# Mathematical Physics

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## Recent submissions

Any replacements are listed farther down

[843] viXra:1903.0255 [pdf] submitted on 2019-03-13 16:31:06

### Resurrection of the Dead and the Organization of the Society of Electronic e-Beings.

Authors: Olga Lyubavina, Alexander Bolonkin

Alexander Bolonkin in his works [1-7] proposed methods of electronic immortality of modern people. He predicted the gradual replacement of biological humanity E-beings, considered their advantages and disadvantages (see List of references in given articles). The author considers methods and modern possibilities of resurrection of long-dead outstanding personalities. It also considers the principles and organization of the new E-society, its goals and conditions of existence.
Category: Mathematical Physics

[842] viXra:1903.0066 [pdf] submitted on 2019-03-04 19:51:11

### Observations of Structure of a Possible Unification Algebra

Authors: Robert G. Wallace

A C-loop algebra is found to have features that suggest it could provide an underlying basis for the standard model of fundamental particles.
Category: Mathematical Physics

[841] viXra:1903.0022 [pdf] submitted on 2019-03-01 10:37:45

### A New Solution of a Singular Quadratic Liénard Equation with Sundman and Lie Symmetry Analysis

Authors: Elémawussi Apédo Doutètien, Akim Boukola Yessoufou, Jean Akande, Marc Delphin Monsia

A fairly and simple exact solution of a well-known singular quadratic Liénard type equation is developed in this paper. The solution is compared with those obtained by Sundman and Lie Symmetry analysis. It is found that the result are in nice agreement.
Category: Mathematical Physics

[840] viXra:1902.0475 [pdf] submitted on 2019-02-27 12:50:06

### Cern no Longer up-to-Date: Back to the Big Bang is Nonsense!

Authors: Dan Visser

The universe never started with a Big Bang. In five original drawings is shown how an higher order universe, called the RTHU, an abbreviation of Rotating Torus Hologram Universe, generates a Big Bang universe as a hologram. This hologram seemingly fools us with an expanding universe increasingly faster. Remarkably the hologram is physically accepted as real reality, however, instead of a Big Bang generating a Big Bang-universe, the RTHU generates a lot of Big Bang holograms at the same time and shifted relative to each other. That is a different definition of parallel. It means these holograms enable transportation from one to the other. This is the future way for travelling without making use of relativistic space-time. In new technology we leave space-time, travel through the RTHU and calculate where to enter space-time again.
Category: Mathematical Physics

[839] viXra:1902.0398 [pdf] submitted on 2019-02-23 11:53:59

### On Highly Relativistic Deep Electrons

Authors: Jean-Luc Paillet, Andrew Meulenberg
Comments: Pages. to be published in JCMNS 2019

We address a number of questions relating to the progress of our study on the relativistic-electron deep orbits (EDOs): - How to combine different EM potentials having two possible versions (attractive and repulsive), while rejecting unrealistic energies? - What about the angular momentum of the deep electrons? How is the Heisenberg Uncertainty Relation satisfied in these EDOs? - From where is extracted the high kinetic energy (of order 100 MeV) of the deep-orbit electrons? - What is the behavior of the effective potential Veff as a function of distance to the nucleus? - What is the order of magnitude of the radiative corrections for the EDO’s? - What is the relation between EDO solutions of the Dirac equation and the high energy resonances (with high binding energies) corresponding to a semi-classical local minimum of energy?
Category: Mathematical Physics

[838] viXra:1902.0345 [pdf] submitted on 2019-02-20 10:08:07

### Memristor Circuit Equations with Periodic Forcing

Authors: Makoto Itoh

In this paper, we show that the dynamics of a wide variety of nonlinear systems such as engineering, physical, chemical, biological, and ecological systems, can be simulated or modeled by the dynamics of memristor circuits. It has the advantage that we can apply nonlinear circuit theory to analyze the dynamics of memristor circuits. Applying an external source to these memristor circuits, they exhibit complex behavior, such as chaos and non-periodic oscillation. If the memristor circuits have an integral invariant, they can exhibit quasi-periodic or non-periodic behavior by the sinusoidal forcing. Their behavior greatly depends on the initial conditions, the parameters, and the maximum step size of the numerical integration. Furthermore, an overflow is likely to occur due to the numerical instability in long-time simulations. In order to generate a non-periodic oscillation, we have to choose the initial conditions, the parameters, and the maximum step size, carefully. We also show that we can reconstruct chaotic attractors by using the terminal voltage and current of the memristor. Furthermore, in many memristor circuits, the active memristor switches between passive and active modes of operation, depending on its terminal voltage. We can measure its complexity order by defining the binary coding for the operation modes. By using this coding, we show that in the forced memristor Toda lattice equations, the memristor's operation modes exhibit the higher complexity. Furthermore, in the memristor Chua circuit, the memristor has the special operation modes.
Category: Mathematical Physics

[837] viXra:1902.0334 [pdf] submitted on 2019-02-21 02:18:14

### Spacetime Transcription of Physical Fields

Authors: Vu B Ho

In this work we discuss possible relationships between physical fields and substructures of the spatiotemporal manifold. We show that physical fields are possibly formed according to designed patterns from the substructures of spacetime in a process may be termed as spacetime transcription. We will formulate and illustrate how spacetime transcriptions can be formulated for the case of the electromagnetic and Dirac field. Even though the formulation in this work is rather suggestive, and a rigorous representation would require a comprehensive development in terms of geometrical and topological dynamics in differential geometry and topology, the work initiates a new approach to establishing intimate relationships between physical fields and spacetime structures.
Category: Mathematical Physics

[836] viXra:1902.0244 [pdf] submitted on 2019-02-13 15:54:17

### Higher Order Universe Saves Two Copies of the Hologram Universe

Authors: Dan Visser

It is possible to do it otherwise: I dared to transpose the dark mass-formula of Professor Erik Verlinde (UvA-NL) into my new universe-model, the RTHU, which is an abbreviation of Rotating Torus Hologram Universe. The RTHU generates the Big Bang Universe (BBU), or BBH in dutch, as a time-spatial hologram. In this setting the BBU is not fundamental, but originated from the RTHU. The RTHU is so to say more fundamental than the BBU and it that sense a ‘higher order universe’. All there is conservatively considered in the BBU is ruled by visible mass, inclusive the belonging coupled forces, and added with dark mass-dynamics and dark energy. However, in this article I show the transposition can lead to an unexpected result. The RTHU leaves a copy of the visible BBU-hologram behind at the open-torus-surface of the RTHU itself, as well as a copy within the light-horizon of black-holes. In this sense black-holes are to be transposed into the RTHU too, as I did. Moreover I show the RTHU needs dark energy for its rotation in order to drive the rotational BBU-hologram. Just as black-holes need dark energy to rotate in the RTHU. Conservatively black-holes are expected to exist in the BBU, but fundamentally considered black-holes are non-existential in the BBU and only reality as rotating black-holes in the RTHU. Inherently the Planck-boundary does not exist in the RTHU, as I described in my former article. Apparently, but theoretically, the two hologram-copies serve to secure the history of the Big Bang Hologram, which rotation causes future-changes in the RTHU and in the black-holes. These future changes seem to be verified in a natural way by the RTHU through the two hologram-copies. I don’t understand, why?
Category: Mathematical Physics

[835] viXra:1902.0205 [pdf] submitted on 2019-02-11 18:02:00

### Formula_of_force

Authors: Vatolin Dm.

