in this paper, we  study the arens regularity properties of module actions. we investigate some properties of topological centers of module actions ${z}^ell_{b^{**}}(a^{**})$ and  ${z}^ell_{a^{**}}(b^{**})$ with some conclusions in group algebras.

In this paper we study the relation between module amenability of $theta$-Lau product $A×_theta B$ and that of Banach algebras $A, B$. We also discuss module biprojectivity of $A×theta B$. As a consequent we will see that for an inverse semigroup $S$, $l^1(S)×_theta l^1(S)$ is module amenable if and only if $S$ is amenable.

A natural Hasse-Schmidt derivation on the exterior algebra of a free module realizes the (small quantum) cohomology ring of the grassmannian Gk(C ) as a ring of operators on the exterior algebra of a free module of rank n. Classical Pieri’s formula can be interpreted as Leibniz’s rule enjoyed by special Schubert cycles with respect to the wedge product.

various methods for parametric interpolation of nurbs curves have been proposed in the past. however, the errors caused by the approximate nature of the nurbs interpolator were rarely taken into account. this paper proposes an integrated look-ahead algorithm for parametric interpolation along nurbs curves. the algorithm interpolates the sharp corners on the curve with the pythagorean-hodograph ...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...

A new algorithm is proposed for the software implementation of modular multiplication, which uses pre-computations with a constant module. The developed modular multiplication algorithm provides high performance in comparison with the already known algorithms, and is oriented at the variable value of the module, especially with the software implementation on micro controllers and smart cards wi...

From the results of two Human behavior studies in small group interactions we constructed iteratively a Collaborative Virtual Environment named “VIRSTORY”. This system is a digital storytelling with speech and 3D gesture recognition technologies using like input devices. It includes several modules: multimodal interaction module, behavior module to animate autonomous expressive characters, etc.

We develop some techniques to the study of exact module categories over some families of pointed finite-dimensional Hopf algebras. As an application we classify exact module categories over the tensor category of representations of the small quantum groups uq(sl2).

Let $R$ be a commutative ring with identity and $M$ be an unitary $R$-module. The intersection graph of an $R$-module $M$, denoted by $Gamma(M)$, is a simple graph whose vertices are all non-trivial submodules of $M$ and two distinct vertices $N_1$ and $N_2$ are adjacent if and only if $N_1cap N_2neq 0$. In this article, we investigate the concept of a planar intersection graph and maximal subm...

let $alpha$ be an endomorphism and $delta$ an $alpha$-derivationof a ring $r$.  in this paper we  study the relationship between an$r$-module $m_r$ and the  general polynomial module  $m[x]$ over theskew polynomial ring $r[x;alpha,delta]$. we introduce the notionsof skew-armendariz modules and skew quasi-armendariz modules whichare generalizations of $alpha$-armendariz modules and extend thecla...