Mathematical Physics

1705 Submissions

[18] viXra:1705.0358 [pdf] submitted on 2017-05-24 13:09:34

Construction of the Lovas-Andai Two-Qubit Function $\tilde{\chi}_2 (\varepsilon )=\frac{1}{3} \varepsilon ^2 \left(4-\varepsilon ^2\right)$ Verifies the $\frac{8}{33}$-Hilbert Schmidt Separability Probability Conjecture

Authors: Paul B. Slater
Comments: 35 pages, 26 figures

We investigate relationships between two forms of Hilbert-Schmidt two-re[al]bit and two-qubit "separability functions''--those recently advanced by Lovas and Andai (arXiv:1610.01410), and those earlier presented by Slater ({\it J. Phys. A} {\bf{40}} [2007] 14279). In the Lovas-Andai framework, the independent variable $\varepsilon \in [0,1]$ is the ratio $\sigma(V)$ of the singular values of the $2 \times 2$ matrix $V=D_2^{1/2} D_1^{-1/2}$ formed from the two $2 \times 2$ diagonal blocks ($D_1, D_2$) of a randomly generated $4 \times 4$ density matrix $D$. In the Slater setting, the independent variable $\mu$ is the diagonal-entry ratio $\sqrt{\frac{d_ {11} d_ {44}}{d_ {22} d_ {33}}}$--with, importantly, $\mu=\varepsilon$ or $\mu=\frac{1}{\varepsilon}$ when both $D_1$ and $D_2$ are themselves diagonal. Lovas and Andai established that their two-rebit function $\tilde{\chi}_1 (\varepsilon )$ ($\approx \varepsilon$) yields the previously conjectured Hilbert-Schmidt separability probability of $\frac{29}{64}$. We are able, in the Slater framework (using cylindrical algebraic decompositions [CAD] to enforce positivity constraints), to reproduce this result. Further, we similarly obtain its new (much simpler) two-qubit counterpart, $\tilde{\chi}_2(\varepsilon) =\frac{1}{3} \varepsilon ^2 \left(4-\varepsilon ^2\right)$. Verification of the companion conjecture of a Hilbert-Schmidt separability probability of $\frac{8}{33}$ immediately follows in the Lovas-Andai framework. We obtain the formulas for $\tilde{\chi}_1(\varepsilon)$ and $\tilde{\chi}_2(\varepsilon)$ by taking $D_1$ and $D_2$ to be diagonal, allowing us to proceed in lower (7 and 11), rather than the full (9 and 15) dimensions occupied by the convex sets of two-rebit and two-qubit states. The CAD's themselves involve 4 and 8 variables, in addition to $\mu=\varepsilon$. We also investigate extensions of these analyses to rebit-retrit and qubit-qutrit ($6 \times 6$) settings.
Category: Mathematical Physics

[17] viXra:1705.0357 [pdf] submitted on 2017-05-24 16:04:15

A Review of Two Derivations of Maxwell-Dirac Isomorphism and a Few Plausible Extensions

Authors: Victor Christianto
Comments: 5 Pages. this paper has been submitted to MDPI - Mathematics

The problem of the formal connection between electrodynamics and wave mechanics has attracted the attention of a number of authors, especially there are some existing proofs on Maxwell-Dirac isomorphism. Here the author will review two derivations of Maxwell-Dirac isomorphism i.e. by Hans Sallhofer and Volodimir Simulik. A few plausible extensions will be discussed too.
Category: Mathematical Physics

[16] viXra:1705.0347 [pdf] submitted on 2017-05-24 01:33:15

About Physical Inadequacy of the Three-Dimensional Navier-Stokes Equation for Viscous Incompressible Fluid.

Authors: Preobrazhenskiy Andrey
Comments: 10 Pages.

ABSTRACT. This paper deals with the analysis of physically possible constructions of a viscous incompressible fluid model. Physical principles that allow to create the only possible construction of this model were found. The new model does not use new constants that characterize properties of the fluid and coincides with the Stokes model only in the plane case. Within the framework of this model, new equations for fluid motion were obtained. The new equations coincide with Navier-Stokes system in the plane case, but do not coincide in the three-dimensional one. The model makes it possible to see why the three-dimensional Navier-Stokes equations cannot physically adequately describe fluids motion, and obliquely confirms the finite time for the existence of its regular solutions.
Category: Mathematical Physics

[15] viXra:1705.0330 [pdf] submitted on 2017-05-22 05:15:16

Nonlinearity, Entropy and Chaos in Music

Authors: Sai Venkatesh Balasubramanian
Comments: 11 Pages.

