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| viXra.org > Mathematical Physics > 2202 |
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[10] viXra:2202.0164 [pdf] submitted on 2022-02-25 07:51:38
Authors: J.A.J. van Leunen
Comments: 2 Pages. This is part of the Hilbert Book Model Project
Confusing metaphors that are popular in use can have disastrous consequences and put science on the wrong track for a long time. It may well be that the fact that in-depth theoretical research is making little progress is caused by the continued use of confusing metaphors.
Category: Mathematical Physics
[9] viXra:2202.0160 [pdf] submitted on 2022-02-23 22:21:04
Authors: Miftachul Hadi
Comments: Written in English, 4 pages, no figure.
The refractive index-curvature relation is formulated using the second rank tensor of Ricci curvature as a consequence of a scalar refractive index. A scalar refractive index describes (an isotropic) linear optics. In (an isotropic) non-linear optics, this scalar refractive index is decomposed into a contravariant fourth rank tensor of non-linear refractive index and a covariant fourth rank tensor of susceptibility. In topological space, both a contravariant fourth rank tensor of non-linear refractive index and a covariant fourth rank tensor of susceptibility, are related to the Euler-Poincare characteristic, a topological invariant.
Category: Mathematical Physics
[8] viXra:2202.0154 [pdf] submitted on 2022-02-24 19:49:30
Authors: Richard D. Lockyer
Comments: 11 Pages. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
The classical definition for the gradient, divergence and curl utilizing the limit as the volume approaches zero, of the ratio of the integral over the enclosing surface divided by the integral over the enclosed volume can be consolidated to form an Ensemble Derivative. This form is constructed initially as a diffeomorphism between two compatible coordinate sets, one representing the intrinsic division algebra basis; u(v) and the other some basis v(u) within which differentiation is defined. The result is the structure for general covariance for division algebra analysis, where covariant differential equations are constructed by full applications of the Ensemble Derivative.
Category: Mathematical Physics
[7] viXra:2202.0146 [pdf] submitted on 2022-02-22 20:18:10
Authors: Jake Brockbank
Comments: 68 Pages.
Consider the Navier-Stokes equation for a one-dimensional and two-dimensional compressible viscous liquid. It is a well-known fact that there is a strong solution locally in time when the initial data is smooth and the initial density is limited down by a positive constant. In this article, under the same hypothesis, I show that the density remains uniformly limited in time from the bottom by a positive constant, and therefore a strong solution exists globally in time. In addition, most existing results are obtained with a positive viscosity factor, but current results are true even if the viscosity factor disappears with density. Finally, I prove that this solution is unique in a class of weak solutions that satisfy the usual entropy inequalities. The point of this work is the new entropy-like inequalities that Bresch and Desjardins introduced into the shallow water system of equations. This discrepancy gives the density additional regularity (assuming such regularity exists first).
Category: Mathematical Physics
[6] viXra:2202.0138 [pdf] replaced on 2022-04-05 01:15:00
Authors: F.M. Sanchez, C. Bizouard, M. Grosmann, V. Kotov
Comments: English 9 pages ; French: 22 pages.
Viewing the Kepler's laws as Diophantine non-local equations introduces the action quantum and the Diophantine Coherence Theorem which generalizes the method of Arthur Haas, which anticipated the Bohr's radius. This leads to a Space quantum breaking the Planck wall by a factor 10^{61} and the associated Holographic Cosmos, identified as the source of the Background Radiation. An Electricity-Gravitation symmetry, connected with the Combinatorial Hierarchy, defines the steady-state Universe with invariant Hubble radius 13.81 Glyr, corresponding to 70.79 (km/s)/Mpc, a value anticipated since 1997 by the Three Minutes Formula, confirmed by the Eddington Number, the Kotov period and the recent Carnegie-Chicago Hubble Program. This specifies G, compatible with the BIPM measurements, and confirms definitely the Anthropic Principle.
Category: Mathematical Physics
[5] viXra:2202.0132 [pdf] replaced on 2022-03-26 16:39:27
Authors: Miftachul Hadi
Comments: Written in English, 4 pages, no figure.
