# Mathematical Physics

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## Recent submissions

Any replacements are listed farther down

[862] viXra:1905.0268 [pdf] submitted on 2019-05-17 17:43:20

### Ecriture Détaillée Des Equations de la Relativité Générale :Cas D’Une Métrique Diagonale

Authors: Abdelmajid Ben Hadj Salem
Comments: 22 Pages. In French.

In this note, we study Einstein equations (EE) of general relativity considering a manifold M with a diagonal metric g_{ij}. We calculate the expression of the components of Ricci and Riemann tensors and the value of the scalar curvature R. Then we give the expression of the (EE) : -a- for the case where g_{ii}=g_i=g_i(x_i); -b- for the case where g_1=g_1(x_1=t) and g_i=g_i(t,x_i) for i=2,3,4$; -c- for the case (b) with x_4=z_0=constant. Category: Mathematical Physics [861] viXra:1905.0142 [pdf] submitted on 2019-05-09 19:53:08 ### (LFs and Gravity Working Paper Variant 1.0 7 Pages 13.04.2019) Life Forms, "Hybrid" Causality, Gravity and Hierarchical Parallel Universes Authors: Andrei Lucian Dragoi Comments: 7 Pages. This paper proposes a new definition of life forms in relation to a new type of “hybrid” causality, gravity and the possible existence of hierarchical parallel universes. Keywords: life forms, gravity, hierarchical parallel universes; Category: Mathematical Physics [860] viXra:1905.0012 [pdf] submitted on 2019-05-01 14:07:09 ### A Mathematical Overview of Mass and Energy Conservation in Modern Physics Authors: Dang Dang Comments: 28 Pages. The idea of energy, matter, and motion has perplexed many philosophers and physicists from antiquity to modern physics, from Plato to Einstein. New and developing physical theories raise different interpretations of energy and matter but no complete theory of everything exists at present. However, there is a law we can almost take for granted: the law of conservation of energy, which states that energy cannot be created nor destroyed although it can be transformed from one form to another. After establishing the foundational theory and history of conservation of energy, this literature review aims to provide an overview of the concept of mass and energy conservation in two of the most fundamental physical theories - quantum mechanics and general relativity. Consequences and challenges of mass-energy conservation and equivalence - dark energy - is studied in an introductory manner Category: Mathematical Physics [859] viXra:1904.0552 [pdf] submitted on 2019-04-28 12:51:07 ### Black Holes in a Rotating Hologram Universe. Authors: Dan Visser Comments: 7 Pages. Black holes are not what it looks like due to postmodern Big Bang interpretations. In my new cosmology black holes are part of a rotating hologram-universe. The black hole mass-density thereto is replaced by my new parameter Tdan, which makes mass-density of a black hole independent of the light speed in vacuum according to general relativity. General relativity has to be extended by refining the Planck-units in a domain below the Planck-boundary. Tdan is that refining-mechanism. Category: Mathematical Physics [858] viXra:1904.0533 [pdf] submitted on 2019-04-27 12:56:38 ### On the Mathematical Formulation of 4D Fock Space Authors: Paul Werbos Comments: 6 Pages. Ordinary Fock space, defined as concatenated combination of three-dimensional spaces is the main workhorse of the canonical version of quantum field theory. It is also fundamental to the modern version of quantum field theory without observers, as in the theory of Everett, Wheeler and Deutsch, which led to the theory of the universal quantum computer. It also has many practical uses, from quantum optics to the closure of turbulence and the derivation of the emergent behavior of space-time dynamical systems. But many of us believe that time and space are interchangeable to some degree, and that methods based on 4D Fock space are needed. This letter describes two simple mathematical tools to help make that possible. It discusses how computing the emergent statistics of such systems is a proper generalization of value function estimation in machine learning, which may therefore carry the same complexities with it. Category: Mathematical Physics [857] viXra:1904.0505 [pdf] submitted on 2019-04-25 07:57:08 ### Riemann's Definition for the Integrals in Mathematical Physics Authors: Louiz Akram Comments: 3 Pages. This is my other work about the riemann Sum as a définition to the integral and the result is really important for many fields. Category: Mathematical Physics [856] viXra:1904.0503 [pdf] submitted on 2019-04-25 08:26:20 ### An Annex and Application for :Mémoire en Physiques. Authors: Louiz Akram Comments: 2 Pages. Mémoire en physiques is a work made since January 2016 by Louiz Akram (an independant researcher). Category: Mathematical Physics [855] viXra:1904.0477 [pdf] submitted on 2019-04-24 08:37:09 ### Mémoire en Physiques Authors: Louiz Akram Comments: 30 Pages. The derivation in the galilean was made in my work differently than the famous steps when dealing with relative rotations. My work gives the results with an accurate uncertainty and it is the only correct derivation for physics' use, hence, It is the solution to avoid the mistakes made when dealing with the Newtonian Mechanics and thus to avoid the relativity of Time. Category: Mathematical Physics [854] viXra:1904.0464 [pdf] submitted on 2019-04-24 15:42:36 ### A Disproof to the Time Dilation . Authors: Louiz Akram Comments: 2 Pages. This a disproof to Einstein's special relativity and to Lorentz' Transformation . Category: Mathematical Physics [853] viXra:1904.0455 [pdf] submitted on 2019-04-23 08:24:27 ### From Maxwell’s Equations to the String Theory and Particle Physics: New Mathematical Connections with Some Sectors of Number Theory Authors: Michele Nardelli, Antonio Nardelli Comments: 179 Pages. In this research thesis we have described some new mathematical connections between Maxwell’s Equations, some sectors of the String Theory and Particle Physics, and some sectors of Number Theory, precisely various Ramanujan’s expressions and equations. Category: Mathematical Physics [852] viXra:1904.0448 [pdf] submitted on 2019-04-23 13:43:14 ### On the Initial Chaos of the Universe: Using Null Deﬂection of Perturbation Element Over ﬂat Geometry Authors: Divyansh Mansukhani Comments: 2 Pages. While the ﬂatness problem, Ω = 1, has been one weighty stand in the modern cosmology to showcase incompetency of BBT, the theory of inﬂation - ﬁrst pioneered by Alan Guth, CTP, MIT (current) - serves to accommodate it in the observed universe. Here, (a) FP is used as a skeleton to attempt for an altogether novel approach involving rudimentary perturbation theory to deﬁne what one may call as ‘initial chaos’, and (b) the corresponding approach is postulated to be lightly rigorous than the other frameworks which propose in the same domain. Category: Mathematical Physics [851] viXra:1904.0340 [pdf] submitted on 2019-04-17 14:26:12 ### Completeness in Physics Authors: Jeremy Dunning-Davies, Richard Lawrence Norman Comments: 3 Pages. Here it is intended to raise some questions surrounding the whole notion of completeness in physics. This does, of course, have bearing on issues raised by the well-known paper by Einstein, Podolsky and Rosen. Category: Mathematical Physics [850] viXra:1904.0268 [pdf] submitted on 2019-04-14 10:05:16 ### Spherical Harmonics and Crystals Authors: Giuliano Bettini Comments: 27 Pages. In Italian The description of Point Groups is made in crystallography, among other, with "character tables". Following my classification work entitled "5 bit 32 crystal classes" and some other curious properties I've noticed, I wanted to try to find a representation with Spherical Harmonics namely: a set of 32 Spherical Harmonics each one representing a Point Group. So the purpose of this work, in a nutshell, is to combine each of the 32 crystal classes with the corresponding Spherical Harmonic that has the same symmetry properties, in a certain sense therefore a "group description". These are among all the Spherical Harmonics the only 32 with which it is possible to create periodic structures with no gaps nor overlapping. A sort of Spherical Harmonics Restriction Theorem. Other possibly interesting connections with the s p d f sub-shells, and with spin, are to be investigated. Category: Mathematical Physics [849] viXra:1904.0206 [pdf] submitted on 2019-04-10 06:49:14 ### The Origin of New Dark Energy. Authors: Dan Visser Comments: 13 Pages. New dark energy is related to a new cosmological model (RTHU). This paper refers to the origin of this new dark energy. As a follow-up this paper considers why CERN (LHC), and other colliders, are relics of the past and why the RTHU-scanner will be the future. The RTHU stands for a rotating hologram universe. The details are anchored in my series of article hosted in the vixra-archive, category mathematical physics. Reach it on www.vixra.org/author/dan_visser. It represents my horizon, my art and my basic-science for the work-out of the new dark energy in the RTHU. Category: Mathematical Physics [848] viXra:1904.0183 [pdf] submitted on 2019-04-09 11:35:38 ### On the Integrability of Liénard Equations Authors: Y.F. J. Kpomahou, M. D. Monsia Comments: 4 pages A simple condition for integrability of Liénard equations is established to compute their general solution explicitly or by quadrature via a nonlocal transformation. Category: Mathematical Physics [847] viXra:1904.0114 [pdf] submitted on 2019-04-05 09:50:38 ### Gravitational and Gravity Constans , and Their Physical Interpretation. Authors: Markos Georgallides Comments: 73 Pages. In