Related papers: The Work of John Tate
The author of this letter to the editor would like to set forth the argument that scientometrics is currently in a phase in which a taxonomic change, and hence a revolution, is taking place. One of the key terms in scientometrics is…
This paper describes a large set of related theorem proving problems obtained by translating theorems from the HOL4 standard library into multiple logical formalisms. The formalisms are in higher-order logic (with and without type…
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…
This is a revised version of NT0505521, a translation of our Japanese expository article that was published under the title `{\it An overview of sieve methods}' in the second issue of the 52nd volume of Sugaku, the Mathematical Society of…
Machine translation (MT) plays an important role in benefiting linguists, sociologists, computer scientists, etc. by processing natural language to translate it into some other natural language. And this demand has grown exponentially over…
This is a short survey illustrating some of the essential aspects of the theory of canonical extensions. In addition some topological results about canonical extensions of lattices with additional operations in finitely generated varieties…
Artificial intelligence and machine learning algorithms have become ubiquitous. Although they offer a wide range of benefits, their adoption in decision-critical fields is limited by their lack of interpretability, particularly with textual…
Any permutation has a disjoint cycle decomposition and concept generates an equivalence class on the symmetry group called the cycle-type. The main focus of this work is on permutations of restricted cycle-types, with particular emphasis on…
This is a survey covering aspects of varied work of the authors with Mohammed Abouzaid, Paul Hacking, and Sean Keel. While theta functions are traditionally canonical sections of ample line bundles on abelian varieties, we motivate, using…
A short overview of various algorithms and technologies that are helpful for big data storage and manipulation. Includes pointers to papers for further reading, and, where applicable, pointers to open source projects implementing a…
This volume contains revised versions of the papers selected for the second volume of the Online Handbook of Argumentation for AI (OHAAI). Previously, formal theories of argument and argument interaction have been proposed and studied, and…
This document is written with the intention to describe in detail a method and means by which a computer program can reason about the world and in so doing, increase its analogue to a living system. As the literature is rife and it is…
The aim here is to continue the investigation in \cite{AB} of Jacobians of a Klein surface and also to correct an error in \cite{AB}.
In a 1983 paper the author has established a (decategorified) Satake equivalence for affine Hecke algebras. In this paper we give new proofs for some results of that paper, one based on the theory of J-rings and one based on the known…
We explain the linear algebraic framework provided by Tate modules of isogenous abelian varieties in a category-theoretic way.
We give a brief historical overview of the famous Pythagoras' theorem and Pythagoras. We present a simple proof of the result and dicsuss some extensions. We follow \cite{thales}, \cite{wiki} and \cite{wiki2} for the historical comments and…
The article is an historical overview of some of the major contributions from different areas of Science with which, for centuries, it has been built up a scientific, sound and consistent vision of the atom. Some experiments that led us to…
This article argues that the most important significance of the AI revolution, especially the rise of large language models, lies not simply in automation, but in a fundamental change in how complex information and human know-how are…
Citations among research papers, and the networks they form, are the primary object of study in scientometrics. The act of making a citation reflects the citer's knowledge of the related literature, and of the work being cited. We aim to…
This is a replacement paper. There are 6 chapters. The first two chapters are introductory. The third chapter is on extremal graph theory. The fourth chapter is about algebra in graph theory. The fifth chapter is focused on algorithms. The…