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In this paper, we introduce the concept of nearly convex set-valued mappings and investigate fundamental properties of these mappings. Additionally, we establish a geometric approach for generalized differentiation of nearly convex…

Optimization and Control · Mathematics 2023-02-20 Nguyen Mau Nam , Nguyen Nang Thieu , Nguyen Dong Yen

In this article we introduce the concept of almost $\mathcal{P}$-numbers. We survey the existing results in literature for almost cyclic numbers and give characterizations for almost abelian and almost nilpotent numbers proving these two…

Group Theory · Mathematics 2024-08-19 Iulia Cătălina Pleşca , Marius Tărnăuceanu

This paper continues the investigation of quasilength, of content of local cohomology with respect to generators of the support ideal, and of robust algebras begun in joint work of Hochster and Huneke. We settle several questions raised by…

Commutative Algebra · Mathematics 2016-09-23 Mel Hochster , Wenliang Zhang

We revisit the notion of probably approximately correct implication bases from the literature and present a first formulation in the language of formal concept analysis, with the goal to investigate whether such bases represent a suitable…

Artificial Intelligence · Computer Science 2017-12-27 Daniel Borchmann , Tom Hanika , Sergei Obiedkov

We develop the basic theory of geometrically closed rings as a generalisation of algebraically closed fields, on the grounds of notions coming from positive model theory and affine algebraic geometry. For this purpose we consider several…

Rings and Algebras · Mathematics 2013-09-24 Jean Berthet

Affine term structure models have gained significant attention in the finance literature, mainly due to their analytical tractability and statistical flexibility. The aim of this article is to present both theoretical foundations as well as…

Pricing of Securities · Quantitative Finance 2008-12-02 Christa Cuchiero , Damir Filipovic , Josef Teichmann

In this paper, eventually totally positive matrices (i.e. matrices all whose powers starting with some point are totally positive) are studied. We present a new approach to eventual total positivity which is based on the theory of…

Spectral Theory · Mathematics 2014-01-07 Olga Y. Kushel

In this paper, we introduce new properties of the relative interior calculus for nearly convex sets, functions, and set-valued mappings. These properties are important for the development of duality theory in optimization. Then we…

Optimization and Control · Mathematics 2023-03-15 Nguyen Quang Huy , Nguyen Mau Nam , Nguyen Dong Yen

We define the notion of an almost polynomial identity of an associative algebra $R$, and show that its existence implies the existence of an actual polynomial identity of $R$. A similar result is also obtained for Lie algebras and Jordan…

Rings and Algebras · Mathematics 2019-10-15 Michael Larsen , Aner Shalev

We provide a self-contained introduction to the classical theory of universal-homogeneous models (also known as generic structures, rich models, or Fra\"iss\'e limits). In the literature, most treatments restrict consideration to embeddings…

Logic · Mathematics 2010-09-10 Silvia Barbina , Domenico Zambella

This article consists in two independent parts. In the first one, we investigate the geometric properties of almost periodicity of model sets (or cut-and-project sets, defined under the weakest hypotheses); in particular we show that they…

Dynamical Systems · Mathematics 2015-12-03 Pierre-Antoine Guihéneuf

There are two ways to turn a categorical model for pure quantum theory into one for mixed quantum theory, both resulting in a category of completely positive maps. One has quantum systems as objects, whereas the other also allows classical…

Category Theory · Mathematics 2015-11-06 Oscar Cunningham , Chris Heunen

We consider closure properties in the class of positively decreasing distributions. Our results stem from different types of dependence, but each type belongs in the family of asymptotically independent dependence structure. Namely we…

In this article we give a classification of the binary, simple, $\omega$-categorical structures with SU-rank 1 and trivial pregeometry. This is done both by showing that they satisfy certain extension properties, but also by noting that…

Logic · Mathematics 2017-04-11 Ove Ahlman

This work deals with almost automorphy of distributions. We give characterizations and main properties of these distributions. We also study the existence of distributional almost automorphic solutions of linear difference-differential…

Functional Analysis · Mathematics 2016-06-17 Chikh Bouzar , Fatima Zohra Tchouar

This work builds upon a well-established research tradition on modal logics of awareness. One of its aims is to export tools and techniques to other areas within modal logic. To this end, we illustrate a number of significant bridges with…

Logic in Computer Science · Computer Science 2023-07-12 Carlo Proietti , Fernando R. Velázquez-Quesada , Antonio Yuste-Ginel

We introduce a general definition of almost $p$-summing mappings and give several concrete examples of such mappings. Some known results are considerably generalized and we present various situations in which the space of almost $p$-summing…

Functional Analysis · Mathematics 2007-05-23 Daniel M. Pellegrino

A deductive system is structurally complete if its admissible inference rules are derivable. For several important systems, like modal logic S5, failure of structural completeness is caused only by the underivability of passive rules, i.e.…

Logic · Mathematics 2014-08-26 Wojciech Dzik , Michal M. Stronkowski

A class of models intended to be as minimal and structureless as possible is introduced. Even in cases with simple rules, rich and complex behavior is found to emerge, and striking correspondences to some important core known features of…

Discrete Mathematics · Computer Science 2020-10-07 Stephen Wolfram

This chapter presents a state-of-the-art survey of relationships, traditionally referred to as `bridges', between interpolation properties for propositional logics -- including superintuitionistic, modal, and substructural logics -- and…

Logic · Mathematics 2025-12-02 George Metcalfe