Related papers: Files for Gabriel-Zisman localization
Context-free language theory is a well-established area of mathematics, relevant to computer science foundations and technology. This paper presents the preliminary results of an ongoing formalization project using context-free grammars and…
A generalized sampling theorem for frequency localized signals is presented. The generalization in the proposed model of sampling is twofold: (1) It applies to various prefilters effecting a "soft" bandlimitation, (2) an approximate…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
The present preprint completes the arXiv preprint #2202.11652, entitled "Pseudodifferential arithmetic and the Riemann hypothesis", devoted to a proof of the conjecture. The first 4 pages of that preprint were devoted to a set of necessary…
In preparing the paper "Some extensions of Hilbert-Kunz multiplicity", we had occasion to perform an intricate set of computations pertaining to a single illustrative example. In the end, we have decided not to include the computations in…
In this article we discuss Bousfield localization, beginning with definitions in terms of mapping spaces and working up to a discussion of how they can be constructed when we have access to the small object argument. We also discuss…
We describe how we connected three programs that compute Groebner bases to Coq, to do automated proofs on algebraic, geometrical and arithmetical expressions. The result is a set of Coq tactics and a certificate mechanism (downloadable at…
This paper describes a formal proof library, developed using the Coq proof assistant, designed to assist users in writing correct diagrammatic proofs, for 1-categories. This library proposes a deep-embedded, domain-specific formal language,…
The present article is devoted to the description of further investigations of the author of this article. These investigations (in terms of various representations of real numbers) include the generalized Salem functions and…
We give a purely cubical argument for the localization theorem for the cubical version of higher Chow groups.
Proof assistants like Coq are increasingly popular to help mathematicians carry out proofs of the results they conjecture. However, formal proofs remain highly technical and are especially difficult to reuse. In this paper, we present a…
We study how to formalize in the Coq proof assistant the smallest projective space PG(3,2). We then describe formally the spreads and packings of PG(3,2), as well as some of their properties. The formalization is rather straightforward,…
This paper introduces a new quantization scheme for real and complex Grassmannian sources. The proposed approach relies on a structured codebook based on a geometric construction of a collection of bent grids defined from an initial mesh on…
In the realm of formal theorem proving, the Coq proof assistant stands out for its rigorous approach to verifying mathematical assertions and software correctness. Despite the advances in artificial intelligence and machine learning, the…
In this paper we give an elementary proof of the Zariski-Lipman conjecture for log canonical spaces.
In this work, we study the codes over the integers with locality constraints. We introduce a weighted notion of locality over $\mathbb{Z}/q_1\mathbb{Z} \times \cdots \times \mathbb{Z}/q_n\mathbb{Z}$ and derive a Singleton-like bound for…
We prove a localization formula for group-valued equivariant de Rham cohomology of a compact G-manifold. This formula is a non-trivial generalization of the localization formula of Berline-Vergne and Atiyah-Bott for the usual equivariant de…
This document provides the supplementary material including a comprehensive related work, the complete proofs and extended evaluation results that support the manuscript, "Unified Characterization and Precoding for Non-Stationary Channels",…
We give a new axiomatization of the N-pseudospace, studied in [2] (Tent(2014)) and [1] (Baudisch,Martin-Pizarro,Ziegler(2014)) based on the zigzags introduced in [2]. We also present a more detailed account of the characterization of…
In this letter some properties of the Gauss decomposition of quantum group $GL_q(n)$ with application to q-bosonization are considered.