Related papers: Some remarks about Cantor sets
In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovitch and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-Packing measures, for the family of dimension functions h, and…
The main results of this paper are generalizations some classical theorems about transversals for families of finite sets to some cases of families of infinite sets.
In this paper we propose a conjecture concerning partial sums of an arbitrary finite subset of an abelian group, that naturally arises investigating simple Heffter systems. Then, we show its connection with related open problems and we…
We obtain the Assouad dimensions of Moran sets under suitable condition. Using the homogeneous set, we also study the Assouad dimensions of Cantor-like sets.
Let $\gamma\in(0;\frac{1}{2}),\tau\geq 1$ and define the "$\gamma,\tau$ Diophantine set" as: $$D_{\gamma,\tau}:=\{\alpha\in (0;1): ||q\alpha||\geq\frac{\gamma}{q^{\tau}}\quad\forall q\in\Bbb{N}\},\qquad||x||:=\inf_{p\in\Bbb{Z}}|x-p|. $$ In…
This is a short note with some (very elementary) remarks concerning realization theory and the choice of inputs for identifying systems. Its goal is to bring some of these facts to the attention of the systems biology community.
We study the relation between the Hurewicz and Menger properties of filters considered topologically as subspaces of P(\omega) with the Cantor set topology.
The point of this short note concerns with two facts on the scheme of secant loci. The first one is an attempt to describe the tangent cone of these schemes globally and the second one is a comparision on the dimension of the tangent spaces…
A by-no-means-complete collection of references for those interested in intonational meaning, with other miscellaneous references on intonation included. Additional references are welcome, and should be sent to [email protected].
In this short note, we briefly discuss the Borel-Cantelli lemma and propose a new generalization of the first part of it.
In this paper, ideas of open ball, closed ball, compact set are introduced and some related basic properties are studied. Some topological properties and some other well known results of metric spaces including Cantor intersection theorem…
This set of notes provides some additional explanatory material on the analytic proof of the finite generation of the canonical ring for a compact complex algebraic manifold of general type.
We discuss some easy statements dealing with linear inhomogeneous Diophantine approximation. Surprisingly, we did not find some of them in the literature.
The purpose of these notes is to collect in one place some facts on the category of finite totally ordered sets and some related categories. More specifically, we collect some results on them which will be useful for the study of iteratedly…
This talk provides a short overview of recent results on possible CPT violation and some associated experimental signatures.
The purpose of this note is to prove that the set of connective constants of Cayley graphs contains a Cantor space.
A compendium for outsiders.
We introduce the notion of specular sets which are subsets of groups called here specular and which form a natural generalization of free groups. These sets are an abstract generalization of the natural codings of linear involutions. We…
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…
In this article one builds a class of recursive sets, one establishes properties of these sets, and one proposes applications.