Related papers: On the half line: K. Ramachandra
A partly autobiographical survey of the development of enumerative and algebraic combinatorics in the 1960's and 1970's.
A k-ary semi-algebraic relation E on R^d is a subset of R^{kd}, the set of k-tuples of points in R^d, which is determined by a finite number of polynomial equations and inequalities in kd real variables. The description complexity of such a…
This is a brief account of the legacy of Ken Wilson in statistical physics, high energy physics, computing and education.
An identity by Ramanujan related to the multisection of Bernoulli numbers is revisited. Two alternative approaches are proposed, both relying on the multisection technique. A geometric approach reveals the role played by the symmetries of…
This paper is a brief overview of the main contributions of Masaki Kashiwara in the domain of microlocal and algebraic analysis.
Kenneth G. Wilson made deep and insightful contributions to statistical physics, particle physics, and related fields. He was also a helpful and thoughtful human being.
For a number field $K$, let $\zeta_{K}(s)$ be the Dedekind zeta function associated to $K$. In this note, we study non-vanishing and transcendence of $\zeta_{K}$ as well as its derivative $\zeta_{K}'$ at $s= 1/2$. En route, we strengthen a…
System of alternatively orthogonalized rational functions of Jacobi type on the half line $[1, \infty)$ is defined and its properties are established. Three subsystems of proper and mixed systems of rational functions with nice properties…
In this short survey we look at a few basic features of p-adic numbers, somewhat with the point of view of a classical analyst. In particular, with p-adic numbers one has arithmetic operations and a norm, just as for real or complex…
David Mumford made groundbreaking contributions in many fields, including the pure mathematics of algebraic geometry and the applied mathematics of machine learning and artificial intelligence. His work in both fields influenced my career…
This article attempts to place the emergence of probabilistic numerics as a mathematical-statistical research field within its historical context and to explore how its gradual development can be related both to applications and to a modern…
In this brief note, there is a short recollection of my scientific interactions with the great Russian mathematician Sergey Konstantinovich Godunov.
We study the properties of a general continued fraction of Ramanujan. In some certain cases we evaluate it completely.
Vladimir Andreevich Uspensky [1930-2018] was one of the Soviet pioneers of the theory of computation and mathematical logic in general (and my teacher and thesis advisor). This paper is the survey of his mathematical works and their…
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).
Contribution of Indian Mathematics since Vedic Period has been recognised by the Historians. Pingala (200 BC) in his book on 'Chandashaastra', a text related to the description and analysis of meters in poetic work, describes algorithms…
We give a brief outline of biography, review 3 of his works on the use of confluent hypergeometric function for description asymmetric relaxation spectrum and provide an overview of the Soviet works of the past (20th) that are in tune with…
This study examines the potential of using math-themed postage stamps in mathematics lessons as a tool to engage students and integrate the subject with history, art, and culture. Since the first mathematical stamps appeared in the early…
Supportive attitudes can bring to a blossoming science, while neglect can quickly make science absent from everyday life and provide a very primitive view of the world. We compare one important Greek achievement, the computation of the…
We briefly review some of Ramanujan's contributions to mathematics, including his $1/\pi$ series, his work on modular forms, and his work on partitions. We briefly review his life, including his collaboration with Hardy. Finally, we give a…