Mechanics Work = Energy = motion is [Force] x[Displacement] and is conserved . In order Motion is conserved as Displacement in all directions , then Displacement must be kept , Quantized , in a Finite Space differently is annihilated .The only possible motion in a Finite -Space is the Periodic-excitation [→ ←] and Revolving motion [(+)↻↺(-)] which is proved define the quality of Particles . Periodic excitation between Space (+) and Anti-Space (-) , may exist only as Collision of Opposite , and this because of the equal and opposite Point-charges that are infinitely close together which create Coulomb Electric dipole-moment in an Electric-field . Motion is captured in a [Box-P] called Stationary-Material-point containing these three elements [ (+) ,[↔], (-)] which are , Space , Energy , Anti-space . The Spin of this Dipole is Stationary and is proved to be the Gravity g . Revolving motion may exist between Space (+) and Anti-Space (-) so the Revolving of Two-Points A(+) and B(-) consist the Material-Point in Segment r = |AB| , and carries the Principal stress , σ , between , A , B , which stress σ as Centripetal acceleration is the Centripetal-force and the minimum Energy becoming from the in-storage [AB] acceleration and is proved to be equal to the Gravity-wave , g . The continually produced Work in this [Box-R] is stored in it as the Golden-ratio-frequency-motion , not eternally but Partially , and the rest superfluous motion is launched out the Box as an Propagating Electromagnetic-Wave , which Out-Wave carries the [Box–R] , and it is called the Photon . Local Spin of [Box-P] is oriented to that of [Box-R] , by a Local-uniform Pressure equal to , g * [Force/Area] = G , which is Newton-Universal-Gravitational-constant G force , such for Macrocosm as for Microcosm , and for both cases Obeying Newtons Laws of motion . It was Proved that Force G is the Pressure on Gravity g , the First-kick-Start , to Enter Planck-cave and formulate in orbit of Plancks cave , the lightest and the less-mass Particle of this universe which is the Hydrogen-cave . In the Undamped Planck`s – Conservative -System , Total-Energy of , -13,6 eV , of Hydrogen , corresponds to the Natural-frequency of the Primary-Particle with the less Negative-charge-frequency, and this is The Electron , e , which mass and frequency follows min.- g . In the Extreme -Three-Body-Problem case ,where any two massive bodies infinitely close together consist a Slit , The-Slit-Focus , is then created a New Structure for Atom as in article [77] which Properties and Configuration anomalies dependent on , e , p , n , numbers. Since Force G is a Uniform-Pointy–Force , therefore needs a Conductor , a Layer , a kind of mass , to be spread and act on it as Stress = Surface-force , which is the Layer or the Conductor of Spin S , or the Stress g , and this because of Stress-Layer, g , where all the Energy-Structures present mass . Gravity acceleration , g , produced from the in Material-points acceleration is equal to the pressure , σ , i.e. the Conductor to all Waves as , Force G - ON-Layer - A , [A = m x g] , = Gravity . Category: Mathematical Physics [846] viXra:1904.0073 [pdf] submitted on 2019-04-03 08:09:11 ### Non-commutativity: Unusual View Authors: Valeriy V. Dvoeglazov Comments: 4 Pages. Prog. Phys. 15 (2019) 48-51 Some ambiguities have recently been found in the definition of the partial derivative (in the case of presence of both explicit and implicit dependencies of the function subjected to differentiation). We investigate the possible influence of this subject on quantum mechanics and the classical/quantum field theory. Surprisingly, some commutators of operators of space-time 4-coordinates and those of 4-momenta are not equal to zero. We postulate the non-commutativity of 4-momenta and we derive mass splitting in the Dirac equation. Moreover, two iterated limits may not commute each other, in general. Thus, we present an example when the massless limit of the function of E, p, m does not exist in some calculations within quantum field theory Category: Mathematical Physics [845] viXra:1903.0429 [pdf] submitted on 2019-03-25 04:20:29 ### On the Wave Motion and Inertial Mass of Quantum Particles Authors: Vu B Ho Comments: 9 Pages. In this work we will discuss the possibility that if a quantum particle possesses a fluid state, as shown in our work on the fluid state of Dirac quantum particles, then the motion of the physical particle in an ambient space may be directly related to its fluid state and therefore it can be explained in terms of the wave motion of physical objects that move in a substrate space with the mechanism similar to that of peristaltic locomotion. In particular, we will also discuss the possibility that the so-called inertial mass of a particle in classical physics may be identified as a form of