| viXra.org > Mathematical Physics > 2503 |
 |
 |
| viXra.org > Mathematical Physics > 2503 |
|
|
[12] viXra:2503.0200 [pdf] submitted on 2025-03-31 20:35:23
Authors: T. L. A. Periat
Comments: 32 Pages.
This paper is part of a series of explorations exposing methods for dividing distorted tensor products by number cubes. Here, the discussion focuses on three-dimensional spaces and anti-symmetric cubes on their low indices, i.e. actually on distorted cross products. The method only delivers the main parts of the divisions. The other documents in the collection complete this investigation. This is a translation made by me of a part of the French version.
Category: Mathematical Physics
[11] viXra:2503.0166 [pdf] submitted on 2025-03-26 22:17:47
Authors: Akira Saito
Comments: 13 Pages.
In this study, we propose a new deterministic solution for the spin glass ground state problem. Our method formulates the Ising spin glass problem as a system of nonlinear equations and determines the ground state by solving those equations. Compared to simulated annealing (SA), the proposed method aims to reduce computational time while achieving energy accuracy that is equal to or better than SA.Through numerical experiments using the Sherrington-Kirkpatrick (SK) model, we confirmed that the proposed method achieves energy values comparable to SA with a reduction in computation time by a factor of 1/3 to 1/15. Furthermore, scaling analysis shows that the computation time of the proposed method grows proportionally to ��1.21, demonstrating superior scalability compared to SA, which depends on ��2.05.The findings of this study suggest new possibilities for solving spin glass ground state problems and may be applied to areas such as combinatorial optimization and machine learning. Future work will focus on improving scalability, introducing methods to avoid local minima, and accelerating computations through GPU parallelization to enhance practical utility.
Category: Mathematical Physics
[10] viXra:2503.0158 [pdf] submitted on 2025-03-26 03:08:39
Authors: David Vickers
Comments: 128 Pages. (Note by viXra Admin: AI assisted content is in general not acceptable)
We present a novel approach to the global existence and smooth-ness problem for the three—dimensional incompressible Navier—Stokes equations based on a Generalized Modular Spectral Theory (GMST).Our method begins with a precise formulation of the Navier—Stokes system in suitable Sobolev and divergence—free function spaces and employs a detailed spectral decomposition of the associated Stokes operator. A key innovation is the introduction of a modular—like (Möbius) transformation applied to the operator’s eigenvalues, which "lifts" potentially dangerous low—frequency modes by enforcing an ex-ponential decay in the spectral density. This spectral transformation is integrated into a recursive fixed—point framework, wherein we establish contraction properties in high—order Sobolev spaces and derive sharp energy inequalities that preclude finite—time blowup. Furthermore,we recast the problem within an axiomatic setting analogous to those used in quantum field theory, thereby providing additional structural insight into the global regularity of solutions. The theoretical findings are supported by comprehensive numerical simulations using a Fourier—Galerkin discretization combined with an Exponential TimeDifferencing Runge—Kutta scheme. Our results offer a promising new perspective on the longstanding Millennium Problem by unifying rigorous spectral analysis, modular invariance, and fixed—point techniques in a single framework.
Category: Mathematical Physics
[9] viXra:2503.0157 [pdf] submitted on 2025-03-25 15:15:15
Authors: Warren D. Smith
Comments: 19 Pages.
Oct.2001 paper by me proving the Turing unsimulability of Navier-Stokes hydrodynamics (or certain other alternatives, but either way, I contend demonstrating the failure of Navier-Stokes as a useful algorithmic physical theory).Now uploaded to vixra for archival purposes.
Category: Mathematical Physics
[8] viXra:2503.0101 [pdf] submitted on 2025-03-17 15:53:09
Authors: Dwight Boddorf
Comments: 2 Pages.
Where N is a counting number, one hundred and thirty-seven is the first prime number to take the form of 2[(2N+2)(2N+2)] + NN , if N equals 3 then prime number is one hundred and thirty-seven.
