[12] **viXra:1404.0473 [pdf]**
*submitted on 2014-04-28 15:17:49*

**Authors:** Yusuf Ziya Umul

**Comments:** 4 Pages.

A three dimensional Green’s function is derived mathematically by using the two dimensional Green’s function, which is obtained as a result of the modified theory of physical optics’ algorithm. The integration of the three dimensional Green’s function leads to the two dimensional one when there spatial symmetry in the scatterer’s geometry and the incident wave. In order to obtain the three dimensional function, the two dimensional Green’s function is mathematically transformed into an infinite integral according to z. The derived Green’s function is generalized and expressed in a scattering integral for soft and hard surfaces.

**Category:** Mathematical Physics

[11] **viXra:1404.0461 [pdf]**
*submitted on 2014-04-25 02:20:25*

**Authors:** Abel Cavaşi

**Comments:** 7 Pages.

A hypothesis on the motion of bodies under the action of forces perpendicular to the trajectory.

**Category:** Mathematical Physics

[10] **viXra:1404.0441 [pdf]**
*replaced on 2016-09-06 09:36:39*

**Authors:** Hans Detlef Hüttenbach

**Comments:** 12 Pages.

It is shown that the action function of a macroscopic adiabatic system of particles described as continuously differentable functions of energy-momentum in space-time, exists, that this is a plane wave, and that this function can in turn be integrated to a 4-vector field, which satisfies the Maxwell equations in the Lorentz gauge. Also, it is shown, how to formulate these results in terms of Functional Analysis of Hilbert spaces. With it, we show a.o. that PCT = -CPT = ±1 holds, which is a strong form of the PCT-theorem; we show that - in order to capture the concept of mass - the standard model gauge group has to be augmented by a factor group U(2), such that the complete gauge group becomes U(4). It is shown that the sourceless action field in itself suffices to describe the long ranged interaction of matter, both, electromagnetic and gravitational. This turns Einstein’s conception of photons as real particles and subsequently the concept of gravitons into physically unproven assumptions, which complicate, but not simplify the theory. The results appear to imply that the fields themselves do not interact with their sources. Though, this has never been checked by an experiment. As shown, a simple experiment could be carried out to answer this question.

**Category:** Mathematical Physics

[9] **viXra:1404.0290 [pdf]**
*replaced on 2016-07-09 03:35:44*

**Authors:** K. Sugiyama

**Comments:** 9 Pages.

This paper constructs the zeta functions of the quaternion and the sporadic finite simple groups.

Although many researchers have tried the proof of the Riemann hypothesis, they have not resulted in the success. The proof of this Riemann hypothesis has been an important issue of mathematics. In this paper, we construct zeta functions of the quaternion and the sporadic finite simple groups as preparation proving the Riemann hypothesis.

**Category:** Mathematical Physics

[8] **viXra:1404.0281 [pdf]**
*replaced on 2016-07-09 03:56:13*

**Authors:** K. Sugiyama

**Comments:** 42 Pages.

In this paper, we derive the reflection integral equation of the zeta function by the complex
analysis.

Many researchers have attempted the proof of the Riemann hypothesis, but have not been
successful. The proof of this Riemann hypothesis has been an important mathematical issue. In
this paper, we attempt to derive the reflection integral equation by the complex analysis as
preparation proving the Riemann hypothesis.

We obtain a generating function of the inverse Mellin-transform. We obtain a new generating
function by multiplying the generating function with exponents and reversing the sign. We derive
the reflection integral equation from the inverse Z-transform of the generating function.

We derive the Faulhaber’s formula, and Nörlund–Rice integral from the reflection integral equation.

