Related papers: Force recurrence near zero

This paper is a survey, with few proofs, of ideas and notions related to self-similarity of groups, semi-groups and their actions. It attempts to relate these concepts to more familiar ones, such as fractals, self-similar sets, and…

We consider real sequences $(f_n)$ that satisfy a linear recurrence with constant coefficients. We show that the density of the positivity set of such a sequence always exists. In the special case where the sequence has no positive…

In this work, we prove the existence of linear recurrences of order M with a non-trivial solution vanishing exactly on the set of gaps (or a subset) of a numerical semigroup S finitely generated by a1 < a2 <...< aN and M = aN. Keywords:…

Here a novel idea to handle imprecise or vague set viz. Pseudo fuzzy set has been proposed. Pseudo fuzzy set is a triplet of element and its two membership functions. Both the membership functions may or may not be dependent. The hypothesis…

We consider integer recurrences of the form a_n = f(a_{n-1}), where f is a quadratic polynomial with integer coefficients. We show, for four infinite families of f, that the set of primes dividing at least one term of such a sequence must…

This short paper introduces an abstraction called Think Again Networks (ThinkNet) which can be applied to any state-dependent function (such as a recurrent neural network).

A connected forcing set of a graph is a zero forcing set that induces a connected subgraph. In this paper, we introduce and study CF-dense graphs -- graphs in which every vertex belongs to some minimum connected forcing set. We identify…

In this article, we consider the notion of almost irredundant sets: A subset $\mathcal{X}$ of a C*-algebra $\mathcal{A}$ is called almost irredundant if and only if for every $a\in \mathcal{X}$, the element $a$ does not belong to the…

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…

A set $A \subseteq \mathbb{N}$ is a set of pointwise recurrence if for all minimal dynamical systems $(X, T)$, all $x \in X$, and all open neighborhoods $U \subseteq X$ of $x$, there exists a time $n \in A$ such that $T^n x \in U$. The set…

We shall address the alternative definition of chain recurrent set for the action of a semigroup of continuous self maps, given by M. Hurley \cite {mh} in noncompact space. Following this, we shall address the characterization of chain…

In the several contexts such as combinatorial number theory, families of sets of positive integers closed under taking subsets have been investigated. Then it is sometimes useful to give bijections between the set of the one-sided infinite…

Hindman and Leader first introduced the notion of Central sets near zero for dense subsemigroups of $((0,\infty),+)$ and proved a powerful combinatorial theorem about such sets. Using the algebraic structure of the Stone-$\breve{C}$ech…

Let $\mathrm{d}(A)$ be the asymptotic density (if it exists) of a sequence of integers $A$. For any real numbers $0\leq\alpha\leq\beta\leq 1$, we solve the question of the existence of a sequence $A$ of positive integers such that…

In the strict semi stable reduction situation, we describe the various filtrations of the perverse sheaf of nearby cycles in terms of irreducible perverse sheaves together with the action of the monodromy operator. We then study the…

A semigroup A is an abelian semigroup with identity 0. A set of positives in A is an ordered down-directed set P containing with every r an element r/2 with r/2 + r/2 = r. A continuity space is an abstract set X equipped with a map d : XxX…

In a couple of previous papers, we initiated a systematic study of semihypergroups and had a thorough discussion on certain analytic and algebraic aspects associated to this class of objects. In this article, we introduce and examine…

Given a dynamical system $(X,T)$ and a family $\mathsf{I}\subseteq \mathcal{P}(\omega)$ of "small" sets of nonnegative integers, a point $x \in X$ is said to be $\mathsf{I}$-strong universal if for each $y \in X$ there exists a subsequence…

In a previous paper, the author introduced the idea of intrinsic density --- a restriction of asymptotic density to sets whose density is invariant under computable permutation. We prove that sets with well-defined intrinsic density (and…

Sofic and hyperlinear groups are the countable discrete groups that can be approximated in a suitable sense by finite symmetric groups and groups of unitary matrices. These notions turned out to be very deep and fruitful, and stimulated in…