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Euclidean-Lorentzian Dichotomy and Algebraic Causality in Finite Ring Continuum [PDF]
EntropyWe present a concise and self-contained extension of the Finite Ring Continuum (FRC) program, showing that symmetry-complete prime shells Fp with p=4t+1 exhibit a fundamental Euclidean-Lorentzian dichotomy.
Yosef Akhtman
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Interval Ranges of Fuzzy Sets Induced by Arithmetic Operations Using Gradual Numbers
Mathematics, 2021 Wu introduced the interval range of fuzzy sets. Based on this, he defined a kind of arithmetic of fuzzy sets using a gradual number and gradual sets. From the point of view of soft computing, this definition provides a new way of handling the arithmetic ...
Qingsong Mao, Huan Huang
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Granular computational homogenisation of composite structures with imprecise parameters
Archives of Mechanics, 2023 The paper presents the formulation of a granular computational homogenisation problem and the proposition of a method to solve it, which enables multiscale analysis of materials with uncertain microstructure parameters.
W. Beluch, M. Hatłas, J. Ptaszny
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Mathematical and Computational Applications, 2022 An interval-based method is presented to evaluate the uncertainty in the computed mechanical properties and the failure assessment of composite unidirectional (UD) laminates.
Dimitris G. Sotiropoulos +1 more
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A Rigorous Extension of the Schönhage-Strassen Integer Multiplication Algorithm Using Complex Interval Arithmetic [PDF]
Electronic Proceedings in Theoretical Computer Science, 2010 Multiplication of n-digit integers by long multiplication requires O(n^2) operations and can be time-consuming. In 1970 A. Schoenhage and V. Strassen published an algorithm capable of performing the task with only O(n log(n)) arithmetic operations over ...
Thomas Steinke, Raazesh Sainudiin
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Numerical Modeling of Heat and Mass Transfer during Cryopreservation Using Interval Analysis
Applied Sciences, 2020 In the paper, the numerical analysis of heat and mass transfer proceeding in an axially symmetrical articular cartilage sample subjected to the cryopreservation process is presented.
Anna Skorupa, Alicja Piasecka-Belkhayat
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Tiling by translates of a function: results and open problems
Discrete Analysis, 2021 Tiling by translates of a function: results and open problems, Discrete Analysis 2021:12, 24 pp. Let $f$ be a function from $\mathbb R$ to $\mathbb R$, and for each $\lambda\in\mathbb R$, let $T_\lambda$ be the translate of $f$ by $\lambda$, that is ...
Mihail N. Kolountzakis, Nir Lev
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Multiple recurrence and large intersections for abelian group actions
Discrete Analysis, 2021 Multiple recurrence and large intersections for abelian group actions, Discrete Analysis 2021:18, 91 pp. In 1975, Szemerédi proved his famous theorem that asserts that for every positive integer $k$ and every $\delta>0$ there exists $n$ such that every ...
Ethan Ackelsberg +2 more
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Approximate Euclidean Ramsey theorems
Journal of Computational Geometry, 2011 According to a classical result of Szemerédi, every dense subset of 1,2,…,N contains an arbitrary long arithmetic progression, if N is large enough. Its analogue in higher dimensions due to Fürstenberg and Katznelson says that every dense subset of {1,2,…
Adrian Dumitrescu
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Journal of Probability and Statistics, 2015 This paper provides explicit formulae for the probability that an arithmetic or a geometric Brownian motion will not cross an absorbing boundary defined as a step function during a finite time interval.
Tristan Guillaume
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