Category: Mathematical Physics
[7] viXra:2503.0081 [pdf] replaced on 2025-03-18 20:46:03
Authors: YoonKi Kim
Comments: 23 Pages. Contact email: yk.reserch@gmail.com
We introduce Alpha Integration, a novel path integral framework that applies to wide range of function including locally integrable functions, distributions, and fields—across arbitrary spaces and n dimensions (n ∈N), while preserving gauge invariance without approximations. This method extend to Rn(n ∈N), smooth manifolds, infinite-dimensional spaces, and complex paths, enabling rigorous integration of all f ∈Du2032 with formal mathematical proofs. This framework is further generalized to infinite-dimensional spaces, complex paths, and arbitrary manifolds,with its consistency validated through extensive testing across diverse functions, fields, and spaces. Alpha Integration thus offers a robust and efficient alternative to traditional path integral techniques, serving as a versatile tool for mathematical and physical analysis.
Category: Mathematical Physics
[6] viXra:2503.0075 [pdf] submitted on 2025-03-12 23:09:49
Authors: Temur Z. Kalanov
Comments: 14 Pages.
The irrefutable proof of the incorrectness of the de Broglie hypothesis (postulate) and the Schrödinger equation (postulate) is proposed. The correct methodological basis for the proof is the unity of formal logic and rational dialectics. The unity of formal logic and rational dialectics is the only correct criterion of truth. The proof leads to the following irrefutable conclusion: the de Broglie hypothesis (idea, postulate) and the Schrödinger equation (idea, postulate) are gross errors in mathematics, physics, formal logic and dialectics. This conclusion is based on the following statements: (1) from the point of view of Euler's formula and the Maclaurin series, the definition of the wave function has neither physical nor mathematical meaning; (2) the substitution of the quantities of energy and momentum, which characterize a quantum (microscopic) particle, into the relationship that describes a macroscopic radiation wave is a gross formal-logical error, because a quantum particle and macroscopic radiation are not identical material objects; (3) in the dialectical and formal-logical points of view, a free classical particle is not identical to a free quantum particle: these particles are non-identical material objects. Therefore, the substitution of the quantities of energy and momentum, characterizing a quantum (microscopic) particle, into the classical relationship that describes the energy and momentum of a classical particle is a gross formal-logical error; (4) in the point of view of formal logic, the concepts of "corpuscular aspect" and "wave aspect" are contradictory (mutually exclusive) concepts. (The concepts of "particle" and "wave" are defined by different essential features of material objects). Therefore, the de Broglie wave function and the Schrödinger wave equation represent a violation of the formal-logical law of lack (absence) of contradiction. This means that the concept of corpuscular-wave dualism is erroneous; (5) The de Broglie wave function and the Schrödinger equation represent a gross dialectical error, because the dimensionless wave function contradicts to the dialectical concept of the measure of a material object (i.e. the dimensionless wave function does not have the qualitative determinacy of a material object, does not characterize the properties of a material object). Therefore, the de Broglie wave function and the Schrödinger equation are meaningless relationships.
Category: Mathematical Physics
[5] viXra:2503.0060 [pdf] replaced on 2025-03-14 14:57:46
Authors: Ervin Goldfain
Comments: 24 Pages.
It was recently conjectured that the Standard Model of particle physics resides on a bifurcation diagram generated by the recursive scaling of the Higgs coupling. This sequel explores the relationship between the bifurcation diagram and the Path Integral (PI) formalism of Quantum Field Theory (QFT). The long-term goal is to base the Feynman diagrams on the properties of the Feigenbaum attractor of either quadratic or cubic maps.
Category: Mathematical Physics
[4] viXra:2503.0043 [pdf] replaced on 2025-03-10 21:19:27
Authors: Vasant Jayasankar
Comments: 36 Pages. (Note by viXra Admin: AI assisted article is in general not acceptable)
The Shannon entropy equation has been foundational in information theory, yet its derivation has historically relied on axiomatic reasoning rather than first principles. In this paper, I propose two derivations of the Shannon entropy equation from fundamental geometric constraints, demonstrating that it emerges naturally as a special case of a deeper information structuring principle. I propose that entropy is fundamentally constrained by geometric projection effects and dimensionality, leading to a formulation that reduces to Shannon’s equation in Euclidean space while extending to structured high-dimensional systems.Further, I introduce a novel connection between optimal information structuring and the All-Pairs Shortest Path (APSP) framework, demonstrating that information processing may follow geodesic constraints in hyperbolic space. This insight suggests that optimal data compression, AI learning, and information retrieval follow geometric constraints, revealing a deeper structural foundation beyond statistical approximations.By unifying entropy, geometric projection constraints, and APSP-based information structuring, I introduce the RTA Framework for Information, which redefines optimal information flow in structured systems and AI architectures. If validated mathematically and empirically, this may have deep implications for AI architectures, compression theory, and quantum information, pointing toward a broader framework that extends beyond classical entropy formulations.