В работе исследуется согласованность обычного релятивистского определения электромагнитной силы с простым механическим движением тел. Формулируются «парадоксы лоренцевой силы». Находится «формула силы», устраняющая парадоксы и приводящая к тем же кинематическим уравнениям для одиночной частицы, что и «старая теория». Находится, что и новая формула не может быть окончательной. Изменение формулы силы сказывается и на определении тензора энергии-импульса электромагнитного поля, и на определении релятивистского импульса тела
Category: Mathematical Physics

[834] viXra:1902.0165 [pdf] submitted on 2019-02-09 11:35:51

### On Forced Parallelism Within Characteristic States

Authors: Divyansh Mansukhani

Characteristic states are shown to necessitate at least one parallel state to fulfil basic normalization. For this, an operator to input arbitrary state is formulated using inner product between dependent states.
Category: Mathematical Physics

[833] viXra:1902.0143 [pdf] submitted on 2019-02-08 12:53:46

### Exact Smooth Solution for General Form of Navier-Stokes Equations

Authors: Sangwha Yi

In Wikipedia “Navier-Stokes existence and smoothness”, we discover the exact smooth solution for general form of Navier-Stokes Equations by Newton potential and timefunction.
Category: Mathematical Physics

[832] viXra:1902.0104 [pdf] submitted on 2019-02-06 08:19:07

### Physics Beyond Catching a Mouse in the Dark: from Big Science to Deep Science

Authors: Victor Christianto, Florentin Smarandache

The Higgs particle has been detected a few years ago, that is what newspapers tell us. For many physicists, the Standard Model of particle physics has accomplished all the jobs. Or to put it simply: The game is over. Is it true? Then some physicists began to ask: can go beyond the Standard Model? Because the supersymmetric extension of the Standard Model has failed. If you feel that theoretical physics is becoming boring, you are not alone. Fortunately, there is good news: a new generation of physicists are doing table-top experiments in their basements. Can we expect new results later?2 If so, what will the future of physics look like? This article discusses this question, starting with a blunt look at the relationship between mathematics and physical reality, written from the perspectives of a mathematician and a cosmologist.
Category: Mathematical Physics

[831] viXra:1902.0003 [pdf] submitted on 2019-02-01 00:12:19

### Explaining Planet Formation and the Initial Mass Function of Stars with a Universe Composed of Mathematics Plus re-Evaluation of the Mass-Gravity Relationship

Authors: Rodney Bartlett

This preprint is a never-print. It can never be printed in a science journal because that approach has often been tried, only to see the submission's ideas repeatedly rejected as too speculative and non-mathematical. Professor John Wheeler used to say the early papers on quantum mechanics were regarded as highly speculative. Nevertheless, editors of the 1920s published them (today's editors would be too timid). Maybe the maths in it doesn't qualify as maths since it isn't complicated (Einstein used to say a theory that can't be explained to a 6-year-old isn't really understood by its author). Or maybe editors believe the only real maths is the squiggly lines of algebra. The distribution of stellar masses at the birth of stars is called the Initial Mass Function or IMF. Why does the IMF favour the production of low-mass stars? There is a clue in the report that most planetary systems seem to outweigh the protoplanetary disks (PPDs) in which they formed, leaving astronomers to re-evaluate planet-formation theories. (AstroNews 2019) Science must always be free to question everything: even the long- established idea that mass is the cause of gravity (by, according to General Relativity (Einstein 1915), warping and curving space-time). Exploration of the reverse, that gravity forms mass, sounds absurd to modern science. Yet, it has the potential to explain planet formation and the IMF. This inverse mass-gravity relation uses the well-accepted idea that the universe is described mathematically, being flexible enough to extend that notion and suggest the universe IS maths. It could be produced by binary digits (base-2 maths) and topology, and the gravity that is the warping of space-time could interact with electromagnetism to form the quantum spin of matter particles (½) via vector-tensor-scalar geometry’s photonic spin of 1 being divided by the gravitonic spin of 2. This geometric attempt at understanding gravity may be seen as related to 4 earlier theories of gravity - Mordehai Milgrom’s 1983 Modified Newtonian Dynamics (MOND), its relativistic generalization known as Jacob Bekenstein’s 2004 Tensor–vector–scalar gravity (TeVeS), the TeVeS extension Bi-scalar tensor vector gravity (BSTV) proposed in 2005 by R.H.Sanders, and John Moffat’s 2006 Scalar–tensor–vector gravity (STVG).
Category: Mathematical Physics

[830] viXra:1901.0431 [pdf] submitted on 2019-01-28 22:50:29

### Generalized Fibonacci Numbers and 4k+1-Fold Symmetric Quasicrystals

Authors: Carlos Castro

Given that the two-parameter $p, q$ quantum-calculus deformations of the integers $[ n ]_{ p, q} = (p^n - q^n)/ ( p - q) = F_n$ coincide precisely with the Fibonacci numbers (integers), as a result of Binet's formula when $p = \tau = { 1 + \sqrt 5 \over 2}$, $q = { \tilde \tau} = { 1 - \sqrt 5 \over 2 }$ (Galois-conjugate pairs), we extend this result to the $generalized$ Binet's formula (corresponding to generalized Fibonacci sequences) studied by Whitford. Consequently, the Galois-conjugate pairs $(p, q = \tilde p ) = { 1\over 2} ( 1 \pm \sqrt m )$, in the very special case when $m = 4 k + 1$ and square-free, generalize Binet's formula $[ n ]_{ p, q} = G_n$ generating integer-values for the generalized Fibonacci numbers $G_n$'s. For these reasons, we expect that the two-parameter $(p, q = \tilde p)$ quantum calculus should play an important role in the physics of quasicrystals with $4k+1$-fold rotational symmetry.
Category: Mathematical Physics

[829] viXra:1901.0421 [pdf] submitted on 2019-01-28 09:38:50

### Exact Solution of Navier-Stokes Equations

Authors: Sangwha Yi

In Navier-Stokes equations, we discover the exact solution by Newton potential and time-function.
Category: Mathematical Physics

[828] viXra:1901.0395 [pdf] submitted on 2019-01-27 03:43:40

### Another View of the Origins of Real Space

Authors: Jan Makopa

This present presentation further explores the nature of Norms which i proposed in part one of this title. The mathematical primacy of the Norm Wave Function forms the foundation stone for the current work and on this basis we set out to erect a formalism of how real space manifests from directional singularities (also Norms).
Category: Mathematical Physics

[827] viXra:1901.0353 [pdf] submitted on 2019-01-24 08:20:12

### A Class of Singular Binomial Eigenvalue Equations

Authors: Elémawussi Apédo Doutètien, Akim Boukola Yessoufou, Kolawolé Kêgnidé Damien Adjaï, Marc Delphin Monsia

This paper shows that a class of binomial equation can be solved as an eigenvalue problem. The major finding is that the solution can be computed in terms of elementary functions.
Category: Mathematical Physics

[826] viXra:1901.0298 [pdf] submitted on 2019-01-19 17:56:09

### Self-Organization Generates Information

Authors: Udo E. Steinemann

Self-orgnization takes place in a specific kind of dynamical systems - e.g. from physics, chemistry or biology - which operate in the view of physics far from thermo-dynamical equilibrium searching for quasi-stable internal states. Such a system can be excited by a wide range of stimuli which it accepts together with influences from outside world as compact input for an internal reflection on its complete actual situation (taking into account the system's total history and actual situation as well). The reflection informs fluently about something that has been created completely new, the system produces information in the fullest sense of the word.
Category: Mathematical Physics

[825] viXra:1901.0260 [pdf] submitted on 2019-01-17 17:12:16

### The Planck-boundary Doesn't Exist

Authors: Dan Visser

My new universe-model, the RTHU, describes the holographical phase as an origin of a Big Bang-universe. This phase is wider acknowledged to exist, but the lay-out of it is nowhere described. In several of my articles I do describe that lay-out by crumbling the Planck-scale and locate it in the world of time smaller than Planck-time and duo-bits. I call that the RTHU, a new universe model. Thereby the after-glow of the Big Bang, the CMB, is no longer considered as the afterglow of the origin of the Big Bang, but considered as separate CMB-system in the RTHU, just like a galaxy or the Sun is. This opens the possibility possible to show the connection with proton-proton-reactions in the Sun, as well as neutrino-neutrino-reactions in galaxies and even duo-bits-reactions in that CMB-system. All are related to the principals of the RTHU, which means duo-bits are the building-stones of the holographical phase and vacuum-energy is variable instead of constant. In order to prove these proclamations the pure exact mass of the Big Bang-universe is needed, however, rather generated by an emergent Big Bang-universe from the RTHU than calculated by its age. In this article I did so. The mass of the emergent Big Bang-universe is 4.5334x10^53 kg instead of 5.68 x 10^53 kg published in lots of different other books or articles. Only in this way a cognitive connection with a holographical origin of the universe is proved in general.
Category: Mathematical Physics

