Related papers: Dynamical IP$^{\star}$-sets in weak rings

We prove a small-gain theorem for interconnections of $n$ nonlinear heterogeneous input-to-state stable (ISS) control systems of a general nature, covering partial, delay and ordinary differential equations. Furthermore, for the same class…

In this paper, we show that the subadditive dual of a feasible conic mixed-integer program (MIP) is a strong dual whenever it is feasible. Moreover, we show that this dual feasibility condition is equivalent to feasibility of the conic dual…

We show that a non-wandering dynamical system with the shadowing property is either equicontinuous or has positive entropy and that in this context uniformly positive entropy is equivalent to weak mixing. We also show that weak mixing…

Let $(R,\mathfrak{m})$ be a regular local ring or a polynomial ring over a field, and let $I$ be an ideal of $R$ which we assume to be graded if $R$ is a polynomial ring. Let astab$(I)$ resp. $\overline{\rm astab}(I)$ be the smallest…

This paper is devoted to studying the multiple recurrent property of topologically mildly mixing systems along generalized polynomials. We show that if a minimal system is topologically mildly mixing, then it is mild mixing of higher orders…

Let $G$ be a connected finite simple graph and let $I_G$ be the edge ideal of $G$. The smallest number $k$ for which $\depth S/I_G^k$ stabilizes is denoted by $\dstab(I_G)$. We show that $\dstab(I_G)<\ell(I_G)$ where $\ell(I_G)$ denotes the…

Let $\mathcal{R}$ be a commutative ring with unity, and let $P$ be a locally finite poset. The aim of the paper is to provide an explicit description of the additive biderivations of the incidence algebra $I(P, \mathcal{R})$. We demonstrate…

We show that certain subrings of the cohomology of a finite p-group P may be realised as the images of restriction from suitable virtually free groups. We deduce that the cohomology of P is a finite module for any such subring. Examples…

We present a method to constrain the potential of the non-axisymmetric components of the Galaxy using the kinematics of stars in the solar neighborhood. The basic premise is that dynamical substructures in phase-space (i.e. due to the bar…

The purpose of this simple note is to provide elementary model-theoretic proofs to some existing results on sumset phenomena and IP sets, motivated by Hrushovski's work on the stabilizer theorem.

We show that, for every finitely generated group with decidable word problem and undecidable domino problem, there exists a sequence of effective subshifts whose inverse limit is not the topological factor of any effective dynamical system.…

It was proved that whenever $\mathbb{N}$ is partitioned into finitely many cells, one cell must contain arbitrary length arithmetic and geometric progression nicely intertwined, so that one cell must be rich in the sense of containing…

We show that if a finite point set $P\subseteq \mathbb{R}^2$ has the fewest congruence classes of triangles possible, up to a constant $M$, then at least one of the following holds. (1) There is a $\sigma>0$ and a line $l$ which contains…

H.Furstenberg and E.Glasner proved that for an arbitrary $k\in\mathbb{N}$, any piecewise syndetic set of integers contains a $k$-term arithmetic progression and the collection of such progressions is itself piecewise syndetic in…

The main goal of this paper is proving the fixed point theorem for finite groups acting on weakly systolic complexes. As corollaries we obtain results concerning classifying spaces for the family of finite subgroups of weakly systolic…

A finite dynamical system with $n$ components is a function $f:X\to X$ where $X=X_1\times\dots\times X_n$ is a product of $n$ finite intervals of integers. The structure of such a system $f$ is represented by a signed digraph $G$, called…

Tao has shown that in any fixed base, a positive proportion of prime numbers cannot have any digit changed and remain prime. In other words, most primes are "digitally delicate". We strengthen this result in a manner suggested by Tao: A…

There is growing interest in termination reasoning for non-linear programs and, meanwhile, recent dynamic strategies have shown they are able to infer invariants for such challenging programs. These advances led us to hypothesize that…

Networked dynamical systems are common throughout science in engineering; e.g., biological networks, reaction networks, power systems, and the like. For many such systems, nonlinearity drives populations of identical (or near-identical)…

Using dynamics, Furstenberg defined the concept of a central subset of positive integers and proved several powerful combinatorial properties of central sets. Later using the algebraic structure of the Stone-\v{C}ech compactification,…