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[22] viXra:2201.0201 [pdf] replaced on 2022-02-21 08:25:10
Authors: J.A.J. van Leunen
Comments: 10 Pages. This is part of the Hilbert Book Model Project
A system of separable quaternionic Hilbert spaces implements a diverse and dynamic universe. Something must connect the members of the system such that these members can interact. This role is taken by state vectors.
Category: Mathematical Physics
[21] viXra:2201.0198 [pdf] submitted on 2022-01-27 01:15:04
Authors: Yoshiki Ueoka
Comments: 11pages, 8 figures
I studied mechanism of shuffle in mahjong, which is a kind of table game. This
research is the first research that focuses on the physical aspect, not the victory or
defeat of mahjong. In physics terms, it is a study of how disordered systems can be
created. I considered whether there is a difference between a completely random
shuffle with random numbers and a shuffle with human hands. I implemented
human shuffle with a new mathematical model. It was found that the equilibrium
reached by human hand shuffle is different from that of completely random shuffle
in the number of shuffles that can be normally assumed. This means that creating
a random state can be difficult in some cases.
Category: Mathematical Physics
[20] viXra:2201.0174 [pdf] submitted on 2022-01-25 19:44:57
Authors: Shlomy Shitrit, David Sidilkover
Comments: 22 Pages.
The discretization process of the full potential equation (FPE) both in the quasi-linear and in
the conservation form, is addressed. This work introduce the rst stage toward a development of
a fast and ecient FPE solver, which is based on the algebraic multigrid (AMG) method. The
mathematical diculties of the problem are associated with the fact that the governing equation changes its type from elliptic (subsonic ow) to hyperbolic (supersonic ow). A pointwise
relaxation method when applied directly to the upwind discrete operator, in the supersonic ow
regime, is unstable. Resolving this diculty is the main achievement of this work. A stable
pointwise direction independent relaxation was developed for the supersonic and subsonic ow
regimes. This stable relaxation is obtained by post-multiplying the original operator by a certain
simple rst order downwind operator. This new operator is designed in such a way that makes
the pointwise relaxation applied to the product operator to become stable. The discretization
of the FPE in the conservation form is based on the body-tted structured grid approach. In
addition the 2D stable operator in the supersonic ow regime was extended to 3D case. We
present a 3D pointwise relaxation procedure that is stable both in the subsonic and supersonic
ow regimes. This was veried by the Von-Neumann stability analysis.
Category: Mathematical Physics
[19] viXra:2201.0173 [pdf] submitted on 2022-01-25 19:46:05
Authors: Shlomy Shitrit, David Sidilkover
Comments: Pages.
This article reports the development of an ecient, and robust full potential equation (FPE) solver
for transonic ow problems, which is based on the algebraic multigrid (AMG) method. AMG method solves algebraic
systems based on multigrid principles but in a way that it is independent on the problem's geometry. The mathematical
diculties of the problem are associated with the fact that the governing equation changes its type from elliptic
(subsonic ow) to hyperbolic (supersonic ow). The ow solver is based of the body-tted structured grid approach
in complex geometries. We demonstrate the AMG performance on various model problems with dierent ow speed
from subsonic to transonic conditions. The computational method was demonstrated to be capable of predicting the
shock formation and achieving residual reduction of roughly an order of magnitude per cycle, both for elliptic and
hyperbolic problems.
Category: Mathematical Physics
[18] viXra:2201.0166 [pdf] replaced on 2022-02-13 15:07:13
Authors: Dan Visser
Comments: 7 Pages.
In this article Dan Visser describes how 6D-time generates the subquantum hologramworld, which is emerging the quantum-world. This is in fact due to his new universemodel, the RTHU, which is an abbreviation for Rotating Torus Hologram Universe. The
RTHU enables seemingly existing dark mass (called dark matter) to be newly written
per surface and per 6D-time. This dimensional extension is combined with Dan’s
Hologram-Formula, which dimensionally generates as well a subquantum- as a
quantum-world by whole numbers (integers). His original related formula shows an
intrinsic connection between seemingly dark matter and sub-quantum dark-matterforce, which is in fact the initiator of dark-gravity in the RTHU. the Hologram-Formula is
related tot this force and enables to calculate dark-matter-force at small scales.