[824] viXra:1901.0212 [pdf] submitted on 2019-01-15 12:07:09

### A Class of Non-autonomous and Nonlinear Singular Liénard Equations

Authors: Akim Boukola Yessoufou, Elémawussi Apédo Doutètien, Ayéna Vignon Régis Yehossou, Marc Delphin Monsia

A class of non-autonomous and nonlinear singular Liénard equation is developed by nonlocal transformation of the linear harmonic oscillator equation. It is shown that it includes some Kamke equations and a nonlinear equation of the general relativity as special cases.
Category: Mathematical Physics

[823] viXra:1901.0156 [pdf] submitted on 2019-01-11 06:19:52

### ¿What is a Strange Attractor?

Authors: Edgar Valdebenito

This note presents a Strange Attractor
Category: Mathematical Physics

[822] viXra:1901.0151 [pdf] submitted on 2019-01-11 07:25:46

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach
Comments: 8 Pages. continued from: viXra:1804.0068

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

[821] viXra:1901.0023 [pdf] submitted on 2019-01-02 07:04:34

### Chiral Solitons: A New Approach to Solitons Over Minkowski Space

Authors: Paul Werbos

This letter proposes a new approach to the unmet challenge of plausibly modeling the electron and other elementary particles as “solitons,” as stable vortices of force fields. This is the only alternative in Minkowski space to the usual model of charged elementary particles as perfect point particles, with an infinite Coulomb energy of self repulsion [1], requiring that elaborate systems of renormalization must be added to the fundamental definition of any quantum field theory. In 1926, Richard Feynmann wrote: “The shell game that we play is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate”.[2] This letter first summarizes previous approaches using topological solitons, and then motivates and outlines the new approach.
Category: Mathematical Physics

[820] viXra:1812.0438 [pdf] submitted on 2018-12-27 18:35:07

### Approximations

Authors: Harry Watson

The set of generating values, {(4 pi), (4 pi-1/pi), (4 pi-2/pi), (4 pi-3/pi), (4 pi-4/pi), (ln(4 pi))}, whose products can be used to approximate the mass ratios of the proton to the electron, the neutron to the electron, and the Higgs boson to the electron. For the proton-electron mass ratio there are several tri-axial ellipsoids whose volume is numerically close to that ratio. harry.watson@att.net
Category: Mathematical Physics

[819] viXra:1812.0293 [pdf] submitted on 2018-12-18 03:37:46

### Error Theory. in 1920, Brown of Norway 9 ＋ 9.～～In1966, 1＋2 Chen Jingrun, China

Authors: 1

Integer theory or fractional theory
Category: Mathematical Physics

[818] viXra:1812.0137 [pdf] submitted on 2018-12-07 10:21:12

### Null-Cone Integral Formulation of QFT

Authors: Julian Brown

In these preliminary notes we show that there exist null cone integral analogues of both the Dirac equation and the U(1) gauge field. We then explore a generalization of this idea through the introduction of a universal scalar, analogous to the lagrangian density of the Standard Model, from which all known particle equations of motion and interactions can be derived in principle, without recourse to either field derivatives or gauge degrees of freedom. The formulation suggests that at least some of the constants appearing in the Standard Model are related to cosmological quantities such as the total number and mass of particles on the past null cone, and that these are the origin of broken gauge symmetry.
Category: Mathematical Physics

[817] viXra:1812.0067 [pdf] submitted on 2018-12-05 04:31:50

### Einstein's Field Theory is Wrong and Nordstr\"om's Correct

Authors: Jorma Jormakka

Gunnar Nordstr\"om published his second gravitation theory in 1913. This theory is today considered to be inconsistent with observations. At this time Einstein was working on his field theory, the General Relativity Theory. Einstein's theory has been accepted as the only theory of gravitation consistent with measurements. The article reconsiders Nordstr\"om's theory and proves the following claims. 1) If gravitation is caused by a scalar field, then the theory is Nordstr\"om's second gravitation, which in a vacuum outside a point mass reduces to his first gravitation theory. Nordstr\"om's scalar field theory gives proper time values that fully agree with gravitational redshift in the Pound-Rebka experiment and with the Shapiro time delay in Shapiro's radar bouncing experiment. Gravitation in Schwarzschild's solution is not a field but a deformed geometry. If proper time is calculated via the General Relativity formula, Schwarzschild's solution fails both the Pound-Rebka redshift and Shapiro time delay tests because the ball in Schwarzschild's solution is deformed and light as measured by an external clock can exceed $c$. 2) The third classical tests of Einstein's theory is the movement of the perihelion of Mercury. Calculations from Schwarzschild's exact solution to Einstein's equations gave a correction that very well fitted the unexplained part of Mercury's movement. However, Schwarzschild's solution as a stationary solution it fails to explain why the orbit of Mercury, or any planet, is an ellipse. It is shown that the customary proof of Kepler's law stating that the orbit is an ellipse is incorrect: under a central stationary Newtonian force the orbit of a two mass system can only be a circle or (almost) a hyperbole because of conservation of energy. This observation invalidates the movement of Mercury as a test of General Relativity: Schwarzschild's solution cannot produce an elliptic orbit, therefore it is not the solution and that it gives a correct size modification to the movement of the perihelion is just a coincidence. Nordstr\"om's theory remains inconclusive in the Mercury test because calculating the orbit is difficult and cannot be done in this article. Nordstr\"om's theory, however, offers a possibility for explaining elliptic orbits: some energy is needed for waves in time-dependent solutions to Nordstr\"om's field equation and this loss of potential energy from the radial potential can lead to elliptic orbits. 3) The fourth classical test is the light bending test. Light bends in Nordstr\"om's theory as light behaves as a test mass in a gravitational field. Calculation of the amount of light bending in Norstrs\"om's theory is similar to calculation of the orbit of planets and beyond the scope of this article. Theoretical consideration of bending of light leads to the conclusion that the stress-energy tensor in the General Relativity is incorrect: the diagonal entries should contain the energy of a stationary gravitational field in the vacuum outside a point mass and therefore diagonal Ricci tensor entries cannot be zeroes. Nordstr\"om's theory passes this theoretical consideration while Einstein's theory fails it.
Category: Mathematical Physics

[816] viXra:1812.0031 [pdf] submitted on 2018-12-02 19:34:05

### Any Even Number Greater Than 2 Must be the Sum of Two Prime

Authors: Tangyin Wu Ye

Abstract simulation,basiclogicof synchronization algorithm, reasoning judgment and hypothesis contradiction [integer theory]
Category: Mathematical Physics

[815] viXra:1811.0453 [pdf] submitted on 2018-11-27 13:17:04

### The Lueverian Model and Easonian Theorem

Authors: Savior F. Eason

Proposes a mathematical formula for measuring and calculating in hyper-space, as well as a theorem for calculating the mandelbrot set of Quantum information making up our universe.
Category: Mathematical Physics

[814] viXra:1811.0428 [pdf] submitted on 2018-11-26 09:54:21

### On the Pythagoras’ and De Gua’s Theorems in Geometric Algebra

Authors: Miroslav Josipović

This small article is intended to be a contribution to the LinkedIn group “Pre-University Geometric Algebra”. The main idea is to show that in geometric algebra we have the Pythagoras’ and De Gua’s theorems without a metric defined. This allows us to generalize these theorems to any dimension and any signature.
Category: Mathematical Physics

[813] viXra:1811.0381 [pdf] submitted on 2018-11-23 06:42:56

### A Poincare Conformal Matrix Lie Algebra

Authors: Richard Shurtleff

The Poincar\'{e} group of spacetime rotations and spacetime translations has been fundamental for over a century. Also a century old are efforts to find alternatives, efforts that include invoking the larger symmetry group of Maxwell's electrodynamics, the conformal group. In this paper an 8x8 matrix representation of the Poincare group is enhanced by defining a 4x4 matrix rep of the conformal group that acts on 4 of the 8 dimensions, a 4-spinor subset of 8-spinors. The matrix generators are described in detail and the commutation relations of the Lie algebra are displayed. There are additional generators needed to keep the enhanced algebra closed. The new generators add new transformations making a group larger than the direct product of the Poincare and conformal groups.
Category: Mathematical Physics