gripping connection between the particle and the substrate, which is the ambient space itself, that is needed for a particle to move in space. This is similar to a tight grip that is needed for a physical object to move on a surface. Category: Mathematical Physics [844] viXra:1903.0419 [pdf] submitted on 2019-03-23 11:42:35 ### On the General Solution for the Quintic Duffing Oscillator Equation Authors: J. Akande, D. K. K. Adjaï, Y. J. F. Kpomahou, M. D. Monsia Comments: 4 pages This paper shows for the first time that exact and general solution for the quintic Duffing oscillator equation may be computed in a straightforward manner within the framework of the generalized Sundman transformation theory introduced recently by authors of this work. A major advantage of the applied method is that it intimately relates such an oscillator equation to the quadratic anharmonic oscillator equation with well-known exact solutions. Category: Mathematical Physics [843] viXra:1903.0385 [pdf] submitted on 2019-03-22 05:56:29 ### The Mathematical Universe Authors: Manjunath.R Comments: 462 Pages. We Humans, a curious beings developed from the Darwin’s principle of natural selection, are accustomed into an inquisition. The question is not ‘do we know everything from the triumph of the Higgs boson to the underlying discomfort of ultimate question of life, the universe, and everything?’ or it is ‘do we know enough?’ But how the creative principle resides in mathematics? There’s something very mathematical about our gigantic Cosmos, and that the more carefully we look, the more equations are built into nature: our universe isn’t just described by math, but that universe is a “grand book” written in the language of mathematics. We find it very appropriate that mathematics has played a striking role in our growing understanding of the events around us, and of our own existence. Category: Mathematical Physics [842] 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 Comments: 9 Pages. 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 [841] viXra:1903.0066 [pdf] submitted on 2019-03-04 19:51:11 ### Observations of Structure of a Possible Unification Algebra Authors: Robert G. Wallace Comments: 29 Pages. 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 [840] 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 Comments: 9pages 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 [839] 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 Comments: 8 Pages. 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 [838] 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 [837] viXra:1902.0345 [pdf] submitted on 2019-02-20 10:08:07 ### Memristor Circuit Equations with Periodic Forcing Authors: Makoto Itoh Comments: 115 Pages. 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 [836] viXra:1902.0334 [pdf] submitted on 2019-02-21 02:18:14 ### Spacetime Transcription of Physical Fields Authors: Vu B Ho Comments: 9 Pages. 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 [835] 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 Comments: 9 Pages. 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 [834] viXra:1902.0205 [pdf] submitted on 2019-02-11 18:02:00 ### Formula_of_force Authors: Vatolin Dm. Comments: 7 Pages. Russian 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 [833] viXra:1902.0165 [pdf] submitted on 2019-02-09 11:35:51 ### On Forced Parallelism Within Characteristic States Authors: Divyansh Mansukhani Comments: 1 Page. 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 [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 Comments: 14 Pages. This paper has been submitted to Prespacetime Journal. Your comments are welcome 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 Comments: 12 Pages. https://doi.org/10.6084/m9.figshare.7658774.v2 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 Comments: 3 Pages. 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 Comments: 6 Pages. Thank you for reading 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 Comments: Pages. 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 Comments: 4 pages 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 Comments: 17 Pages. 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 Comments: 7 Pages. 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 Comments: 5 pages 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 Comments: 4 Pages. 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 Comments: 4 Pages. 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 Comments: 3 Pages. 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 Comments: 3 Pages. 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 Comments: 2 Pages. 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 Comments: 33 Pages. 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
Comments: 23 Pages.

