Results 11 to 20 of about 941 (218)
Localic separation and the duality between closedness and fittedness [PDF]
, 2023 There are a number of localic separation axioms which are roughly analogous to the $T_1$-axiom from classical topology. For instance, besides the well-known subfitness and fitness, there are also Rosicky-Smarda's $T_1$-locales, totally unordered locales ...
Arrieta, Igor
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PROPOSED IS A COUNTEREXAMPLEFOR THE DIAGONAL METHOD OF GEORG CANTOR
, 2022 The diagonal method proposed by Georg Cantor is a proof that unenumerable sets exist. For example, the set of all subsets of the set of all natural numbers; or the set of all binary sequencies; or the set of all decimals fractions belong in gto the ...
Stukach, Mykola
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A New Diagonal Separation and its Relations With the Hausdorff Property
, 2022 Let P be a property of subobjects relevant in a category C. An object X∈C is P -separated if the diagonal in X×X has P; thus e.g. closedness in the category of topological spaces (resp. locales) induces the Hausdorff (resp. strong Hausdorff) axiom.
Picado, Jorge +2 more
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Unifying Cubical Models of Univalent Type Theory [PDF]
, 2020 We present a new constructive model of univalent type theory based on cubical sets. Unlike prior work on cubical models, ours depends neither on diagonal cofibrations nor connections.
Mörtberg, Anders +3 more
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From the Universality of Mathematical Truth to the Interoperability of Proof Systems [PDF]
, 2022 International audienceThe development of computerized proof systems, such as Coq, Matita, Agda, Lean, HOL 4, HOL Light, Isabelle/HOL, Mizar, etc. is a major step forward in the never ending quest of mathematical rigor. But it jeopardizes the universality
Dowek, Gilles, Gilles Dowek
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Results on R-Diagonal Operators in Bi-Free Probability Theory and Applications of Set Theory to Operator Algebras [PDF]
, 2023 The contents of this dissertation lie in the branch of pure mathematics known as functional analysis and are focused on the theory of bi-free probability and on the interplay between set theory and the field of operator algebras.
Katsimpas, Georgios
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Time-reversal invariance and irreversibility in time-asymmetric quantum mechanics [PDF]
, 2005 The aim of this paper is to analyze the concepts of time-reversal invariance and irreversibility in the so-called 'time-asymmetric quantum mechanics'. We begin with pointing out the difference between these two concepts.
Castagnino, Mario +5 more
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Advanced Science, EarlyView.An interpretable machine learning framework integrating SHAP and PDP analysis identifies critical design descriptors from 139 physicochemical features for Nb─Si alloys. The framework achieves <7% prediction error and guides the discovery of Nb38.5Ti38.5Si3Zr18V2 alloy with 22.791 MPa·m1/2 fracture toughness, breaking the 20 MPa·m1/2 barrier.
Dezhi Chen +7 more
wiley +1 more source
AI‐Driven Cancer Multi‐Omics: A Review From the Data Pipeline Perspective
Advanced Intelligent Discovery, EarlyView.The exponential growth of cancer multi‐omics data brings opportunities and challenges for precision oncology. This review systematically examines AI's role in addressing these challenges, covering generative models, integration architectures, Explainable AI for clinical trust, clinical applications, and key directions for clinical translation.
Shilong Liu, Shunxiang Li, Kun Qian
wiley +1 more source
Lattice-valued convergence spaces and regularity
, 2008 We define a regularity axiom for lattice-valued convergence spaces where the lattice is a complete Heyting algebra. To this end, we generalize the characterization of regularity by a ”dual form” of a diagonal condition.
Jäger, Gunter, Jäger, G.
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