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| viXra.org > General Mathematics > 2504 |
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[6] viXra:2504.0183 [pdf] submitted on 2025-04-28 20:37:51
Authors: Hongbo Sun
Comments: 13 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper presents a novel framework for probability theory, leveraging the geometric partitioning of Voronoi diagrams and topological measure theory to derive the fundamental properties of probability—nonnegativity, normalization, and additivity—without relying on the traditional Kolmogorov axioms. We reveal the abstract nature of probability: it is independent of specific entities and determined solely by the squared modulus of complex coefficients |ci|2. By treating Voronoi cells as phase circles and mapping them to Hilbert space basis vectors, we provide a geometric interpretation for classical probability and a topological foundation for quantum probability, expressed as P(|ei⟩) = |ci|2. We extend this framework to continuous distributions using three-dimensional tubular structures, and incorporate conditional probability and Bayesian inference, demonstrating its versatility. This framework unifies classical and quantum probability, highlighting the universal nature of probability, with potential applications in quantum information processing, random geometry, and statistical physics.
Category: General Mathematics
[5] viXra:2504.0103 [pdf] submitted on 2025-04-15 04:21:45
Authors: Mirzakhmet Syzdykov
Comments: 2 Pages.
As we have presented our functional hypothesis of complexity classes in previous review, we are to present the full mathematical proof of the relations between complexity classes.
Category: General Mathematics
[4] viXra:2504.0084 [pdf] submitted on 2025-04-12 22:30:15
Authors: Zhi Li, Hua Li
Comments: 18 Pages.
In the process of solving the roots of higher-order equations, it is found that the numbers with multi-layer radical forms obtained by special methods are not the roots of the equations, but only the approximate values of the roots of the equations. It is found that the numbers formed by the square root of non-rational numbers are inaccurate numbers. Among them, quantum numbers can be directly proved to be unordered. Further research has found quantum superposition numbers. This new discovery breaks the view that "numbers are accurate". New research shows that the rational numbers in the real number system have some non-rational counterparts. The non-rational numbers are those that cannot be expressed as ratios of integers but are roots of polynomials with rational coefficients.The numbers with double-layer square roots obtained by solving the equations by the Cardan method are inaccurate numbers. They are not real numbers under the classical definition, but only approximate values of the roots of the equations. The mainstream view is that the roots of the equations belong to the real numbers under the classical definition, which proves the general formula that there are no roots for cubic equations of one variable, and at the same time proves that the Galois group theory is wrong in its discussion of the roots of equations. In the function of finding non-trivial zeros in the Riemann hypothesis, there are a large number of square roots of transcendental numbers π, which are similar to multi-layer radical numbers. These numbers are not real numbers under the classical definition, and have no accurate values. After participating in the operation, the calculation results must not be zero. Therefore, it can be proved that there is no "non-trivial zero point" and no polynomial root with a real part value of 1/2, which negates the Riemann hypothesis.The discovery and proof of quantum numbers and quantum superposition numbers have broadened human thinking about the nature of nature. It provides a reference for human understanding of the behavior of the microscopic world, making our understanding of mathematics, physics and even the entire universe more profound and comprehensive. The discovery and proof of quantum numbers and quantum superposition numbers reveal the ultimate mystery of the universe. That is, some laws of the universe cannot be perfectly expressed by functions, nor can they be accurately expressed by mathematical formulas. Some conclusions derived from quantum numbers are consistent with current quantum theory.
Category: General Mathematics
[3] viXra:2504.0077 [pdf] submitted on 2025-04-11 19:30:39
Authors: Shiping Gu, Haitao Gu
Comments: 8 Pages. (Note by viXra Admin: Please submit article written with AI assistance to ai.viXra.org)
This paper introduces a new branch of mathematics, multilayer interface mathematics.A mathematical model describing the energy of multilayer interfaces is constructed based on the variational method, which includes constructing the total energy functional from interface free energy, electrochemical energy, and diffusion transport energy. The orresponding Euler-Lagrange equations are derived. Eachstep of the mathematical derivation is explained in detail, clearly introducing howperturbation methods, the chain rule, and integration by parts are used to rigorouslyderive the target equations. The performance of fuel cells and lithium-ion batteries is largely limited by the rapid exchange efficiency of key ions in multilayer interfaces. Based on traditional models, we further introduce physical equations describing proton transport in hydrogen fuel cells and the rapid exchange of lithium ions in multilayer interfaces, providing quantitative design guidance for the fastestexchange of protons in fuel cell membrane electrodes and lithium ions in lithium-ionbatteries through specific numerical examples and parameter sensitivity analysis.
Category: General Mathematics
[2] viXra:2504.0061 [pdf] submitted on 2025-04-09 16:07:46
Authors: Mirzakhmet Syzdykov, Yannick Leon Kardeis
Comments: 31 Pages.
We propose a simple and intuitive algorithm for solving md-DFA problem using algorithm concepts within extended operators, our approach shows quadratic polynomial time and hence proves the equivalence between polynomial and non-polynomial classes, we have also shown that minimal non-emptiness of automata problem can be solved in polynomial time with help of modified subset construction, rather that building a product automaton, which lead to factorial size of the memory and time, in this work we also have used many non-tractable existing examples and computed them in polynomial time, which guarantees that our algorithm solves NP-complete problem in almost linear polynomial time, we have also avoided the problem of product automata by an algorithmic approach, we are also giving the starting ground for the proof of back-reference problem which was discussed before, notion to the globally local increment is also given as the main argument towards the resolution of "P versus NP" theorem, which coincides with the finitarity term in general mathematics.
Category: General Mathematics
[1] viXra:2504.0020 [pdf] submitted on 2025-04-03 16:44:25
Authors: Edgar Valdebenito
Comments: 2 Pages.
In this note, we give some formulas related to Wallis's constant.
Category: General Mathematics
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