Results 41 to 50 of about 4,013,096 (184)
Efficient solution of linear diophantine equations
Journal of Symbolic Computation, 1989 The paper gives a new method for finding complete information about all nonnegative solutions of a linear homogeneous or inhomogeneous diophantine equation \[ \sum_{i=1}^{m}a_ix_i- \sum_{j=1}^{n}b_jy_j=c, \] where the \(a_i's\) and \(b_j's\) are positive integers and \(c\) is \(0\) resp. a positive integer.
Michael Clausen, Albrecht Fortenbacher
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Grain Boundary Structure Ordering via Electroshock Treatment Enhances Strength‐Ductility Synergy
Advanced Science, EarlyView.Electroshock treatment triggers atomic rearrangement, transforming disordered grain boundaries into ordered states without inducing recrystallization. This grain boundary ordering effectively relieves strain concentration and strengthens boundaries, enabling a simultaneous improvement in both strength and ductility.
Jiancheng Chen +6 more
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Real-world applications of number theory [PDF]
ریاضی و جامعهThe above abstract has been extracted by the translator from the original article (J. Klaška, Real-world applications of number theory, South Bohemia Mathematical Letters, 25 no.
Rahim Rahmati-Asghar
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Counting monochromatic solutions to diagonal Diophantine equations
Discrete Analysis, 2021 Counting monochromatic solutions to diagonal Diophantine equations, Discrete Analysis 2021:14, 47 pp. An important subfield of Ramsey theory concerns questions of the following type: for which systems of equations $E_1,\dots,E_k$ in variables $x_1,\dots,
Sean Prendiville
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Communications on Pure and Applied Mathematics, Volume 79, Issue 9, Page 2107-2157, September 2026.ABSTRACT The leading‐order asymptotic behavior of the solution of the Cauchy initial‐value problem for the Benjamin–Ono equation in L2(R)$L^2(\mathbb {R})$ is obtained explicitly for generic rational initial data u0$u_0$. An explicit asymptotic wave profile uZD(t,x;ε)$u^\mathrm{ZD}(t,x;\epsilon)$ is given, in terms of the branches of the multivalued ...
Elliot Blackstone +3 more
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On 7‐adic Galois representations for elliptic curves over Q$\mathbb {Q}$
Proceedings of the London Mathematical Society, Volume 133, Issue 2, August 2026.Abstract In recent years, significant progress has been made on Mazur's Program B, with many authors beginning a systematic classification of all possible images of p$p$‐adic Galois representations attached to elliptic curves over Q$\mathbb {Q}$. Currently, the classification is only complete for p∈{2,3,13,17}$p \in \lbrace 2,3,13,17\rbrace$.
Lorenzo Furio, Davide Lombardo
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Fourier Expansion‐Based Approach to the Parameter Space of Classical Systems
Annalen der Physik, Volume 538, Issue 7, July 2026.ABSTRACT We propose a new approach to compute the classical metric tensor (CMT) and the Hannay curvature using Fourier series expansions in action‐angle variables. This approach circumvents the need for complex time‐domain integrals or the construction of generating functions, replacing them with algebraic combinations of Fourier coefficients. We prove
Marcos J. Hernández +3 more
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Unified linear time-invariant model predictive control for strong nonlinear chaotic systems
Nonlinear Analysis, 2016 It is well known that an alone linear controller is difficult to control a chaotic system, because intensive nonlinearities exist in such system. Meanwhile, depending closely on a precise mathematical modeling of the system and high computational ...
Yuan Zhang, Mingwei Sun, Zengqiang Chen
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On the moments of exponential sums over r$r$‐free polynomials
Bulletin of the London Mathematical Society, Volume 58, Issue 7, July 2026.Abstract Let Fq[t]${\mathbb {F}}_q[t]$ denote the ring of polynomials over the finite field Fq${\mathbb {F}}_q$. Building off of techniques of Balog and Ruzsa and of Keil in the integer setting, we determine the precise order of magnitude of k$k$th moments of exponential sums over r$r$‐free polynomials in Fq[t]${\mathbb {F}}_q[t]$ for all k>0$k>0$.
Ben Doyle
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An elegant model of the geodesic flow on the modular surface
Journal of the London Mathematical Society, Volume 114, Issue 1, July 2026.Abstract Caroline Series' [The modular surface and continued fractions, J. Lond. Math. Soc. (2), 31, no. 1, (1985), 69–80] gives a clear framework linking, in a deceptively simple way, the dynamics of the geodesic flow on the modular surface with the dynamics of the regular continued fraction, through a well‐chosen symbolic coding.
Pierre Arnoux, Thomas A. Schmidt
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