‎in this text we prove that in generalized shift dynamical system $(x^gamma,sigma_varphi)$‎ ‎for finite discrete $x$ with at least two elements‎, ‎infinite countable set $gamma$ and‎ ‎arbitrary map $varphi:gammatogamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(x^gamma,sigma_varphi)$ is‎ li-yorke chaotic;‎ - the dynamical system $(x^gamma,sigma_varphi)$ has‎ an scr...

‎In this text we prove that in generalized shift dynamical system $(X^Gamma,sigma_varphi)$‎ ‎for finite discrete $X$ with at least two elements‎, ‎infinite countable set $Gamma$ and‎ ‎arbitrary map $varphi:GammatoGamma$‎, ‎the following statements are equivalent‎: ‎ - the dynamical system $(X^Gamma,sigma_varphi)$ is‎ Li-Yorke chaotic;‎ - the dynamical system $(X^Gamma,sigma_varphi)$ has‎ an scr...

In this paper, we study the linear dynamical properties of shift operators on some classes Segal algebras. Moreover, characterize hypercyclic generalized bilateral standard Hilbert module.

‎in the following text for arbitrary $x$ with at least two elements‎, ‎nonempty countable set $gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(x^gamma,sigma_varphi)$ where $varphi:gammatogamma$ is an arbitrary self-map‎. ‎we pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding devaney‎, ‎exact dev...

A countable collection X of functions in L2(IR ) is said to be a Bessel system if the associated analysis operator T ∗ X : L2(IR ) → `2(X) : f 7→ (〈f, x〉)x∈X is well-defined and bounded. A Bessel system is a fundamental frame if T ∗ X is injective and its range is closed. This paper considers the above two properties for a generalized shift-invariant system X. By definition, such a system has t...

‎In the following text for arbitrary $X$ with at least two elements‎, ‎nonempty countable set $Gamma$‎ ‎we make a comparative study on the collection of generalized shift dynamical systems like $(X^Gamma,sigma_varphi)$ where $varphi:GammatoGamma$ is an arbitrary self-map‎. ‎We pay attention to sub-systems and combinations of generalized shifts with counterexamples regarding Devaney‎, ‎exact Dev...

This paper presents generators based on decimated sequences of Generalized Feedback Shift Register (GFSR) generators. The equivalence relation between decimated GFSR generators and Tausworthe generators are presented and a k-distributed initialization scheme is derived. We present decimated GFSR generators that are maximally equidistributed. Timing results of these generators are presented.