Related papers: On totally disconnected generalised Sierpinski car…
Let C be a projective Gorenstein curve over an algebraically closed field of characteristic 0. A generalized linear system on C is a pair (I,f) consisting of a torsion-free, rank-1 sheaf I on C and a map of vector spaces f to the space of…
We investigate the structure of the generalized Weierstrass semigroups at several points on a curve defined over a finite field. We present a description of these semigroups that enables us to deduce properties concerned with the…
A new n-dimensional family of Poisson structures is globally characterized and analyzed, including the construction of its main features: the symplectic structure and the reduction to the Darboux canonical form. Examples are given and…
We study the problem of quasisymmetrically embedding spaces homeomorphic to the Sierpi\'nski carpet into the plane. In the case of so called dyadic slit carpets, several characterizations are obtained. One characterization is in terms of a…
We answer a question of Banakh, Jab\l{}o\'nska and Jab\l{}o\'nski by showing that for $d\ge 2$ there exists a compact set $K \subseteq \mathbb{R}^d$ such that the projection of $K$ onto each hyperplane is of non-empty interior, but $K+K$ is…
We determine the degree sequence of the generalized Sierpinski graph and its general first Zagreb index in terms of the same parameters of the base graph G.
In this note we provide a quasisymmetric taming of uniformly perfect and uniformly disconnected sets that generalizes a result of MacManus from 2 to higher dimensions. In particular, we show that a compact subset of $\mathbb{R}^n$ is…
We show, for every $r>d\ge 0$ or $r=d\ge 2$, the existence of a Baire generic set of $C^d$-families of $C^r$-maps $(f_a)_{a\in (-1,1)^k}$ of a manifold $M$ of dimension $\ge 2$, so that for every $a$ small the map $f_a$ has infinitely many…
We introduce a model of the set of all Polish (=separable complete metric) spaces: the cone $\cal R$ of distance matrices, and consider geometric and probabilistic problems connected with this object. The notion of the universal distance…
We study notions of generic and coarse computability in the context of computable structure theory. Our notions are stratified by the $\Sigma_\beta$ hierarchy. We focus on linear orderings. We show that at the $\Sigma_1$ level all linear…
We provide a rich family of self-similar sets, called locally symmetric polygon-based self-similar sets, as examples of metric spaces having conductive homogeneity, which was introduced as a sufficient condition for the construction of…
Let $\Gamma$ be a countable abelian group, let $k\geq 1$, and let $\mathrm{X}=(X,\mathcal{X},\mu,T)$ be an ergodic $\Gamma$-system of order $k$ in the sense of Host--Kra--Ziegler. The $\Gamma$-system $\mathrm{X}$ is said to be totally…
Generalised polynomials are maps constructed by applying the floor function, addition, and multiplication to polynomials. Despite superficial similarity, generalised polynomials exhibit many phenomena which are impossible for polynomials.…
Iterated planar contact manifolds are a generalization of three dimensional planar contact manifolds to higher dimensions. We study some basic topological properties of iterated planar contact manifolds and discuss several examples and…
Given any polynomial $p$ in $C[X]$, we show that the set of irreducible matrices satisfying $p(A)=0$ is finite. In the specific case $p(X)=X^2-nX$, we count the number of irreducible matrices in this set and analyze the arising sequences…
The supersymmetric Poisson Sigma model is studied as a possible worldsheet realization of generalized complex geometry. Generalized complex structures alone do not guarantee non-manifest N=(2,1) or N=(2,2) supersymmetry, but a certain…
We prove that, up to scalar multiples, there exists only one local regular Dirichlet form on a generalized Sierpinski carpet that is invariant with respect to the local symmetries of the carpet. Consequently for each such fractal the law of…
In this paper we consider a generalized Kuramoto-Sivashinsky equation. The equivalence group of the class under consideration has been constructed. This group allows us to perform a comprehensive study and a clear and concise formulation of…
We introduce the generalized upper box dimension which is defined for any set, whether the set is bounded or unbounded. We study basic properties of the generalized upper box dimension. We prove that the generalized upper box and upper box…
This paper presents a study of generic elements in full isometry groups of Polish ultrametric spaces. We obtain a complete characterization of Polish ultrametric spaces X whose isometry group Iso(X) contains an open subgroup H with ample…