Related papers: Research Problems in Function Theory (New Edition)
A brief overview of publications in approximation theory of functions known to the author and connected with scientific publications by V.~K.~Dzyadyk (1919--1998).
In this survey article we revisit Hilbert's $19^{\text{th}}$ problem concerning the regularity of minimizers of variational integrals. We first discuss the classical theory (that is, the statement and resolution of Hilbert's problem in all…
The original version of the paper was published in Contemporary Mathematics 378 ``Groups, Languages, Algorithms''; 2005, pp. 319-348. This is a modified version with Appendix that holds a corrected formulation of Proposition 4.1.
This book consists of material originally appearing in the Problem Section of the journal Topology Proceedings since 1976 as well as some other well-known problem lists in general topology from the 1970's that have some connection to the…
This is my working paper on a proposed logical framework for the practice of mathematics, which is paralleled by philosophical considerations and a computer implementation (a variant of Automath). Updated 10/27/2016 with a version from…
Text generation has become more accessible than ever, and the increasing interest in these systems, especially those using large language models, has spurred an increasing number of related publications. We provide a systematic literature…
Increasing interest in reasoning models has led math to become a prominent testing ground for algorithmic and methodological improvements. However, existing open math datasets either contain a small collection of high-quality, human-written…
Identifying critical research within the growing body of academic work is an intrinsic aspect of conducting quality research. Systematic review processes used in evidence-based medicine formalise this as a procedure that must be followed in…
The progress in text summarization techniques has been remarkable. However the task of accurately extracting and summarizing necessary information from highly specialized documents such as research papers has not been sufficiently…
Systematic reviews traditionally have taken considerable amounts of human time and energy to complete, in part due to the extensive number of titles and abstracts that must be reviewed for potential inclusion. Recently, researchers have…
The vast proliferation of sensor devices and Internet of Things enables the applications of sensor-based activity recognition. However, there exist substantial challenges that could influence the performance of the recognition system in…
Simulation studies are commonly used in methodological research for the empirical evaluation of data analysis methods. They generate artificial data sets under specified mechanisms and compare the performance of methods across conditions.…
The Nyman-Beurling criterion, equivalent to the Riemann hypothesis (RH), is an approximation problem in the space of square integrable functions on $(0,\infty)$, involving dilations of the fractional part function by factors…
This is the second volume of a textbook for a two-semester course in mathematical analysis. This second volume is about analysis of multi-variable functions. The topics covered include Euclidean spaces, convergence of sequences, open sets…
Cost functions provide a framework for constructions of sets Turing below the halting problem that are close to computable. We carry out a systematic study of cost functions. We relate their algebraic properties to their expressive…
Deep learning techniques have become the method of choice for researchers working on algorithmic aspects of recommender systems. With the strongly increased interest in machine learning in general, it has, as a result, become difficult to…
We introduce FinanceMath, a novel benchmark designed to evaluate LLMs' capabilities in solving knowledge-intensive math reasoning problems. Compared to prior works, this study features three core advancements. First, FinanceMath includes…
In this paper a small survey is presented on eighteen new functions and four new sequences, such as: Inferior/Superior f-Part, Fractional f-Part, Complementary function with respect with another function, S-Multiplicative, Primitive…
In this paper, we introduce new classes of functions that extend the known classes of functions of complex variable, such as entire functions, meromorphic functions, rational functions and polynomial functions and take values in the set of…
This survey paper is an expanded version of lectures given at the Clay Mathematics Academy ; see http://www.claymath.org/programs/outreach/academy/colloquium2005.php These lectures were intended to very young (and motivated) college…