In 2006, Czeizler et.al. introduced parallel communicating Watson-Crick automata system. They showed that parallel communicating Watson-Crick automata system can accept the non-regular unary language L={ , > 1} using non-injective complementarity relation and three components. In this paper, we improve on Czeizler et.al. work by showing that parallel communicating Watson-Crick automata system c...

We show that every λm-injectivity class (i.e., the class of all the objects injective with respect to some class of λ-presentable morphisms) is a weakly reflective subcategory determined by a functorial weak factorization system cofibrantly generated by a class of λ-presentable morphisms. This was known for small-injectivity classes, and referred to as the “small object argument”. An analogous ...

A ring $R$ is called right CSP if the sum of any two closed ideals also a ideal $R$. Left rings can be defined similarly. An example given to show that left may not CSP. It shown matrix over proved $\mathbb{M}_{2}(R)$ and only self-injective von Neumann regular. The equivalent characterization for trivial extension $R\propto R$

In this paper an algebraic star product and differential one defined on a regular coadjoint orbit of a compact semisimple group are compared. It is proven that there is an injective algebra homomorphism between the algebra of polynomials with the algebraic star product and the algebra of differential functions with the differential star product structure. Investigation supported by the Universi...

Let F be a family of graphs and let d be large enough. For every d-regular graph G, we study the existence of a spanning F -free subgraph of G with large minimum degree. This problem is wellunderstood if F does not contain bipartite graphs. Here we provide asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartite graphs. To prove these results, we s...

In this paper, after recalling the category {\bf PosAct}-$S$ of all poset acts over a pomonoid $S$; an $S$-act in Pos} posets, with action preserving monotone maps between them, some categorical properties are considered. particular, we describe limits and colimits such as products, coproducts, equalizers, coequalizers etc. category. Also, several kinds epimorphisms monomorphisms characterized ...

Abstract We prove that many, but not all, injective factors arise as crossed products by nonsingular Bernoulli actions of the group $\mathbb {Z}$ . obtain this result proving a completely general on ergodicity, type and Krieger’s associated flow for shifts with arbitrary base spaces. must satisfy structural property infinite divisibility. Conversely, we all almost periodic flows, well many othe...

We prove a max-min theorem for weak containment in the context of algebraic actions. Namely, we show that given an action $G$ on $X,$ there is maximal, closed $G$-invariant subgroup $Y$ $X$ so weakly contained Bernoulli shift. This also minimal any shift $G\curvearrowright X/Y$-ergodic presence X$. give several applications, including major simplification proof measure entropy equals topologica...

we study topological von neumann regularity and principal von neumann regularity of banach algebras. our main objective is comparing these two types of banach algebras and some other known banach algebras with one another. in particular, we show that the class of topologically von neumann regular banach algebras contains all $c^*$-algebras, group algebras of compact abelian groups and cer...