‎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...

in this paper, the notion of fully idempotent modules is defined and it is shown that this notion inherits most of the essential properties of the usual notion of von neumann's regular rings. furthermore, we introduce the dual notion of fully idempotent modules (that is, fully coidempotent modules) and investigate some properties of this class of modules.

In this paper we present a novel approach to delay-testing of VLSl logic chips based on the level-sensitive scan design (LSSD) methodology. The objective of the delay test is to reduce significantly the failures of multi-chip modules at system integration test while minimizing the complexity and cost of subassembly testing. Because system timing data are used to derive test specifications, the ...

Let $R$ be a commutative ring with identity. The purpose of this paper is to introduce and study two classes of modules over $R$, called $mbox{Max}$-injective and $mbox{Max}$-strongly top modules and explore some of their basic properties. Our concern is to extend some properties of $X$-injective and strongly top modules to these classes of modules and obtain some related results.

background: repeated implantation failure (rif) is defined as pregnancy failure after two to six times with at least ten high grade embryo transfer to uterus. a variety of causes have been anticipated for rif, including anatomical, autoimmune, genetics, endocrine and thrombotic anomalies. factors responsible for rif have important implication regarding treatment however in many couples a perfec...

‎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 $c_2=0$.

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In this work, performance of hollow fiber membrane photobioreactor (HFMPB) on the growth of Dunaliella Salina (G26) at various aeration rates (0.1 and 0.2 VVm) and medium re-circulation flow rates (500 and 1000 mL/h) were studied. Cultivation was carried out at both batch and semi-continuous modes in HFMPBs containing neat and hydrophilized in-house fabricated poly ethylene (PE) membranes at fi...

The purpose of this paper is to introduce some new classes of rings and modules that are closely related to the classes of almost Dedekind domains and almost Dedekind modules. We introduce the concepts of $\phi$-almost Dedekind rings and $\Phi$-almost Dedekind modules and study some properties of this classes. In this paper we get some equivalent conditions for $\phi$-almost Dedekind rings and ...