In this paper we introduce a new class of modules which is closely related to the class of Noetherian modules. Let $R$ be a commutative ring with identity and let $M$ be an $R$-module such that $Nil(M)$ is a divided prime submodule of $M$. $M$ is called a Nonnil-Noetherian $R$-module if every nonnil submodule of $M$ is finitely generated. We prove that many of the properties of Noetherian modul...

‎we introduce a generalization of the notion of‎ depth of an ideal on a module by applying the concept of‎ local cohomology modules with respect to a pair‎ ‎of ideals‎. ‎we also introduce the concept of $(i,j)$-cohen--macaulay modules as a generalization of concept of cohen--macaulay modules‎. ‎these kind of modules are different from cohen--macaulay modules‎, as an example shows‎. ‎also an art...

Self-reconfigurable robots are designed so that they can change their external shape without human intervention. One general way to achieve such functionality is to build a robot composed of multiple, identical unit modules. If the modules are designed so that they can be assembled into rigid structures, and so that individual units within such structures can be relocated within and about the s...

Self-reconfigurable robots are designed so that they can change their external shape without human intervention. One general way to achieve such functionality is to build a robot composed of multiple, identical unit modules. If the modules are designed so that they can be assembled into rigid structures, and so that individual units within such structures can be relocated within and about the s...

Besides the mature and steadily growing datacom market for which VCSELs are key components in Transceivers, Active Optical Cables (AOC), Mid Board Optical Modules (MBOM) or Embedded Optical Modules (EOM), VCSELs have proven to be key components also for other volume applications. Laser mice emerged 2004, just after the burst of the dotcom bubble and the related downturn in the Datacom industry,...

Copyright # 20 ABSTRACT: This review focuses on how the mechanistic approach of physical organic chemistry can be used to elucidate the mechanisms behind complex biochemical networks. The dynamics of biochemical reaction networks is difficult to describe by considering their individual reactions, just as the dynamics of organic reactions is difficult to describe by considering individual electr...

‎Highest weight modules of the double affine Lie algebra $widehat{widehat{mathfrak{sl}}}_{2}$ are studied under a‎ ‎new triangular decomposition‎. ‎Singular vectors of Verma modules are‎ ‎determined using a similar condition with horizontal affine Lie‎ ‎subalgebras‎, ‎and highest weight modules are described under the‎ ‎condition $c_1>0$ and $c_2=0$.

This paper is concerned with the relation between local cohomology modules defined by a pair of ideals and the Serre subcategories of the category of modules. We characterize the membership of local cohomology modules in a certain Serre subcategory from lower range or upper range.

System of Mobile Devices (SyD) is a middleware we developed that can be used for implementing collaborative, mobile, and distributed applications over heterogeneous devices, data stores, and computing environments. Current prototype implementation of SyD consists of five modules. These modules provide ease of programming in the areas of distributed communication, remote method invocation, servi...

Abstract. Certain facts about frames and generalized frames (g- frames) are extended for the g-frames for Hilbert C*-modules. It is shown that g-frames for Hilbert C*-modules share several useful properties with those for Hilbert spaces. The paper also character- izes the operators which preserve the class of g-frames for Hilbert C*-modules. Moreover, a necessary and suffcient condition is ob- ...