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

**Authors:** Mesut Kavak

**Comments:** 7 Pages.

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

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

**Authors:** Jan Makopa

**Comments:** 6 Pages.

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

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

**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

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

**Authors:** Wan-Chung Hu

**Comments:** 1 Page.

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

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

**Authors:** Takahiro Kajisa

**Comments:** 8 Pages.

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

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

**Authors:** Dan Visser

**Comments:** 16 Pages.

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

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

**Authors:** Vu B Ho

**Comments:** 24 Pages.

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

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

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

**Comments:** 244 Pages. dubinyansky@mail.ru

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

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

**Authors:** Pan Zhang

**Comments:** 11 Pages.

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

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

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

**Comments:** 17 Pages.

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

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

**Authors:** Pan Zhang

**Comments:** 10 Pages.

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

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

**Authors:** Yélomè J. F. Kpomahou, Damien K. K. Adjaï, J. Akande, Marc D. Monsia

**Comments:** 7 pages

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

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

**Authors:** Amit Kumar Jha

**Comments:** 3 Pages.

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

**Category:** Mathematical Physics

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

**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