are spacetime surface entities that use the time axis as a pseudospatial dimension. The (pseudo)cyclides are the inversions of (pseudo)quadrics in hyperpseudospheres. An operation for the directed non-uniform scaling (anisotropic dilation) of the 2-vector general quadric entities is defined using the boost operator and a spatial projection. Quadric surface entities can be boosted into moving surfaces with constant velocities that display the Thomas-Wigner rotation and length contraction of special relativity. DCSTA is an algebra for computing with general quadrics and their inversive geometry in spacetime. For applications or testing, G(4,8) DCSTA can be computed using various software packages, such as the symbolic computer algebra system SymPy with the GAlgebra module.

**Category:** Mathematical Physics

[527] **viXra:1708.0226 [pdf]**
*replaced on 2018-04-20 05:33:43*

**Authors:** Vu B Ho

**Comments:** 6 Pages.

Investigations into the nature of the principle of least action have shown that there is an intrinsic relationship between geometrical and topological methods and the variational principle in classical mechanics. In this work, we follow and extend this kind of mathematical analysis into the domain of quantum mechanics. First, we show that the identification of the momentum of a quantum particle with the de Broglie wavelength in 2-dimensional space would lead to an interesting feature; namely the action principle δS=0 would be satisfied not only by the stationary path, corresponding to the classical motion, but also by any path. Thereupon the Bohr quantum condition possesses a topological character in the sense that the principal quantum number n is identified with the winding number, which is used to represent the fundamental group of paths. We extend our discussions into 3-dimensional space and show that the charge of a particle also possesses a topological character and is quantised and classified by the homotopy group of closed surfaces. We then discuss the possibility to extend our discussions into spaces with higher dimensions and show that there exist physical quantities that can be quantised by the higher homotopy groups. Finally we note that if Einstein’s field equations of general relativity are derived from Hilbert’s action through the principle of least action then for the case of n=2 the field equations are satisfied by any metric if the energy-momentum tensor is identified with the metric tensor, similar to the case when the momentum of a particle is identified with the curvature of the particle’s path.

**Category:** Mathematical Physics

[526] **viXra:1708.0184 [pdf]**
*replaced on 2017-09-18 07:37:47*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 11 Pages.

In a previous work I have derived the theory of everything (ToE) in a 74 pages paper. To make the theory more accessible, in this work, I derive the equation for the ToE on one page. I then follow the derivation with a few pages of discussion.

**Category:** Mathematical Physics

[525] **viXra:1708.0184 [pdf]**
*replaced on 2017-09-07 09:50:53*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 11 Pages.

In a previous work I have derived the theory of everything (ToE) in a 74 pages paper. To make the theory more accessible, in this work, I derive the equation for the ToE on one page. I then follow the derivation with a few pages of discussion.

**Category:** Mathematical Physics

[524] **viXra:1708.0149 [pdf]**
*replaced on 2017-09-09 17:23:30*

**Authors:** Alexandre Harvey-Tremblay

**Comments:** 39 Pages.

According to the second law of thermodynamics, a physical system will tend to increase its entropy over time. In this paper, I investigate a universal Turing machine (UTM) running multiple programs in parallel according to a scheduler. I found that if, over the course of the computation, the scheduler adjusts the work done on programs so as to maximize the entropy in the calculation of the halting probability Ω, the system will follow the laws of physics. Specifically, I show that the computation will obey algorithmic information theory (AIT) analogues to general relativity, entropic dark energy, the Schrödinger equation, a maximum computation speed analogous to the speed of light, the Lorentz's transformation, light cone, the Dirac equation for relativistic quantum mechanics, spins, polarization, etc. As the universe follows the second law of thermodynamics, these results would seem to suggest an affinity between an "entropic UTM" and the laws of physics.

**Category:** Mathematical Physics

[523] **viXra:1708.0147 [pdf]**
*replaced on 2017-08-28 07:33:28*

**Authors:** Harry Watson

**Comments:** 2 Pages.

Consider the product (4pi)(4pi-1/pi)(4pi-2/pi)(4pi-2/pi)(4pi-4/pi). The product of the first three terms is 1836.15. The product of the last two terms is 134.72. The mass ratio of the proton to the electron is 1836.15. We may sharpen the result by letting the last two terms be (4pi-3/pi)(4pi-4/pi) = 131.13. harry.watson@att.net

**Category:** Mathematical Physics

[522] **viXra:1708.0147 [pdf]**
*replaced on 2017-08-19 12:51:05*

**Authors:** Harry Watson

**Comments:** 2 Pages.

Consider the product (4pi)(4pi-1/pi)(4pi-2/pi)(4pi-2/pi)(4pi-4/pi). The product of the first three terms is 1836.15. The product of the last two terms is 134.72. The mass ratio of the proton to the electron is 1836.15. We may sharpen the result by letting the last two terms be (4pi-3/pi)(4pi-4/pi) = 131.13. harry.watson@att.net

**Category:** Mathematical Physics

[521] **viXra:1708.0031 [pdf]**
*replaced on 2017-09-17 22:28:49*

**Authors:** Hideki Mutoh

**Comments:** 6 Pages.

Dirac equation includes the 4 x 4 complex differential operator matrix, which is one of square roots of d' Alembertian with spin. We found another 4 x 4 complex differential matrix as a spinless square root of d' Alembertian, which we call diamond operator. The extended Maxwell's equations including charge creation-annihilation field and the linear gravitational field equations including energy creation-annihilation field can be simply written by using the diamond operator. It is shown that the linear gravitational field equations derive Klein-Gordon equation, time independent Schrödinger equation, and the principle of quantum mechanics.

**Category:** Mathematical Physics

[520] **viXra:1708.0031 [pdf]**
*replaced on 2017-08-04 07:06:47*

**Authors:** Hideki Mutoh

**Comments:** 5 Pages.

Dirac equation includes the 4 x 4 complex differential operator matrix, which is one of square roots of d' Alembertian with spin. We found another 4 x 4 complex differential matrix as a spinless square root of d' Alembertian, which we call diamond operator. The extended Maxwell's equations including charge creation-annihilation field and the linear gravitational field equations including energy creation-annihilation field can be simply written by using the diamond operator. It is shown that the linear gravitational field equations derive Klein-Gordon equation, time independent Schrödinger equation, and the principle of quantum mechanics.

**Category:** Mathematical Physics

[519] **viXra:1708.0011 [pdf]**
*replaced on 2017-10-03 00:04:34*

**Authors:** Hong Lai Zhu

**Comments:** 53 Pages.

In this paper, using proposed three new transformation methods we have solved general solutions and exact solutions of the problems of definite solutions of the Laplace equation, Poisson equation, Schrödinger equation, the homogeneous and non-homogeneous wave equations, Helmholtz equation and heat equation. In the process of solving, we find that in the more general case, general solutions of partial differential equations have various forms such as basic general solution, series general solution, transformational general solution, generalized series general solution and so on.

**Category:** Mathematical Physics

[518] **viXra:1708.0011 [pdf]**
*replaced on 2017-09-04 08:14:07*

**Authors:** Hong Lai Zhu

**Comments:** 53 Pages.

In this paper, using proposed three new transformation methods we have solved general solutions and exact solutions of the problems of definite solutions of the Laplace equation, Poisson equation, Schrödinger equation, the homogeneous and non-homogeneous wave equations, Helmholtz equation and heat equation. In the process of solving, we find that in the more universal case, general solutions of partial differential equations have various forms such as basic general solution, series general solution, transformational general solution, generalized series general solution and so on.

**Category:** Mathematical Physics