Related papers: Research Problems in Function Theory (New Edition)
This book is a compilation of notes from a two-week international workshop on the "The Functional Analysis of Quantum Information Theory" that was held at the Institute of Mathematical Sciences during 26/12/2011-06/01/2012. The workshop was…
The purpose of this paper is to update the review of Bornmann and Daniel (2008) presenting a narrative review of studies on citations in scientific documents. The current review covers 41 studies published between 2006 and 2018. Bornmann…
In this note, we highlight the impact of the paper G. H. Hardy, A theorem concerning Fourier transforms, J. Lond. Math. Soc. (1) 8 (1933), 227--231 in the community of harmonic analysis in the last 90 years, reviewing, on the one hand, the…
How much large language models (LLMs) can aid scientific discovery, notably in assisting academic peer review, is in heated debate. Between a literature digest and a human-comparable research assistant lies their practical application…
In his famous presentation at the International Congress of Mathematicians held in Paris in 1900, David Hilbert included the Riemann Hypothesis on zeros of $\zeta -$function as number 8 in his list of 23 challenging problems published…
During years 2008 to 2011 author gives several courses on Foundations of Scientific Research at Computer Science Faculty of the National Aviation University in Kiev. This text presents material to lectures of the courses. It consists of 18…
A sketch of the chapter appearing under the same heading in the book ``New Optimization Algorithms in Physics'' (A.K. Hartmann and H. Rieger, Eds.) is given. After a general introduction to spin glasses, important aspects of heuristic…
With the advent of large language models (LLMs), there is a growing interest in applying LLMs to scientific tasks. In this work, we conduct an experimental study to explore applicability of LLMs for configuring, annotating, translating,…
In this paper, we study uniqueness problems for an entire function that shares small functions of finite order with their difference operators. In particular, we give a generalization of results in [2,3,13].
Recent advancements in artificial intelligence (AI), particularly in large language models (LLMs) such as OpenAI-o1 and DeepSeek-R1, have demonstrated remarkable capabilities in complex domains such as logical reasoning and experimental…
Scientific writing builds upon already published papers. Manual identification of publications to read, cite or consider as related papers relies on a researcher's ability to identify fitting keywords or initial papers from which a…
This thesis is concerned with investigations into the "complexity of term rewriting systems". Moreover the majority of the presented work deals with the "automation" of such a complexity analysis. The aim of this introduction is to present…
We discuss various problems in frame theory that have been open for some years. A short discussion of frame theory is also provided, but it only contains the information that is necessary in order to understand the open problems and their…
Analytic perturbation theory for matrices and operators is an immensely useful mathematical technique. Most elementary introductions to this method have their background in the physics literature, and quantum mechanics in particular. In…
In this paper I present a brief survey of the active area of Special Functions associated with Root Systems. The article is intended for a general mathematical audience. It will not suppose prerequisites on either special functions or root…
Fast-growing scientific publications present challenges to the scientific community. In this paper, we describe their implications to researchers. As references form explicit foundations for researchers to conduct a study, we investigate…
The aim of the paper is to investigate the solutions of special inhomogeneous linear functional equations by using spectral analysis in a translation invariant closed linear subspace of additive/multiadditive functions containing the…
Below is a translation from my Russian paper. I added references, unavailable to me in Moscow. Similar results have been also given in [Schnorr Stumpf 75] (see also [Lynch 75]). Earlier relevant work (classical theorems like Compression,…
Large formal mathematical libraries consist of millions of atomic inference steps that give rise to a corresponding number of proved statements (lemmas). Analogously to the informal mathematical practice, only a tiny fraction of such…
We aim to conduct a systematic mapping in the area of testing ML programs. We identify, analyze and classify the existing literature to provide an overview of the area. We followed well-established guidelines of systematic mapping to…