In a two-dimensional space, a refractive index-curvature relation is formulated using the second rank tensor of Ricci curvature. A scalar refractive index describes an isotropic linear optics. In a fibre bundle geometry, a scalar refractive index is related to an Abelian (a linear) curvature form. The Gauss-Bonnet-Chern theorem is formulated using a scalar refractive index. Because the Euler-Poincare characteristic is the topological invariant then a scalar refractive index is also a topological invariant.
Category: Mathematical Physics
[4] viXra:2202.0072 [pdf] submitted on 2022-02-12 14:01:47
Authors: Richard D. Lockyer
Comments: 13 Pages. Keywords: Hadamard matrices, division algebras, Cayley-Dickson algebras, Cayley-Dickson doubling, Octonion Algebra
The iteration that builds systematic forms for Hadamard matrices doubles the dimension each application equivalent to the Cayley-Dickson algebra doubling process. These systematic forms have a row or column composition rule where the composition of any two rows(columns) is closed for the matrix, such that for sequentially assigned column and row indexes from 0 up, the index of the result is the binary bit-wise exclusive or (xor) of the indexes for the two rows(columns) participating. The Exclusive Or Group of order 2 exponent n and all of its subgroups is isomorphic to the product tables for order 2 exponent n Cayley-Dickson algebra and all of its subalgebras when all resultant –1 signs are dropped. The Boolean xor operator thus forms the bridge between Cayley-Dickson algebras and Hadamard matrices, but only for the division algebra subset. The dimension 8 Hadamard matrix is ubiquitous within Octonion algebraic structure by specifying optimal enumerations of, and relationships between; basis elements, Quaternion subalgebra triplets, proper Octonion orientations, Octonion Algebraic Invariance and Variance.
Category: Mathematical Physics
[3] viXra:2202.0055 [pdf] submitted on 2022-02-10 03:26:24
Authors: Shlomy Shitrit
Comments: 21 Pages.
The most suited air breathing vehicle to hypersonic flight is the supersonic combustion ramjet, or
scramjet. One of the many challenges to scramjets is being able to operate efficiently over a wide
range of flight conditions. Under the extreme pressure and heat experienced at these flight
conditions there is a high degree of shape uncertainty. Numerous phenomena such as inlet unstart,
extreme load, boundary-layer effects and shear layer interaction, restrict scramjet design and limit
their performance. Such problems are the main motivation for surface sensitivities that can be
used for aerodynamic shape optimization. The objective of the present paper is to document lessons
learned from aerodynamic shape optimization of the HiFire scramjet configuration under
supersonic flow conditions. Mesh warping and geometry parametrization is accomplished by
using surface control points embedded with free-form deformation (FFD) volumes. The
aerodynamic model solves the RANS equations with Spallart-Almaras turbulence model. A
gradient based optimization algorithm is used with an adjoint method in order to compute the
objectives and constraints derivatives with respect to the design variables. The main purpose of
this study is to suggest an approach for aerodynamic shape optimization of scramjet inlet and
mainly to present two optimization problem formulations which includes different objectives:
pressure recovery and thrust, by using a polynomial approach which reflects a low fidelity model
of the combustion and expansion process. The results of optimization are presented, including the
tradeoff between the two approaches.
Category: Mathematical Physics
[2] viXra:2202.0031 [pdf] submitted on 2022-02-05 19:53:21
Authors: Taha Khaled
Comments: 8 Pages. The foundations and some details are what got explained and nothing more. [Corrections made by viXra Admin to conform with the requirements on the Submission Form]
Why there are repeated concepts in reality? And why mathematics is capable of dealing with them? There is such a weird structure that connects these two events. This structure is so fundamental that every single being looks so complex compared to it. The true start is not when objects appeared but rather when this structure appeared. And this paper tries to explain such a thing.
Category: Mathematical Physics
[1] viXra:2202.0004 [pdf] submitted on 2022-02-01 00:46:36
Authors: N. Gurappa
Comments: 3 pages, no figures
A polynomial power series is constructed for the one-sided step function using a modified Taylor series, whose derivative results in a new representation for Dirac $\delta$-function.
Category: Mathematical Physics
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