Related papers: A note on badly approximable affine forms and winn…
We show that badly approximable matrices are exactly those that, for any inhomogeneous parameter, can not be inhomogeneous approximated at every monotone divergent rate, which generalizes Ram\'irez's result (2018). We also establish some…
We give a brief proof of a recent result of Avron, Seiler and Simon.
We prove that the set of (r_1,r_2,..,r_{d})-badly approximable vectors is a winning set if r_1=r_2=...=r_{d-1}\geq r_{d}.
We give a new proof of a classical theorem on approximation of continuous functions on totally real sets
Modifying an idea of E. Brietzke we give simple proofs for the recurrence relations of some sequences of binomial sums which have previously been obtained by other more complicated methods.
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We confirm several conjectures of Guo, Jouhet and Zeng concerning the factors of alternative binomials sums.
We establish a strong form of Littlewood's conjecture with inhomogeneous shifts, for a full-dimensional set of pairs of badly approximable numbers on a vertical line. We also prove a uniform assertion of this nature, generalising a strong…
Following T. H. Chan, we consider the problem of approximation of a given rational fraction a/q by sums of several rational fractions a_1/q_1, ..., a_n/q_n with smaller denominators. We show that in the special cases of n=3 and n=4 and…
In this paper, we provide a new scheme for approximating the weakly efficient solution set for a class of vector optimization problems with rational objectives over a feasible set defined by finitely many polynomial inequalities. More…
In this letter, we prove an inequality involving alternating binomial logarithmic sums by exploiting the variance of the logarithm of the maximum of independent and identically distributed exponential random variables. This inequality was…
Certain new inequalities for the sums of factorials are presented.
In this paper, sharp results on operator Young's inequality are obtained. We first obtain sharp multiplicative refinements and reverses for the operator Young's inequality. Secondly, we give an additive result, which improves a well-known…
Motivated by a wonderful paper by Ngoc Ai Van Nguyen, Anthony Po\"els and Damien Roy, where a powerful method was introduced, we prove a criterion for a vector $\pmb{\alpha}\in \mathbb{R}^d$ to be a badly approximable vector. Moreover we…
An technically interesting proof of a known theorem.
We prove some extensions of Andrews inequality.
We answer a question of Serre from the 1980s on rational points of bounded height on projective thin sets, in degree at least $4$. For degrees $2$ and $3$ we improve the known bounds in general. The focus is on thin sets of type II, namely…
We develop the theory of Diophantine approximation for systems of simultaneously small linear forms, which coefficients are drawn from any given analytic non-degenerate manifolds. This setup originates from a problem of Sprind\v{z}uk from…
In twisted Diophantine approximation, for a fixed $m\times n$ matrix $\boldsymbol\alpha$ one is interested in sets of vectors $\boldsymbol\beta\in\mathbb R^m$ such that the system of affine forms $\mathbb R^n \ni \mathbf q \mapsto…
In this note we prove a weighted version of the Khintchine inequalities.