Related papers: Extending valuations to formal completions

Although the notion of a concept as a collection of objects sharing certain properties, and the notion of a conceptual hierarchy are fundamental to both Formal Concept Analysis and Description Logics, the ways concepts are described and…

In this paper we consider the problem of optimization of approximate integration of set-valued functions from the class defined by given majorant of their moduli of continuity, using values of the functions at $n$ fixed or free points of…

I discuss (ontologies_and_ontological_knowledge_bases / formal_methods_and_theories) duality and its category theory extensions as a step toward a solution to Knowledge-Based Systems Theory. In particular I focus on the example of the…

We give an informal introduction to formal and rigid geometry over complete discrete valuation rings, and we discuss some applications in algebraic and arithmetic geometry and singularity theory, with special emphasis on recent applications…

The purpose of this overview is to explain the enormous impact of Les Valiant's eponymous short conference contribution from 1979 on the development of algebraic complexity.

In this paper, we undertake a systematic model and valuation theoretic study of the class of ordered fields which are dense in their real closure. We apply this study to determine definable henselian valuations on ordered fields, in the…

We present three projects concerned with applications of proof assistants in the area of programming language theory and mathematics. The first project is about a certified compilation technique for a domain-specific programming language…

Let $(K, \nu)$ be a valued field, the notions of \emph{augmented valuation}, of \emph{limit augmented valuation} and of \emph{admissible family} of valuations enable to give a description of any valuation $\mu$ of $K [x]$ extending $\nu$.…

This paper gives a survey on a valuation theoretical approach to local uniformization in positive characteristic, the model theory of valued fields in positive characteristic, and their connection with the valuation theoretical phenomenon…

Reference prices have long been studied in applied economics and business research. One of the classic formulations of the reference price is in terms of an iterative function of past prices. There are a number of limitations of such a…

We recall the space of seminorms discussed by Payne in \cite{P} and define a slight modification, the space of graded valuations. After explaining how these spaces relate to tropical geometry, we describe examples of graded valuations which…

This article is written with the hope to draw attention to a method that uses integral transforms to find exact values for a large class of convergent series (and, in particular, series of rational terms). We apply the method to some series…

This is a continuation of a previous paper by the same authors. In the former paper, it was proved that in order to obtain local uniformization for valuations centered on local domains, it is enough to prove it for rank one valuations. In…

A concise review of the notions of elliptic functions, modular forms, and theta-functions is provided, devoting most of the paper to applications to Conformal Field Theory (CFT), introduced within the axiomatic framework of quantum field…

We define an extension of operator-valued positive definite functions from the real or complex setting to topological algebras, and describe their associated reproducing kernel spaces. The case of entire functions is of special interest,…

The formal system lambda-delta is a typed lambda calculus that pursues the unification of terms, types, environments and contexts as the main goal. lambda-delta takes some features from the Automath-related lambda calculi and some from the…

Lecture notes of a course on birational geometry (taught at College de France, Winter 2011, with the support of Fondation Sciences Math\'ematiques de Paris). Topics covered: introduction into the subject, contractions and extremal rays,…

In this paper we present characterizations of the sets of key polynomials and abstract key polynomials for a valuation $\mu$ of $K(x)$, in terms of (ultrametric) balls in the algebraic closure $\overline K$ of $K$ with respect to $v$, a…

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…

We develop Boolean-valued domain theory and show how the lambda-calculus can be interpreted in using domain-valued random variables. We focus on the reflexive domain construction rather than the language and its semantics. The notion of…