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For a finite lattice L, let EL denote the reflexive and transitive closure of the join-dependency relation on L, defined on the set J(L) of all join-irreducible elements of L. We characterize the relations of the form EL, as follows:…

General Mathematics · Mathematics 2016-08-16 George Grätzer , Friedrich Wehrung

Determining the index of the Simon congruence is a long outstanding open problem. Two words $u$ and $v$ are called Simon congruent if they have the same set of scattered factors, which are parts of the word in the correct order but not…

Combinatorics · Mathematics 2022-02-17 Pamela Fleischmann , Lukas Haschke , Annika Huch , Annika Mayrock , Dirk Nowotka

We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focusing on complete and finitely generated semilattices and…

Commutative Algebra · Mathematics 2025-11-25 Fernando Martin-Maroto , Antonio Ricciardo , David Mendez , Gonzalo G. de Polavieja

We establish new results concerning endomorphisms of a finite chain if the cardinality of the image of such endomorphism is no more than some fixed number. The semiring of all such endomorphisms can be seen as a simplex whose vertices are…

Rings and Algebras · Mathematics 2015-06-18 Ivan Trendafilov

Attribute and size reductions are key issues in formal concept analysis. In this paper, we consider a special kind of equivalence relation to reduce concept lattices, which will be called local congruence. This equivalence relation is based…

Data Structures and Algorithms · Computer Science 2024-09-25 Roberto G. Aragón , Jesús Medina , Eloísa Ramírez-Poussa

We apply the notion of a full convex subcategory to a wide range of algebras including tilted, quasi-tilted, shod, weakly shod, left and right glued, laura, simply connected, strongly simply connected, left supported, and cluster-tilted. In…

Representation Theory · Mathematics 2020-06-30 Stephen Zito

For a measurable space $(X,\mathcal{A})$, let $\mathcal{M}^+(X,\mathcal{A})$ be the commutative semiring of non-negative real-valued measurable functions with pointwise addition and pointwise multiplication. We show that there is a lattice…

Functional Analysis · Mathematics 2024-08-21 Pronay Biswas , Sagarmoy Bag , Sujit Kumar Sardar

We consider finite element approximations of ill-posed elliptic problems with conditional stability. The notion of {\emph{optimal error estimates}} is defined including both convergence with respect to mesh parameter and perturbations in…

Numerical Analysis · Mathematics 2024-03-25 Erik Burman , Mihai Nechita , Lauri Oksanen

The context of this work is that of partial frames; these are meet-semilattices where not all subsets need have joins. A selection function, S, specifies, for all meet-semilattices, certain subsets under consideration, which we call the…

General Topology · Mathematics 2023-06-22 Anneliese Schauerte , John Frith

Given a formal context, an ordinal factor is a subset of its incidence relation that forms a chain in the concept lattice, i.e., a part of the dataset that corresponds to a linear order. To visualize the data in a formal context, Ganter and…

Artificial Intelligence · Computer Science 2023-06-21 Dominik Dürrschnabel , Gerd Stumme

The paper glosses different forms of an introducing of higher order tangent-like functors, especially functors derived from higher order nonholonomic tangent functors. A special attention is devoted to higher order osculating bundles: their…

Differential Geometry · Mathematics 2012-02-15 Miroslav Kureš

For a finite lattice L, the congruence lattice Con L of L can be easily computed from the partially ordered set J(L) of join-irreducible elements of L and the join-dependency relation D\_L on J(L). We establish a similar version of this…

General Mathematics · Mathematics 2007-05-23 Friedrich Wehrung

A hemiimplicative semilattice is a bounded semilattice $(A, \wedge, 1)$ endowed with a binary operation $\to$, satisfying that for every $a, b, c \in A$, $a \leq b \to c$ implies $a \wedge b \leq c$ (that is to say, one of the conditionals…

Logic · Mathematics 2016-11-30 José Luis Castiglioni , Hernán Javier San Martín

We study the properties of the two-point spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a…

chao-dyn · Physics 2009-10-31 Jens Bolte , Stefan Keppeler

Factorization models express a statistical object of interest in terms of a collection of simpler objects. For example, a matrix or tensor can be expressed as a sum of rank-one components. However, in practice, it can be challenging to…

Methodology · Statistics 2022-12-06 Lorenzo Schiavon , Antonio Canale , David B. Dunson

The principle of finding an integrating factor for a none exact differential equations is extended to a class of third order differential equations. If the third order equation is not exact, under certain conditions, an integrating factor…

Classical Analysis and ODEs · Mathematics 2017-06-21 Mohammadkheer Al-Jararha

We introduce semidistrim lattices, a simultaneous generalization of semidistributive and trim lattices that preserves many of their common properties. We prove that the elements of a semidistrim lattice correspond to the independent sets in…

Combinatorics · Mathematics 2021-11-17 Colin Defant , Nathan Williams

The notion of unboundedly order converges has been recieved recently a particular attention by several authors. The main result of the present paper shows that the notion is efficient and deserves that care. It states that a vector lattice…

Functional Analysis · Mathematics 2017-10-10 Youssef Azouzi

This paper proposes a new factor rotation for the context of functional principal components analysis. This rotation seeks to re-represent a functional subspace in terms of directions of decreasing smoothness as represented by a generalized…

Methodology · Statistics 2014-07-18 Giles Hooker , Steven Roberts

We survey three methods for proving that the characteristic polynomial of a finite lattice factors over the nonnegative integers and indicate how they have evolved recently. The first technique uses geometric ideas and is based on…

Combinatorics · Mathematics 2007-05-23 Bruce E. Sagan