Related papers: Achievement sets -- current results and open probl…
The talk contains a brief introduction string theory, followed by a discussion of some of the recent developments.
We review some selected recent results concerning selection principles in topology and their relations with several topological constructions.
We collect here various conjectures on congruences made by the author in a series of papers, some of which involve binary quadratic forms and other advanced theories. Part A consists of 100 unsolved conjectures of the author while…
To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is…
An overview of the results of new exhaustive computations of gaps between primes in arithmetic progressions is presented. We also give new numerical results for exceptionally large least primes in arithmetic progressions.
We provide an overview of some recent progress on the complexity of election systems. The issues studied include the complexity of the winner, manipulation, bribery, and control problems.
The paper focuses on some versions of connected dominating set problems: basic problems and multicriteria problems. A literature survey on basic problem formulations and solving approaches is presented. The basic connected dominating set…
In this paper, we study sequences of positive numbers preserving summability. In particular, the open set property for such a family of sequences is shown. Several classes of sequences preserving summability, including polynomials, sums of…
This is a structured compilation of some of my favourite open problems.
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.
In this work, I use a survey of senior visualization researchers and thinkers to ideate about the notion of progress in visualization research: how are we growing as a field, what are we building towards, and are our existing methods…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
We present a new fragment of axiomatic set theory for pure sets and for the iteration of power sets within given transitive sets. It turns out that this formal system admits an interesting hierarchy of models with true membership relation…
Expanding upon recent work, a new class of $A$-functions is introduced that can be viewed as an appropriate generalization of the class of regular $A$-functions, the class of structured $A$-functions, and the class of perfect $A$-functions.…
Statistical models have seen a significant rise in popularity in recent years. Despite their undeniable success in various industry use cases such as sabermetrics, investment portfolio management, and artificial intelligence, there has been…
Our objective is to determine which subsets of $\mathbb{R}^d$ arise as escaping sets of continuous functions from $\mathbb{R}^d$ to itself. We obtain partial answers to this problem, particularly in one dimension, and in the case of open…
We survey recent developments in the theory and applications of the broken ray transforms. Furthermore, we discuss some open problems.
This paper is devoted to the investigation of an important issue recently brought into attention by a recent paper of Arutyunov: the relation between openness of composition of set-valued maps and fixed point results. More precisely, we…
We present a treasure trove of open problems in matrix and operator inequalities, of a functional analytic nature, and with various degrees of hardness.
The purpose of this short paper is to identify the mathematical essence of the superiorization methodology. This methodology has been developed in recent years while attempting to solve specific application-oriented problems. Consequently,…