This article explores the nonlinear aspects underlying music , particularly focusing on melody. By using the concept of scale as the basis, the article explores ways to formulate and study the features and 'feature richness' of a given melody or Raga, and to do this, the Raga scale is represented as a 1-Dimensional array. The Signature graph of a Raga plotted as Interval as a function of Note position, established a graphic visualization of the Raga. The progression and trend of intervals was computed using the Second Level Interval Array. This trend graph reveals the complexity in a Raga structure, through looping, crowded and intricate curves in the graph. Next, the concept of chaos in the context of melody is explored, fundamentally by performing a sensitivity test, which analyzes that given a Raga, and a particular evolution path, how starting at two nearby Swaras results in two entirely different ending Swaras, when sampled after a certain period in time. As a measure of the complexity in a Raga, the entropy, a measure of uncertainty is proposed, and computed using the interval arrays as bases for an occurrence array yielding empirical probabilities. The entropy is seen as a measure of richness, a measure of variety of inter-Swara intervals that a given Raga possesses. One notes that Ragas with high entropy, on account of their interval richness, usually fall under the category of pleasant, appealing and melodious Ragas. These are also the Ragas one finds being employed in film music, clearly owing to their pleasant feel.
Category: Mathematical Physics

[14] viXra:1705.0300 [pdf] replaced on 2017-05-23 08:56:56

Mnozenje Vektora I Struktura 3D Euklidskog Prostora

Authors: Miroslav Josipović
Comments: 80 Pages. geometric algebra

This is the translation of the article "Multiplication of Vectors and Structure of 3D Euclidean Space" to Croatian.
Category: Mathematical Physics

[13] viXra:1705.0274 [pdf] replaced on 2017-05-23 14:09:54

An Axiomless Derivation of the Theory of Everything

Authors: Alexandre Harvey-Tremblay
Comments: 48 Pages.

Plato recognized that most of the disagreement in philosophy is ultimately linked to the choice of axioms made by the parties involved. He believed that by grinding away at the assumptions made for any argument, one could recover a kind universal truth. He believed that this universal truth, comprised of whatever survives the grinding process, could ultimately be used to build a logical framework in a manner that is entirely irrefutable. This is the axiomless position. In this work, I present such a derivation. Part I of this work is the axiomless derivation of the theory of everything in physics. From this derivation I obtain a master equation relating the notions of truth, knowledge and information to that of entropy. Part II is the thesis that this master equation is indeed the theory of everything in physics. To convince you of that, I recover, again in an axiomless manner, the exact mathematical formulation of the major theories of physics; including statistical mechanics, quantum mechanics, special and general relativity. These equations are entirely derived from pure reason with no appeal to physical observations. The work here can also be interpreted as a constructive proof of René Descartes' cogito ergo sum. Where-as he proved the existence of the thinking self by contradiction, it is here proven by construction.
Category: Mathematical Physics

[12] viXra:1705.0262 [pdf] submitted on 2017-05-18 03:29:30

An Extension to the Theory of Trigonometric Functions as Exact Periodic Solutions to Quadratic Liénard Type Equations

Authors: D. K. K. Adjaï, L. H. Koudahoun, J. Akande, Y. J. F. Kpomahou, M. D. Monsia
Comments: 11 Pages. 1-11

This paper slightly extends the theory of exact trigonometric periodic solutions to quadratic Liénard type equations introduced earlier by the authors of the present contribution. The extended theory is used to determine the general periodic solutions to the Duffing equation and to some Painlevé-Gambier equations as illustrative examples. Finally the mathematical equivalence between the Duffing equation and the Painlevé-Gambier XIX equation has been highlighted by means of the proposed extended theory.
Category: Mathematical Physics

[11] viXra:1705.0261 [pdf] submitted on 2017-05-18 03:29:03

On the Complex Function Basis of Maxwell Equations

Authors: Zhi Cheng
Comments: 14 Pages. Include Chinese version

In this paper, we propose a concept of vector complex function to prove that the whole world can be reduced to a very simple function f(Z) = F + iG by introducing the knowledge of complex function theories. We can also derive Maxwell equations through the differential and integral analysis of the vector complex function.
Category: Mathematical Physics

[10] viXra:1705.0251 [pdf] submitted on 2017-05-16 19:11:11

Six Easy Pieces in Computational Physics

Authors: Victor Christianto
Comments: 39 Pages. This paper has not been submitted to a journal

The present book consists of 6 papers that I and some colleagues developed throughout the last 3-4 years. The subjects discussed cover wireless energy transmission, soliton model of DNA, cosmology, and also solutions of Navier-Stokes equations both in 2D and 3D. Some additional graphical plots for solution of 3D Navier-Stokes equations are also given. Hopefully the readers will find these papers at least interesting to ponder.
Category: Mathematical Physics

[9] viXra:1705.0212 [pdf] submitted on 2017-05-14 02:26:57

Correcting for Relativity in GPS makes no sense

Authors: Sjaak Uitterdijk
Comments: 3 Pages.

