Results 51 to 60 of about 20,123 (196)
Arithmetic progressions at the Journal of the LMS
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract We discuss the papers P. Erdős and P. Turán, On some sequences of integers, J. London Math. Soc. (1) 11 (1936), 261–264 and K. F. Roth, On certain sets of integers, J. London Math. Soc. (1) 28 (1953), 104–109, both foundational papers in the study of arithmetic progressions in sets of integers, and their subsequent influence.
Ben Green
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Diophantine tuples and product sets in shifted powers
Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.Abstract Let k⩾2$k\geqslant 2$ and n≠0$n\ne 0$. A Diophantine tuple with property Dk(n)$D_k(n)$ is a set of positive integers A$A$ such that ab+n$ab+n$ is a k$k$th power for all a,b∈A$a,b\in A$ with a≠b$a\ne b$. Such generalizations of classical Diophantine tuples have been studied extensively.
Ernie Croot, Chi Hoi Yip
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Integral geometry on discrete matrices
Moroccan Journal of Pure and Applied Analysis, 2021 In this note, we study the Radon transform and its dual on the discrete matrices by defining hyperplanes as being infinite sets of solutions of linear Diophantine equations. We then give an inversion formula and a support theorem.
Attioui Abdelbaki
doaj +1 more source
Symmetric Diophantine Equations
Rocky Mountain Journal of Mathematics, 2004 The author describes a method to obtain infinite parametric solutions of some Diophantine equations of type \(f(x,y)=f(u,v)\) where \(f\) is a form (usually the product of some linear and quadratic forms) with rational coefficients. The main idea is to apply a non-singular linear transformation \(x=\alpha u+\beta v\), \(y=\gamma u+\delta v\) such that ...
openaire +2 more sources
Optimising Wave Energy Plant Location Through Neutrosophic Multi‐Criteria Group Decision‐Making
CAAI Transactions on Intelligence Technology, Volume 11, Issue 1, Page 167-189, February 2026.ABSTRACT The global shift towards sustainable energy has intensified research into renewable sources, particularly wave energy. Pakistan, with its long coastline, holds significant potential for wave energy development. However, identifying optimal locations for wave energy plants involves evaluating complex, multi‐faceted criteria.
Hafiz Muhammad Athar Farid +4 more
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A universal example for quantitative semi‐uniform stability
Journal of the London Mathematical Society, Volume 113, Issue 2, February 2026.Abstract We characterise quantitative semi‐uniform stability for C0$C_0$‐semigroups arising from port‐Hamiltonian systems, complementing recent works on exponential and strong stability. With the result, we present a simple universal example class of port‐Hamiltonian C0$C_0$‐semigroups exhibiting arbitrary decay rates slower than t−1/2$t^{-1/2}$.
Sahiba Arora +3 more
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Multivariate Diophantine equations with many solutions
, 2001 We show that for each n-tuple of positive rational integers (a_1,..,a_n) there are sets of primes S of arbitrarily large cardinality s such that the solutions of the equation a_1x_1+...+a_nx_n=1 with the x_i all S-units are not contained in fewer than ...
Evertse, J. -H. +3 more
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Plank theorems and their applications: A survey
Bulletin of the London Mathematical Society, Volume 58, Issue 1, January 2026.Abstract Plank problems concern the covering of convex bodies by planks in Euclidean space and are related to famous open problems in convex geometry. In this survey, we introduce plank problems and present surprising applications of plank theorems in various areas of mathematics.
William Verreault
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The Davenport–Heilbronn method: 80 years on
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract The Davenport–Heilbronn method is a version of the circle method that was developed for studying Diophantine inequalities in the paper (Davenport and Heilbronn, J. Lond. Math. Soc. (1) 21 (1946), 185–193). We discuss the main ideas in the paper, together with an account of the development of the subject in the intervening 80 years.
Tim Browning
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The dimension of well approximable numbers
Journal of the London Mathematical Society, Volume 113, Issue 1, January 2026.Abstract In this survey article, we explore a central theme in Diophantine approximation inspired by a celebrated result of Besicovitch on the Hausdorff dimension of well approximable real numbers. We outline some of the key developments stemming from Besicovitch's result, with a focus on the mass transference principle, ubiquity and Diophantine ...
Victor Beresnevich, Sanju Velani
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