相关论文: Some Questions around The Hilbert 16th Problem

The main purpose of this note is to pose a couple of problems which are easily formulated thought some seem to be not yet solved. These problems are of general interest for discrete mathematics including a new twig of a bough of theory of…

In this paper a new variational approach concerning functions (continuous) over Hilbert spaces is presented.

This paper is a contribution to the problem of particle localization in non-relativistic Quantum Mechanics. Our main results will be (1) to formulate the problem of localization in terms of invariant subspaces of the Hilbert space, and (2)…

We examine an elementary problem on prime divisibility of binomial coefficients. Our problem is motivated by several related questions on alternating groups.

The present report, has been inspired by the need of the author and its colleagues to understand the underlying theory of Wirtinger's Calculus and to further extend it to include the kernel case. The aim of the present manuscript is…

We give some results and conjectures about recurrence relations for certain sequences of binomial sums.

In preparing the paper "Some extensions of Hilbert-Kunz multiplicity", we had occasion to perform an intricate set of computations pertaining to a single illustrative example. In the end, we have decided not to include the computations in…

We survey recent results on Calderon's inverse problem with partial data, focusing on three and higher dimensions.

I give a short overview of Chiral Perturbation Theory, its underlying assumptions and underpinnings. A few examples are included.

In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.

This paper discusses some topics of enquiry concerning fractals, functions on them, and so on.

In this paper, we study some combinations of the degenerate and incomplete Stirling numbers of the second kind. We use a combinatorial approach and provide some asymptotic results.

We show how to efficiently compute Hilbert modular forms as orthogonal modular forms, generalizing and expanding upon the method of Birch.

In the paper we present some new inversion formulas and two new formulas for Stirling numbers.

We suggest an approach for description of integrable cases of the Abel equations. It is based on increasing of the order of equations up to the second one and using equivalence transformations for the corresponding second-order ordinary…

We discuss some aspects of Extrapolation theory. The presentation includes many examples and open problems.

The purpose of this paper is to establish the solvability results to direct and inverse problems for time-fractional pseudo-parabolic equations with the self-adjoint operators. We are especially interested in proving existence and…

We give a brief description of the Birch and Swinnerton-Dyer Conjecture which is one of the seven Clay problems.

We obtain some new inequalities of Chebyshev Type.

We introduce more generalizations of BCI, BCK and of Hilbert algebras, with proper examples, and show the hierarchies existing between all these algebras, old and new ones. Namely, we found thirty one new generalizations of BCI and BCK…