Related papers: The Work of John Tate
In this paper, authors study the convexity and concavity properties of real-valued function with respect to the classical means, and prove a conjecture posed by Bruce Ebanks in \cite{e}.
We show that the $\ell$-adic Tate conjecture for divisors on smooth proper varieties over finitely generated fields of positive characteristic follows from the $\ell$-adic Tate conjecture for divisors on smooth projective surfaces over…
In this paper we give an ordinal analysis of the theory of second order arithmetic. We do this by working with proof trees -- that is, "deductions" which may not be well-founded. Working in a suitable theory, we are able to represent…
We present an English translation of a third 1918 paper by Felix Klein which follows up on his earlier work.
Summaries are important when it comes to process huge amounts of information. Their most important benefit is saving time, which we do not have much nowadays. Therefore, a summary must be short, representative and readable. Generating…
The present text is an introduction to \'Ecalle's theory of resurgent functions and alien calculus, in connection with problems of exponentially small separatrix splitting. An outline of the resurgent treatment of Abel's equation for…
There has been a long history of research into the structure and evolution of mankind's scientific endeavor. However, recent progress in applying the tools of science to understand science itself has been unprecedented because only recently…
This article (which appeared with illustrations) was the astrophysics/cosmology contribution to the historical series ``Pathways of Discovery'' which appeared in ``Science'' during last year.
Software now lies at the heart of scholarly research. Here we argue that as well as being important from a methodological perspective, software should, in many instances, be recognised as an output of research, equivalent to an academic…
New title and minor adjustments. To appear in the Journal of Pure and Applied Algebra
Tate objects have been studied by many authors. They allow us to deal with infinite dimensional spaces by identifying some more structure. In this article, we set up the theory of Tate objects in stable $(\infty,1)$-categories, while the…
The authors' ATR programming formalism is a version of call-by-value PCF under a complexity-theoretically motivated type system. ATR programs run in type-2 polynomial-time and all standard type-2 basic feasible functionals are ATR-definable…
This paper presents a type theory with a form of equality reflection: provable equalities can be used to coerce the type of a term. Coercions and other annotations, including implicit arguments, are dropped during reduction of terms. We…
The purpose of this book is to lay out certain aspects of descriptive set theory. After initially establishing notation and generalities we proceed to the following topics: partitions, semirings, rings, $\sigma$-rings, $\delta$-rings,…
The goal of this chapter is to support teachers in holistically introducing graduate students to literature reviews, with a particular focus on secondary research. It provides an overview of the overall literature review process and the…
Fields such as the philosophy of language, continental philosophy, and literary studies have long established that human language is, at its essence, ambiguous and that this quality, although challenging to communication, enriches language…
Completion is one of the most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In this paper we present new correctness proofs of abstract completion, both for finite and infinite runs. For the…
The main purpose of the present article is to give some new Hilbert's sum type inequalities, which in special cases yield the classical Hilbert's inequalities. Our results provide some new estimates to these types of inequalities.
This paper presents general syntactic conditions ensuring the strong normalization and the logical consistency of the Calculus of Algebraic Constructions, an extension of the Calculus of Constructions with functions and predicates defined…
This book chapter attempts to counter anxieties in the humanities and social science about the role of big data in research by focusing on approaches which, by being firmly grounded in the traditional values of disciplines, enhance existing…