The purpose of this note is to describe when a general complex algebraic $^*$-algebra pre-$C^*$-normed, and investigate their structure the $^*$-algebras are Baer $^*$-rings in addition algebraicity. As main result we prove following theorem for $^*$-algebras: every kind can be decomposed as direct sum $M\oplus B$, where $M$ finite dimensional $B$ commutative $^*$-algebra. summand $^*$-isomorph...

Let R be a commutative ring with identity and Mbe a unitary R-module. In this paper we generalize the conceptmultiplicatively closed subset of R and we study some propertiesof these genaralized subsets of M. Among the many results in thispaper, we generalize some well-known theorems about multiplicativelyclosed subsets of R to these generalized subsets of M. Alsowe show that some other well-kno...

background: lymphocyte subsets enumeration is considered prominent in the management of primary and acquired immunodeficiency disorders. because of local variations due to race, age, gender, and environmental conditions on lymphocyte subsets, and to improve the accuracy of interpretation of laboratory findings, reference intervals must be determined in every population. objective: to establish ...

1 Glossary Almost equicontinuous CA has an equicontinuous configuration. Attractor: omega-limit of a clopen invariant set. Blocking word interrupts information flow. Closing CA: distinct asymptotic configurations have distinct images. Column subshift: columns in space-time diagrams. Cross section: one-sided inverse map. ∗Université de Nice Sophia Antipolis, Département d’Informatique, Parc Valr...

We define a function f : X → Y to be slightly β-continuous if for every clopen set V of Y , f−1(V)⊂ Cl(Int(Cl(f−1(V)))). We obtain several properties of such a function. Especially, we define the notion of ultra-regularizations of a topology and obtain interesting characterizations of slightly β-continuous functions by using it. 2000 Mathematics Subject Classification. 54C08.

C0-semigroups of linear operators play a crucial role in the solvability of evolution equations in the classical context. This paper is concerned with a brief conceptualization of C0-semigroups on (ultrametric) free Banach spaces E. In contrast with the classical setting, the parameter of a given C0-semigroup belongs to a clopen ball Ωr of the ground field K. As an illustration, we will discuss...

Answer Set Programming (ASP) and ontology languages like Description Logics (DLs) play leading roles in Knowledge Representation and Reasoning (KR&R). ASP and DLs have largely orthogonal features because they make very different assumptions regarding the completeness of information, and thus reasoning techniques and algorithms that are deployed in ASP are significantly different from the ones u...

Abstract Given a dynamical simplex K on Cantor space X , we consider the set $G_K^*$ of all homeomorphisms which preserve elements and have no non-trivial clopen invariant subset. Generalizing theorem Yingst, prove that for generic element g measures is equal to . We also investigate when there exists conjugacy class in this happens exactly has only one element, unique measure associated some o...

In the topos approach to quantum physics, a functor known as the spectral presheaf of a von Neumann algebra plays the role of a generalized state space. Mathematically, the spectral presheaf also provides an interesting generalization of the Gelfand spectrum, which is only defined for abelian von Neumann algebras, to the nonabelian case. A partial duality result, analogous to Gelfand duality, e...

A non-erasing morphism σ is said to be recognizable on x if there exists ` such that, for each m ∈ Cσ(x), m′ ∈ Z, y[m−`,m+`) = y[m′−`,m′+`) implies that m′ ∈ Cσ(x), with y = σ(x). Is the Thue-Morse substitution σ : a 7→ ab, b 7→ ba recognizable on σ∞(a)? Same question for the Fibonacci substitution τ : a 7→ ab, b 7→ a. Let σ be a primitive morphism that is recognizable on some x and injective o...