Category: Mathematical Physics
[3] viXra:2503.0032 [pdf] submitted on 2025-03-05 21:18:44
Authors: Shlomy Shitrit, Eran Arad
Comments: 30 Pages.
The transition of a boundary layer from laminar to turbulent impacts the characteristics of aflow field, but its underlying physics has yet to be well understood. This literature review aims to give an overview of the more widely used approaches to model transition in ComputationalFluid Dynamics (CFD). Several different methods are reviewed: the linear stability analysismethod, the low Reynolds number turbulent closure approach, the correlation-based methods,the intermittency transport method and the laminar fluctuation energy method. The approaches are compared to one another, highlighting their respective advantages and drawbacks.
Category: Mathematical Physics
[2] viXra:2503.0029 [pdf] submitted on 2025-03-04 22:01:18
Authors: James Fruit
Comments: 8 Pages. Copyright Licensed under CC BY 4.0. NC © 2025 James Fruit.
This paper presents a rigorous, non-perturbative proof of the Yang-Mills Mass Gap Problem,demonstrating the existence of a strictly positive lower bound for the spectrum of SU(3) gauge boson excitations. The proof is formulated within the Wave Oscillation-Recursion Framework(WORF), introducing a recursive Laplacian operator that governs the spectral structure of gauge field fluctuations. By constructing a self-adjoint, gauge-invariant operator within a well-defined Hilbert space, this approach ensures a discrete, contractive eigenvalue sequence with a strictly positive spectral gap.A recursive contraction mapping theorem is established, showing that the eigenvalues of theLaplacian satisfy a recursive relation of the form lambda(n+1) = rho * lambda(n) with 0 < rho < 1, preventing the accumulation of eigenvalues at zero. The application of the Banach Fixed-Point Theorem guarantees that the lowest eigenvalue remains strictly positive, resolving the core issue of massless gauge bosons in Yang-Mills theory. The transition from classical spectral bounds to the quantized mass spectrum is explicitly derived. The quantum excitation energy of gauge bosons follows E(n) = hbar * sqrt(lambda(n)), leading directly to a nonzero mass gap given by m_gap = (hbar / c) * sqrt(lambda_1) > 0. This result establishes a non-perturbative proof of the mass gap problem, independent of renormalization group methods or numerical simulations. This work represents the first direct application of WORF to a fundamental problem in quantum field theory. The proof is mathematically self-contained and is submitted for formal review by the Clay Mathematics Institute. If validated, this approach provides a transformative new methodfor addressing open problems in high-energy physics and gauge theory.
Category: Mathematical Physics
[1] viXra:2503.0028 [pdf] submitted on 2025-03-04 21:53:40
Authors: Dara O. Shayda
Comments: 8 Pages.
In March of 1845 Gauss described the conception of an action at a distance, propagated with a finite velocity, the natural generalization to electrodynamics view of Newtonian force. Unsuccessfully, Wheeler and Feynman attempted a new theory for Absorber in 1945 [9]. In their paper there is a detailed reference provided by Prof. Einstein about a relatively unknown physicist named Hugo Tetrode[10,11] and quoted: "The sun would not radiate if it were alone in space and no other bodies could absorb its radiation... If for example I observed through my telescope yesterday evening that star which let us say is 100 lights years away, then not only did I know that the light which it allowed to reach my eyes was emitted 100 years ago, but also the star or individual atoms of it knew already 100 years ago that ‘I’, who then did not even exit, would view it yesterday evening at such and such timeu2026"[11]. The process by which the verb "knew"occurs is modelled by the Noetic morphisms of the arr(Decay) Arrow Category. However this treatise is not about energy emission absorption in nature, rather about their mechanism of information knowledge exchange to make the emission possible.This treatise and its categorical constructions, Universal Properties and symbols pave the way for grammars and functions and operators and Formal Systems (algebras, calculi) of de novo programming languages to describe the nature of specific Emitter Absorber coupling.
Category: Mathematical Physics
| Third-Party Links: |
|