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

To this day, the two-slit electron interference pattern remains shrouded in an inordinate mystery. It continues to defy a logical and rational explanation. This paper will postulate a new "characteristic" pertaining to the electron. If this…

In this paper we consider the notions of binomial thinning, binomial mixing, their generalizations, certain interplay between them, associated limit theorems and provide various examples.

Some formulas and speculations are presented relative to integrable systems and quantum mechanics.

The relativistic Wigner function for spin 1/2 particles is the subject of active research due to diverse applications. However, further progress is hindered by the fabulous complexity of the integro-differential equations of motion. We…

In this paper we present 43 new inequalities related to integer part and fractional part.

A brief report on recent work on the sphere-packing problem.

In this note some philosophical thoughts and observations about mathematics are expressed, arranged as challenges to some common claims.

I discuss computational challenges in the relativistic few-nucleon problem and the resolution of some of these challenges. I also discuss the outlook for the future.

In this note, necessary and sufficient conditions are obtained for unilateral weighted shifts to be near subnormal . As an application of the main results, many answers to the Hilbert space problem 160 are presented at the end of the paper.

We consider matrix problems in Hilbert spaces (orthoscalar representations of quivers and posets). A criterion of tameness of the problem of classification of indecomposable orthoscalar representations of a quiver is given.

In this paper, we introduce a system of split variational inequality problems in real Hilbert spaces. Using projection method, we propose an iterative algorithm for the system of split variational inequality problems. Further, we prove that…

After a short description of various classical solutions of Plateau's problem, we discuss other ways to model soap films, and some of the related questions that are left open. A little more attention is payed to a more specific model, with…

Some notes and questions about the concept of time are exposed. Particular reference is given to the problem in quantum mechanics, in connection with the indeterminacy principle.

There are several versions of Bell's inequalities, proved in different contexts, using different sets of assumptions. The discussions of their experimental violation often disregard some required assumptions and use loose formulations of…

We pose 22 relatively general questions about quantization in the operator algebra setting. In the process we briefly survey some recent developments.

Two variable speed of light models and their physical consequences are investigated.

This paper considers overdetermined boundary problems. Firstly, we give a proof to the Payne-Schaefer conjecture about an overdetermined problem of sixth order in the two dimensional case and under an additional condition for the case of…

Hilbert's first problem is of importance in relation to work being done in computational systems. It is the question of equipollence of natural and real numbers. By construction equipollence is established for real numbers in open interval…

We discuss various recent advances on weak forms of the Twin Prime Conjecture.

The aim of this paper is to share with the mathematical community a list of 33 problems that I have found along the years during my research. I believe that it is worth to think about them and, hopefully, it will be possible either to solve…