Let R be a commutative ring with unity 1 6= 0, and let M be a unitary left module over R. In this paper we introduce the notion of epiform∗ modules. Various properties of this class of modules are given and some relationships between these modules and other related modules are introduced.

In this paper, we introduce and study a new concept named couniform modules, which is a dual notion of uniform modules, where an R-module M is said to be couniform if every proper submodule N of M is either zero or there exists a proper submodule N1 of N such that is small submodule of Also many relationships are given between this class of modules and other related classes of modules. Finally, we consider the hereditary property between R-module M and R-module R in case M is couniform.

Throughout this paper we introduce the notion of coextending module as a dual of the class of extending modules. Various properties of this class of modules are given, and some relationships between these modules and other related modules are introduced.

During more than (50) years past, India has achieved considerable social and economic progress. It is also generally assumed that the future progress will be even more rapid and that India will be an important player in the global market. India has only (2.5) percent of global land whereas it has to provide home for one-sixth of world's population .On examining the past trends of India's population ,it may be observed that during the latter half of the twentieth century ,about (650) million populations were added to the country ,thus living in a country with a high population density and high growth rate , India in need a transition from high fertility high mortality to a low fertility low mortality and towards stable population situatio

In line with the advancement of hardware technology and increasing consumer demands for new functionalities and innovations, software applications grew tremendously in term of size over the last decade. This sudden increase in size has a profound impact as far as testing is concerned. Here, more and more unwanted interactions among software systems components, hardware, and operating system are to be expected, rendering increased possibility of faults. To address this issue, many useful interaction-based testing techniques (termed t-way strategies) have been developed in the literature. As an effort to promote awareness and encourage its usage, this chapter surveys the current state-of-the-art and reviews the state-of-practices in t

In line with the advancement of hardware technology and increasing consumer demands for new functionalities and innovations, software applications grew tremendously in term of size over the last decade. This sudden increase in size has a profound impact as far as testing is concerned. Here, more and more unwanted interactions among software systems components, hardware, and operating system are to be expected, rendering increased possibility of faults. To address this issue, many useful interaction-based testing techniques (termed t-way strategies) have been developed in the literature. As an effort to promote awareness and encourage its usage, this chapter surveys the current state-of-the-art and reviews the state-of-practices in t