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[11] viXra:2105.0163 [pdf] submitted on 2021-05-27 01:56:07
Authors: Miftachul Hadi
Comments: 6 Pages. Written in English, 1 Figure.
The refractive index and curved space relation is formulated using the Riemann-Christoffel curvature tensor. As a consequence of the fourth rank tensor of the Riemann-Christoffel curvature tensor, the refractive index should be a second rank tensor. The second rank tensor of the refractive index describes a linear optics. In case of a non-linear optics, if susceptibility is a fourth rank tensor, then the refractive index is a sixth rank tensor. In a topological space, the linear and non-linear refractive indices are related to the Euler-Poincare characteristic. Because the Euler-Poincare characteristic is a topological invariant then the linear and non-linear refractive indices are also topological invariants.
Category: Mathematical Physics
[10] viXra:2105.0155 [pdf] replaced on 2021-09-22 14:02:58
Authors: Andreas Martin
Comments: 13 Pages.
This publication takes a mathematical approach to a general solution to the Navier-Stokes equations. The basic idea is a mathematical analysis of the unipolar induction according to Faraday with the help of the vector analysis. The vector analysis enables the unipolar induction and the Navier-Stokes equations to be related physically and mathematically, since both formulations are mathematically equivalent. Since the unipolar induction has proven itself in practice, it can be used as a reference for describing the Navier-Stokes equations.
Category: Mathematical Physics
[9] viXra:2105.0148 [pdf] submitted on 2021-05-24 03:42:56
Authors: Makoto Itoh
Comments: 40 Pages.
The two-dimensional autonomous cellular neural networks (CNNs) having one layer or two layers of memristor coupling can exhibit many interesting nonlinear waves and bifurcation phenomena.
In this paper, we study the nonlinear waves (solitons) in the one-dimensional CNN difference equations.
From our computer simulations, we found that the CNN difference equations can exhibit many interesting behaviors.
The most remarkable thing is that the first-order linear CNN difference equation can exhibit a train of solitary waves, if the initial condition is given by the unit step function. Furthermore, the second-order linear CNN difference equation can exhibit soliton-like behavior, if the initial condition is given by a pulse wave.
That is, the solitary waves pass through one another and emerge from the collision.
Furthermore, the solution exhibits the area-preserving behavior, and it returns exactly to its initial state (the recurrence of the initial state).
In the case of the nonlinear CNN difference equation, we observed the following interesting behaviors.
In the Korteweg-de Vries CNN difference equation, the three-dimensional plot of the interaction of the solitary waves looks like a chicken cockscomb.
In the Toda lattice CNN difference equation, a train of solitary waves with a negative amplitude interact with a train of solitary waves with a positive amplitude, and they emerge from the collisions.
Furthermore, after a certain period of time, the solution breaks down.
In the Sine-Gordon CNN difference equation, the solution moves at constant speed, and it emerges from the collision.
Furthermore, the solution returns the state which is roughly similar to the initial state.
In the memristor CNN difference equations, the three-dimensional plots of solitary waves exhibit more complicated (chaotic or distorted) behavior.
Category: Mathematical Physics
[8] viXra:2105.0126 [pdf] replaced on 2021-07-21 15:23:19
Authors: Ervin Goldfain
Comments: 20 Pages.
Fractals and multifractals are well-known trademarks of nonlinear dynamics and classical chaos. The goal of this work is to tentatively uncover the unforeseen path from multifractals and selfsimilarity to the framework of effective field theory (EFT). An intriguing finding is that the partition function of multifractal geometry includes a signature analogous to that of gravitational interaction. Our results also suggest that multifractal geometry may offer insights into the non-renormalizable interactions presumed to develop beyond the Standard Model scale.
Category: Mathematical Physics
[7] viXra:2105.0121 [pdf] submitted on 2021-05-20 20:49:11
Authors: Miroslav Pardy
Comments: 4 Pages. original article
We will consider the string, the left end of which is fixed at the beginning of the
coordinate system, the right end is fixed at point l and mass m is interstitial between the ends of the string. We determine the vibration of such system. The proposed model can be also related to the problem of the Moessbauer effect, or, recoilless nuclear resonance fluorescence, being resonant and recoilfree emission and absorption of gamma radiation by atomic nuclei bound in a solid (Moessbauer,1958).
