Zobrazeno 1 - 10
of 21
pro vyhledávání: '"Rao, Anurag"'
For an m by n real matrix A, we investigate the set of badly approximable targets for A as a subset of the m-torus. It is well known that this set is large in the sense that it is dense and has full Hausdorff dimension. We investigate the relationshi
Externí odkaz:
http://arxiv.org/abs/2402.00196
Editing knowledge in large language models is an attractive capability to have which allows us to correct incorrectly learnt facts during pre-training, as well as update the model with an ever-growing list of new facts. While existing model editing t
Externí odkaz:
http://arxiv.org/abs/2401.07453
Publikováno v:
Comb. Number Th. 13 (2024) 207-224
We introduce a novel concept in topological dynamics, referred to as $k$-divergence, which extends the notion of divergent orbits. Motivated by questions in the theory of inhomogeneous Diophantine approximations, we investigate this notion in the dyn
Externí odkaz:
http://arxiv.org/abs/2307.09054
Autor:
Kleinbock, Dmitry, Rao, Anurag
Given a norm $\nu$ on $\mathbb{R}^2$, the set of $\nu$-Dirichlet improvable numbers $\mathbf{DI}_\nu$ was defined and studied in the papers of Andersen-Duke (Acta Arith. 2021) and Kleinbock-Rao (Internat. Math. Res. Notices 2022). When $\nu$ is the s
Externí odkaz:
http://arxiv.org/abs/2210.09299
Autor:
Kleinbock, Dmitry, Rao, Anurag
Following the development of weighted asymptotic approximation properties of matrices, we introduce the analogous uniform approximation properties (that is, study the improvability of Dirichlet's Theorem). An added feature is the use of general norms
Externí odkaz:
http://arxiv.org/abs/2111.07115
Autor:
Kleinbock, Dmitry, Rao, Anurag
Publikováno v:
Moscow J. Comb. Number Th. 11 (2022) 97-114
In a recent paper of Akhunzhanov and Shatskov the two-dimensional Dirichlet spectrum with respect to Euclidean norm was defined. We consider an analogous definition for arbitrary norms on $\mathbb{R}^2$ and prove that, for each such norm, the set of
Externí odkaz:
http://arxiv.org/abs/2107.10298
Let $K$ be a bounded convex domain in $\mathbb{R}^2$ symmetric about the origin. The critical locus of $K$ is defined to be the (non-empty compact) set of lattices $\Lambda$ in $\mathbb{R}^2$ of smallest possible covolume such that $\Lambda \cap K= \
Externí odkaz:
http://arxiv.org/abs/2003.13829
Autor:
Kleinbock, Dmitry, Rao, Anurag
We study a norm sensitive Diophantine approximation problem arising from the work of Davenport and Schmidt on the improvement of Dirichlet's theorem. Its supremum norm case was recently considered by the first-named author and Wadleigh, and here we e
Externí odkaz:
http://arxiv.org/abs/1910.00126
Akademický článek
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Publikováno v:
In Indagationes Mathematicae May 2021 32(3):719-728
