We consider the broadcasting problem for one-dimensional grid graphs with a given neighborhood template. There are two different models that have been considered-shouting (a node informs all of its neighbors in one step) and whispering (a node informs a single neighbor in one step). Let a(t) (respectively a(t)) denote the maximum number of nodes that can be reached in t steps by shouting (respe...

‎let $omega$ be a class of unital‎ ‎$c^*$-algebras‎. ‎we introduce the notion of a local tracial $omega$-algebra‎. ‎let $a$ be an $alpha$-simple unital local tracial $omega$-algebra‎. ‎suppose that $alpha:gto $aut($a$) is an action of a finite group $g$ on $a$‎ ‎which has a certain non-simple tracial rokhlin property‎. ‎then the crossed product algebra‎ ‎$c^*(g,a,alpha)$ is a unital local traci...

A Heyting algebra is a distributive lattice with implication and a dual $BCK$-algebra is an algebraic system having as models logical systems equipped with implication. The aim of this paper is to investigate the relation of Heyting algebras between dual $BCK$-algebras. We define notions of $i$-invariant and $m$-invariant on dual $BCK$-semilattices and prove that a Heyting semilattice is equiva...

Suppose that $A$ is a semi-simple and commutative Banach algebra. In this paper we try to characterize the character space of the Banach algebra $C_{rm{BSE}}(Delta(A))$ consisting of all  BSE-functions on $Delta(A)$ where $Delta(A)$ denotes the character space of $A$. Indeed, in the case that $A=C_0(X)$ where $X$ is a non-empty locally compact Hausdroff space, we give a complete characterizatio...

In this paper, we introduce the notions of expansion of ideals in $MV$-algebras, $ (tau,sigma)- $primary, $ (tau,sigma)$-obstinate  and $ (tau,sigma)$-Boolean  in $ MV- $algebras. We investigate the relations of them. For example, we show that every $ (tau,sigma)$-obstinate ideal of an $ MV-$ algebra is $ (tau,sigma)$-primary  and $ (tau,sigma)$-Boolean. In particular, we define an expansion $ ...

The division algebra of real quaternions, as the only noncommutative normed division real algebra up to isomorphism of normed algebras, is of great importance. In this note, first we present a brief introduction to quaternion matrices and quaternion linear algebra. This, among other things, will help us present the counterpart of a theorem of Herman Auerbach in the setting of quaternions. More ...

For a Banach algebra $A$, $A''$ is $(-1)$-Weakly amenable if $A'$ is a Banach $A''$-bimodule and $H^1(A'',A')={0}$. In this paper, among other things,  we study the relationships between the $(-1)$-Weakly amenability of $A''$ and the weak amenability of $A''$ or $A$. Moreover, we show that the second dual of every $C^ast$-algebra is $(-1)$-Weakly amenable.

In this paper we review the concepts of the superalgebra, superderivation and some properties of them. We will define algebraic and differential superderivations on a superalgebra and will prove some theorems about them, Then we consider a superalgebra bundle, that is an algebra bundle which its fibers are superalgebras and then characterize the superderivations of the algebra of sections of th...