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

## Replacements of recent Submissions

[667] viXra:1904.0533 [pdf] replaced on 2019-04-28 11:29:31

### On the Mathematical Formulation of 4D Fock Space

Authors: Paul Werbos
Comments: 6 Pages. word screwed up eq 2 in v1. Replaced word equation with image object.

Ordinary Fock space, defined as concatenated combination of three-dimensional spaces is the main workhorse of the canonical version of quantum field theory. It is also fundamental to the modern version of quantum field theory without observers, as in the theory of Everett, Wheeler and Deutsch, which led to the theory of the universal quantum computer. It also has many practical uses, from quantum optics to the closure of turbulence and the derivation of the emergent behavior of space-time dynamical systems. But many of us believe that time and space are interchangeable to some degree, and that methods based on 4D Fock space are needed. This letter describes two simple mathematical tools to help make that possible. It discusses how computing the emergent statistics of such systems is a proper generalization of value function estimation in machine learning, which may therefore carry the same complexities with it.
Category: Mathematical Physics

[666] viXra:1904.0315 [pdf] replaced on 2019-05-23 07:38:21

### Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 9 Pages. Comments welcome.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold. To that end, I suggest three proposals relevant to Mathematics and mathematical physics.
Category: Mathematical Physics

[665] viXra:1904.0315 [pdf] replaced on 2019-05-19 17:38:04

### Time and Continuum: Zenon Manifold

Authors: D. Chakalov
Comments: 8 Pages. Comments welcome.

Ensuing from first principles, I suggest pre-geometric theory of spacetime, in which the apex of light cone ‘here and now’ is not modeled with dimensionless point, but with non-trivial mathematical object along null intervals, endowed with brand new structure, topology and dynamics, and defined on so-called Zenon manifold.
Category: Mathematical Physics

[664] viXra:1904.0268 [pdf] replaced on 2019-04-21 10:22:35

### Spherical Harmonics and Crystals

Authors: Giuliano Bettini
Comments: 27 Pages. In English. Updated.

The description of Point Groups is made in crystallography, among other, with "character tables". Following my classification work entitled "5 bit 32 crystal classes" and some other curious properties I've noticed, I wanted to try to find a representation with Spherical Harmonics namely: a set of 32 Spherical Harmonics each one representing a Point Group. So the purpose of this work, in a nutshell, is to combine each of the 32 crystal classes with the corresponding Spherical Harmonic that has the same symmetry properties, in a certain sense therefore a "group description". These are among all the Spherical Harmonics the only 32 with which it is possible to create periodic structures with no gaps nor overlapping. A sort of Spherical Harmonics Restriction Theorem. Other possibly interesting connections with the s p d f sub-shells, and with spin, are to be investigated.
Category: Mathematical Physics

[663] viXra:1904.0268 [pdf] replaced on 2019-04-20 01:43:00

### Spherical Harmonics and Crystals

Authors: Giuliano Bettini
Comments: 27 Pages. In Italian. This is the update to the Italian version v1.

