[8] **viXra:1512.0458 [pdf]**
*submitted on 2015-12-28 10:27:37*

**Authors:** Markos Georgallides

**Comments:** 33 Pages. The Unsolved ancient-Greek Problems , The Unsolved Special E-Problems

The Special Problems of E-geometry consist the Quantization Moulds of Euclidean Geometry in it , to become → The Basic monad , through mould of Space –Anti-space in itself , which is the material dipole in inner monad Structure which is Identical with the Electromagnetic cycloidal field → Linearly , through mould of Parallel Theorem , which are the equal distances of common Line-meter between the points of parallel and line → In Plane , through mould of Squaring the circle , where the two equal and perpendicular monads consist a Plane acquiring the common Plane-meter ,pi,→ and in Space ,(volume) , through mould of the Duplication of the Cube , where any two Un-equal and perpendicular monads acquire the common Space-meter ³√2 ,to be twice each other , as this in analytical methods explained . The article consist a provocation to all scarce today Geometers and mathematicians in order to give an answer to these Old-age standing Unsolved Problems.
All Geometrical solutions are clearly Exposed and presented on Dr-Geo machine , and unveill the pass-over-faults of Relativity . E-Geometry is proved to be the base of all natural sciences and also the reflective logic from the objective reality , which is nature , to us

**Category:** Mathematical Physics

[7] **viXra:1512.0443 [pdf]**
*submitted on 2015-12-26 14:29:46*

**Authors:** Dan Visser

**Comments:** 11 Pages.

The formulation of the Einstein-field equations are changed: Herewith I present dynamical formulations for the multiplication of Big Bang-universes embedded in an eternal rotating holographic universe. This is beyond the current assumption the universe could be a hologram; that assumption was made without detailed knowledge of shape and deeper dynamics of a holographic universe. The new formulations introduce a dynamical process of deeper dynamics by which an object or subject could be transformed to another part of the holographic universe. This may happen by recalculation. But how? The recalculation described here is based on an amount of ‘duo-bits of dark matter’, which recalculate the quantum-dynamics. The recalculation-process emerges from a domain below the Planck-scale. The ‘duo-bit recalculation’ starts for a calculated lower-limit of Planck-areas. From my calculation follows, for example: 17 x 10^53 ‘duo-bits’ can recalculate 64 x 10^6 Planck-areas. This subquantum informational process is embedded in the modified Einstein-field-equations by a geometrical ratio of quantum-gravity and Planck-areas. This ratio is correlated to an additional energy-tensor of dark matter-energy. The geometrical ratio is more refined than the Einstein cosmological constant, which is only a number. The refined ratio replaces the cosmological constant. Therefore the main-issue in this paper is, that the accelerated space-expansion in the current Big Bang-universe is based on a ‘fake-dynamic’ due to one of many possible quasi Big Bang-universes that directly exist in physical reality. Or in other words: Directly existing parallel universes are part of the holographic dynamics. According to the new formulations parallel universes do not exist outside the conservative Big Bang-universe. In an appendix a description is added for the media written in Dutch.

**Category:** Mathematical Physics

[6] **viXra:1512.0401 [pdf]**
*submitted on 2015-12-22 11:25:45*

**Authors:** Sergey V. Ershkov

**Comments:** 10 Pages. Keywords: Arnold-Beltrami-Childress (ABC) flow, helical flow, stationary points

The existence of stationary points for the dynamical system of ABC-flow is considered.
The ABC-flow, a three-parameter velocity field that provides a simple stationary solution of Euler's equations in three dimensions for incompressible, inviscid fluid flows, is the prototype for the study of turbulence (it provides a simple example of dynamical chaos).
But, nevertheless, between the chaotic trajectories of the appropriate solutions of such a system we can reveal the stationary points, the deterministic basis among the chaotic behaviour of ABC-flow dynamical system. It has been proved the existence of 1 point for two partial cases of parameters {A, B, C}: 1) A = B = 1; 2) C = 1 (A² + B² = 1). Moreover, dynamical system of ABC-flow allows 3 points of such a type, depending on the meanings of parameters {A, B, C}.

**Category:** Mathematical Physics

[5] **viXra:1512.0341 [pdf]**
*submitted on 2015-12-16 14:56:32*

**Authors:** Branko Zivlak

**Comments:** 3 Pages. 1 Formula, 1 Table

The formula connecting fundamental physical constants has been verified based on the 2010 and 2014 recommended CODATA values of physical constants.

