[6] **viXra:1611.0293 [pdf]**
*submitted on 2016-11-20 13:15:56*

**Authors:** Nicolas Poupart

**Comments:** 6 Pages.

It will be demonstrated in this paper that dark mass is a necessary consequence of the relativistic mechanics. This demonstration disregards the forces of physics and is therefore a purely mechanical explanation. The Tully-Fisher relation will be deduced naturally, without appealing to any new physics, and it is therefore possible to derive this law without modifying the Newtonian gravity or general relativity. In addition, a theoretical prediction on a new form of frequency shift will be carried out which makes it possible to refute or confirm this theory.

**Category:** Mathematical Physics

[5] **viXra:1611.0214 [pdf]**
*submitted on 2016-11-14 10:00:31*

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

**Comments:** 11 pages

A mathematical model describing the nonlinear oscillations in elastic structures is proposed. The Energy Balance Method (EBM) is applied to solve the generalized nonlinear Duffing equation obtained in absence of excitation. The numerical results show an excellent agreement with the periodic solutions obtained through the Energy Balance Method. Finally the effects of different parameters on the system behavior are studied.

**Category:** Mathematical Physics

[4] **viXra:1611.0212 [pdf]**
*replaced on 2017-10-03 18:23:05*

**Authors:** William O. Straub

**Comments:** 5 Pages. Inserted a missing factor of 2 on the RHS of Equation (3.7)

n Riemannian geometry there is a unique combination of the Riemann-Christoffel curvature tensor, Ricci tensor and Ricci scalar that defines a fourth-order Lagrangian for conformal gravity theory. This Lagrangian can be greatly simplified by eliminating the curvature tensor term, leaving a unique combination of just the Ricci tensor and scalar. The resulting formalism and the associated equations of motion provide a tantalizing alternative to Einstein-Hilbert gravity that may have application to the problems of dark matter and dark energy without the imposition of the cosmological constant or extraneous scalar, vector and spinor terms typically employed in attempts to generalize the Einstein-Hilbert formalism. Gauss-Bonnet gravity specifies that the full Lagrangian hides an ordinary divergence (or surface term) that can be used to eliminate the curvature tensor term. In this paper we show that the overall formalism, outside of surface terms necessary for integration by parts, does not involve any such divergence. Instead, it is the Bianchi identities that are hidden in the formalism, and it is this fact that allows for the simplification of the conformal Lagrangian.

**Category:** Mathematical Physics

[3] **viXra:1611.0163 [pdf]**
*submitted on 2016-11-11 08:42:21*

**Authors:** M.E. Hassani

**Comments:** 8 Pages;8 References

In 1916, Johannes Droste independently found an exact (vacuum) solution to the Einstein's (gravitational) field equations in empty space. Droste's solution is quasi-comparable to Schwarzschild's one . Droste published his paper entitled “The field of a single centre in Einstein's theory of gravitation, and the motion of a particle in that fieldˮ. The paper communicated (in the meeting of May 27, 1916) by Prof. H.A. Lorentz, and published in ʻProceedings of the Royal Netherlands Academy of Arts and Science. 19 (1): 197-215 (1917)ʼ. In the present article, the Droste's solution is scrutinized and proven to be invalid purely and simply because the procedure used by Droste is mathematically questionable since he had systematically, deliberately, and without any justification ‒removed the constant coefficient ʻ2ʼ from the differential term (v'w') in Eq.(6) and added the differential term (wv'') to the same Eq.(6) in order to obtain Eq.(7) which was and is his principal objective, that is, the desired solution. Consequently, Eqs.(6,7) had clearly been falsified.

**Category:** Mathematical Physics

[2] **viXra:1611.0162 [pdf]**
*replaced on 2017-01-13 07:30:24*

**Authors:** Biswanath Rath, Pravanjan Mallick, Jean Akande, D.K.K. Adjay, L.H. Koudahoun, Y.J.F Kpomahou, Marc D. Monsia

**Comments:** 18 pages

We generate a general model of Liénard type of second order differential equation and study
its classical solution. We also generate Hamiltonian from the differential equation and study
its stable eigenvalues.

**Category:** Mathematical Physics

[1] **viXra:1611.0146 [pdf]**
*submitted on 2016-11-11 00:07:25*

**Authors:** Biswanath Rath

**Comments:** 07 Pages. A new Eigenvalue mathod sing fractional matrix has been introduced .

A new member in Matrix representation has been introduced under
the name Fractional − Matrix and defined properly. Further we show
how one can address spectral analysis using this Fractional − Matrix.
Interesting examples have been considerd .

**Category:** Mathematical Physics