Related papers: A note on Kronecker's approximation theorem

We establish a quantitative version of Oppenheim's conjecture for generic ternary indefinite quadratic forms using an analytic number theory approach. The statements come with power gains and in some cases are essentially optimal

We show the pointwise version of the Ste\v{c}kin theorem on approximation by de la Vall\'ee-Poussin means. The result on norm approximation is also derived.

We give derivations of some basic results for the Bernstein approximation in $n$ variables that are useful in investigating copulas. It is shown that Bernstein approximations of copulas are again copulas. We exhibit a stochastic…

We give a counterexample to a recently conjectured variant of the Penrose inequality.

Leopardi introduced the notion of a Kronecker quotient in [Paul Leopardi. A generalized FFT for Clifford algebras. Bulletin of the Belgian Mathematical Society, 11:663--688, 2005.]. This article considers the basic properties that a…

In this short note we improve the best to date bound in Godbersen's conjecture, and show some implications for unbalanced difference bodies.

In this short note, we prove that the one-dimensional Kronecker sequence $i\alpha \bmod 1, i=0,1,2,\ldots,$ is quasi-uniform if and only if $\alpha$ is a badly approximable number. Our elementary proof relies on a result on the three-gap…

The reduced Kronecker coefficients are particular instances of Kronecker coefficients that contain enough information to recover them. In this notes we compute the generating function of a family of reduced Kronecker coefficients. We also…

We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.

We prove some extensions of Andrews inequality.

Kronecker's 1856 paper contains a solvability theorem that is useful to construct unsolvable algebraic equations. We show how Kronecker's solvability theorem can be derived naturally via a polynomial complete decomposition method. This…

We survey recent developments on the Restriction conjecture.

We study approximations of theories both in general context and with respect to some natural classes of theories. Some kinds of approximations are considered, connections with finitely axiomatizable theories and minimal generating sets of…

In this paper, we give direct theorems on point wise and global approximation by new variants of Bernstein-Durrmeyer operator, introduced by A.-M. et al.[1].

We present Korovkin approximation theorems that incorporate summability methods. These result allows us to obtain a unified treatment of several previous results, focusing on the underlying structure and the properties that a summability…

An alternative computational approach to the Collatz (3n+1) conjecture is presented that may be theoretically capable of confirming the conjecture.

We explain why the conventional argument for deriving the time-dependent Born-Oppenheimer approximation is incomplete and review recent mathematical results, which clarify the situation and at the same time provide a systematic scheme for…

In this note, we demonstrate the convergence of the Demailly approximation of a general (weakly) upper semi-continuous weight.

We first propose two conjectural estimates on Diophantine approximation of logarithms of algebraic numbers. Next we discuss the state of the art and we give further partial results on this topic.

An equivalent but useful version on the Homological Nerve Theorem is proved.