相关论文: Analysis on disconnected sets

This article was prepared in connection with the 2009 Barnett lecture at the University of Cincinnati, and deals with various classes of fractal sets and analysis on them.

We begin the study of character sheaves on a not necessarily connected reductive group, extending the known theory for connected groups.

The present article is devoted to some examples of functions whose arguments represented in terms of certain series of the Cantor type.

Prompted by a recent question of G. Hjorth as to whether a bounded Urysohn space is indivisible, that is to say has the property that any partition into finitely many pieces has one piece which contains an isometric copy of the space, we…

Abstrct: In this note, by considering fractionally linear functions over a finite field and consequently developing an abstract sequence, we study some of its properties.

Sets in R^n in which every pair of elements x, y can be connected by a path in the set of length bounded by a constant multiple of the distance between x and y are considered.

Concept-based explanations have emerged as a popular way of extracting human-interpretable representations from deep discriminative models. At the same time, the disentanglement learning literature has focused on extracting similar…

The set of all separable quantum states is compact and convex. We focus on the two-qubit quanum system and study the boundary of the set. Then we give the criterion to determine whether a separable state is on the boundary. Some…

In this article, we study disjoint universality for certain sequences of operators, that are connected with the differential operator. Actually, the motivation to study such sequences comes from Universal Taylor series, if you change the…

A way to add an extra dimension is briefly discussed.

Separation systems are posets with additional structure that form an abstract setting in which tangle-like clusters in graphs, matroids and other combinatorial structures can be expressed and studied. This paper offers some basic theory…

It is known that there are many notions of largeness in a semigroup that own rich combinatorial properties. In this paper, we focus on partition and almost disjoint properties of these notions. One of the most remarkable results with…

In this article, we consider the concept of the decay of the Favard length of $\varepsilon$-neighborhoods of purely unrectifiable sets. We construct non-self-similar Cantor sets for which the Favard length decays arbitrarily with respect to…

A relational structure is called reversible iff every bijective endomorphism of that structure is an automorphism. We give several equivalents of that property in the class of disconnected binary structures and some its subclasses. For…

We introduce and study the notion of overcomplete set in a Banach space, that subsumes and extends the classical concept of overcomplete sequence in a (separable) Banach space. We give existence and non-existence results of overcomplete…

We explore the properties of non-piecewise syndetic sets with positive upper density, which we call "discordant", in countably infinite amenable (semi)groups. Sets of this kind are involved in many questions of Ramsey theory and manifest…

This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…

Motivated by questions arising in the study of the spectral theory of models of aperiodic order, we investigate sums of functions of semibounded closed subsets of the real line. We show that under suitable thickness assumptions on the sets…

We introduce a class of self-similar sets which we call {\em twofold Cantor sets} $K_{pq}$ in $\mathbb R$ which are totally disconnected, do not have weak separation property and at the same time have isomorphic self-similar structures.

We present a survey of some aspects and new results on configurations, i.e. disjoint unions of constellations of infinitely near points, local and global theory, with some applications and results on generalized Enriques diagrams, singular…