Showing that the Special Theory of Relativity is an untenable theory, many times leads to the reaction that the GPS is so accurate thanks to the STR corrections. This article shows that the supposed relativity errors are by far negligible relative to the errors caused by atmospheric circumstances.
Category: Mathematical Physics

[8] viXra:1705.0203 [pdf] submitted on 2017-05-12 22:53:16

The Relations Between Ancient China’s Taoism And Modern Mathematics & Physics

Authors: ShengYu.Shu
Comments: 62 Pages.

I have mainly analyzed the mathematical meaning of non-classical mathematical theory for three fundamental physics equations - Maxwell’s equations, Dirac’s equations, Einstein’s equations from the quantized core theory of ancient China’s Taoism, and found they have some structures described in the core of the theory of ancient China’s Taoism, especially they all obviously own the yin-yang induction structure. This reveals the relations between the ancient China’s Taoism and modern mathematics and physics in a way, which may help us to understand some problems of the fundamental theory of physics.
Category: Mathematical Physics

[7] viXra:1705.0133 [pdf] submitted on 2017-05-08 07:55:21

The Recursive Future And Past Equation Based On The Ananda-Damayanthi Similarity Measure Considered To Exhaustion (New)

Authors: Ramesh Chandra Bagadi
Comments: 2 Pages.

In this research investigation, the author has presented a Recursive Past Equation and a Recursive Future Equation based on the Ananda-Damayanthi Similarity Measure considered to Exhaustion [1].
Category: Mathematical Physics

[6] viXra:1705.0104 [pdf] submitted on 2017-05-04 12:18:15

The Recursive Past Equation Based On The Ananda-Damayanthi Similarity Measure. The Recursive Future Equation Based On The Ananda-Damayanthi Similarity Measure

Authors: Ramesh Chandra Bagadi
Comments: 4 Pages.

In this research investigation, the author has presented a Recursive Past Equation based on the Ananda-Damyanthi Similarity Measure [1]. Also, in this research investigation, the author has presented a Recursive Future Equation based on the Ananda-Damyanthi Similarity Measure [1].
Category: Mathematical Physics

[5] viXra:1705.0095 [pdf] submitted on 2017-05-03 22:01:08

A Detailed Analysis of Geometry Using Two Variables

Authors: John Peel
Comments: 6 Pages. The sets at the end are important

Calculating certain aspects of geometry has been difficult. They have defied analytics. Here I propose a method of analysing shape and space in terms of two variables (n,m).
Category: Mathematical Physics

[4] viXra:1705.0091 [pdf] submitted on 2017-05-04 06:15:57

The Recursive Future Equation (Final)

Authors: Ramesh Chandra Bagadi
Comments: 2 Pages.

The author has presented a Recursive Future Equation
Category: Mathematical Physics

[3] viXra:1705.0035 [pdf] replaced on 2017-05-04 02:31:50

Solving Numerically a System of Coupled Riccati ODEs for Incompressible Non-Stationary 3D Navier-Stokes Equations

Authors: Victor Christianto, Sergey Ershkov
Comments: 11 Pages. This paper is to be submitted to Royal Society Open Access journal. Your comments are welcome.

In a recent paper, Ershkov derived a system of two coupled Riccati ODEs as solution of non-stationary incompressible 3D Navier-Stokes equations. Now in this paper, we solve these coupled Riccati ODEs using: a) Maxima and b) Mathematica 11 computer algebra packages. The result seems to deserve further investigation in particular in comparison with rigid body motion, which will be discussed elsewhere.
Category: Mathematical Physics

[2] viXra:1705.0012 [pdf] submitted on 2017-05-01 22:52:24

The Recursive Equation Connecting Future And Past

Authors: Ramesh Chandra Bagadi
Comments: 3 Pages.

In this research manuscript, the author has presented a Recursive Equation Connecting Future And Past
Category: Mathematical Physics

[1] viXra:1705.0011 [pdf] submitted on 2017-05-01 23:45:14

An Introduction to Ontological-Phase Topological Field Theory in Relation to Newton-Einstein G-Duality and Dirac-Majorana Doublet Fusion

Authors: Richard L. Amoroso
Comments: 14 Pages. Version to be published in 10th proceedings honoring mathematical physicist Jean-Pierre Vigier by World Scientific

Ontological-Phase Topological Field Theory (OPTFT) under seminal development to formally describe 3rd regime Unified Field Mechanics (UFM) (classical-Quantum-UFM) is extended to relate the duality of Newton-Einstein gravitation theory by added degrees of freedom in a semi-quantum limit enabling insight into topological Dirac-Majorana doublet fusion supervening the uncertainty principle.
Category: Mathematical Physics