**Category:** Mathematical Physics

[7] **viXra:1404.0116 [pdf]**
*submitted on 2014-04-13 19:03:13*

**Authors:** Victor Christianto

**Comments:** 8 Pages. This paper has been submitted to Prespacetime Journal. Comments are welcome

In a recent paper, M. Zubair et al. described a novel approach for fractional space generalization of the differential electromagnetic equations. A new form of vector differential operator Del, and its related differential operators, is formulated in fractional space. Using these modified vector differential operators, the classical Maxwell equations have been worked out for fractal media. In the meantime, there are other papers discussing fractional Maxwell equations. However, so far there is no derivation of Proca equations and Proca-type equations for GEM in fractional space. Therefore in this paper I present for the first time a derivation of GravitoElectroMagnetic (GEM) Proca-type equations in fractional space. Considering that Proca equations may be used to explain some electromagnetic effect in superconductor, then fractional GEM Proca-type equations may be expected to explain some gravitomagnetic effects of superconductor for fractal media. It is our hope, that this paper may stimulate further investigation and experiments in particular with respect to gravitomagnetic effects.

**Category:** Mathematical Physics

[6] **viXra:1404.0104 [pdf]**
*submitted on 2014-04-12 12:24:45*

**Authors:** Michail Zak

**Comments:** 2 Pages.

A new class of dynamical systems that have random solutions with chaotic
probability densities is discovered.

**Category:** Mathematical Physics

[5] **viXra:1404.0088 [pdf]**
*submitted on 2014-04-11 11:47:03*

**Authors:** Solomon I. Khmelnik

**Comments:** 14 Pages. in Russian

An explanation is offered of the mechanism of turbulent flows emergence, based of the Maxwell-like gravitation equations, updated after some known experiments. It is shown that the moving molecules of flowing liquid interact like electrical charges. The forces of such interaction can be calculated and included to the Navier-Stokes equations as mass forces. Navier-Stocks equations complemented by these forcesbecome equations of hydrodynamics for turbulent flow. For the calculations of turbulent flows the known methods of Navier-Stokes equations solution may be used. // Предлагается объяснение механизма возникновения турбулентных течений, которое основано на максвеллоподобных уравнениях гравитации, уточненных на основе известных экспериментов. Показывается, что движущиеся молекулы текущей жидкости взаимодействуют между собой аналогично движущимся электрическим зарядам. Силы такого взаимодействия могут быть расчитаны и включены в уравнения Навье-Стокса как массовые силы. Уравнения Навье-Стокса, дополненные такими силами, становятся уравнениями гидродинамики для турбулентного течения. При этом для расчета турбулентных течений можно использовать известные методы решения уравнений Навье-Стокса.

**Category:** Mathematical Physics

[4] **viXra:1404.0034 [pdf]**
*submitted on 2014-04-05 00:13:33*

**Authors:** Abel Cavaşi

**Comments:** 3 Pages.

A corollary of the reccurence theorem of the Frenet formulas: the darbuzian of any order depends only on variations of the lancretians of lower order.

**Category:** Mathematical Physics

[3] **viXra:1404.0030 [pdf]**
*submitted on 2014-04-04 07:43:10*

**Authors:** Arm Boris Nima

**Comments:** 9 Pages.

We check that the relation between the angle
and the radius of the movement of an
object following a logarithm
spiral of
p
p
SO(2)
is constant.

