[5] **viXra:1701.0533 [pdf]**
*submitted on 2017-01-18 05:02:17*

**Authors:** J. Dunning-Davies, J. P. Dunning-Davies

**Comments:** 7 Pages.

Ever since Oliver Heaviside's suggestion of the possible existence of a set of equations, analogous to Maxwell's equations for the electromagnetic field, to describe the gravitational field, others have considered and built on the original notion. However, if such equations do exist and really are analogous to Maxwell's electromagnetic equations, new problems could arise related to presently accepted notions concerning special relativity. This note, as well as offering a translation of a highly relevant paper by Carstoiu, addresses these concerns in the same manner as similar concerns regarding Maxwell's equations were.

**Category:** Mathematical Physics

[4] **viXra:1701.0523 [pdf]**
*submitted on 2017-01-17 04:41:39*

**Authors:** Grushka Ya.I.

**Comments:** 158 Pages. Mathematics Subject Classification: 03E75; 70A05; 83A05; 47B99

This work lays the foundations of the theory of kinematic changeable sets ("abstract kinematics"). Theory of kinematic changeable sets is based on the theory of changeable sets. From an intuitive point of view, changeable sets are sets of objects which, unlike elements of ordinary (static) sets, may be in the process of continuous transformations, and which may change properties depending on the point of view on them (that is depending on the reference frame). From the philosophical and imaginative point of view the changeable sets may look like as "worlds" in which evolution obeys arbitrary laws.
Kinematic changeable sets are the mathematical objects, consisting of changeable sets, equipped by different geometrical or topological structures (namely metric, topological, linear, Banach, Hilbert and other spaces). In author opinion, theories of changeable and kinematic changeable sets (in the process of their development and improvement), may become some tools of solving the sixth Hilbert problem at least for physics of macrocosm. Investigations in this direction may be interesting for astrophysics, because there exists the hypothesis, that in the large scale of Universe, physical laws (in particular, the laws of kinematics) may be different from the laws, acting in the neighborhood of our solar System. Also these investigations may be applied for the construction of mathematical foundations of tachyon kinematics.
We believe, that theories of changeable and kinematic changeable sets may be interesting not only for theoretical physics but also for other fields of science as some, new, mathematical apparatus for description of evolution of complex systems.

**Category:** Mathematical Physics

[3] **viXra:1701.0309 [pdf]**
*replaced on 2017-01-08 17:30:17*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 5 Pages. added comment on mass gap.

This paper is on the mathematical structure of space, time, and gravity. It is shown that electrodynamics is neither charge inversion invariant, nor is it time inversion invariant.

**Category:** Mathematical Physics

[2] **viXra:1701.0299 [pdf]**
*replaced on 2017-01-15 11:21:14*

**Authors:** William O. Straub

**Comments:** 13 Pages. Finalized, with typos fixed in Equations (6.2.2) and (6.3.2)

A very elementary overview of the spinor concept, intended as a guide for undergraduates.

**Category:** Mathematical Physics

[1] **viXra:1701.0166 [pdf]**
*submitted on 2017-01-03 13:20:03*

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

**Comments:** 6 pages

In quantum mechanics, the wave function and energy are required for the complete characterization of fundamental properties of a physical system subject to a potential energy. It is proved in this work, the existence of a Schrödinger equation with position-dependent mass having the prolate spheroidal wave function as exact solution, resulting from a classical quadratic Liénard-type oscillator equation. This fact may allow the extension of the current one-dimensional model to three dimensions and increase the understanding of analytical features of quantum systems.

**Category:** Mathematical Physics