The description of Point Groups is made in crystallography, among other, with "character tables". Following my classification work entitled "5 bit 32 crystal classes" and some other curious properties I've noticed, I wanted to try to find a representation with Spherical Harmonics namely: a set of 32 Spherical Harmonics each one representing a Point Group. So the purpose of this work, in a nutshell, is to combine each of the 32 crystal classes with the corresponding Spherical Harmonic that has the same symmetry properties, in a certain sense therefore a "group description". These are among all the Spherical Harmonics the only 32 with which it is possible to create periodic structures with no gaps nor overlapping. A sort of Spherical Harmonics Restriction Theorem. Other possibly interesting connections with the s p d f sub-shells, and with spin, are to be investigated.
Category: Mathematical Physics

[662] viXra:1904.0218 [pdf] replaced on 2019-04-19 07:37:16

### Back to Cosmos

Authors: F.M. Sanchez, V. Kotov, M. Grosmann, D. Weigel, R. Veysseyre, C. Bizouard, N. Flawisky, D. Gayral, L. Gueroult
Comments: 27 Pages. To be published in Progress in Physics

To the memory of Sir Michael Atiyah Abstract. The ancestral concept of Cosmos is rediscovered through the idea of a Tachyonic Grandcosmos Multibasis Computer, inversing the Anthropic Principle and reestablishing the Laplace Determinism. The observed fine tuning between physical dimensionless parameters is interpreted as relations between optimal calculation basis, announcing a dramatic progress in computer software. Three type of mathematical constants are considered: Large, Intermediate and close to unity. The famous Large Number problem is resolved by Eddington's statistical theory and the gravitational Hydrogen Molecule model, leading to the visible Universe horizon radius R ≈ 13.812 Giga ligth-years. The extension of the double cosmic correlation defines a Topological Axis using Euler-Napier constant e as primary basis, confirming String Theory, Cartan-Bott periodicity and the 30 holic dimensions corresponding to the simplest space-time-matter diophantine equation T^2 = L^3 = M^5 = N^30. This dimension n = 30 corresponds to the common time, about 10^58 s, given by two mandatory dimensional analysis, interpreted as the Supercycle period. The visible Universe wavelength 'Topon' 2Għ/Rc3 ≈ 4 × 10^-96 m corresponds to n ≈ 2ee and enters the 1D mono-radial holographic extension of the Bekenstein-Hawking Universe entropy, implying the critical condition, and breaking the Planck wall by a factor 1061, justifying the Hawking trans-planckian frequencies. The monochrome holographic extension leads to a Grandcosmos, larger than the visible Universe by the same factor 10^61. A toponic quantization justifies the Cosmos vastness in a scanned Universe, justifying the entropy factor 1/4. This implies a tachyonic speed in the same ratio by respect to c, justifying the Planck re-normalisation of the vacuum energy, independently checked by the Casimir effect. The couple Universe-Grandcosmos is confirmed by a dramatic geo-dimensional analysis, where Length, Time and Mass ratios are considered as unit vectors in a 3D Super-space. A matter-antimatter 10^104 Hz Oscillatory Bounce unifies standard Single Bang with steady-state cosmology, but suppress Relativity in cosmology at large, reestablishing the Newton Absolute Space realized by the Microwave Cosmic Radiation, while Kotov cycle defines a quasi-absolute clock. This new scanning space-time structure is confirmed by single-electron cosmology, connected with Kotov period, and relying Sternheimer Biological scale factor and Atiyah constant, which appear as privileged computation basis, as well as e, p and a ≈ 137.036, in liaison with the sporadic groups. The Atiyah constant enters dramatic ppb precision relations with particle data. This unifies mathematics, physics, chemistry, biology and philosophy. It is predicted that the future telescopes will find mature galaxies in the very far range, instead of a Dark Space, ruining the standard evolutionary cosmology, ill-founded on an imperfect Cosmological Principle.
Category: Mathematical Physics

[661] viXra:1904.0218 [pdf] replaced on 2019-04-17 12:18:01

### Back to Cosmos

Authors: F.M. Sanchez, V. Kotov, M. Grosmann, D. Weigel, R. Veysseyre, C. Bizouard, N. Flawisky, D. Gayral, L. Gueroult
Comments: 26 Pages. Accepted by Progress in Ohysics, Avril 2019