Category: Mathematical Physics
[6] viXra:2105.0098 [pdf] submitted on 2021-05-18 21:39:34
Authors: Dan Visser
Comments: 30 Pages.
In this article I summerize a new perception of the Universe, called the “Rotational Torus Hologram Universe (RTHU)”, which is related to all of my articles in www.vixra.org/author/dan_visser . The RTHU predicts the Big Bang is not the origin of the Universe. The RTHU behaves like a "Hologram Carrousel". It is a bunch of materialized reality-holograms rotating as an inner torus, which is surrounded and intertwined by a dark energy second torus, while in each of these holograms the impression of a Big Bang-universe is performed. In an additional manuscript is also dimensionally shown how I modified the Einstein-equation by implementing a “Hologram Tensor”. This DAN-Tensor predicts a dark matter force by “duo-bits”, which replace and extend the Planck-boundary through “sub-quantum-kinetica”. In this way gravity and dark gravity have become normal in the RTHU and offers an additional fifth-force and new movement in vacuum. This article and manuscript are autentically written in Dutch for the benifit of collectors, because I also make paintings, which are related to my new universe-ideology. The original manuscript is in my possesion.
Category: Mathematical Physics
[5] viXra:2105.0097 [pdf] submitted on 2021-05-17 08:51:04
Authors: Debasis Biswas
Comments: 3 Pages.
In this paper a simple derivation of Euler-Bohlin invariant is given without any kind of symmetry analysis.
Category: Mathematical Physics
[4] viXra:2105.0060 [pdf] replaced on 2022-06-08 05:24:40
Authors: Paul R. Gerber
Comments: 7 Pages. Interpretation of the representation space was not fully correct in version one.
The Lorentz group is a non-compact group. Consequently, it’s representations cannot be expected to be equivalent to representations of a unitary group. Actually, they act on a large-component space and a separated small-component space, in some sense analogous to 4-vectors. In contrast to representations of compact groups state vectors carry the actual value of the non-compact variables, the boost-vector. In the non-boosted state the small components vanish and the large components transform according to a representation of the rotation subgroup. Application of a boost then generates small components, a process that preserves norms. However, the norm now has a growing positive contribution from the large-components and a negative contribution from the small-components, growing absolutely to keep the total unchanged. General transformations are described in detail. The freedom to assign boost directions to the phases of small components leads to a topological symmetry with flavor-generating representations for two-sheeted representations.
Category: Mathematical Physics
[3] viXra:2105.0039 [pdf] submitted on 2021-05-09 10:38:48
Authors: Debasis Biswas
Comments: 3 Pages.
In this paper a new proof of functional equation of Riemann Zeta function is given using analytical expression of Riemann Xi function.
Category: Mathematical Physics
[2] viXra:2105.0027 [pdf] submitted on 2021-05-05 18:21:25
Authors: Yuji Masuda
Comments: 1 Page.
I think that in addition to the fact that atoms are represented by electrons, protons and
neutrons, the discovery of "mesons" in modern physics has had a significant impact on
modern physics, especially quantum mechanics. In this paper, I will discuss the uncertainty principle, which is the fundamental equation
of quantum mechanics, from my definitions.
Category: Mathematical Physics
[1] viXra:2105.0002 [pdf] submitted on 2021-05-02 20:35:01
Authors: Abdelmajid Ben Hadj Salem
Comments: 49 Pages. In French. Comments welcome.
[Note: This is Henri Poincare's paper edited by Abdelmajid Ben Hadj Salem]
This article is a numerical version of the first chapter of the long paper of Henri Poincar\'e " The Three-Body Problem and the Equations of Dynamics " published by the celebrate journal \textit{Acta Mathematica} (Vol.13, n$^{\circ}1-2$, 1889), created by the Swedish mathematician Gösta Mittag-Leffler in 1882, and he was the Editor-in-Chief. The new version kept the original text with some minimal changes and adding the bibliography which summarizes all the references cited in the article.| Third-Party Links: |
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