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Special Set Systems
A set system is a collection of subsets of a set X. Frequently X is called the ground set or base set of the set system. Set systems are often...
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On the set of Gibbs measures for model with a countable set of spin values on Cayley trees
In this paper we show that the set of Gibbs measures for models with countable set of spin values is convex and compact. Also, by using analogue of...
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Parameterized Complexity of Weighted Target Set Selection
Consider a graph G where each vertex has a threshold. A vertex v in G is activated if the number of active vertices adjacent to v is at least as many...
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Mathematical analysis of modified level-set equations
The linear transport equation allows to advect level-set functions to represent moving sharp interfaces in multiphase flows as zero level-sets. A...
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Maximum Estimates for Solutions to Elliptic and Parabolic Equations on a Book-Type Stratified Set
Studying PDEs on the sets of complicated structure and, in particular, stratified sets has been gaining popularity since recently. This article...
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Disjoint Stable Matchings in Linear Time
We show that given a Stable Matching instance \(G\) as input, we...
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Topological and Geometric Properties of the Set of 1-Nonconvexity Points of a Weakly 1-Convex Set in the Plane
We consider a class of generalized convex sets in the real plane known as weakly 1-convex sets. For a set in the real Euclidean space ℝ n , n ≥ 2 , we...
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Incidence hypergraphs: the categorical inconsistency of set-systems and a characterization of quiver exponentials
This paper considers the difficulty in the set-system approach to generalizing graph theory. These difficulties arise categorically as the category...
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On a Result of Hayman Concerning the Maximum Modulus Set
The set of points where an entire function achieves its maximum modulus is known as the maximum modulus set . In 1951, Hayman studied the structure of...
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Two disjoint and infinite sets of solutions for a nonlocal problem involving a Hardy potential and critical growth with concave nonlinearities
In this paper, we consider the following problem involving fractional Laplacian with a Hardy potential...
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On the measure of products from the middle-third Cantor set
We prove upper and lower bounds for the Lebesgue measure of the set of products xy with x and y in the middle-third Cantor set. Our method is...
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Set of Uniqueness for Cantorvals
The main result is that the celebrated Guthrie–Nymann’s Cantorval has comeager set of uniqueness. On the other hand many other Cantorvals have meager...
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B-Points of a Cantor-Type Set
We study the behavior of the harmonic continuation u to the upper half-plane of the characteristic function for a Cantor-type set E of positive...
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Intuitionistic sets and numbers: small set theory and Heyting arithmetic
It has long been known that (classical) Peano arithmetic is, in some strong sense, “equivalent” to the variant of (classical) Zermelo–Fraenkel set...
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Set Theory
Modern analysis, like most other subfields of modern mathematics, is concerned with numbers, sets, and geometry. We have already introduced one type...
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