相关论文: Overlapping self-affine sets

In this paper we study the set of digit frequencies that are realised by elements of the set of $\beta$-expansions. The main result of this paper demonstrates that as $\beta$ approaches $1,$ the set of digit frequencies that occur amongst…

We show that any equicontractive, self-similar measure arising from the IFS of contractions $(S_{j})$, with self-similar set $[0,1]$, admits an isolated point in its set of local dimensions provided the images of $S_{j}(0,1)$ (suitably)…

A family of permutations $\mathcal{F} \subseteq S_n$ is even-cycle-intersecting if $\sigma \pi^{-1}$ has an even cycle for all $\sigma,\pi \in \mathcal{F}$. We show that if $\mathcal{F} \subseteq S_n$ is an even-cycle-intersecting family of…

Let $\mathcal{F}$ be a family of subsets of $[n]=\{1,\ldots,n\}$ and let $L$ be a set of nonnegative integers. The family $\mathcal{F}$ is \emph{$L$-intersecting} if $|F\cap F'|\in L$ for every two distinct members $F,F'\in\mathcal{F}$; and…

The notion of a complete Boolean algebra, although completely legitimate in constructive mathematics, fails to capture some natural structures such as the lattice of subsets of a given set. Sambin's notion of an overlap algebra, although…

In the context of the cohomological deformation theory, infinitesimal description of one-parametric families of Backlund transformations of special type including classical examples is given. It is shown that any family of such a kind…

Let G be a finite subgroup of GL_n(C). G-constellations are a scheme-theoretic generalization of orbits of G in C^n. We study flat families of G-constellations parametrised by an arbitrary resolution of the quotient space C^n/G. We develop…

We study the concept of density for sets of natural numbers in some lacunary $A$-convergent sequence spaces. Also we are trying to investigate some relation between the ordinary convergence and module statistical convergence for evey…

The contour of a family of filters along a filter is a set-theoretic lower limit. Topologicity and regularity of convergences can be characterized with the aid of the contour operation. Contour inversion is studied, in particular, for…

We introduce and study a new family of extensions for the Borsuk-Ulam and topological Radon type theorems. The defining idea for this new family is to replace requirements of the form `a subset that is large in some sense goes to a…

We obtain closed form expressions for convolutions of scale transformations within a certain subset of Appell polynomials. This subset contains the Bernoulli, Apostol-Euler, and Cauchy polynomials, as well as various kinds of their…

Let $n>2r>0$ be integers. We consider families $\mathcal{F}$ of subsets of an $n$-element set, in which the union of any two members has size at most $2r$. One of our results states that for $n\geq 6r$ the number of members of size…

In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…

Following D. Sobota we call a family $\mathcal F$ of infinite subsets of $\mathbb N$ a Rosenthal family if it can replace the family of all infinite subsets of $\mathbb N$ in classical Rosenthal's Lemma concerning sequences of measures on…

In this article we carry out a detailed investigation of the geometric nature of the points at infinity of Minkowski superspace. It turns out that there are several sets of points forming the superconformal boundary of Minkowski superspace:…

We investigate the relation between p-adic Galois representations and overconvergent (phi,Gamma)-modules in families. Especially we construct a natural open subspace of a family of (phi,Gamma)-modules, over which it is induced by a family…

We identify a family of numbers for which the Bernoulli convolution is singular. Within this family we find two countable collections of Salem numbers in the interval $(1,2)$, and another Salem number and an algebraic integer that is…

Previous study of the Assouad dimension of planar self-affine sets has relied heavily on the underlying IFS having a `grid structure', thus allowing for the use of approximate squares. We study the Assouad dimension of a class of…

In this note we study a conjecture by Jer\'onimo-Castro, Magazinov and Sober\'on which generalized a question posed by Dol'nikov. Let $F_1,F_2,\dots,F_n$ be families of translates of a convex compact set $K$ in the plane so that each two…

Understanding convergent learning -- the degree to which independently trained neural systems -- whether multiple artificial networks or brains and models -- arrive at similar internal representations -- is crucial for both neuroscience and…