[7] **viXra:1309.0212 [pdf]**
*submitted on 2013-09-30 16:38:40*

**Authors:** Jeremy Dunning-Davies

**Comments:** 4 Pages. Again it is hoped this short note will provoke more examination of this topic.

Here two derivations of Hamilton’s equations of motion are examined and found to depend crucially on both the system being conservative and the mass being constant. It is speculated that these derivations might be extended to the case where, as well as the system being conservative, the mass varies purely with time. However, at this stage, other generalisations seem unlikely and, if that is so, the usefulness of the Hamilton approach in mechanics would appear to be limited.

**Category:** Mathematical Physics

[6] **viXra:1309.0210 [pdf]**
*submitted on 2013-09-30 14:46:09*

**Authors:** Jeremy Dunning-Davies

**Comments:** 6 Pages. It is hoped this short note will provoke further examination of the topic discussed.

In most, if not all, introductions to classical mechanics, the mass is assumed to be constant. Usually this is mentioned and often attention is drawn to such systems as rocket motion to indicate that, in practice, the mass is not always a constant. In truth, many students actually meet a varying mass for the first time when introduced to the Special Theory of Relativity. However, varying masses do occur in nature when relativistic effects are not important. Here an attempt is made to draw together some common results of classical mechanics with a variable mass taken into account. Particular attention will be drawn to a perceived change in the expression for the kinetic energy and to crucial changes in the basic form of Lagrange’s equations of motion.

**Category:** Mathematical Physics

[5] **viXra:1309.0141 [pdf]**
*submitted on 2013-09-19 10:13:47*

**Authors:** John Frederick Sweeney

**Comments:** 37 Pages. De – Constructing De Marrais Series

The late Robert Marrais wrote of 3 distinct aspects of Sedenion Space: one belonging to the E8 x E8 Super – Symmetry of the embattled Super String Theory, one belonging to Icosahedral Rotation Groups or H3, and a third belonging to O. V. Lyashko. In addition, this paper discusses methods to classify and to categorize the Sedenions.

**Category:** Mathematical Physics

[4] **viXra:1309.0116 [pdf]**
*submitted on 2013-09-17 10:54:11*

**Authors:** John Frederick Sweeney

**Comments:** 34 Pages.

This paper examines a point of intersection between the work of the late Robert de Marrais and Vedic Physics. Specifically, de Marrais discussed the concept of Lissajous Figures in relation to Sedenions and his 42 Assessors, in his first paper about Box Kites. Later, John Baez took up a related subject, the problem of epicycloids, apparently without having read the work of de Marrais. This paper examines this intersection between leading - edge mathematical physics and Vedic Physics in order to further illuminate the higher algebras - the Octonions, Sedenions and Trigintaduonions.

**Category:** Mathematical Physics

[3] **viXra:1309.0087 [pdf]**
*replaced on 2013-09-14 21:55:02*

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

**Comments:** 10 Pages.

The following article briefly lays out a plausible alternative to the P=NP problem, and defines a general physical approach to the computational physics involved. It makes a conjecture that the underlying differences between quantum systems and classical mechanics can be bridged by a newer and novel mathematical parameter.

**Category:** Mathematical Physics

[2] **viXra:1309.0008 [pdf]**
*replaced on 2014-09-03 14:10:22*

**Authors:** Algirdas Antano Maknickas

**Comments:** 8 Pages.

It was proposed new gauge invariant Lagrangian, where the gauge field interact with the charged electromagnetic fields. Gauge invariance was archived by replacing of particle mass with new one invariant of the field $F_{\mu\nu}F^{\mu\nu}$ multiplied with calibration constant $\alpha_g$. It was shown that new proposed Lagrangian generates similar Dirac and electromagnetic field equations. Solution of Dirac equations for a free no massless particle answers to the 'question of the age' why free particle deal in experiments like a de Broil wave. Resulting wave functions of the new proposed Lagrangian will describe quantized list of bespinor particles of different masses. Finally, it was shown that renormalization of the new proposed Lagrangian is similar to QED in case similarity of new proposed Lagrangian to classic QED.

**Category:** Mathematical Physics

[1] **viXra:1309.0002 [pdf]**
*submitted on 2013-09-02 05:33:45*

**Authors:** José Francisco García Juliá

**Comments:** 1 Page.

The existence of the waves proves the existence of the special relativity.

**Category:** Mathematical Physics