Category: Mathematical Physics
[17] viXra:2201.0130 [pdf] replaced on 2022-09-11 03:21:37
Authors: Zhengxi Wang
Comments: 11 pages
Through the logical analysis of the numbers 0 and 1, continuously split the number 1, split to infinitesimal, a logarithmic function is established. The matter break-up and space, let their set is a logarithmic function. After the introduction of Planck length, the model of the universe is established. Conclusions are drawn from the model: Our universe opens from 1 (There is), the universe is finite, max 1/(1.6×10-35 )meters. The whole process is： contraction → the origin → the universe opens → expansion → Big Rip, end. The di-mension on cosmic original point space is invalid, and there is no external space. Direction and matter cannot be positive at the same time. We are opposite to the direction of the symmetrical universe. Infer: The break-up of matter produces space and expands the universe. There is a multiverse.
Category: Mathematical Physics
[16] viXra:2201.0126 [pdf] submitted on 2022-01-18 22:20:56
Authors: Anamitra Palit
Comments: 7 Pages.
The brief article explores the Christoffel symbols starting from its transformation rules and by such an exploration demonstrates the fact that only linear transformations are possible. It derives that Christoffel symbols behave like rank three tensors[with one upper index and two lower ones] since the term standing in the way of such behavior vanishes.
Category: Mathematical Physics
[15] viXra:2201.0125 [pdf] submitted on 2022-01-19 05:54:54
Authors: Jose Salvador Ruiz Fargueta
Comments: 6 Pages.
In this letter we analyze the vacuum energy as a simple fractal. With elementary mathematics and a novel approach, we will study its properties.
Category: Mathematical Physics
[14] viXra:2201.0120 [pdf] replaced on 2022-01-29 15:24:59
Authors: Ervin Goldfain
Comments: 9 Pages.
The motivation for the continuous dimensionality of spacetime near the Fermi scale stems from two premises, namely, 1) dimensional regularization of perturbative quantum field theory (QFT), 2) the existence of non-trivial fixed points of Renormalization Group equations. Here we discuss a third reason, rooted in the behavior of non-equilibrium phase-space flows.
Category: Mathematical Physics
[13] viXra:2201.0111 [pdf] submitted on 2022-01-18 02:08:51
Authors: Anamitra Palit
Comments: 3 Pages.
The article explores the transformation of rank two tensors to bring out the fact that tensor transformations should be linear .Tensors of a diagonal nature have been used to this end.
Category: Mathematical Physics
[12] viXra:2201.0110 [pdf] submitted on 2022-01-18 02:12:41
Authors: Anamitra Palit
Comments: 10 Pages.
In this article the Riemann tensor has been discussed in two sections. The first section considers two formulas to project results that are inconsistent in their nature. The next section considering tensor transformations and the linear homogeneous equations proves that the Riemann tensor is the rank four null tensor
Category: Mathematical Physics
[11] viXra:2201.0107 [pdf] submitted on 2022-01-18 13:09:37
Authors: Michele Nardelli, Antonio Nardelli
Comments: 16 Pages.
In this paper, we analyze two Maxwell’s equations and describe the possible mathematical connections with some sectors of Number Theory.
Category: Mathematical Physics
[10] viXra:2201.0104 [pdf] replaced on 2022-12-01 01:40:26
Authors: Abhishek Majhi
Comments: 39 Pages. Foundations of Science (2022) [Online Only], https://doi.org/10.1007/s10699-022-09875-9
Einstein's theory of general relativity, which Newton's theory of gravity is a part of, is fraught with the problem of singularity that has been established as a theorem by Hawking and Penrose, the later being awarded the Nobel Prize in recent years. The crucial {\it hypothesis} that founds the basis of both Einstein's and Newton's theories of gravity is that bodies with unequal magnitudes of masses fall with the same acceleration under the gravity of a source object. Since, the validity of the Einstein's equations is one of the assumptions based on which Hawking and Penrose have proved the theorem, therefore, the above hypothesis is implicitly one of the founding pillars of the singularity theorem.
