[6] **viXra:1406.0173 [pdf]**
*replaced on 2016-03-10 06:39:59*

**Authors:** Sergey G. Fedosin

**Comments:** 20 pages. OALib Journal, Vol. 3, P. 1-15 (2016). http://dx.doi.org/10.4236/oalib.1102459.

A hypothesis is suggested that the fields associated with macroscopic bodies, such as classical electromagnetic and gravitational fields, acceleration field, pressure field, dissipation field, strong interaction field and weak interaction field, are the manifestations of a single general field. Using the generalized four-velocity as the four-potential of the general field, with the help of the principle of least action it is shown that each of these seven fields contributes linearly to the formation of the total four-force density. The general field equations, equation of the particles’ motion in this field, equation for the metric and the system’s energy are determined. It should be noted that the stress-energy tensor of the general field includes not only the stress-energy tensors of these seven fields, but also the cross terms with the products of various field strengths. As a result, the energy and momentum of the system with several fields can differ from the classical values, not taking into account such cross terms in the general field energy and momentum.

**Category:** Mathematical Physics

[5] **viXra:1406.0130 [pdf]**
*replaced on 2016-07-09 03:08:00*

**Authors:** K. Sugiyama

**Comments:** 19 Pages.

We derive the reflection integral equation of the zeta function by the quaternionic analysis.

Many researchers have attempted proof of the Riemann hypothesis, but they 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 from the quaternionic analysis as preparation proving the Riemann hypothesis.

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

Probability is proportional to the number of elementary events, and the number of elementary events is the square of the number of elementary state. The number of elementary states is proportional to the surface area of the manifold, and the surface area of the manifold is the absolute value of the wave function. Therefore, the probability is proportional to the absolute square of the wave function.

**Category:** Mathematical Physics

[4] **viXra:1406.0125 [pdf]**
*submitted on 2014-06-19 17:56:51*

**Authors:** M. D. Sheppeard

**Comments:** 4 Pages.

A concise algebraic definition of the associahedra and permutohedra polytopes is given in terms of canonical coordinates for discrete simplices.

**Category:** Mathematical Physics

[3] **viXra:1406.0065 [pdf]**
*replaced on 2014-06-12 09:28:02*

**Authors:** Valdir Monteiro dos Santos Godoi

**Comments:** 2 Pages.

We analyze the solution of Schwarzschild Equation taking mathematically the observation that the motion of bodies can be a spiral modulated by trigonometric functions, which may be something more important than simply mean a shift of perihelion.

**Category:** Mathematical Physics

[2] **viXra:1406.0063 [pdf]**
*submitted on 2014-06-10 10:50:27*

**Authors:** Markos Georgallides

**Comments:** 14 Pages.

In prior articles was shown that all Monads are Dipole , z = (a+i.v)^ n =1/w, on nth power where
issues their Binomial nature and also on exponential power of the natural logarithm base ,e, as
→ z^n = (s +v̄ i )¹/ w = |zo| ̄ w. [cos.(φ+2kπ)/w + i.sin.(φ+2kπ)/w] = |zo| ̄ w .e^ i.(φ+2kπ) / w ←
meaning that these are of wave and sinusoidal nature . This Quaternion exponential form of the quantized Spaces , Anti-Spaces , Sub-Spaces and Energy as logarithm on decimal base ,b, is the
,Monads geometrical interpretation, measured on the three natural and constant numbers e , π , i ,
on bases which are independent of any Space and coordinate system one of them is Planck length's
Lp = 8,906.10 ^ -35 m (10 - 35 m).
Moreover , Diffraction cavities are created for storing Energy of all types , and for Temperature in
the Tank cavity Lt = 1,781.10 ^ -7 m (10-7m) from where is then dissipated and damped in Planck's Tank cavity Lp following the two ideal Gas equations [Λ= nRT/V] of Entropy in Thermodynamics
(perfectly elastic) and the Temperature of the Black-body which is quantized and dissipated per circle ( from the Balance Tank energy ) following Stefan - Boltzmann law Wd = σ.T 4 where then
the Temperature in this Ideal Tank T t = 2,213.1010 K which absorbs and emits all types of the electromagnetic radiations .
Energy (Heat ) causes Monads (molecules) to vibrate . More Heat creates higher frequency vibrations and increasing also the Intensity = Pressure of the radiation . Boltzmann's constant
σ = 5,67.10– 8 (W/m².K 4) = 1,38066.10– 23(J/K) is the quantized Energy [Vibration in magnitude L < 3,9698.10 – 62 m , under Heat cause] into a new monad , the Intensity . In this magnitude is emitted Graviton particle (radiation) in Gravity's Length Lg = e ^ -i.(9π/2).b = e - i.( 9π/2 ).10 =
e ̄ ( 141,372 ) = 3,969.10 ̄ 62 m , and now Gravity is Incorporated into Quantum mechanics .

**Category:** Mathematical Physics

[1] **viXra:1406.0017 [pdf]**
*replaced on 2015-08-11 09:18:56*

**Authors:** Sergey G. Fedosin

**Comments:** 13 pages. International Journal of Thermodynamics. Vol. 18 (No. 1), pp. 13-24, 2015. http://dx.doi.org/10.5541/ijot.5000034003.

From the principle of least action the equation of motion for viscous compressible and charged fluid is derived. The viscosity effect is described by the 4-potential of the energy dissipation field, dissipation tensor and dissipation stress-energy tensor. In the weak field limit it is shown that the obtained equation is equivalent to the Navier-Stokes equation. The equation for the power of the kinetic energy loss is provided, the equation of motion is integrated, and the dependence of the velocity magnitude is determined. A complete set of equations is presented, which suffices to solve the problem of motion of viscous compressible and charged fluid in the gravitational and electromagnetic fields.

**Category:** Mathematical Physics