Mathematical Physics

2012 Submissions

[8] viXra:2012.0200 [pdf] submitted on 2020-12-28 11:18:23

Exact Solution of Some Non-Autonomous Nonlinear ODEs of Second Order

Authors: E. A. Doutètien, K. K. D. Adjaï, M. D. Monsia
Comments: 10 pages

This paper shows the exact integrability analysis of two classes of non-autonomous and nonlinear differential equations. It has been possible to recover some equations of general relativity from the first class of equations and consequently to compute their solution in fashion way. The second class is shown to include the Emden-Fowler equation and its integrability analysis, performed with the first integral theory developed by Monsia et al. [16] allowed to compute the exact solution of some subclasses of Emden-Fowler equations.
Category: Mathematical Physics

[7] viXra:2012.0190 [pdf] submitted on 2020-12-25 23:17:29

Transformation of the Covariant Derivative

Authors: Anamitra Palit
Comments: 3 Pages.

The article considers the transformation of the covariant derivative of a rank one contravariant tensor to bring out a conflicting aspect of the theory in that we arrive at an impossible equation.
Category: Mathematical Physics

[6] viXra:2012.0156 [pdf] replaced on 2020-12-23 11:09:59

On the Existence of Identical Periodic Solutions Between Differential Equations

Authors: J. Akande, K. K. D. Adjaï, A.V. R. Yehossou, M. D. Monsia
Comments: 5 pages

We present for the first time a singular quadratic Lienard type equation having the linear harmonic oscillator solution. We show also the existence of a singular quadratic Lienard type equation having the solution of the Ermakov-Pinney equation. Consequently, these equations may be used as truly nonlinear oscillators.
Category: Mathematical Physics

[5] viXra:2012.0117 [pdf] submitted on 2020-12-14 19:28:18

On Truly Nonlinear Oscillator Equations of Ermakov-Pinney Type

Authors: M. Nonti, K.K.D. Adjaï, J. Akande, M.D. Monsia
Comments: 17 Pages.

In this paper we present a general class of differential equations of Ermakov-Pinney type which may serve as truly nonlinear oscillators. We show the existence of periodic solutions by exact integration after the phase plane analysis. The related quadratic Lienard type equations are examined to show for the first time that the Jacobi elliptic functions may be solution of second-order autonomous non-polynomial differential equations.
Category: Mathematical Physics

[4] viXra:2012.0104 [pdf] submitted on 2020-12-14 12:54:13

Existence of Non-Periodic Real-Valued and Complex-Valued Solutions of Mathews-Lakshmanan Oscillator Equation

Authors: J. Akande, K.K. D. Adjaï, L.H. Koudahoun, M.D. Monsia
Comments: 7 pages

We show in this paper the existence of non-periodic real-valued and complex-valued solutions of the Mathews-Lakshmanan oscillator equation. The theory allows also to find the sinusoidal periodic solution given by the authors. As an oscillator can only have periodic solutions for the same model parameters, we conclude that the Mathews-Lakshmanan equation is a pseudo-oscillator.
Category: Mathematical Physics

[3] viXra:2012.0061 [pdf] submitted on 2020-12-09 09:13:31

The Soft Shadow of Physical Reality

Authors: Deep Bhattacharjee, Aruna Harikant
Comments: 4 Pages. 1 Figure

Combining the ‘Holographic Principles’ of Leonard Susskind and ‘Simulation Theory’ of Nick Bostrom, a theory has been reproduced in this paper dictating the negation of the relative entropy persistent in the present, thereby forbidding their collapse as subject to increment of entropy while moving forward in time and decrement of entropy while moving backward in time, preventing a phase of state before the Big Bang or the collapse of the convergence. The universe in its own way diverges taking the simultaneous array of ‘Past, Present and Future’ with the ‘Bread-Slice’ concept of time, the reality being augmented by some future advanced civilizations to create a Spatio-Temporal 3D ‘Hologram’ on a 2D Canvas, projecting through a simulation, thus creating exponential channels of realistic layers with a certain percentile of errors, which are so minimal in present stage, that, the universal constants of nature, G,c,ℏ remains unaltered, which may alter in future if the error fragmentation over simulation takes growth, censoring the future reality in a state of complete superposition excluding us, who are residing in the exponential shadows of simulations
Category: Mathematical Physics

[2] viXra:2012.0029 [pdf] submitted on 2020-12-05 22:27:21

On Properties of Solutions of a Generalized Quadratic Lienard Quation

Authors: Elémawussi Apédo Doutètien, K. K. Damien Adjaï, Jean Akandé, Marc Delphin Monsia
Comments: 1 Page.

We present a quadratic Lienard equation which contains several nonlinear equations as special cases. The equation is exactly and explicitly integrable despite of the presence of quadratic term. The general solution is expressed as a power law of a sine function of time. This allows to compare the properties of solutions with those obtained by phase plane analysis.
Category: Mathematical Physics

[1] viXra:2012.0002 [pdf] replaced on 2021-08-03 12:08:26

Operational Definition of Electric Charge and Derivation of Coulomb’s Law

Authors: Muntafa Mubarrat Mahi
Comments: 6 Pages.

The paper focuses on the part of the Coulomb’s Law that is just a definition and provides one possible mechanism for operationally defining electric charge based on the concept of force(action at a distance). Then a derivation of Coulomb’s law from the definition is presented and the sign of the charges are defined. Finally, the paper concludes with a discussion on the conservation of charge.
Category: Mathematical Physics