In this work, I demonstrate how one can possibly write a non-singular theory of gravity which manifests that the above mentioned hypothesis is only valid in an approximate sense in the ``large distance'' scenario. To mention a specific instance, under the gravity of the earth, a $5$ kg and a $500$ kg fall with accelerations which differ by approximately $113.148\times 10^{-32}$ meter/sec$^2$ and the more massive object falls with less acceleration. Further, I demonstrate why the concept of gravitational field is not definable in the ``small distance'' regime which automatically justifies why the Einstein's and Newton's theories fail to provide any ``small distance'' analysis. In course of writing down this theory, I demonstrate why the continuum hypothesis as spelled out by Goedel, is undecidable. The theory has several aspects which provide the following realizations: (i) Descartes' self-skepticism concerning exact representation of numbers by drawing lines (ii) Born's wish of taking into account ``natural uncertainty in all observations'' while describing ``a physical situation'' by means of ``real numbers'' (iii) Klein's vision of having ``a fusion of arithmetic and geometry'' where ``a point is replaced by a small spot'' (iv) Goedel's assertion about ``non-standard analysis, in some version'' being ``the analysis of the future''.
A major drawback of this work is that it can easily appear to the authorities of modern science as too simple to believe in. This is, firstly due to the origin of the motivations being rooted to the truthfulness of the language in which physics is written and secondly due to the lucidity of the calculations involved. However, at the same time, this work can also appear as a fresh and non-standard approach to do physics from its roots, where the problem of singularity is not even there to begin with. The credibility of this work depends largely on whether the reader is willing adopt the second mindset.
Category: Mathematical Physics
[9] viXra:2201.0095 [pdf] submitted on 2022-01-16 15:18:18
Authors: Richard D. Lockyer
Comments: 10 Pages.
It is impossible to fully represent a non-associative algebra using group theory due to the associativity requirement for the group operation. This precludes a full group theoretical cover of Cayley-Dickson algebras beginning with the generally non-associative Octonion Algebra doubling count. However, if we “forget” the sign attached to the result of the product of any two basis elements, every Cayley-Dickson algebra of doubling count n: CD(n) is modelled by the Exclusive Or group X(n), up to ignored sign of fixed nature or orientation choice. This paper explores the bijective correspondence between every CD(n) algebra and all of its subalgebras, and every X(n) group and all of its subgroups. A recursion relationship for determining the number of subalgebras of order 2 exponent m for any CD(n), which is equivalent to the number of subgroups of order 2 exponent m for the corresponding group X(n), is presented.
Category: Mathematical Physics
[8] viXra:2201.0054 [pdf] replaced on 2022-01-17 16:48:32
Authors: J.A.J. van Leunen
Comments: 7 Pages.
In onze leefomgeving spelen een aantal groepen rekenregels een essentiële rol. Elke groep bedient een getalsysteem. Sommige van deze getalsystemen kunnen samengevoegd worden. Samen kunnen de getalsystemen ons heelal op allerlei wijzen overdekken. Deze overdekkingen bepalen de inhoud en de werking van het heelal.
Een systeem van Hilbertruimten die allemaal dezelfde onderliggende vectorruimte gebruiken, beschrijft de structuur en het gedrag van wat wij ons universum noemen.
Category: Mathematical Physics
[7] viXra:2201.0053 [pdf] replaced on 2022-01-17 16:51:18
Authors: J.A.J. van Leunen
Comments: 7 Pages.
In our living environment, several groups of calculation rules play an essential role. Each group operates a number system. Some of these number systems can be combined. Together, the number systems can cover our universe in many kinds of ways. These coverings determine the content and operation of the universe. A system of Hilbert spaces that all use the same underlying vector space describes the structure and behavior of what we call our universe.