[812] viXra:1811.0373 [pdf] submitted on 2018-11-23 23:21:08

### A Method for Detecting Lagrangian Coherent Structures (LCSs) using Fixed Wing Unmanned Aircraft System (UAS)

Authors: Peter J. Nolan, Hunter McClelland, Craig Woolsey, Shane D. Ross
Comments: 25 Pages. In preparation for journal submission

The transport of material in the atmosphere is a problem with important implications for agriculture, aviation, and human health. Given the turbulent nature of the atmosphere it can be difficult to predict where a particle, such as a plant pathogen, will wind up. Tools from dynamical systems theory, such as Lagrangian coherent structures (LCSs), can help us to understand how particles in a flow will evolve. The study of atmospheric transport from a dynamical systems perspective has long focused on the study of large scale phenomena. This has been largely due to the larger scale grid spacing of readily available atmospheric model data and the lack of high resolution atmospheric measurements on a scale large enough to calculate Lagrangian data. Furthermore, few works have attempted to find ways to detect LCSs in the field. In the authors used wind velocity measurements from a dopler LiDAR to detect LCS which had passed through Hong Kong International Airport. Rather than measure the wind velocity to try and detect LCSs, the authors in looked at sudden changes in pathogen concentrations in the atmosphere. They were then able to link those changes to the passage of LCSs using atmospheric velocity data from the North American Mesoscale (NAM) model. Yet to date, we are unaware of any attempts to develop a means of directly sense LCSs which could be readily implemented by operators in the field. Recent advances in dynamical systems theory, such as new Eulerian diagnostics, and new atmospheric sensing technology, such as unmanned aircraft systems (UAS), have brought the local detection of LCSs within reach.
Category: Mathematical Physics

[811] viXra:1811.0363 [pdf] submitted on 2018-11-24 05:07:10

### About Non-Closedness of the Three-Dimensional Navier-Stokes Equations System for the Viscous Incompressible Fluid

Authors: Preobrazhenskiy Andrey

ABSTRACT. In this paper it is shown that the system of four equations formed by three-dimensional Navier-Stokes equations system for incompressible fluid and equation of continuity, is not closed, equation of continuity is excessive. This is because the three-dimensional Navier-Stokes equations system cannot have a bounded at infinity solutions to the Cauchy problem with a non-zero velocity field divergence.
Category: Mathematical Physics

[810] viXra:1811.0357 [pdf] submitted on 2018-11-22 09:55:14

### A Factorial Identity Resulting from the Orthogonality Relation of the Associated Laguerre Polynomials

Authors: Spiros Konstantogiannis

Plugging the closed-form expression of the associated Laguerre polynomials into their orthogonality relation, the latter reduces to a factorial identity that takes a simple, non-trivial form for even-degree polynomials.
Category: Mathematical Physics

[809] viXra:1811.0289 [pdf] submitted on 2018-11-18 09:39:36

### The Mathematical Octal Numbering System(not Computing Numbering System)

In this paper we will talk about I numbering system I want to invent which is based on the knowledge of true and false being 1 and 0 (true and false) Lets take a look at our hands it has 10 fingers which uses the decimal system its ok Lets take out the true and false which are the 1 and 0 (one and zero) from the decimal system leaving eight numbers which are 2 3 4 5 6 7 8 9 but first lets take a look at how I thought of this These are 10 mathematical stuff made from 1 and 0 or the true and false below 1*1/1*1=1(true fact or something) 1*0/1*1=0 0*1/1*1=0 0*0/1*1=0 1*1/0*0=not understood 1*1/1*0=not understood 1*1/0*1=not understood 0*1/0*0=not understood 1*0/0*0= not understood 0*0/0*0= totally not understood When looking at this you see that if you take the true and false which are 1*1/1*1=1 and 0*0/0*0=totally not understood you are left with 8 of the 10 Now to see how you can apply this new numbering system you should look at what follows Lets start counting in this numbering system with 2 and end with 8 so we say 2 3 4 5 6 7 8 9 Lets do this mathematical trick 2*3*4*5/6=120/6=20 which is 2*10=20 Lets try an easier one which is 3*4*5/6=60/6=10 you see the trick? Adding a truth to false and another truth(which is my theory!!!!) which all amounts to 3 (2 truths and one false) which starts with 3 in this one you get to the numbering system in your hand or 10 in the second easier mathematical trick and also in the mathematical trick starting with 2 ends with 20 which when divided by 10 you get 2 which is the number you started with!!!!!
Category: Mathematical Physics

[808] viXra:1811.0036 [pdf] submitted on 2018-11-02 10:41:52

### Incompatibility of the Dirac-Like Field Operators with the Majorana Anzatzen

Authors: Valeriy V. Dvoeglazov
Comments: 19 Pages. Extended version of viXra:1809.0241 to include spin 1.

In the present article we investigate the spin-1/2 and spin-1 cases in different bases. Next, we look for relations with the Majorana-like field operator. We show explicitly incompatibility of the Majorana anzatzen with the Dirac-like field operators in both the original Majorana theory and its generalizations. Several explicit examples are presented for higher spins too. It seems that the calculations in the helicity basis give mathematically and physically reasonable results only.
Category: Mathematical Physics

[807] viXra:1810.0502 [pdf] submitted on 2018-10-30 18:06:51

### Short Note on Unification of Field Equations and Probability

Authors: Mesut Kavak

Is math in harmony with existence? Is it possible to calculate any property of existence over math? Is exact proof of something possible without pre-acceptance of some physical properties? This work is realized to analysis these arguments somehow as simple as possible over short cuts, and it came up with some compatible results finally. It seems that both free space and moving bodies in this space are dependent on the same rule as there is no alternative, and the rule is determined by mathematics
Category: Mathematical Physics

[806] viXra:1810.0467 [pdf] submitted on 2018-10-29 02:08:45

### The Imaginary Norm

Authors: Jan Makopa

It is known that the direction of rotation of a position vector in Polar Coordinates is not continuous for angles ʘ = π(a + 1/2). The fallacy has algebraic origins and as a increases, the direction of the position vector at ʘ is oscillating between two opposite discontinuous points we shall call Norms . The pertinent Literature can be argued, as has been done by others in the past that – the direction of a position vector at ʘ cannot be real thence must carry an imaginary component also to justify the occurrence of discontinuities along the Polar plane. To understand how Norms oscillate, we propose the “Norm Wave Function” whose exposition we give herein is based on the geometric expansion of Norms. The once speculative Mohammed Abubakr- proposition on Calpanic Numbers, can now find full justification as a fully-fledged proposition. At the end of it all our contribution in the present work – if any; is that we demonstrate that the hypothetical Norm proposed herein, is imaginary and Norms carry unique properties that may have the potential for strong application in Quantum Theory of the Spinning Photon. This current text is part one of two. This text is a proposition of a Norm Wave Function and it discusses the philosophy behind the discontinuities of rotations while part two will apply the formulation in Quantum Mechanics of Spinning Photons.
Category: Mathematical Physics

[805] viXra:1810.0458 [pdf] submitted on 2018-10-27 13:21:47

### Methods for Derivation of Generalized Equations in the (S,0)+(0,S) Representations of the Lorentz Group

Authors: Valeriy V. Dvoeglazov
Comments: 13 Pages. Some parts of this paper have been presented at the XI Escuela de DGFM SMF, Dec. 5-9, 2016, Playa del Carmen, QRoo, M\'exico, the IARD2018, June 4-7, 2018, M\'erida, Yuc., M\'exico and the MG15 Meeting, July 1-7, Rome, Italy.