**Category:** Mathematical Physics

[4] **viXra:1512.0334 [pdf]**
*replaced on 2017-07-03 01:48:23*

**Authors:** A. A. Frempong

**Comments:** 47 Pages. Copyright © by A. A. Frempong

Over nearly a year and half ago, the Navier-Stokes (N-S) equations in 3-D for incompressible fluid flow were analytically solved by the author. However, some of the solutions contained implicit terms. In this paper, the implicit terms have been expressed explicitly in terms of x, y, z and t. The author proposed and applied a new law, the law of definite ratio for incompressible fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It was mathematically shown that without gravity forces on earth, there would be no incompressible fluid flow on earth as is known, and also, there would be no magnetohydrodynamics. In addition to the usual method of solving these equations, the N-S equations were also solved by a second method in which the three equations in the system were added to produce a single equation which was then integrated. The solutions by the two methods were identical, except for the constants involved. Ratios were used to split-up the equations; and the resulting sub-equations were readily integrable; and even, the nonlinear sub-equations were readily integrated. The examples in the preliminaries show everyday examples on using ratios to divide a quantity into parts, as well as possible applications of the solution method in mathematics, science, engineering, business, economics, finance, investment and personnel management decisions. The x-direction Navier-Stokes equation was linearized, solved, and the solution analyzed. This solution was followed by the solution of the Euler equation of fluid flow. The Euler equation represents the nonlinear part of the Navier-Stokes equation. Following the Euler solution, the Navier-Stokes equation was solved essentially by combining the solutions of the linearized equation and the Euler solution. For the Navier-Stokes equation, the linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions and relations revealed the role of each term of the Navier-Stokes equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the parabolic and forward motion of fluids. The pressure gradient term is also involved in the parabolic motion. The viscosity terms are involved in the parabolic, periodic and decreasingly exponential motion. Periodicity increases with viscosity. The variable acceleration term is also involved in the periodic and decreasingly exponential motion. The fluid flow in the Navier-Stokes solution may be characterized as follows. The x-direction solution consists of linear, parabolic, and hyperbolic terms. The first three terms characterize parabolas. If one assumes that in laminar flow, the axis of symmetry of each parabola for horizontal velocity flow profile is in the direction of fluid flow, then in turbulent flow, the axes of symmetry of some of the parabolas would be at right angles to that for laminar flow. The characteristic curve for the integral of the x-nonlinear term is such a parabola whose axis of symmetry is at right angles that of laminar flow. The integral of the y-nonlinear term is similar, parabolically, to that of the x-nonlinear term. The characteristic curve for the integral of the z-nonlinear term is a combination of two similar parabolas and a hyperbola. If the above x-direction flow is repeated simultaneously in the y-and z-directions, the flow is chaotic and consequently turbulent.
For a spin-off, the smooth solutions from above are specialized and extended to satisfy the requirements of the CMI Millennium Prize Problems, and thus prove the existence of smooth solutions of the Navier-Stokes equations.

**Category:** Mathematical Physics

[3] **viXra:1512.0333 [pdf]**
*replaced on 2015-12-16 22:38:15*

**Authors:** A. A. Frempong

**Comments:** 10 Pages. Copyright © A. A. Frempong

The system of magnetohydrodynamic (MHD) equations has been solved analytically in this paper. The author applied the technique used in solving the Navier-Stokes equations and applied a new law, the law of definite ratio for MHD. This law states that in MHD, the other terms of the system of equations divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. It is shown that without gravity forces on earth, there would be no magnetohydrodynamics on earth as is known. The equations in the system of equations were added to produce a single equation which was then integrated. Ratios were used to split-up this single equation into sub-equations which were readily integrated, and even, the non-linear sub-equations were readily integrated. Twenty-seven sub-equations were integrated. The linear part of the relation obtained from the integration of the linear part of the equation satisfied the linear part of the equation; and the relation from the integration of the non-linear part satisfied the non-linear part of the equation. The solutions revealed the role of each term in magnetohydrodynamics. In particular, the gravity term is the indispensable term in magnetohydrodynamics. The solutions of the MHD equations were compared with the solutions of the N-S equations, and there were similarities and dissimilarities.

