[8] **viXra:1409.0122 [pdf]**
*replaced on 2016-11-12 22:35:43*

**Authors:** Reinhard Frischbier

**Comments:** an 8th page has been added with an appendix

Since the proof given by Wang Qiu-Dong on Dirichlet's assertion
is based on the successive approximations objections to assumptions
of the global solution of this problem have to be raised.

**Category:** Mathematical Physics

[7] **viXra:1409.0109 [pdf]**
*replaced on 2017-05-09 15:51:46*

**Authors:** Doug Jensen

**Comments:** 22 Pages.

Spin is introduced - a new field of mathematics that gives us a deeper look into quantum physics.

**Category:** Mathematical Physics

[6] **viXra:1409.0105 [pdf]**
*submitted on 2014-09-13 12:25:36*

**Authors:** Zafar Turakulov

**Comments:** 6 Pages.

Arguments in favor of existence of Green's functions for all linear equations are analyzed. In case of equation for electromagnetic field, these arguments have been widely used through formal considerations according to which electromagnetic field equations are nothing but some non-covariant scalar equations. We criticize these considerations and show that justification of applying the method of Green's functions to equations of classical electrodynamics are invalid. Straightforward calculations are presented which show that in case of dipole radiation the method gives incorrect results.

**Category:** Mathematical Physics

[5] **viXra:1409.0050 [pdf]**
*replaced on 2015-01-11 06:55:05*

**Authors:** J.A.J. van Leunen

**Comments:** 45 Pages.

It is possible to derive a model from a set of well selected first principles. After a series of extensions of this foundation the model shows many similarities with what we know from observing reality.
The first principles formulate a skeleton relational structure that is mathematically known as an orthocomplemented weakly modular lattice. It can be considered as part of a recipe for modular construction. When starting from this foundation it is mathematically inescapable evident that this model confines to a quaternionic space-progression model that proceeds with model-wide progression steps through an ordered sequence of sub-models that each represent a static status quo of the whole model.
This base model is a hybrid construct that consists of a sub model that treats all discrete objects and a continuum based sub model that embeds the discrete objects. The discrete part of the model keeps its data in an infinite dimensional separable Hilbert space. The continuum part stores its data in a corresponding non-separable Hilbert space.
An extra mechanism that controls the coherence and the scheduling of dynamics applies the recurrent embedding of the discrete objects into appropriate continuums.
Despite the fact that the target of the model is planned to reach a level in which it shows many features and phenomena that we know from observing reality, this model is not claimed to be a model of physics. The reason for this restriction is that many of its aspects cannot be observed and will never become observable. Physicists tend to deny completely or largely deduced models.
The deduced model appears to own built-in restrictions that guard against uncontrolled growth of the complexity of the model.

**Category:** Mathematical Physics

[4] **viXra:1409.0047 [pdf]**
*replaced on 2016-03-21 12:30:57*

**Authors:** DT Froedge

**Comments:** 26 Pages. This paper is the quest of a lifetime that will never be noticed.

The purpose of this paper is to develop a single solution to both the Klein-Gordon & Dirac equations that expresses both the QM and the classical aspects of particles. It is found that this can be done, but only in the context of a system that has an initial event (T = 0) and is expanding at c, thus it is consistent with a big bang representation of the universe. The equations are defined in geometric algebraic, and the KGD equation will be considered a single equation factorable into linear products of the two linear Dirac expressions, with a solution defined analogously to path integrals. The solution has botha Gaussian shaped amplitude, (classical), and phase, (QM) components satisfying the quadratic KG equation, and the linear Dirac expression. The equation differentials are not restricted to representing the normal QM operator replacement of p and E, applicable to the linear equation, but have a broader context in operating on the more complex function with amplitude and phase factors. The solutions represent the particle at a single event, thus the standard view of the solution being a probability amplitude field over spacetime is not applicable, but an alternate observational field is illustrated that demonstrates the connection of the solutions to the observed wave characteristics. The phase factors are as usual cyclic, but the amplitude factors exist only in the context of the entire interval. The amplitude factor of the solution is proportional to mass and thus should offer insight into particle mass ratios.