We continue the discussion of several explicit examples of generalizations in relativistic quantum mechanics. We discussed the generalized spin-1/2 equations for neutrinos and the spin-1 equations for photon. The equations obtained by means of the Gersten-Sakurai method and those of Weinberg for spin-1 particles have been mentioned. Thus, we generalized the Maxwell and Weyl equations. Particularly, we found connections of the well-known solutions and the dark 4-spinors in the Ahluwalia-Grumiller elko model. They are also not the eigenstates of the chirality and helicity. The equations may lead to the dynamics which are different from those accepted at the present time. For instance, the photon may have non-transverse components and the neutrino may be {\it not} in the energy states and in the chirality states. The second-order equations have been considered too. They have been obtained by the Ryder method.
Category: Mathematical Physics

[804] viXra:1810.0435 [pdf] submitted on 2018-10-25 06:20:51

### Yang-Mills Theory is the Typical Form of Torsion Tensor

Authors: Wan-Chung Hu

In the single page of this article, I stated that Yang-Mills theory (the foundation of standard model) is actually the typical form of torsion tensor. Since electromagnetic field is also the torsion tensor without the [x,y] part. We can easily unite strong force field, weak force field, and electromagnetic field by integrating these torsion tensors. This provides the proof of Yang-Mills theory existence. And, I also solved Yang-Mills mass gap problem in strong interaction in my previous study. Thus, the grand unified theories can be finished.
Category: Mathematical Physics

[803] viXra:1810.0403 [pdf] submitted on 2018-10-25 02:40:01

### The Formulation Of Thermodynamical Path Integral

Authors: Takahiro Kajisa

In a non-equilibrium thermodynamical physics, there has been al- most no universal theory for representing the far from equilibrium sys- tems. In this work, I formulated the thermodynamical path integral from macroscopic view, using the analogy of optimal transport and large deviations to calculate the non-equilibrium indicators quantita- tively. As a result, I derived Jarzynski equality, fluctuation theorem, and second law of thermodynamics as its corollaries of this formula. In addition, the latter result implies the connection between non- equilibrium thermodynamics and Riemannian geometry via entropic flow.
Category: Mathematical Physics

[802] viXra:1810.0386 [pdf] submitted on 2018-10-23 12:05:16

### New Universe Model, Evidence and Future.

Authors: Dan Visser

In this article an overview-abstract is given about a new universe model according to a series articles by the author, wherein he describes step by step in rather easy mathematics and not affiliated to the university-world, how he came to his new cosmological model. The overview-abstract contains an amount of subjects being found important for a better understanding of his new model in addition to his former articles. His articles are hosted in the viXra-archive in the UK and free to read. The new universe model is called RTHU instead of Big Bang. The main issue is that the RTHU generates the Big Bang-universe, although at the same time the RTHU also contains a lot of other Big Bang-universes shifted relative to each other, however all generated by the RTHU. The generator is the rotation of the RTHU, which has no beginning of time, but uses duo-bits to crumble the Planck-scale. The RTHU therefore is much bigger than a single self-supporting Big Bang-universe. The total new dynamics give other insights in unsolved problems, but make it possible to understand several phenomena better than solving them just only in a single Big Bang-universe. The author pleads for physics and cosmology in the token of the RTHU. Therefore evidence is available, which has been already presented in several of his articles. Moreover it will pinpoint the future for cosmology in a better way. He describes a new perception of time and future. The author also launches a new insight, based on his new cosmological model, which not has been earlier being involved in the problems around climate-change.
Category: Mathematical Physics

[801] viXra:1810.0300 [pdf] submitted on 2018-10-20 04:55:25

### Topological Transformation of Quantum Dynamics

Authors: Vu B Ho

In this work we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. A rigorous approach would be a complete formulation of wave dynamics on two and three-dimensional geometries that are classified according to the uniformisation theorem of Riemannian surfaces and the Thurston geometrisation conjecture on three-dimensional differentiable manifolds. However, for the purpose of physical illustration, we will follow a modest approach in which we will present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. The wave dynamics on a circle can also be described in terms of projective elliptic geometry. Since a circle is a 1-sphere which is also a 1-torus therefore the Bohr model of the hydrogen atom can also be viewed as a standing wave on a 1-torus. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In particular, we show that when the wave dynamics on a projective plane is described in terms of projective elliptic geometry then it is identical to the wave dynamics on a 2-sphere. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K×S^1 defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube therefore in three-dimensions the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K×S^1. We also discuss a transformation of a stationary wave on the fundamental cube into a stationary wave on a 3-sphere despite it still remains unknown whether a 3-sphere can be constructed directly from a cube by gluing its opposite faces. In spite of this uncertainty, however, we speculate that mathematical degeneracy in which an element of a class of objects degenerates into an element of a different but simpler class may play an important role in quantum dynamics. For example, a 2-sphere is a degenerate 2-torus when the axis of revolution passes through the centre of the generating circle. Therefore, it seems reasonable to assume that if an n-torus degenerates into an n-sphere then wavefunctions on an n-torus may also be degenerated into wavefunctions on an n-sphere. Furthermore, since an n-sphere can degenerate itself into a single point, therefore the mathematical degeneracy may be related to the concept of wavefunction collapse in quantum mechanics where the classical observables such as position and momentum can only be obtained from the collapse of the associated wavefunctions for physical measurements. This consideration suggests that quantum particles associated with differentiable manifolds may possess the more stable mathematical structures of an n-torus rather than those of an n-sphere.
Category: Mathematical Physics

[800] viXra:1810.0274 [pdf] submitted on 2018-10-17 13:33:42

### Universe is a Solid Elastic Continuum.

Authors: Alexander I.Dubinyansky, Pavel Churlyaev.

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

[799] viXra:1810.0263 [pdf] submitted on 2018-10-16 07:43:15

### Semistable Holomorphic Bundles Over Compact bi-Hermitian Manifolds

Authors: Pan Zhang

In this paper, by using Uhlenbeck-Yau's continuity method, we prove that the existence of approximation $\alpha$-Hermitian-Einstein strusture and the $\alpha$-semi-stability on $I_{\pm}$-holomorphic bundles over compact bi-Hermitian manifolds are equivalent.
Category: Mathematical Physics

[798] viXra:1810.0181 [pdf] submitted on 2018-10-11 16:51:13

### The Task of the Panrelativistic Discrete Wave Mechanics

Authors: I. M. Saharov, G. I. Saharov

The paper presents a mathematical study of sub-nuclear particles (nucleons) by a singular mathematical structure, which is a unique compatibility of singular integers with their binding functions, demonstrating the connection of the transcendent and integer, continuous and discrete. The four-dimensional space-time was tested to find the original effective unit, the coefficients of the dominant angles and the main singular number. Representation of a particle as a spatial wave objects (rotating waves) made it possible to find geometric and numeric expressions to their relative mass in units of electron mass with a precision within the limits of the uncertainty principle. Submitted to the consideration of the law effective wave of the relationships governing the stability of subnuclear particles. An approximate expression of the ratio of the magnetic moments of nucleons in vector form based on the ratio of the functions of dominant angles is shown.
Category: Mathematical Physics

[797] viXra:1810.0157 [pdf] submitted on 2018-10-10 07:45:13

### Dirichlet Problem for Hermitian-Einstein Equations Over bi-Hermitian Manifolds

Authors: Pan Zhang

In this paper, we solve the Dirichlet problem for $\alpha$-Hermitian-Einstein equations on $I_{\pm}$-holomorphic bundles over bi-Hermitian manifolds. As a corollary, we obtain an analogue result about generalized holomorphic bundles on generalized K\"{a}hler manifolds.
Category: Mathematical Physics

[796] viXra:1810.0146 [pdf] submitted on 2018-10-09 10:40:20

### A New Trigonometric Function Solution with Amplitude-Dependent Frequency for the Linear Harmonic Oscillator Equation

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

It is well known that amplitude-dependent frequency features only nonlinear dynamical systems. This paper shows that, however, within the framework of the theory of nonlinear differential equations introduced recently by the authors of this work, such a property may also characterize the linear harmonic oscillator equation. In doing so it has been found as another major result that the linear harmonic oscillator is nothing but the nonlocal transformation of equation of the free particle motion under constant forcing function.
Category: Mathematical Physics

[795] viXra:1810.0116 [pdf] submitted on 2018-10-07 08:50:44

### Identity Featuring Gamma Function: Ramanujan's Integration

Authors: Amit Kumar Jha

In this short 3 page Pdf I am giving you method to prove Ramanujan's identity
Category: Mathematical Physics

[794] viXra:1809.0599 [pdf] submitted on 2018-09-30 10:53:19

### The Mathematical Principles of the Scale Relativity Physics I. History and Physics

Authors: Nicolae Mazilu, Maricel Agop

Even though a physical theory, the Scale Relativity Theory (SRT) means more than physics, as its creator noticed himself. In fact it targets the very foundation of the entire positive knowledge, and we are set here to prove this fact. Mathematically one needs the description of a transition between infrafinite, finite and transfinite orders, while physically one needs a transition between microcosmos, daily world (quotidian cosmos) and universe. With SRT the mathematical categories of infrafinite, finite and transfinite, become differentias of the same general concept of ‘finite’. As it turns out, there is a parallelism of the physical transition between the worlds and the mathematical transition between degrees of ‘finite’: it is followed here historically and logically, in a first part of the present work, with the benefit of extracting the mathematical principles of a physical description of matter.
Category: Mathematical Physics

