Related papers: Extending valuations to formal completions
Let $K\to L$ be an algebraic field extension and $\nu$ a valuation of $K$. The purpose of this paper is to describe the totality of extensions $\left\{\nu'\right\}$ of $\nu$ to $L$ using a refined version of MacLane's key polynomials. In…
A concise explanations on the results given by Non-local Markovian Symmetric Forms on Infinite Dimensional Spaces I, CMP 2021, by Sergio Albeverio, Minoru W. Yoshida, et.al., and Non-local Markovian Symmetric Forms on Infinite Dimensional…
This is the first part of a series of articles where we are going to develop theory of valuations on manifolds generalizing the classical theory of continuous valuations on convex subsets of a linear space. In this article we still work…
We introduce a local multifractal formalism adapted to functions, measures or distributions which display multifractal characteristics that can change with time, or location. We develop this formalism in a general framework and we work out…
We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
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…
EvalRS aims to bring together practitioners from industry and academia to foster a debate on rounded evaluation of recommender systems, with a focus on real-world impact across a multitude of deployment scenarios. Recommender systems are…
Koya's and author's approach to the higher local reciprocity map as a generalization of the classical class formations approach to the level of complexes of Galois modules.
Refining a constructive combinatorial method due to MacLane and Schilling, we give several criteria for a valued field that guarantee that all of its maximal immediate extensions have infinite transcendence degree. If the value group of the…
This paper presents an operational semantics for UML activity diagrams. The purpose of this semantics is three-fold: to give a robust basis for verifying model correctness; to help validate model transformations; and to provide a…
Autoformalization, the process of transforming informal mathematical propositions into verifiable formal representations, is a foundational task in automated theorem proving, offering a new perspective on the use of mathematics in both…
The formal system $\lambda\delta$ is a typed lambda calculus derived from $\Lambda_\infty$, aiming to support the foundations of Mathematics that require an underlying theory of expressions (for example the Minimal Type Theory). The system…
This paper summarizes our rather lengthy paper, "Algebra of the Infrared: String Field Theoretic Structures in Massive ${\cal N}=(2,2)$ Field Theory In Two Dimensions," and is meant to be an informal, yet detailed, introduction and summary…
These are expanded notes of the mini-courses on Pila's work that Yuri Bilu gave in Basel in April 2011, Yaroslavl in August 2011 and Chennai in February 2012. The topics covered include the Bombieri-Pila theorem, its extensions and…
This is an introduction to the author theory of cyclic p-extensions of an absolutely unramified complete discrete valuation field K with arbitrary residue field of characteristic p. In this theory a homomorphism is constructed from the…
In this paper we develop the theory of the depth of a simple algebraic extension of valued fields $(L/K,v)$. This is defined as the minimal number of augmentations appearing in some Mac Lane-Vaqui\'e chain for the valuation on $K[x]$…
This paper provides foundations for strong (that is, possibly under abstraction) call-by-value evaluation for the lambda-calculus. Recently, Accattoli et al. proposed a form of call-by-value strong evaluation for the lambda-calculus, the…
The main goal of this paper is to characterize the module of K\"ahler differentials for an extension of valuation rings. More precisely, we consider a simple algebraic valued field extension $(L/K,v)$ and the corresponding valuation rings…
We revisit a classical theme of (general or translation invariant) valuations on convex polyhedra. Our setting generalizes the classical one, in a ``dual'' direction to previously considered generalizations: while previous research was…