**Category:** Mathematical Physics

[2] **viXra:1512.0332 [pdf]**
*replaced on 2016-04-18 01:01:43*

**Authors:** A. A. Frempong

**Comments:** 12 Pages. Copyright © A. A. Frempong

This paper covers the solutions of the Euler equations in 3-D and 4-D for incompressible fluid flow. The solutions are the spin-offs of the author's previous analytic solutions of the Navier-Stokes equations (vixra:1405.0251 of 2014). However, some of the solutions contained implicit terms. In this paper, the implicit terms have been expressed explicitly in terms of x, y, z and t.
The author applied a new law, the law of definite ratio for fluid flow. This law states that in incompressible fluid flow, the other terms of the fluid flow equation divide the gravity term in a definite ratio, and each term utilizes gravity to function. The sum of the terms of the ratio is always unity. This law evolved from the author's earlier solutions of the Navier-Stokes equations. In addition to the usual approach of solving these equations, the Euler equations have also been solved by a second method in which the three equations in the system are added to produce a single equation which is then integrated. The solutions by the two approaches are identical, except for the constants involved. From the experience gained in solving the linearized Navier-Stokes equations, only the equation with the gravity term as the subject of the equation was integrated. The experience was that when each of the terms of the Navier-Stokes equation was used as the subject of the equation, only the equation with the gravity term as the subject of the equation produced a solution. Ratios were used to split-up the x-direction Euler equation with the gravity term as the subject of the equation. The resulting five sub-equations were readily integrable, and even, the non-linear sub-equations were readily integrated. The integration results were combined. The combined results satisfied the corresponding equation. This equation which satisfied its corresponding equation would be defined as the driver equation; and each of the other equations which would not satisfy its corresponding equation would be called a supporter equation. A supporter equation does not satisfy its corresponding equation completely, but provides useful information which is not apparent in the solution of the driver equation. The solutions and relations revealed the role of each term of the Euler equations in fluid flow. The gravity term is the indispensable term in fluid flow, and it is involved in the forward motion of fluids. The pressure gradient term is also involved in the forward motion. The variable acceleration term is also involved in the forward motion. The fluid flow behavior in the Euler solution may be characterized as follows. The x-direction solution consists of linear, parabolic, and hyperbolic terms. If one assumes that in laminar flow, the axis of symmetry of the parabola for horizontal velocity flow profile is in the direction of fluid flow, then in turbulent flow, the axis of symmetry of the parabola would have been rotated 90 degrees from that for laminar flow. The characteristic curve for the x-nonlinear term is such a parabola whose axis of symmetry has been rotated 90 degrees from that of laminar flow. The y-nonlinear term is similar parabolically to the x-nonlinear term. The characteristic curve for the z-nonlinear term is a combination of two similar parabolas and a hyperbola. If the above x-direction flow is repeated simultaneously in the y-and z-directions, the flow is chaotic and consequently turbulent.

**Category:** Mathematical Physics

[1] **viXra:1512.0261 [pdf]**
*submitted on 2015-12-07 21:43:24*

**Authors:** Rodney Bartlett

**Comments:** 6 Pages.

The Fields Medal is an award established in 1924 by the ICM (International Congress of Mathematicians) and is restricted to mathematicians up to the age of 40. It recognizes both existing work and future promise, and is equivalent to the Nobel Prize.
A trick is shown in this article that proves 1=2. However, during the steps division by zero is used. Since this is not allowed, the conclusion is false. Or it would be unless zero could be shown not to be nothing. Zeros are something because they're paired with ones to compose the binary digits essential to the formation of everything in space-time. This means zero has been misunderstood throughout history, division by zero is indeed permitted and the conclusion that 1=2 is correct. In turn, this means that while 1+1=2, 1+1 must also equal 1. This mathematically validates the centuries-long march of physics towards unification of everything in this cosmos. Unification occurs not just in the present but the entire past and future are naturally part of this one entity/event.
The article then explores possible consequences for 1) Einstein being correct to divide by zero, 2) Hidden Variables and Determinism, 3) that zero is not nothing but actually something, 4) that zero redefines the term infinity, 5) that there really is another explanation for the origin of the universe besides the Big Bang, 6) and another explanation for black holes, 7) possibilities regarding life after death and life before conception.

**Category:** Mathematical Physics