[4] **viXra:1211.0143 [pdf]**
*replaced on 2014-04-19 05:52:35*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 10 Pages.

ABSTRACT: We study a given exponential potential
aebx on the Real half-line which is possible
related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method
to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue
staircase includes the oscillatory and smooth part of the Number of Riemann zeros.
In this paper and for simplicity we use units so 2m1
Keywords: = Riemann Hypothesis, WKB semiclassical approximation, exponential potential

**Category:** Mathematical Physics

[3] **viXra:1211.0140 [pdf]**
*submitted on 2012-11-24 02:12:29*

**Authors:** Guowu Meng

**Comments:** 13 Pages.

Let ${\mathbb R}^{2k+1}_*={\mathbb R}^{2k+1}\setminus\{\vec 0\}$ ($k\ge 1$) and $\pi$: ${\mathbb R}^{2k+1}_*\to \mathrm{S}^{2k}$ be the map sending $\vec r\in {\mathbb R}^{2k+1}_*$ to ${\vec r\over |\vec r|}\in \mathrm{S}^{2k}$. Denote by $P\to {\mathbb R}^{2k+1}_*$ the pullback by $\pi$ of the canonical principal $\mathrm{SO}(2k)$-bundle $\mathrm{SO}(2k+1)\to \mathrm{S}^{2k} $. Let $E_\sharp\to {\mathbb R}^{2k+1}_*$ be the associated co-adjoint bundle and $E^\sharp\to T^*{\mathbb R}^{2k+1}_*$ be the pullback bundle under projection map $T^*{\mathbb R}^{2k+1}_*\to {\mathbb R}^{2k+1}_*$. The canonical connection on $\mathrm{SO}(2k+1)\to \mathrm{S}^{2k} $ turns $E^\sharp$ into a Poisson manifold.
The main result here is that the real Lie algebra $\mathfrak{so}(2, 2k+2)$ can be realized as a Lie subalgebra of the Poisson algebra $(C^\infty(\mathcal O^\sharp), \{, \})$, where $\mathcal O^\sharp$ is a symplectic leave of $E^\sharp$ of special kind. Consequently, in view of the earlier result of the author, an extension of the classical MICZ Kepler problems to dimension $2k+1$ is obtained. The hamiltonian, the angular momentum, the Lenz vector and the equation of motion for this extension are all explicitly worked out.

**Category:** Mathematical Physics

[2] **viXra:1211.0051 [pdf]**
*replaced on 2013-04-02 13:59:43*

**Authors:** Hosein Nasrolahpour

**Comments:** 7 Pages. A few formulas and references added.

We investigate the time evolution of the fractional electromagnetic waves by using the time
fractional Maxwell's equations. We show that electromagnetic plane wave has amplitude which
exhibits an algebraic decay, at asymptotically long times.

**Category:** Mathematical Physics

[1] **viXra:1211.0048 [pdf]**
*submitted on 2012-11-10 00:53:16*

**Authors:** Jian-zhong Zhao

**Comments:** 10 Pages.

Violating the law of energy conservation, Zanaboni Theorem is invalid and Zanaboni's proof is wrong. Zanaboni's mistake of " proof " is analyzed. Energy Theorem for Zanaboni Problem is suggested and proved. Equations and conditions are established in this paper for Zanaboni Problem, which are consistent with , equivalent or identical to each other. Zanaboni Theorem is, for its invalidity , not a mathematical formulation or
proof of Saint-Venant's Principle.
AMS Subject Classifications: 74-02, 74G50

**Category:** Mathematical Physics