Results 61 to 70 of about 1,197 (263)
Algorithmic search for integer Abelian roots of a polynomial with integer Abelian coefficients [PDF]
Известия Саратовского университета. Новая серия: Математика. Механика. ИнформатикаIn this work, we consider the operations over Abelian integers of rank $n$. By definition, such numbers are elements of the complex field and have the form of polynomials with integer coefficients from the $n$th degree primitive root of 1.
Tsybulya, Liliya Mikhailovna
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Additive number theory and the ring of quantum integers [PDF]
Electronic Notes in Discrete Mathematics, 2005 LaTex.
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Advanced Science, EarlyView.We introduce AutomataGPT, a generative pretrained transformer (GPT) trained on synthetic spatiotemporal data from 2D cellular automata to learn symbolic rules. Demonstrating strong performance on both forward and inverse tasks, AutomataGPT establishes a scalable, domain‐agnostic framework for interpretable modeling, paving the way for future ...
Jaime A. Berkovich +2 more
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The Fourier restriction and Kakeya problems over rings of integers modulo $N$
Discrete Analysis, 2018 The Fourier restriction and Kakeya problems over rings of integers modulo $N$, Discrete Analysis 2018:11, 18 pp. The _Fourier restriction problem_ is the following general question.
Jonathan Hickman, James Wright
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Consensus Formation and Change are Enhanced by Neutrality
Advanced Science, EarlyView.Neutral agents are shown to enhance both the formation and overturning of consensus in collective decision‐making. A general mathematical model and experiments with locusts and humans reveal that neutrality enables robust consensus via simple interactions and accelerates consensus change by reducing effective population size.
Andrei Sontag +3 more
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Graphs Induced by W-Regular Rings With Application to Zpn
International Journal of Mathematics and Mathematical SciencesA ring R is called W-regular if for any non-nilpotent element a of R, there exists an element b of R such that a=aba. This ring is generalized to a regular ring and is a special type of π-regular ring; therefore, some results on rings that are regular ...
Mostafa Amer Khattab +2 more
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A Perspective on Interactive Theorem Provers in Physics
Advanced Science, EarlyView.Into an interactive theorem provers (ITPs), one can write mathematical definitions, theorems and proofs, and the correctness of those results is automatically checked. This perspective goes over the best usage of ITPs within physics and motivates the open‐source community run project PhysLean, the aim of which is to be a library for digitalized physics
Joseph Tooby‐Smith
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Certain near-rings are rings, II
International Journal of Mathematics and Mathematical Sciences, 1986 We investigate distributively-generated near-rings R which satisfy one of the following conditions: (i) for each x,y∈R, there exist positive integers m, n for which xy=ymxn; (ii) for each x,y∈R, there exists a positive integer n such that xy=(yx)n. Under
Howard E. Bell
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Additive maps preserving determinant on module of symmetric matrices over Zm
Journal of Hebei University of Science and Technology, 2018 In order to characterize the additive maps preserving of modulus of symmetric matrices over residue class rings, these maps are firstly proved to be linear in fact, then they are classified and discussed by means of contract transformation, number theory
Yuqiu SHENG +4 more
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Elimination theory for the ring of algebraic integers.
Journal für die reine und angewandte Mathematik (Crelles Journal), 1988 Let \(\mathcal R\) be the ring of all algebraic integers, \(\mathcal R\subset\mathbb C\). The author proves the following elimination theorem: Each elementary problem about \(\mathcal R\) can be effectively reduced to a finite number of ideal membership questions about the algebraic integers constructed by a simple algorithm from the parameters of the ...
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