To the memory of Sir Michael Atiyah Abstract. The ancestral concept of Cosmos is rediscovered through the idea of a Tachyonic Grandcosmos Multibasis Computer, inversing the Anthropic Principle and reestablishing the Laplace Determinism. The observed fine tuning between physical dimensionless parameters is interpreted as relations between optimal calculation basis, announcing a dramatic progress in computer software. Three type of mathematical constants are considered: Large, Intermediate and close to unity. The famous Large Number problem is resolved by Eddington's statistical theory and the gravitational Hydrogen Molecule model, leading to the visible Universe horizon radius R ≈ 13.812 Giga ligth-years. The extension of the double cosmic correlation defines a Topological Axis using Euler-Napier constant e as primary basis, confirming String Theory, Cartan-Bott periodicity and the 30 holic dimensions corresponding to the simplest space-time-matter diophantine equation T2 = L3 = M5 = N30. This dimension n = 30 corresponds to the common time, about 10^58 s, given by two mandatory dimensional analysis, interpreted as the Supercycle period. The visible Universe wavelength 'Topon' 2Għ/Rc3 ≈ 4 × 10^-96 m corresponds to n ≈ 2ee and enters the 1D mono-radial holographic extension of the Bekenstein-Hawking Universe entropy, implying the critical condition, and breaking the Planck wall by a factor 10^61, justifying the Hawking trans-planckian frequencies. The monochrome holographic extension leads to a Grandcosmos, larger than the visible Universe by the same factor 10^61. A toponic quantization justifies the Cosmos vastness in a scanned Universe, justifying the entropy factor 1/4. This implies a tachyonic speed in the same ratio by respect to c, justifying the Planck re-normalisation of the vacuum energy, independently checked by the Casimir effect. The couple Universe-Grandcosmos is confirmed by a dramatic geo-dimensional analysis, where Length, Time and Mass ratios are considered as unit vectors in a 3D Super-space. A matter-antimatter 10^104 Hz Oscillatory Bounce unifies standard Single Bang with steady-state cosmology, but suppress Relativity in cosmology at large, reestablishing the Newton Absolute Space realized by the Microwave Cosmic Radiation, while Kotov cycle defines a quasi-absolute clock. This new scanning space-time structure is confirmed by single-electron cosmology, connected with Kotov period, and relying Sternheimer Biological scale factor and Atiyah constant, which appear as privileged computation basis, as well as e, p and a ≈ 137.036, in liaison with the sporadic groups. The Atiyah constant enters dramatic ppb precision relations with particle data. This predicts unification of mathematics, informatics, physics, chemistry, biology and philosophy. The future telescopes will find mature galaxies in the very far range, instead of a Dark Space, ruining the standard evolutionary cosmology, ill-founded on an imperfect Cosmological Principle.
Category: Mathematical Physics

[660] viXra:1903.0066 [pdf] replaced on 2019-05-12 06:53:09

### Observations of a Possible Unification Algebra

Authors: Robert G. Wallace
Comments: 29 Pages.

A C-loop algebra is assembled as the product 0f a Clifford algebra and a Cayley-Dickson algebra. Once the principle of spatial equivalence is invoked, a sub-algebra is identified with features that suggest it could provide an underlying basis for the standard model of fundamental particles.
Category: Mathematical Physics

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

### Observations of a Possible Unification Algebra

Authors: Robert G Wallace
Comments: 29 Pages.

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

[658] 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

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

### Memristor Circuit Equations with Periodic Forcing

Authors: Makoto Itoh
Comments: 114 Pages.

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

[656] viXra:1902.0205 [pdf] replaced on 2019-04-12 09:23:43

### Formula of Force

Authors: Vatolin. Dm
Comments: 6 Pages. Russian

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

[655] viXra:1902.0205 [pdf] replaced on 2019-04-11 07:06:18

### Formula of Force

Authors: Vatolin Dm.
Comments: 6 Pages. Rusian

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

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

### Formula of Force

Authors: Vatolin Dm.
Comments: 6 Pages. Russian

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.
Comments: 7 Pages. Russian

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: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
Comments: 5 pages

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

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

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach
Comments: 9 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

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

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach
Comments: 9 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

[649] 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

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

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach
Comments: 9 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

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

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach
Comments: 8 Pages. Minor correction

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 2019-01-13 14:02:11

### Algebraic Invariants of Gravity

Authors: Hans Detlef Hüttenbach
Comments: 8 Pages. Minor correction

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

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

Authors: Paul Werbos
Comments: 4 Pages.

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