Related papers: Typical self-affine sets with non-empty interior

We characterize inclusions of compact noncommutative convex sets with the property that every continuous affine function on the smaller set can be extended to a continuous affine function on the larger set with a uniform bound. As an…

In this paper we study the existence of at least one non-inner automorphism of order p of a finite thin p-group, for any prime p.

Efficient methods for computing with matrices over finite fields often involve randomised algorithms, where matrices with a certain property are sought via repeated random selection. Complexity analyses for these algorithms require…

We compute explicitly the automorphism and outer automorphism group of all large-type free-of-infinity Artin groups. Our strategy involves reconstructing the associated Deligne complexes in a purely algebraic manner, i.e. in a way that is…

We will review the main results concerning the automorphism groups of saturated structures which were obtained during the two last decades. The main themes are: the small index property in the countable and uncountable cases; the…

Finite dimensional matrices having more columns than rows have no left inverses while those having more rows than columns have no right inverses. We give generalizations of these simple facts to bi--infinite matrices and use those to obtain…

We consider linear iterated function systems with a random multiplicative error on the real line. Our system is $\{x\mapsto d_i + \lambda_i Y x\}_{i=1}^m$, where $d_i\in \R$ and $\lambda_i>0$ are fixed and $Y> 0$ is a random variable with…

For $V$ a vector space over a field, or more generally, over a division ring, it is well-known that every $x\in\mathrm{End}(V)$ has an <i>inner inverse</i>, i.e., an element $y\in\mathrm{End}(V)$ satisfying $xyx=x.$ We show here that a…

Consider the algebra M(n,F) of n x n matrices over an infinite field F of arbitrary characteristic. An identity for M(n,F) with forms is such a polynomial in n x n generic matrices and in \sigma_k(x), 0<k\leq n, coefficients in the…

A visceral structure on M is given by a definable base for a uniform topology on its universe in which all basic open sets are infinite and any infinite definable subset X of M has non-empty interior. This context includes o-minimal ordered…

In this paper, it is shown that for a minimal system $(X,T)$ and $d,k\in \mathbb{N}$, if $(x,x_i)$ is regionally proximal of order $d$ for $1\leq i\leq k$, then $(x,x_1,\ldots,x_k)$ is $(k+1)$-regionally proximal of order $d$. Meanwhile, we…

If L is a Tonelli Lagrangian defined on the tangent bundle of a compact and connected manifold whose dimension is at least 2, we associate to L the tiered Aubry set and the tiered Mane set (defined in the article). We prove that the tiered…

It is well-known that a function on an open set in $\mathbb R^d$ is smooth if and only if it is arc-smooth, i.e., its composites with all smooth curves are smooth. In recent work, we extended this and related results (for instance, a real…

We show that if a polynomial filled Julia set has empty interior, then it is computable.

Let $J\subset S=K[x_0,...,x_n]$ be a monomial strongly stable ideal. The collection $\Mf(J)$ of the homogeneous polynomial ideals $I$, such that the monomials outside $J$ form a $K$-vector basis of $S/I$, is called a {\em $J$-marked…

A conjecture of Kalai asserts that for $d\geq 4$, the affine type of a prime simplicial $d$-polytope $P$ can be reconstructed from the space of affine $2$-stresses of $P$. We prove this conjecture for all $d\geq 5$. We also prove the…

We study random independent and identically distributed iterations of functions from an iterated function system of homeomorphisms on the circle which is minimal. We show how such systems can be analyzed in terms of iterated function…

Inspired by nonstandard analysis, we define and study internal subsets and internal functions in algebras of Colombeau generalized functions. We prove a saturation principle for internal sets and provide applications to Colombeau algebras.

Reachability sets of linear switching dynamical systems (systems of ODE with time-dependent matrices that take values from a given compact set) are analysed. An eigenset is a non-trivial compact set M that possesses the following property:…

Let $(\mathcal{M}, c_k,n_k)$ be a class of Moran sets. We assume that the convex hull of any $E\in (\mathcal{M}, c_k,n_k)$ is $[0,1]$. Let $A,B$ be two non-empty sets in $\mathbb{R}$. Suppose that $f$ is a continuous function defined on an…