[8] **viXra:1507.0169 [pdf]**
*submitted on 2015-07-21 15:48:24*

**Authors:** M. D. Sheppeard

**Comments:** 20 Pages.

These introductory lectures on affine and quantum algebras are motivated by the idea that triality and exceptional structures are crucial to gravity and color symmetry. We start with the ADE classification.

**Category:** Mathematical Physics

[7] **viXra:1507.0157 [pdf]**
*replaced on 2016-01-25 10:00:53*

**Authors:** Arm Boris Nima

**Comments:** 18 Pages.

We give an expression of the Arm function which gives rise to the definition of the Arm binomial coefficient and the corresponding Arm triangle.

**Category:** Mathematical Physics

[6] **viXra:1507.0139 [pdf]**
*submitted on 2015-07-17 22:04:16*

**Authors:** Harry Watson

**Comments:** 3 Pages.

A Single Model for Various Shapes of the Proton. Experiments have indicated that the proton may be shaped as a sphere, an oblate spheroid, a peanut, a dumbbell, an hourglass, or a torus. A model is presented that satisﬁes each of the above. The model also provides an estimate of the mass ratio of the proton to the electron.
(4π)(4π−1/pi)(4π−2/π)=1836.15 (1)
If we assume that the electron is a perfect ball with radius equal to one, the model becomes a ball of radius (4π−1/π) with a sector or non-overlapping sectors removed. The total curved surface area of the removed sector(s) is 4/π.
harry.watson@att.net

**Category:** Mathematical Physics

[5] **viXra:1507.0112 [pdf]**
*replaced on 2015-09-21 08:38:09*

**Authors:** Andrei P. Kirilyuk

**Comments:** 10 pages, 4 eqs, 15 refs; Paper presented at the FQXi essay contest 2015, http://fqxi.org/community/forum/topic/2398; Main text without change, discussion summary from the paper site is added as Appendices in v2

The current crisis in exact description of fundamental and applied systems has the well-defined origin and rigorously substantiated resolution in the form of qualitatively extended, unified mathematical framework of unreduced dynamic complexity. It is based on the unreduced universal solution of arbitrary interaction problem revealing the new, extended qualities with respect to traditional mathematical constructions. We describe the origin of the problem, the proposed causally complete solution and its mathematical novelties confirmed by problem-solving applications in fundamental and applied sciences.

**Category:** Mathematical Physics

[4] **viXra:1507.0111 [pdf]**
*submitted on 2015-07-14 22:03:42*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 4 Pages.

We're going to model the grand unification scheme base on a restricted and primitive set of mathematical properties. This procedure carries limitations but using current day tools will unveil unique insights.

**Category:** Mathematical Physics

[3] **viXra:1507.0108 [pdf]**
*submitted on 2015-07-14 10:12:10*

**Authors:** Valeri V. Dvoeglazov

**Comments:** 2 Pages. http://spacetime.narod.ru/13.html

Misconceptions have recently been found in the definition of a partial
derivative (in the case of the presence of both explicit and implicit
dependencies of the function subjected to differentiation) in the classical
analysis. We investigate the possible influence of this discovery on quantum
mechanics and the classical/quantum field theory. Surprisingly, some
commutators of operators of space-time 4-coordinates do not equal to zero.
Thus, we provide the bases for new-fashioned noncommutative field theory.

**Category:** Mathematical Physics

[2] **viXra:1507.0086 [pdf]**
*replaced on 2015-12-07 17:03:44*

**Authors:** Miroslav Josipović

**Comments:** 9 Pages. v3

Geometric algebra is a powerful mathematical tool for description of physical phenomena. The article [3] gives a thorough analysis of functions of multivectors in Cl3 relaying on involutions, especially Clifford conjugation and complex structure of algebra. Here is discussed another elegant way to do that, relaying on complex structure and idempotents of algebra. Implementation of Cl3 using ordinary complex algebra is briefly discussed.

**Category:** Mathematical Physics

[1] **viXra:1507.0056 [pdf]**
*submitted on 2015-07-08 20:25:25*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 5 Pages.

The manuscript will prove and describe the trust head theorem [TrHT].

**Category:** Mathematical Physics