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| viXra.org > Mathematical Physics > 2008 |
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[9] viXra:2008.0226 [pdf] replaced on 2021-05-12 07:47:46
Authors: Stephen H. Jarvis
Comments: 59 Pages.
The application of the Calculus of Infinitesimals (differentials/integrals) to physical analysis, given the paradoxical lack of precise particle definition it grants the study of the elementary particles, despite the precision of such mathematics itself, and therefore its application to particle physics, is questioned. To offer more mathematical precision of definition to the elementary particles, a new proposal for the mathematics of time and space, as an application of mathematics to the paradigm of time, is proposed, as the calculus of time-points in space, here as “Temporal Calculus”, a calculus not focusing on space primarily, yet time. As a standard of reference, this time-algorithm is based on the human temporal perception ability in the three paradigms most commonly associated to the human temporal perception ability, namely time-before, time-now, and time-after, assigning mathematical values to those qualities that then give rise to the “golden-ratio” equation, which when applied to 3-d space forms a fractal (golden-ratio) lattice of time-points that is able to derive all the known equations and constants of physical phenomena, from mass to charge, particle energy to particle spin, elementary and standard particles, presenting the case not for an infinitely metrically expanding universe, yet a steady-state time-space system that successfully links the CMBR with the vacuum permittivity and permeability, together with calculating the Yang-Mills mas gap and associated elementary particle phenomena, while finally explaining the existence of antimatter, all via a field of time-points in space.
Category: Mathematical Physics
[8] viXra:2008.0221 [pdf] submitted on 2020-08-30 10:31:33
Authors: Federico Pagano
Comments: 9 Pages.
The problem of integration technique over integrands of the form f(t)/t^n, can be solved by differentiation(n times) by using Leibniz's rule to get rid of t^n, that leads to integrate back (n times) to end the game which it's harder than the original problem.This work focuses on the derivation of the formula (Pagano's Theorem) which is a perfect tool to avoid that hard task. It allows to change the difficult n iterated integrals into a more outstanding easier problem which consists of n -1 derivatives.The Pagano's Theorem is a generalization of the Dirichlet integral with a strong conection with Cauchy's residue theorem.
Category: Mathematical Physics
[7] viXra:2008.0199 [pdf] submitted on 2020-08-27 21:06:50
Authors: Saburou Saitoh
Comments: 18 Pages. In order to show some power of the division by zero calculus we will give several simple applications to physics. Recall that Oliver Heaviside: {\it Mathematics is an experimental science, and definitions do not come first, but later on.}
In order to show some power of the division by zero calculus we will give several simple applications to physics. Recall that Oliver Heaviside: {\it Mathematics is an experimental science, and definitions do not come first, but later on.}
Category: Mathematical Physics
[6] viXra:2008.0111 [pdf] replaced on 2020-08-26 04:29:51
Authors: Stephen H. Jarvis
Comments: 35 Pages.
The application of the Calculus of Infinitesimals (differentials/integrals) to physical analysis, given the paradoxical lack of precise spatial and temporal relevance it grants the study of the elementary particles in both quantum and relativistic aspects of determination, despite the precision of such mathematics, is questioned. To offer more precise relevance to time and space and associated phenomena, a new proposal for the mathematics of time and space, as an application of mathematics to the paradigm of time, is proposed, as the calculus of time-points in space (Temporal Calculus), a calculus that does not focus on space primarily, yet time. The temporal calculus presented here explains two basic features regarding the proposed mechanics between time and space, namely indeterminism (here as defined by the uncertainty between time and space), and the idea of time mandating a spherical wave-function for any point in space. As a standard of reference, this time-algorithm is based o n the human temporal perception ability in the three paradigms most commonly associated to the human temporal perception ability, namely time-before, time-now, and time-after, assigning mathematical values to those qualities that then give rise to the “golden-ratio” equation, which when applied to 3-d space forms a fractal (golden-ratio) lattice of time-points that is able to derive all the known equations and constants of physical phenomena, from mass to charge, particle energy to particle spin, presenting the case not for an infinitely metrically expanding universe, yet a steady-state time-space system that successfully links the CMBR with the vacuum permittivity and permeability, governing the redshift of light in space.
Category: Mathematical Physics
[5] viXra:2008.0080 [pdf] replaced on 2020-09-30 04:42:22
Authors: Giuliano Bettini
Comments: 27 Pages. In English. Appendices 7 and 8 added.
In addition to the classification of crystals in 32 Crystal Classes divided into 6 (or 7) Crystal Systems, I propose a second further classification. The 32 Crystal Classes are rearranged in a 8x4=32 table having 8 row and 4 columns so they are constituted by eight Groups, each of them having four Classes.
