Related papers: Research Problems in Function Theory (New Edition)
Due to the growing complexity of software systems, there has been a dramatic increase and industry demand for tools and techniques on software refactoring in the last ten years, defined traditionally as a set of program transformations…
Over the decades, Functional Analysis has been enriched and inspired on account of demands from neighboring fields, within mathematics, harmonic analysis (wavelets and signal processing), numerical analysis (finite element methods,…
One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks. Almost no computational tasks in real life are…
The material of this work is aimed at mathematics educators, as well as math specialists with a keen interest in progressions. In this paper, we study the subject of arithmetic, geometric, mixed, and harmonic progressions or sequences. Some…
Software is foundationally important to scientific and social progress, however, traditional acknowledgment of the use of others' work has not adapted in step with the rapid development and use of software in research. This report outlines…
Estimating the coefficient functionals on various classes of holomorphic functions traditionally forms an important field of geometric complex analysis and its mathematical and physical applications. These coefficients reflect fundamental…
This book is not meant to be another compendium of select inequalities, nor does it claim to contain the latest or the slickest ways of proving them. This project is rather an attempt at describing how most functional inequalities are not…
The present article is an extended version of [6] containing new results and an updated list of references. We review the notion of polar analyticity introduced in a previous paper and succesfully applied in Mellin analysis and quadrature…
Recent years have seen tremendous growth in the amount of verified software. Proofs for complex properties can now be achieved using higher-order theories and calculi. Complex properties lead to an ever-growing number of definitions and…
Functional integrals are central to modern theories ranging from quantum mechanics and statistical thermodynamics to biology, chemistry, and finance. In this work we present a new method for calculating functional integrals based on a…
With extensive pre-trained knowledge and high-level general capabilities, large language models (LLMs) emerge as a promising avenue to augment reinforcement learning (RL) in aspects such as multi-task learning, sample efficiency, and…
This is the introduction I wrote for the multi-authored book "From Riemann to differential geometry and relativity", edited by L. Ji, A. Papadopoulos and S. Yamada (Berlin, Springer verlag, 2017). The book consists of twenty chapters,…
The subject of this textbook is the analysis of Boolean functions. Roughly speaking, this refers to studying Boolean functions $f : \{0,1\}^n \to \{0,1\}$ via their Fourier expansion and other analytic means. Boolean functions are perhaps…
This book is intended for teaching Signal Analysis methods and Inverse Problems theory. It is completely open access and will remain free. It is currently illustrated with examples that we have actually encountered in geophysics, but will…
Recent progress in large language models (LLMs) has enabled the deployment of many generative NLP applications. At the same time, it has also led to a misleading public discourse that ``it's all been solved.'' Not surprisingly, this has, in…
In this paper we turn the spotlight on a class of lexicographic ranking functions introduced by Bradley, Manna and Sipma in a seminal CAV 2005 paper, and establish for the first time the complexity of some problems involving the inference…
Fermi Problems (FPs) are mathematical reasoning tasks that require human-like logic and numerical reasoning. Unlike other reasoning questions, FPs often involve real-world impracticalities or ambiguous concepts, making them challenging even…
This article is a theoretical study on the effectiveness of educational research in the context of Philosophy of science. This topic of discussion, in the area of educational research, has been the subject of intellectual debate and arises…
One might think that, once we know something is computable, how efficiently it can be computed is a practical question with little further philosophical importance. In this essay, I offer a detailed case that one would be wrong. In…
We correct mistakes in the paper Kuhlmann, F.-V.: Value groups, residue fields and bad places of rational function fields, Trans. Amer. Math. Soc. 356 (2004) [arXiv:1003.5685] and report on recent new developments which settle cases left…