**Category:** Mathematical Physics

[3] **viXra:1409.0038 [pdf]**
*submitted on 2014-09-06 09:20:35*

**Authors:** Markos Georgallides

**Comments:** 14 Pages.

This paper shows in a rigorous description, how nature is produced only from Euclidean Geometry , and that is not needed any attempt ion to establish any Philosophy or axioms as these of theories. All physical laws such as Momentum Newton`s second law of gravity, Maxwell`s equations of fields, conservation laws, Spring from geometry logic and are common to, the Large and Short scale distances without any exclusion principles or assumptions. Existing of everything follows the only one conservation law, that of Virtual work and not any logical starting point . [STPL] line (cylinder) is a geometrical mechanism , the only passage (mould = Tensor) from, Common Circle of Space , Anti-Space (which is a Plane) to Particles (reflected evanescent waves) with real part (s) and imaginary part (± v.i) and without any assumption , that reflected waves have an unknown phase shift . Reflected wave is equal to the incident wave (the real part to the real place and the imaginary part to the imaginary place with all incident properties (spin) included) , i.e. different properties create distinct kinds of waves as these are the Fermions and Quarks of scalar magnitudes with ½ spin and Bosons of vector magnitudes with 1 spin. In Common circle circumference, the components of light waves interfere with each other to produce a ,Color , Spectrum because of Birefringence, a property of the (Centripetal) stress material with more than two indices, n, of refraction. [Retardation is the phase difference between the two light vectors through the material at different velocities (fast, slow) and determines color Bands and as Retardation and stress (σ) go up then the colors cycle through a more or less repeating Pattern and the Intensity of the colors diminishes] . In Common Circle of equilibrium Space Anti-Space with different angular velocity vector, v = w r, in the absence of applied Torques produces the Color Spectrum which is, the < Color Forces > → Gluon Red, Gluon Green, Gluon Blue and velocity of light on the circumference. Planck`s length Lp in Einstein's theory of General Relativity is approximately implicated to the properties of physical Spaces instead that of Lp = e i.( - 5π / 2).10 = 8,906.10 35 m which is based on the three natural constants ,e, i, π , only . Lame`s stress ellipsoid represent Cauchy stress quadric of the Stress State at a point . Mohr circle can be applied to any symmetric 2x2 or 3x3 Tensor matrix and is graphically (geometrically) representing Cauchy stress Tensor. [STPL] line can be applied to any 3x3 symmetric Tensor (which are Spaces , Anti-Spaces and Sub-Spaces) and is graphically representing the passage (mould = Tensor 6x3) from , Common Circle of the Gravity Cave, in Lg = 3,969.10 62 m = 2r (a Plane) to Particles in Planck`s Cave Lp , with Velocities (v = wr) that of light ,c, tending to zero . For rotations in caves Lc > Lg then exist Velocities (vc = wr)
faster than that of light ,c, [vc > c ] tending to ∞. The hidden pattern of universe is ,STPL- line,
which is off the Spaces and connect them ( maintain , conserve , and support all universe ) ,
so , it is the Navel string of galaxies.

**Category:** Mathematical Physics

[2] **viXra:1409.0030 [pdf]**
*replaced on 2015-01-02 06:40:47*

**Authors:** Algirdas Antano Maknickas

**Comments:** 4 Pages.

The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed into full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Velocity and outer forces densities components were expressed in form of curl for obtaining solutions satisfying continuity condition specifying divergence of velocities equality to zero. Finally, solution in 3D space for any shaped boundary was expressed in terms of 3D Green function and inverse Laplace transform accordantly.

**Category:** Mathematical Physics

[1] **viXra:1409.0020 [pdf]**
*replaced on 2014-12-22 13:27:22*

**Authors:** DT Froedge

**Comments:** 10 Pages.

For most purposes in physics the concept of mass particles and photons are treated as though they are completely separate and distinct entities having little connection accept through collision interactions. This paper explores the concept of a mass particle being viewed as a pair of trapped photons in a mass-less box demonstrating proper relativistic dynamics, Lorentz covariance, and gravitational properties. The mechanism of trapping of the photons in the particle is not herein defined; however the lack of sufficient spin to properly constitute a photon would be a containment factor. Although this presentation is primarily focused on electrons, presumably it would be applicable to any particle with primary constituents consisting of particles that travel at light speed along null vectors. This illustrates the concept of the equivalence of mass and energy, and why mass velocity cannot exceed the speed of light.
It is asserted and illustrated; that the gravitational effect on particles and photons can be can be effectuated by a simple gradient in the speed of light. This allows the assertion that gravitation is a local alteration of c generated by the presence of matter and could be a QFT effect.

**Category:** Mathematical Physics