[6] **viXra:1712.0419 [pdf]**
*submitted on 2017-12-12 13:58:40*

**Authors:** Nikola Samardzija

**Comments:** 16 Pages. This review paper was written in 2014, and since has raised quite a few eyebrows in academia. The simplicity of the globotoroid model is far reaching, and alters some central themes in mathematics and sciences - Namely, the singularity based theories.

Mathematical models can give us invaluable insights into natural phenomena, and as such play an important role in science. The intent of this paper is to give a high-level overview of a simple continuous dynamical model that offers an insight into a qualitative behavior seldom reported or discussed. This model has no equilibrium or singular points, yet its phase space unveils four distinct topological features: a limit cycle, a torus, a sphere and a wormhole. Each of these features results from model solutions that can be periodic, quasi-periodic and chaotic, which collectively form a space-time structure referred to as the globotoroid. The model generalizes the energy behavior of many processes of interest, and consequently is reshaping contemporary systems theory to fit more completely with different natural phenomena. Specifically, the globotoroid is the simplest 3-dimensional dynamic model that exposes the concept of the wormhole, which embodies an important energy behavior throughout our universe. The fields of science that may benefit from this modeling approach are many, including physics, cosmology, biology, chemistry, engineering, cognitive sciences, economics, politics, and business and finance. This is demonstrated by reviewing some well-known phenomena in natural and social sciences.

**Category:** Mathematical Physics

[5] **viXra:1712.0404 [pdf]**
*submitted on 2017-12-13 03:42:44*

**Authors:** Vu B Ho

**Comments:** 12 Pages.

In this work, we discuss a method to derive Dirac equation and other equations, such as the Cauchy-Riemann equations, from a general system of linear first order partial differential equations, with the hope that when studied more thoroughly the general system may provide deeper insights into geometrical and topological structures of quantum particles and fields.

**Category:** Mathematical Physics

[4] **viXra:1712.0399 [pdf]**
*submitted on 2017-12-12 03:53:52*

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

**Comments:** 3 pages

This paper shows, for the first time, that the explicit and exact solution to the Troesch nonlinear two-point boundary value problem may be computed in a direct and straightforward fashion from the general solution obtained by a generalized Sundman transformation for the related differential equation, which appeared to be a special case of a more general equation. As a result, various initial and boundary value problems may be solved explicitly and exactly.

**Category:** Mathematical Physics

[3] **viXra:1712.0364 [pdf]**
*submitted on 2017-12-10 07:52:18*

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

**Comments:** 3 pages

This paper shows, for the first time, that the mathematical pendulum and generalized mathematical pendulum initial and boundary value problems may be computed from the explicit and exact general solution to the corresponding differential equation in a straightforward fashion by a direct method.

**Category:** Mathematical Physics

[2] **viXra:1712.0149 [pdf]**
*submitted on 2017-12-06 10:01:43*

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

**Comments:** 13 pages

A generalized Bratu equation is established in the framework of Sundman transformation. The well-known exact solution to the Bratu boundary value problem is deduced from the obtained explicit and exact general solution which may be also used to compute the exact solution to Bratu type initial and boundary value problems.

**Category:** Mathematical Physics

[1] **viXra:1712.0082 [pdf]**
*submitted on 2017-12-04 05:04:28*

**Authors:** Dmitri Martila

**Comments:** 3 Pages.

Derived the integral of motion for perfect fluid. It reduces the number of valid equations of state: must be p=0.

**Category:** Mathematical Physics