**Category:** Mathematical Physics

[2] **viXra:1404.0023 [pdf]**
*submitted on 2014-04-03 09:19:10*

**Authors:** Marcos Georgallides

**Comments:** 13 Pages.

In prior articles , the position of points in Spaces creates Momentum [Λ] which is bounded
in the three constant Energy Layer States k1,2,3 [10] . This rotating energy E = Λ λ is transformed into the Acceleration al and Rotational Ellipsoid , and radiated away ,by loosing angular momentum E = r.m.vr and conserved as momentum E = M.v where emission of linear momentum creates vector v of generalized mass M . When vector v = 0 , this rotating Energy is generalized mass M which is mapped on the perpendicular to Λ plane as velocity v̄r which creates Newton smallest equilibrium accelerations (a f + a p = 0) from Centrifugal (Ff) and Centripetal (Fp) forces . On the infinite points of [PNS] and on the infinite dipole AiBi this acceleration vectors create the Wave motion of the infinite dipole AiBi which dipole are composed of the wavelength λ and the rotating Energy Λ . From this Position , Time enters in equations of motion as the meter of changes only .This rotating Energy is interchanged on dipole A B = (λ , Λ= mv) in the Configuration of co variants λ , m , v̄ as ellipsoid in the two perpendicular fields E = [(/x) + (/dy) + (/z)] . Λ and B = [(/x) + (/dy) + (/z)] xΛ following conservation laws only. Classical theories are confined in Space -Time and Planck-time (which are not assessing the outer reality of Spaces ) , with Time , which is only a meter of changes , and not existing differently . Spaces are composed of infinite points which are related each other with a quantum of Work ( Energy ) .The Norm is the Equation of Total Energy State of Monads equal to → ET = •[(k/ λv) .vE ²] ² + [Λ.vB +ΛxvB ] ² = • [(k/λv) .vE.² ]² + T ² ← which is completely refining Time and leaving only λ Λ = k which indicates a Space Energy Universe . Energy in a Vibrating system is either dissipated into Heat (temperature) which is another type of energy { Energy E as momentum vector Λλ is damped on the perpendicular to Λ plane , as it is like a < Spring-mass System with viscous dumping > , on the basic three co-variants of , Energy E , Lagranges generalized mass M = m , and velocity v̄ with Norm the wavelength λ , and secondly on the rotating Energy Λ= r̄.M.ūr } or radiated away. Newton's laws have a Universal application in all Configuration Systems instead of the referred as the Inertial ones . Even also to the smallest circular motion , ( anywhere that exists momentum ) , exists also Centrifugal and Centripetal forces which create acceleration and the Oscillatory motion . Since also velocity v maybe equal to 0 → c → ∞ then the velocity of light is not the faster in universe . In Black Holes Configuration a new Type of light is needed with a greater velocity than that of light to see what is happening . Light which is a quaternion is travelling either as wave ( photon Λ) either as particle (E =Mv̄= r.m.v̄r ) and in both cases as , a travelling Energy λ.Λ = k interchanged in the two perpendicular forced fields E = . Λ and B = x Λ
( Electromagnetic fields ) following conservation laws . Gauss laws spring from this property.
Oscillatory motion is the simplest case of Energy dissipation of Work embodied in dipole .
In the vibratory system , Energy k = λΛ is Spin of Dipole , dissipated on ⊥ to Λ plane and damped as momentum vector λ.mv̄ . Monad ĀB is the ENTITY and [ A ,B – PA , P B ] is the LAW , so Entities are embodied with the Laws . Entity is quaternion A B , and law |AB| = length of points A,B and imaginary part forces PA , P B . Dipole A B = [ λ , Λ ] in [PNS] are composed of the two elements λ , Λ which are created from points A ,B only where Real part |AB| = λ = wavelength (dipoles ) and from the embodied work , λ Λ , the Imaginary part
W = ∫ P.ds =(r.dP) = r̄xp = I.w = [λ.p] = λ.Λ = k2 , where momentum Λ = p= m.v and Forces
dP = P B –P A are the stationary sources of the Space Energy field . The moving charges is velocity v created from the rotating Energy momentum vector [ Ω = (λ.P) = ± Spin ] which creates the Centrifugal force (Ff) , the equal and opposite to it Centripetal force (Fp) and the acceleration ā mapped (damped ) on the perpendicular to Λ plane as → v E||dP and v B dP. F = q.E + q.v̄ x B = q.[ E + v̄ x B ] is Lorentz force in Electromagnetic crossed fields E and B . Since (dP ± Λ ) the work occurring from momentum p = mv = Λ acting on force dP is zero so when v E =0 , momentum Λ = mv only , is exerting the velocity vector v B to the dipole ,
, λ , and the generalized mass M ( the reaction to the change of velocity v̄ ) which creates the component forces , FE || dP .v and FB dP x v .

**Category:** Mathematical Physics

[1] **viXra:1404.0017 [pdf]**
*submitted on 2014-04-02 22:35:49*

**Authors:** Abel Cavaşi

**Comments:** 3 Pages. Contains an English translation from Romanian

We define the generalized helix of order k, then we make a link with movement on the generalized helix.

**Category:** Mathematical Physics