[793] viXra:1809.0450 [pdf] submitted on 2018-09-20 16:03:08

### How Gas and Force Work Together to Create Geometrical Dispersed Patterns Based On an Object's Shape

Authors: Andrew Dente

This unique mathematical method for understanding the flow of gas through each individual objects shape will show us how we can produce physical functions for each object based on the dissemination of gas particles in accordance to its shape. We analyze its continuum per shape of the object and the forces acting on the gas which in return produces its own unique function for the given object due to the rate at which forces were applied to the gas. We also get to examine the different changes in the working rate due to the effect of its volume and mass from the given objects shape with our working equation discovered through green’s and gaussian functions.
Category: Mathematical Physics

## Replacements of recent Submissions

[657] viXra:1903.0066 [pdf] replaced on 2019-03-05 21:14:17

### Observations of a Possible Unification Algebra

Authors: Robert G Wallace

A C-loop algebra is found to have features that suggest it could provide an underlying basis for the standard model of fundamental particles.
Category: Mathematical Physics

[656] viXra:1902.0398 [pdf] replaced on 2019-03-02 03:26:20

### On Highly Relativistic Deep Electrons

Authors: Jean-Luc Paillet, Andrew Meulenberg
Comments: 16 Pages. To be published in JCMNS 29 (2019)

We address a number of questions relating to the progress of our study on the relativistic-electron deep orbits (EDOs): - How to combine different EM potentials having two possible versions (attractive and repulsive), while rejecting unrealistic energies? - What about the angular momentum of the deep electrons? How is the Heisenberg Uncertainty Relation satisfied in these EDOs? - From where is extracted the high kinetic energy (of order 100 MeV) of the deep-orbit electrons? - What is the behavior of the effective potential Veff as a function of distance to the nucleus? - What is the order of magnitude of the radiative corrections for the EDO’s? - What is the relation between EDO solutions of the Dirac equation and the high energy resonances (with high binding energies) corresponding to a semi-classical local minimum of energy?
Category: Mathematical Physics

[655] viXra:1902.0345 [pdf] replaced on 2019-02-24 19:26:10

### Memristor Circuit Equations with Periodic Forcing

Authors: Makoto Itoh

In this paper, we show that the dynamics of a wide variety of nonlinear systems such as engineering, physical, chemical, biological, and ecological systems, can be simulated or modeled by the dynamics of memristor circuits. It has the advantage that we can apply nonlinear circuit theory to analyze the dynamics of memristor circuits. Applying an external source to these memristor circuits, they exhibit complex behavior, such as chaos and non-periodic oscillation. If the memristor circuits have an integral invariant, they can exhibit quasi-periodic or non-periodic behavior by the sinusoidal forcing. Their behavior greatly depends on the initial conditions, the parameters, and the maximum step size of the numerical integration. Furthermore, an overflow is likely to occur due to the numerical instability in long-time simulations. In order to generate a non-periodic oscillation, we have to choose the initial conditions, the parameters, and the maximum step size, carefully. We also show that we can reconstruct chaotic attractors by using the terminal voltage and current of the memristor. Furthermore, in many memristor circuits, the active memristor switches between passive and active modes of operation, depending on its terminal voltage. We can measure its complexity order by defining the binary coding for the operation modes. By using this coding, we show that the memristor's operation modes exhibit the higher complexity, in the forced memristor Toda lattice equations and the forced memristor Van der Pol equations. Furthermore, the memristor has the special operation modes in the memristor Chua circuit.
Category: Mathematical Physics

[654] viXra:1902.0205 [pdf] replaced on 2019-03-11 18:38:14

### Formula of Force

Authors: Vatolin Dm.

The paper investigates the consistency of the usual relativistic definition of electromagnetic force with a simple mechanical movement of bodies. “Paradoxes of Lorentz force” are formulated. The “formula of force” is found, eliminating paradoxes and leading to the same kinematic equations for a single particle as the “old theory”. It is found that the new formula can not be final. The change in the force formula affects both the determination of the energy-momentum tensor of the electromagnetic field and the definition of the relativistic body momentum
Category: Mathematical Physics

[653] viXra:1902.0205 [pdf] replaced on 2019-02-21 20:34:51

### Formula of Force

Authors: Vatolin Dm.

В работе исследуется согласованность обычного релятивистского определения электромагнитной силы с простым механическим движением тел. Формулируются «парадоксы лоренцевой силы». Находится «формула силы», устраняющая парадоксы и приводящая к тем же кинематическим уравнениям для одиночной частицы, что и «старая теория». Находится, что и новая формула не может быть окончательной. Изменение формулы силы сказывается и на определении тензора энергии-импульса электромагнитного поля, и на определении релятивистского импульса тела
Category: Mathematical Physics

[652] viXra:1902.0143 [pdf] replaced on 2019-03-08 20:46:24

### Exact Smooth Solution for General Form of Navier-Stokes Equations

Authors: Sangwha Yi

In Wikipedia “Navier-Stokes existence and smoothness”, we discover the exact smooth solution for general form of Navier-Stokes Equations by Newton potential and timefunction.
Category: Mathematical Physics

[651] viXra:1901.0212 [pdf] replaced on 2019-01-17 10:26:56

### A Class of Non-autonomous and Nonlinear Singular Liénard Equations

Authors: Akim Boukola Yessoufou, Elémawussi Apédo Doutètien, Ayéna Vignon Régis Yehossou, Marc Delphin Monsia

A class of non-autonomous and nonlinear singular Liénard equation is developed by nonlocal transformation of the linear harmonic oscillator equation. It is shown that it includes some Kamke equations and a nonlinear equation of the general relativity as special cases.
Category: Mathematical Physics

[650] viXra:1901.0151 [pdf] replaced on 2019-03-16 10:11:46

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach

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

[649] viXra:1901.0151 [pdf] replaced on 2019-03-05 10:48:07

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach

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

[648] viXra:1901.0151 [pdf] replaced on 2019-02-25 05:45:25

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach
Comments: 9 Pages. Minor correction as to the non-relativistic limit of interacting particles.

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

[647] viXra:1901.0151 [pdf] replaced on 2019-02-07 04:46:10

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach

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

[646] viXra:1901.0151 [pdf] replaced on 2019-01-23 05:15:59

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach

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

[645] viXra:1901.0151 [pdf] replaced on 2019-01-13 14:02:11

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach

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

[644] viXra:1901.0023 [pdf] replaced on 2019-01-02 07:33:40

### Chiral Solitons: A New Approach to Solitons Over Minkowski Space

Authors: Paul Werbos

This letter proposes a new approach to the unmet challenge of plausibly modeling the electron and other elementary particles as “solitons,” as stable vortices of force fields. This is the only alternative in Minkowski space to the usual model of charged elementary particles as perfect point particles, with an infinite Coulomb energy of self repulsion [1], requiring that elaborate systems of renormalization must be added to the fundamental definition of any quantum field theory. Richard Feynmann has written: “The shell game that we play is technically called 'renormalization'. But no matter how clever the word, it is still what I would call a dippy process! Having to resort to such hocus-pocus has prevented us from proving that the theory of quantum electrodynamics is mathematically self-consistent. It's surprising that the theory still hasn't been proved self-consistent one way or the other by now; I suspect that renormalization is not mathematically legitimate”.[2] This letter first summarizes previous approaches using topological solitons, and then motivates and outlines the new approach.
Category: Mathematical Physics

