Related papers: A separation property for iterated function system…

In this paper, we show that \phi is a dependent formula if and only if all \phi-types have an extension to a \phi-isolated \phi-type that is an "elementary \phi-extension" (see Definition 2.3 in the paper). Moreover, we show that the domain…

An approach is proposed which, given a family of linearly independent functions, constructs the appropriate biorthogonal set so as to represent the orthogonal projector operator onto the corresponding subspace. The procedure evolves…

This paper concerns the local connectedness of components of self-similar sets. Given an equal partition of the unit square into n*n small squares, we may choose arbitrarily two or more of them and form an iterated function system. The…

In this paper the dynamics of an economic system with foreign financing, of integer or fractional order, are analyzed. The symmetry of the system determines the existence of two pairs of coexisting attractors. The integer-order version of…

Iterated function systems (IFSs) are one of the most important tools for building examples of fractal sets exhibiting some kind of `approximate self-similarity'. Examples include self-similar sets, self-affine sets etc. A beautiful variant…

We introduce a sufficient and necessary condition for the separability of a specific class of $N$ $d$-dimensional system (qudits) states, namely special generalized Werner state (SGWS): $W^{[d^N]}(v)=(1-v)\frac{I^{(N)}}{d^N}+v|\psi…

The problem of non-iterative one-shot and non-destructive correction of unavoidable mistakes arises in all Artificial Intelligence applications in the real world. Its solution requires robust separation of samples with errors from samples…

It is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous counterpart and…

In this paper are investigated strictly self-similar fractals that are composed of an infinite number of regular star-polygons, also known as Sierpinski $n$-gons, $n$-flakes or polyflakes. Construction scheme for Sierpinsky $n$-gon and…

We study countable compact spaces as potential attractors of iterated function systems. We give an example of a convergent sequence in the real line which is not an IFS-attractor and for each countable ordinal $\delta$ we show that a…

Let $n$ be a positive integer. A collection $\cal S$ of subsets of $[n]=\{1,\ldots,n\}$ is called {\it symmetric} if $X\in {\cal S}$ implies $X^\ast\in {\cal S}$, where $X^\ast:=\{i\in [n]\colon n-i+1\notin X\}$. We show that in each of the…

Let $M$ be a $2\times2$ real matrix with both eigenvalues less than~1 in modulus. Consider two self-affine contraction maps from $\mathbb R^2 \to \mathbb R^2$, \begin{equation*} T_m(v) = M v - u \ \ \mathrm{and}\ \ T_p(v) = M v + u,…

We provide necessary and sufficient conditions for separability of mixed states. As a result we obtain a simple criterion of separability for $2\times2$ and $2\times3$ systems. Here, the positivity of the partial transposition of a state is…

Let $F(x)$ be a function of the form $ \sum_{i=1}^r d_i x^{\rho_i}$ where $d_1,\ldots,d_r\in\mathbb{R}$, $0 \leq \rho_1 < \ldots < \rho_r,$ $\rho_r \not\in \mathbb{Z},\rho_i \in \mathbb{R}$ for $ 1 \leq i \leq r$ and $d_r\not=0$. We prove…

We consider the asymmetric exclusion process (ASEP) in one dimension on sites $i = 1,..., N$, in contact at sites $i=1$ and $i=N$ with infinite particle reservoirs at densities $\rho_a$ and $\rho_b$. As $\rho_a$ and $\rho_b$ are varied, the…

The structure of the graph defined by the interactions in a Boolean network can determine properties of the asymptotic dynamics. For instance, considering the asynchronous dynamics, the absence of positive cycles guarantees the existence of…

Filtered probability spaces (called "filtrations" for short) are shown to satisfy such a topological zero-one law: for every property of filtrations, either the property holds for almost all filtrations, or its negation does. In particular,…

We show that a family of extremely thin sets satisfy the Erd\H{o}s similarity conjecture. These examples lie outside the range covered by recent work of Shmerkin and Yavicoli \cite{ShmerkinYavicoli2025}. As we shall see, they have small…

Colloidal particles, amphiphiles, and functionalized nanoparticles are examples of systems that frequently exhibit short-range attractions coupled with long-range repulsions. In this work, we observe striking differences in the dynamics of…

Feng and Wang showed that two homogeneous iterated function systems in $\mathbb{R}$ with multiplicatively independent contraction ratios necessarily have different attractors. In this paper, we extend this result to graph directed iterated…