[8] **viXra:1706.0572 [pdf]**
*submitted on 2017-06-30 11:04:20*

**Authors:** Gary D. Simpson

**Comments:** 11 Pages.

This text continues the development of pentuples begun in Part – 2 of these works. Matrix formulations are presented that are easily inverted. The presentation of a pentuple is similar to the form of a quaternion. A functionality is presented in Equation 4.2 that mimics wave-function collapse. Octonion multiplication is shown to be very similar irrespective of whether the complex i commutes normally or anti-commutes.

**Category:** Mathematical Physics

[7] **viXra:1706.0456 [pdf]**
*submitted on 2017-06-23 18:05:12*

**Authors:** Mauro Bernardini

**Comments:** 44 Pages. Comment (Abstract) replacement

This is a brief summary of the Theory of Transcendent Reality (TTR), which describes the main postulates and mathematics used to describe and support the rationality of the Alef's model as unique and absolute being container of all the existences. This first issiue allow to describe the real physical composition of all the parallel universes contained in Alef's body. Universes that are logically and rationally constituted exclusively by Particles of Existence with a mass equal to that of a Proton and which generate an "apparent" existence since they are interpreted as existent only by the under-dimensional beings they generate in each single universe. Highlighting therefore that the Particles of Existence present in every universe are in fact 11 dimensional body slices of the Points of Alef, which, in turn, are the only real components of Alef's body: and, therefore, Particles of Existence that never really born nor died.

**Category:** Mathematical Physics

[6] **viXra:1706.0416 [pdf]**
*submitted on 2017-06-21 09:12:37*

**Authors:** Miroslav Josipović

**Comments:** 1 Page.

There is an erroneous formula in the article Functions of multivectors in 3D Euclidean geometric algebra via spectral decomposition (for physicists and engineers).

**Category:** Mathematical Physics

[5] **viXra:1706.0193 [pdf]**
*replaced on 2017-07-15 21:47:18*

**Authors:** A. A. Frempong

**Comments:** 19 Pages. Copyright © by A. A. Frempong

Coincidences. The US Supreme Court consists of nine members, one of whom is the Chief Justice of the Court. So also, a one-direction Navier-Stokes equation consists of nine members, one of which is the indispensable gravity term, without which there would be no incompressible fluid flow as shown by the solutions of the N-S equations (viXra:1512.0334). Another coincidence is that numerologically, the number, 9, is equivalent to the 1800's (1 + 8 + 0 + 0 = 9) time period during which the number of the members of the Supreme Court became fixed at 9, while the formulation of the nine-term N-S equations was completed. Also, another coincidence is that the solutions of the N-S equations were completed (viXra:1512.0334) by the author in the year, 2016 (2 + 0 +1+ 6 = 9). Using a new introductory approach, this paper covers the author's previous solutions of the N-S equations (viXra:1512.0334). In particular, the N-S solutions have been compared to the equations of motion and liquid pressure of elementary physics. The N-S solutions are (except for the constants involved) very similar or identical to the equations of motion and liquid pressure of elementary physics. The results of the comparative analysis show that the N--S equations have been properly solved. It could be stated that the solutions of the N-S equations have existed since the time the equations of motion and liquid pressure of elementary physics were derived. A one-direction Navier-Stokes equation has also been derived from the equations of motion and liquid pressure of elementary physics. Insights into the solutions include how the polynomial parabolas, the radical parabolas, and the hyperbolas interact to produce turbulent flow. It is argued that the solutions and methods of solving the N-S equations are unique, and that only the approach by the author will ever produce solutions to the N-S equations. By a solution, the equation must be properly integrated and the integration results must be tested in the original equation for identity before the integration results are claimed as solutions

**Category:** Mathematical Physics

[4] **viXra:1706.0189 [pdf]**
*submitted on 2017-06-15 03:48:11*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 6 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Normalized Similarity Measure considered to Exhaustion [1] (please see the addendum of [1] as well).

**Category:** Mathematical Physics

[3] **viXra:1706.0137 [pdf]**
*replaced on 2017-06-14 12:16:22*

**Authors:** Marcellin Nonti, Fernando Y. J. Kpomahou, Jean Akande, Damien K. K. Adjaï, Lucas H. Koudahoun, Marc D. Monsia

**Comments:** 4 pages

Hamiltonian dynamics and exact Gibbs statistical mechanics of a system of quadratic Liénard type oscillators have been investigated. The work has shown that the canonical ensemble for the harmonic oscillator is a particular case of the Gibbs ensemble theory developed in this paper.

**Category:** Mathematical Physics

[2] **viXra:1706.0123 [pdf]**
*submitted on 2017-06-09 01:36:02*

**Authors:** Ramesh Chandra Bagadi

**Comments:** 8 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Normalized Similarity Measure considered to Exhaustion [1] (please see the addendum of [1] as well).

**Category:** Mathematical Physics

[1] **viXra:1706.0034 [pdf]**
*submitted on 2017-06-05 02:03:41*

**Authors:** Richard L Amoroso, Georges Lemaitre

**Comments:** 13 Pages. Lemaitre's 1948 paper translated from original French, ACTA, Vol. XII, No. 8, pp. 57-80

The author applies the notion of quaternions, as practiced by Klein in the Erlangen program, to determine the fundamental
properties of elliptical space.

**Category:** Mathematical Physics