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

**Authors:** Hongbing Zhang

**Comments:** 30 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Hongbing Zhang

**Comments:** 7 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Hongbing Zhang

**Comments:** 6 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Antoine Balan

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

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

**Category:** Mathematical Physics

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

**Authors:** Harry Watson

**Comments:** 2 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Markos Georgallides

**Comments:** 89 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Louai Hassan Elzein Bashier

**Comments:** 22 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Moises Dominguez-Espinosa

**Comments:** 5 Pages.

There is a paradigm in Quantum Mechanics that explains quantization through normal vibration modes called Eigenstates that arise from Schrödinger wave equation. In this contribution we propose an alternative methodology of quantization by using basic concepts of mechanics and chaos from which a Toy Model is built.

**Category:** Mathematical Physics

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

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

**Comments:** 3 Pages.

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

**Category:** Mathematical Physics

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

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

**Comments:** 16 pages

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

**Category:** Mathematical Physics

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

**Authors:** Andrei P. Kirilyuk

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

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

**Category:** Mathematical Physics

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

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 20 Pages.

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

**Category:** Mathematical Physics

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

**Authors:** Spiros Konstantogiannis

**Comments:** 28 Pages.

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

**Category:** Mathematical Physics