Results 21 to 30 of about 102 (92)
Simultaneous inhomogeneous diophantine approximation on manifolds [PDF]
Journal of Mathematical Sciences, 2012 Dedicated to A.O.
Beresnevich, V. V., Velani, S. L.
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On simultaneous inhomogeneous Diophantine approximation [PDF]
Acta Arithmetica, 2006 In this paper, the authors study inhomogeneous problems in metrical Diophantine approximation. For a tuple \(\underline{\alpha} = (\alpha_1, \dots, \alpha_k) \in {\mathbb R}^k\) and real numbers \(v,w>0\), let \({\mathcal V}_v(\underline{\alpha})\) denote the set of \(\xi \in {\mathbb R}\) for which there is a \(c > 0\) such that the inequality ...
Bugeaud, Yann, Chevallier, Nicolas
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On a problem in simultaneous Diophantine approximation: Schmidt's conjecture [PDF]
Annals of Mathematics, 2011 For any $i,j \ge 0$ with $i+j =1$, let $\bad(i,j)$ denote the set of points $(x,y) \in \R^2$ for which $ \max \{\|qx\|^{1/i}, \|qy\|^{1/j} \} > c/q $ for all $ q \in \N $. Here $c = c(x,y)$ is a positive constant. Our main result implies that any finite intersection of such sets has full dimension. This settles a conjecture of Wolfgang M. Schmidt in
Badziahin, Dzmitry +2 more
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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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Energy Science &Engineering, Volume 14, Issue 7, Page 3250-3271, July 2026.This study introduces bipolar q‐fractional fuzzy sets and new aggregation operators to support renewable energy selection under uncertainty. The proposed decision‐making framework effectively integrates positive and negative evaluations, ensuring consistent ranking and robust performance, as demonstrated through practical analysis and comparative ...
Sagvan Y. Musa +3 more
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Kripke on Gödel Incompleteness
Theoria, Volume 92, Issue 3, June 2026.ABSTRACT This paper surveys six of Saul Kripke's highly creative ideas and results on Gödel incompleteness, from when he was an undergraduate to last publications. These include his extension of incompleteness from sentences to predicates, his model‐theoretic proof of incompleteness of arithmetic, his compelling analysis of incompleteness in terms of ...
Daniel Isaacson
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Simultaneous diophantine approximation of rational numbers [PDF]
Acta Arithmetica, 1972 For any real number \(x\), let \(\Vert x\Vert\) denote the distance from \(x\) to the nearest integer. Let \(n\) be any positive integer and let \(\sigma = (s_1, \ldots, s_n)\) denote an arbitrary point in the set \(S^n\) of \(n\)-dimensional points all of whose coordinates are rational noninteger numbers.
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Generalized free wreath products and their operator algebras
Journal of the London Mathematical Society, Volume 113, Issue 6, June 2026.Abstract We develop a new approach on free wreath products, generalizing the constructions of Bichon and of Fima‐Pittau. We show stability properties for certain approximation properties such as exactness, Haagerup property, hyperlinearity, and K‐amenability. We study qualitative properties of the associated von Neumann algebra: factoriality, primeness,
Pierre Fima, Arthur Troupel
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Liminf Sets in Simultaneous Diophantine Approximation [PDF]
Journal de théorie des nombres de Bordeaux, 2017 Let 𝒬 be an infinite set of positive integers. Denote by W τ ,
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Successive Minima and Best Simultaneous Diophantine Approximations [PDF]
Monatshefte für Mathematik, 2005 We study the problem of best approximations of a vector $α\in{\mathbb R}^n$ by rational vectors of a lattice $Λ\subset {\mathbb R}^n$ whose common denominator is bounded. To this end we introduce successive minima for a periodic lattice structure and extend some classical results from geometry of numbers to this structure.
Aliev, Iskander, Henk, Martin
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