Related papers: A note on badly approximable affine forms and winn…

We give a simple proof of a recently result concerning Hardy $q$-inequalities.

We prove an easy statement about inhomogeneous approximation in metric theory of Diophantine Approximation.

The convergence analysis for least-squares finite element methods led to various adaptive mesh-refinement strategies: Collective marking algorithms driven by the built-in a posteriori error estimator or an alternative explicit…

We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.

We give a reformuation of the Tate conjecture for a surface over a finite field in terms of suitable affine open subsets. We then present three attempts to prove this reformulation, each of them falling short. Interestingly, the last two…

Let $v$ be an odd real polynomial (i.e. a polynomial of the form $\sum_{j=1}^\ell a_jx^{2j-1}$). We utilize sets of iterated differences to establish new results about sets of the form $\mathcal…

Recent progress building on the groundbreaking work of Mabillard and Wagner has shown that there are important differences between the affine and continuous theory for Tverberg-type results. These results aim to describe the intersection…

We perform the a posteriori error analysis of residual type of a transmission problem with sign changing coefficients. According to [6] if the contrast is large enough, the continuous problem can be transformed into a coercive one. We…

This paper presents an approach for obtaining approximate solutions to quasi-variational inequalities in a real Hilbert space by modifying Tseng's scheme, which was originally designed for variational inequalities. The study explores the…

The paper presents a counterexample to the Hodge conjecture.

This short note provides a new and simple proof of the convergence rate for Peng's law of large numbers under sublinear expectations, which improves the corresponding results in Song [15] and Fang et al. [3].

This note provides a new approach to a result of Foregger and related earlier results by Keilson and Eberlein. Using quite different techniques, we prove a more general result from which the others follow easily. Finally, we argue that the…

We show an analogue of a theorem of An, Ghosh, Guan, and Ly on weighted badly approximable vectors for totally imaginary number fields. We show that for $G=\mathrm{SL}_2(\mathbb{C})\times\dots\times\mathrm{SL}_2(\mathbb{C})$ and $\Gamma<G$…

This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, which both allows to fully exploit the unique…

We obtain simple proofs of certain inequalites for bivariate means.

We give alternative proofs to certain results in the paper "Weak limits of almost invariant projections" by using ultraproducts of operators.

We improve a result of Bennett concerning certain sequences involving sums of powers of positive integers.

We give a proof of a result of Bonet, Engli\v{s} and Taskinen filling in several details and correcting some flaws.

In this two-part paper we prove an existence result for affine buildings arising from exceptional algebraic reductive groups. Combined with earlier results on classical groups, this gives a complete and positive answer to the conjecture…

We explore and refine techniques for estimating the Hausdorff dimension of exceptional sets and their diffeomorphic images. Specifically, we use a variant of Schmidt's game to deduce the strong C^1 incompressibility of the set of badly…