[643] viXra:1811.0373 [pdf] replaced on 2019-02-06 23:48:53

### A Method for Detecting Lagrangian Coherent Structures (LCSs) using Fixed Wing Unmanned Aircraft System (UAS)

Authors: Peter J. Nolan, Hunter McClelland, Craig Woolsey, Shane D. Ross

The transport of material through the atmosphere is an issue with wide ranging implications for fields as diverse as agriculture, aviation, and human health. Due to the unsteady nature of the atmosphere, predicting how material will be transported via Earth's wind field is challenging. Lagrangian diagnostics, such as Lagrangian coherent structures (LCSs), have been used to discover the most significant regions of material collection or dispersion. However, Lagrangian diagnostics can be time consuming to calculate and often rely on weather forecasts that may not be completely accurate. Recently, Eulerian diagnostics have been developed which can provide indications of LCS and have computational advantages over their Lagrangian counterparts. In this paper, a methodology is developed for estimating local Eulerian diagnostics from wind velocity data measured by a fixed wing unmanned aircraft system (UAS) flying in circular arcs. Using a simulation environment, it is shown that the Eulerian diagnostic estimates from UAS measurements approximate the true local Eulerian diagnostics, therefore also predicting the passage of LCSs. This methodology requires only a single flying UAS, making it more easy to implement in the field than existing alternatives.
Category: Mathematical Physics

[642] viXra:1811.0363 [pdf] replaced on 2018-12-16 05:44:46

### About Non-Closedness of the Three-Dimensional Navier-Stokes Equations System for the Viscous Incompressible Fluid

Authors: Preobrazhenskiy Andrey

In this paper it is shown that the system of four equations formed by three-dimensional Navier-Stokes equations system for incompressible fluid and equation of continuity, is not closed, equation of continuity is excessive. This is because the three-dimensional Navier-Stokes equations system cannot have a bounded at infinity solutions to the Cauchy problem with a non-zero velocity field divergence.
Category: Mathematical Physics

[641] viXra:1811.0357 [pdf] replaced on 2018-11-28 03:57:18

### A Factorial Identity Resulting from the Orthogonality Relation of the Associated Laguerre Polynomials

Authors: Spiros Konstantogiannis

Plugging the closed-form expression of the associated Laguerre polynomials into their orthogonality relation, the latter reduces to a factorial identity that takes a simple, non-trivial form for even-degree polynomials.
Category: Mathematical Physics

[640] viXra:1810.0502 [pdf] replaced on 2018-11-11 06:27:01

### Short Note on Unification of Field Equations and Probability

Authors: Mesut Kavak

Is math in harmony with existence? Is it possible to calculate any property of existence over math? Is exact proof of something possible without pre-acceptance of some physical properties? This work is realized to analysis these arguments somehow as simple as possible over short cuts, and it came up with some compatible results finally. It seems that both free space and moving bodies in this space are dependent on the same rule as there is no alternative, and the rule is determined by mathematics.
Category: Mathematical Physics

[639] viXra:1810.0502 [pdf] replaced on 2018-11-06 10:08:35

### Short Note on Unification of Field Equations and Probability

Authors: Mesut Kavak

Is math in harmony with existence? Is it possible to calculate any property of existence over math? Is exact proof of something possible without pre-acceptance of some physical properties? This work is realized to analysis these arguments somehow as simple as possible over short cuts, and it came up with some compatible results finally. It seems that both free space and moving bodies in this space are dependent on the same rule as there is no alternative, and the rule is determined by mathematics.
Category: Mathematical Physics

[638] viXra:1810.0502 [pdf] replaced on 2018-11-02 09:02:35

### Short Note on Unification of Field Equations and Probability

Authors: Mesut Kavak

Is math in harmony with existence? Is it possible to calculate any property of existence over math? Is exact proof of something possible without pre-acceptance of some physical properties? This work is realized to analysis these arguments somehow as simple as possible over short cuts, and it came up with some compatible results finally. It seems that both free space and moving bodies in this space are dependent on the same rule as there is no alternative, and the rule is determined by mathematics.
Category: Mathematical Physics

[637] viXra:1810.0502 [pdf] replaced on 2018-11-01 13:01:26

### Short Note on Unification of Field Equations and Probability

Authors: Mesut Kavak

Is math in harmony with existence? Is it possible to calculate any property of existence over math? Is exact proof of something possible without pre-acceptance of some physical properties? This work is realized to analysis these arguments somehow as simple as possible over short cuts, and it came up with some compatible results finally. It seems that both free space and moving bodies in this space are dependent on the same rule as there is no alternative, and the rule is determined by mathematics.
Category: Mathematical Physics

[636] viXra:1810.0502 [pdf] replaced on 2018-10-31 07:34:22

### Short Note on Unification of Field Equations and Probability

Authors: Mesut Kavak

Is math in harmony with existence? Is it possible to calculate any property of existence over math? Is exact proof of something possible without pre-acceptance of some physical properties? This work is realized to analysis these arguments somehow as simple as possible over short cuts, and it came up with some compatible results finally. It seems that both free space and moving bodies in this space are dependent on the same rule as there is no alternative, and the rule is determined by mathematics.
Category: Mathematical Physics

[635] viXra:1810.0467 [pdf] replaced on 2019-01-27 03:36:34

### The Imaginary Norm

Authors: Jan Makopa

It is known that the direction of a position vectors located along the imaginary dimension of the Euler coordinate system distorts the symmetry of the Euler cycle. The pertinent Literature in context has algebraic origins but yet can be argued as has been done by others in the past that – the direction of the singularities cannot be real and therefore must carry an imaginary component. To understand how Norms oscillate, we propose the “Norm Wave Function” whose exposition we give herein is based on the geometric expansion of Norms. The once speculative Mohammed Abubakr- proposition on Calpanic Numbers, can now find full justification as a fully-fledged proposition. At the end of it all our contribution in the present work – if any; is that we shall here in Part One demonstrate that directional singularities that distorts Euler rotations are imaginary state vectors that are cyclic in nature and in Part two of this proposition we will further demonstrate that the hypothetical Norm in proposal carry unique attributes that may have the potential to explain the manifestation of real space from the imaginary realm.
Category: Mathematical Physics

[634] viXra:1810.0386 [pdf] replaced on 2019-01-15 10:22:13

### New Universe Model, Evidence and Future.

Authors: Dan Visser

In this article an overview-abstract is given about a new universe model according to a series articles by the author, wherein he describes step by step in rather easy mathematics and not affiliated to the university-world, how he came to his new cosmological model. The overview-abstract contains an amount of subjects being found important for a better understanding of his new model in addition to his former articles. His articles are hosted in the viXra-archive in the UK and free to read. The new universe model is called RTHU instead of Big Bang. The main issue is that the RTHU generates the Big Bang-universe, although at the same time the RTHU also contains a lot of other Big Bang-universes shifted relative to each other, however all generated by the RTHU. The generator is the rotation of the RTHU, which has no beginning of time, but uses duo-bits to crumble the Planck-scale. The RTHU therefore is much bigger than a single self-supporting Big Bang-universe. The total new dynamics give other insights in unsolved problems, but make it possible to understand several phenomena better than solving them just only in a single Big Bang-universe. The author pleads for physics and cosmology in the token of the RTHU. Therefore evidence is available, which has been already presented in several of his articles. Moreover it will pinpoint the future for cosmology in a better way. He describes a new perception of time and future. The author also launches a new insight, based on his new cosmological model, which not has been earlier being involved in the problems around climate-change.
Category: Mathematical Physics

[633] viXra:1810.0386 [pdf] replaced on 2018-12-09 15:58:58

### New Universe Model, Evidence and Future.

Authors: Dan Visser

In this article an overview-abstract is given about a new universe model according to a series articles by the author, wherein he describes step by step in rather easy mathematics and not affiliated to the university-world, how he came to his new cosmological model. The overview-abstract contains an amount of subjects being found important for a better understanding of his new model in addition to his former articles. His articles are hosted in the viXra-archive in the UK and free to read. The new universe model is called RTHU instead of Big Bang. The main issue is that the RTHU generates the Big Bang-universe, although at the same time the RTHU also contains a lot of other Big Bang-universes shifted relative to each other, however all generated by the RTHU. The generator is the rotation of the RTHU, which has no beginning of time, but uses duo-bits to crumble the Planck-scale. The RTHU therefore is much bigger than a single self-supporting Big Bang-universe. The total new dynamics give other insights in unsolved problems, but make it possible to understand several phenomena better than solving them just only in a single Big Bang-universe. The author pleads for physics and cosmology in the token of the RTHU. Therefore evidence is available, which has been already presented in several of his articles. Moreover it will pinpoint the future for cosmology in a better way. He describes a new perception of time and future. The author also launches a new insight, based on his new cosmological model, which not has been earlier being involved in the problems around climate-change.
Category: Mathematical Physics