This is no more a hypothesis. This is a fact, unanbiguously based on physical properties.
It took me almost forty years to get here.
Aside from all the various ruminations many of which I’ve posted elsewhere, the final decisive step was the following:
even the second column classes ("center", bit c) share a common physical property.
This property is: "non-polar" or "non-pyro", that is, enough isotropically distributed around the center not to be pyroelectric.
No invention here, but only a rereading of what is possible for all to see, exactly written in crystallography books. Interpreted, of course.
Category: Mathematical Physics
[4] viXra:2008.0034 [pdf] submitted on 2020-08-06 06:04:00
Authors: Dan Visser
Comments: 13 Pages.
The Big Bang universe is not just only a ‘hologram’, but eventually a ‘Hologram Carrousel’. That says (the 72-year old) Dan Visser, scientist, independent cosmologist and art-painter in the Netherlands. He introduces a ‘hologram tensor’, through which the dimension-structure of the universe-hologram can be determined. The layout shows how the hologram tensor is related to dark matter and dark energy. According to DAN dark matter is also no solid particle, but a force-particle, which takes part in the hologram tensor. This replaces the Planckborder (boundary) and the refined information-domain below as well. This is whereon the new universe-model is pillard, under the name Rotating Torus Hologram Universe (RTHU). This replaces the classical Big Bang universe. Moreover DAN describes how an ‘ufo’ can be understood, based on his new cosmological ideology.
Category: Mathematical Physics
[3] viXra:2008.0033 [pdf] submitted on 2020-08-06 06:47:28
Authors: Radhakrishnamurty Padyala
Comments: 10 Pages. Figures 5
Given three points one can find a fourth point such that the sum of its distances from the three points is minimal, using any of the many methods available in the literature. The solution point is called Fermat’s Point (FP). The solution points to, two special cases. One is when the triangle formed from the three given points contains an angle equal to 120°. The other is when the triangle contains an angle greater than 120°. In both these cases the sum of the two distances i.e. the sum of the lengths of the sides containing that angle is minimum. This is well known. It is also well known that light travels between two given points by the minimum distance path viz. along the straight line connecting two points. If it suffers reflection at a point enroute, it travels by a two-segment broken line path. The path followed is such that the sum of the two segments is a minimum. The reflection phenomenon is governed by Snell’s law of reflection. Reflection offers us an example of a natural phenomenon with three points and two distances connecting them. Therefore, we can compare the two minimal sums of distances given by FP and Snell’s law. In this paper, we compare them and show that the two results are contradictory. Therefore, it follows that FP violates Snell’s law. Snell’s law of reflection and refraction are so connected that if one is violated the other is also violated.
Category: Mathematical Physics
[2] viXra:2008.0021 [pdf] replaced on 2020-09-08 19:54:42
Authors: Andrew Alexander Logan
Comments: 9 Pages. 4 figures, typos corrected
This paper investigates the onset of turbulence in incompressible viscous fluid flow over a flat plate by looking at the pressure gradients implied by the Blasius solution for laminar fluid flow and adjusting the predicted flow, leading to a mathematically predictable flow separation in the boundary layer and the onset of turbulence (including both transition and fully turbulent regions - both with and without the presence of a flat plate). It then considers the implications for potential analytic solutions to the Navier-Stokes Equations of the fact that it is possible to predict turbulence and a singularity for many flows (at any velocity).
Category: Mathematical Physics
[1] viXra:2008.0005 [pdf] submitted on 2020-08-02 06:59:30
Authors: Miroslav Josipović
Comments: 7 Pages.
This article is intended as an addition to the book [10], since, in the first edition, I was double minded whether to introduce the Dirac theory for young students. Now I am quite sure that it should be introduced, and for several reasons. First, the Cl3 formulation of the Dirac theory is simple and the derivation of the Dirac’s formula is straightforward. Second, it is relatively easy to show that gamma matrices are not the only possibility in linearizing the Klein-Gordon equation (we even do not need it in Cl3). Finally, the fact that it is possible to use the same mathematical (3D) formalism for classical mechanics, the special (and general) theory of relativity (without Minkowski space), electromagnetism, and both non-relativistic and relativistic quantum mechanics (without the imaginary unit) is remarkable. Not to mention the geometric clarity and possibilities of unifications, as well as generalizations. Moreover, all this without coordinates, matrices, tensors… In addition, we should appreciate the new concept of oriented numbers and simple fact that Cl3 contains complex, hypercomplex, and dual numbers, quaternions, spinors, etc. Geometric algebra of 3D Euclidean vector space (Cl3) is truly rich in structure and the question remains as to how physics would have developed had the ideas of Grassmann and Clifford been accepted in the late nineteenth and early twentieth centuries.
Category: Mathematical Physics
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