Category: Mathematical Physics
[6] viXra:2201.0043 [pdf] replaced on 2023-10-30 06:12:25
Authors: Stephen H. Jarvis
Comments: 48 Pages.
A key feature of physics theory formulation is the "thought experiment", an instrumental key with specific conditions to unlocking the mechanics of physical phenomena, conditions as this paper highlights that have been overlooked by Einstein’s own thought experiments with his works of Special and General Relativity. To demonstrate such, two processes shall be presented here, the first being an analysis of contemporary physics which holds physical phenomena (namely momentum-inertia-mass) as the basis for physics theory, and the second approach (Temporal Mechanics) using the temporal and spatial perception ability of human consciousness and associated proposed formalism of mathematical logic as the basis for physics theory. The two approaches shall be compared based on what they can both achieve, here the results showing that making physical phenomena the key theoretic basis of physics theory itself leads to paradoxes of temporal and spatial mathematical interplay, whereas making the temporal and spatial human consciousness ability and associated formalism of mathematical logic as the key theoretic basis, as the proposed fundamental time-equation thought experiment, avoids those temporal and spatial abstractions and paradoxes of dimensional analysis for physical phenomena.
Category: Mathematical Physics
[5] viXra:2201.0034 [pdf] replaced on 2022-01-12 18:17:14
Authors: F. M. Sanchez
Comments: 3 Pages. in French
The third Keper law is shown to be the simplest Physical Diophantine Equation, leading to the critical Universe mass in the steady-state cosmology without any numerical parameter, whose 3/10 part is the Eddingtron Number times the neutron mass, suggesting that black matter is mater-antimater vibration in quadrature, and that the dark energy must be replaced by the 5th force of Fred Hoyle.
Category: Mathematical Physics
[4] viXra:2201.0029 [pdf] submitted on 2022-01-06 17:55:44
Authors: Liu Yajun
Comments: 9 Pages.
In this paper, we get a Space characteristic equation with a 1/2 fixed point and an entropy form.Base on this Space, We setup a model to describe a photon with the velocity of light C pushed by one unit en-ergy h. and we find that it is interesting when considering the intensity of field1/aF as the curvature of the Quantum Time-Space with ener-gy, then we get a Unified Field Equation.We hope to throw a little bit light on the big picture of uniting the quantum mechanics and General relative theory.
Category: Mathematical Physics
[3] viXra:2201.0020 [pdf] replaced on 2022-12-25 03:29:18
Authors: Kronberger Reinhard
Comments: 5 Pages.
The formula found by Hans de Vries for the fine structure constant is very elegant and accurate but there exists no explanation for it. In this paper, I try to give an interpretation. It is also shown why we have a electromagnetic field and why we have the value for the fine structure constant.
Category: Mathematical Physics
[2] viXra:2201.0009 [pdf] replaced on 2022-03-27 17:05:46
Authors: J.A.J. van Leunen
Comments: 80 Pages. This is part of the Hilbert Book Model Project
Hilbert spaces are relevant because these extensions of vector spaces are capable of archiving sets of numbers in a structured way such that these data can be retrieved in a well-organized way.
Textbooks about Hilbert spaces do not contain all subjects that make Hilbert spaces interesting and relevant. This paper adds some valuable aspects of Hilbert spaces that you will not easily find in regular textbooks about Hilbert spaces.
The section on conclusions shows that advanced Hilbert space technology leads to other results than mainstream physics does.
Category: Mathematical Physics
[1] viXra:2201.0006 [pdf] submitted on 2022-01-02 15:21:02
Authors: Miroslav Josipović
Comments: 3 Pages.
The problem of base vectors rotation appeared in the formulation of the theory of AC circuits in the language of geometric algebra ([4]). In [4], it is shown how to get the desired rotor in a few steps. Here we show that it is possible to find a 4D rotor in a closed form.
Category: Mathematical Physics
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