[632] viXra:1810.0300 [pdf] replaced on 2019-02-14 01:38:54

### A Topological Transformation of Quantum Dynamics

Authors: Vu B Ho
Comments: 26 Pages. This paper has been published in Journal of Modern Physics

In this work we discuss the topological transformation of quantum dynamics by showing the wave dynamics of a quantum particle on different types of topological structures in various dimensions from the fundamental polygons of the corresponding universal covering spaces. This is not the view from different perspectives of an observer who simply uses different coordinate systems to describe the same physical phenomenon but rather possible geometric and topological structures that quantum particles are endowed with when they are identified with differentiable manifolds that are embedded or immersed in Euclidean spaces of higher dimension. We present our discussions in the form of Bohr model in one, two and three dimensions using linear wave equations. In one dimension, the fundamental polygon is an interval and the universal covering space is the straight line and in this case the standing wave on a finite string is transformed into the standing wave on a circle which can be applied into the Bohr model of the hydrogen atom. In two dimensions, the fundamental polygon is a square and the universal covering space is the plane and in this case the standing wave on the square is transformed into the standing wave on different surfaces that can be formed by gluing opposite sides of the square, which include a 2-sphere, a 2-torus, a Klein bottle and a projective plane. In three dimensions, the fundamental polygon is a cube and the universal covering space is the three-dimensional Euclidean space. It is shown that a 3-torus and the manifold K×S^1 defined as the product of a Klein bottle and a circle can be constructed by gluing opposite faces of a cube therefore in three-dimensions the standing wave on a cube is transformed into the standing wave on a 3-torus or on the manifold K×S^1. We also suggest that the mathematical degeneracy may play an important role in quantum dynamics and be associated with the concept of wavefunction collapse in quantum mechanics.
Category: Mathematical Physics

[631] viXra:1810.0274 [pdf] replaced on 2018-11-09 19:32:17

### Universe is a Solid Elastic Continuum.

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

Abstract. 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

[630] viXra:1810.0181 [pdf] replaced on 2018-12-14 15:11:08

### The Task of the Panrelativistic Discrete Wave Mechanics

Authors: I. M. Saharov, G. I. Saharov

The paper presents a mathematical study of sub-nuclear particles (nucleons) by a singular mathematical structure, which is a unique compatibility of singular integers with their binding functions, demonstrating the connection of the transcendent and integer, continuous and discrete. The four-dimensional space-time was tested to find the original effective unit, the coefficients of the dominant angles and the main singular number. Representation of a particle as a spatial wave objects (rotating waves) made it possible to find geometric and numeric expressions to their relative mass in units of electron mass with a precision within the limits of the uncertainty principle. Submitted to the consideration of the law effective wave of the relationships governing the stability of subnuclear particles. An approximate expression of the ratio of the magnetic moments of nucleons in vector form based on the ratio of the functions of dominant angles is shown.
Category: Mathematical Physics

[629] viXra:1810.0023 [pdf] replaced on 2018-12-10 14:33:10

### Finite-Time Lyapunov Exponent Field in the Infinitesimal Time Limit

Authors: Peter J. Nolan, Shane D. Ross
Comments: 8 Pages. In preparation for journal submission

Lagrangian analysis using techniques such as the finite-time Lyapunov exponent (FTLE) field or Lagrangian coherent structures can be very informative as to the dynamics of a system, however these methods can be time consuming to integrate and tricky to interpret. Recent developments in dynamical systems theory have generated new Eulerian methods, such as objective Eulerian coherent structures (OECS), for the anaylsis of dynamical systems. In this paper we will build upon this previous work by connecting OECS to FTLE, and providing a new method for the visualization of OECS.
Category: Mathematical Physics

[628] viXra:1809.0599 [pdf] replaced on 2019-01-20 08:37:07

### The Mathematical Principles of the Scale Relativity Physics I. History and Physics

Authors: Nicolae Mazilu, Maricel Agop

Even though a physical theory, the Scale Relativity Theory (SRT) means more than physics, as its creator noticed himself. In fact it targets the very foundation of the entire positive knowledge, and we are set here to prove this fact. Mathematically one needs the description of a transition between infrafinite, finite and transfinite orders, while physically one needs a transition between microcosmos, daily world (quotidian cosmos) and universe. With SRT the mathematical categories of infrafinite, finite and transfinite, become differentiae of the same general concept of ‘finite’. As it turns out, there is a parallelism of the physical transition between the worlds and the mathematical transition between degrees of ‘finite’: it is followed here historically and logically, in a first part of the present work, with the benefit of extracting the mathematical principles of a physical description of matter.
Category: Mathematical Physics

[627] viXra:1809.0599 [pdf] replaced on 2018-12-26 04:12:36

### The Mathematical Principles of the Scale Relativity Physics I. History and Physics

Authors: Nicolae Mazilu, Maricel Agop

Even though a physical theory, the Scale Relativity Theory (SRT) means more than physics, as its creator noticed himself. In fact it targets the very foundation of the entire positive knowledge, and we are set here to prove this fact. Mathematically one needs the description of a transition between infrafinite, finite and transfinite orders, while physically one needs a transition between microcosmos, daily world (quotidian cosmos) and universe. With SRT the mathematical categories of infrafinite, finite and transfinite, become differentiae of the same general concept of ‘finite’. As it turns out, there is a parallelism of the physical transition between the worlds and the mathematical transition between degrees of ‘finite’: it is followed here historically and logically, in a first part of the present work, with the benefit of extracting the mathematical principles of a physical description of matter.
Category: Mathematical Physics

[626] viXra:1809.0599 [pdf] replaced on 2018-11-14 08:46:32

### The Mathematical Principles of the Scale Relativity Physics I. History and Physics

Authors: Nicolae Mazilu, Maricel Agop

Even though a physical theory, the Scale Relativity Theory (SRT) means more than physics, as its creator noticed himself. In fact it targets the very foundation of the entire positive knowledge, and we are set here to prove this fact. Mathematically one needs the description of a transition between infrafinite, finite and transfinite orders, while physically one needs a transition between microcosmos, daily world (quotidian cosmos) and universe. With SRT the mathematical categories of infrafinite, finite and transfinite, become differentiae of the same general concept of ‘finite’. As it turns out, there is a parallelism of the physical transition between the worlds and the mathematical transition between degrees of ‘finite’: it is followed here historically and logically, in a first part of the present work, with the benefit of extracting the mathematical principles of a physical description of matter.
Category: Mathematical Physics

[625] viXra:1809.0599 [pdf] replaced on 2018-10-05 13:27:53

### The Mathematical Principles of the Scale Relativity Physics

Authors: Nicolae Mazilu, Maricel Agop

Even though a physical theory, the Scale Relativity Theory (SRT) means more than physics, as its creator noticed himself. In fact it targets the very foundation of the entire positive knowledge, and we are set here to prove this fact. Mathematically one needs the description of a transition between infrafinite, finite and transfinite orders, while physically one needs a transition between microcosmos, daily world (quotidian cosmos) and universe. With SRT the mathematical categories of infrafinite, finite and transfinite, become differentias of the same general concept of ‘finite’. As it turns out, there is a parallelism of the physical transition between the worlds and the mathematical transition between degrees of ‘finite’: it is followed here historically and logically, in a first part of the present work, with the benefit of extracting the mathematical principles of a physical description of matter.
Category: Mathematical Physics

[624] viXra:1809.0450 [pdf] replaced on 2018-09-23 14:57:31

### How Gas and Force Work Together to Create Geometrical Dispersed Patterns Based On an Object's Shape

Authors: Andrew Dente
Comments: 9 Pages. This manuscript has no operational errors confirmed by reviewers and outside reviewers.

This unique mathematical method for understanding the flow of gas through each individual objects shape will show us how we can produce physical functions for each object based on the dissemination of gas particles in accordance to its shape. We analyze its continuum per shape of the object and the forces acting on the gas which in return produces its own unique function for the given object due to the rate at which forces were applied to the gas. We also get to examine the different changes in the working rate due to the effect of its volume and mass from the given objects shape with our working equation discovered through Green’s and Gaussian functions.
Category: Mathematical Physics