module over a ring is a general mathematical concept for many examples of mathematicalobjects that can be added to each other and multiplied by scalar numbers.in this paper, we consider a module over a ring as a universe and by using the notion of reference points, we provide local approximations for  subsets of the universe.

To date, the role of gender in speaking tests has received limited attention in language testing research. It is possible in oral interviews, for instance, that both interviewing and rating may be highly gendered processes. In tests like the IELTS interview, where the interviewer also acts as the rater, this poses the question of whether a gender effect, if it exists, stems from the interview i...

The extraction of oil and gas from deep water is one of the most important challenges of the oil and gas industry today. FPSO is one of the leading platforms for deep waters. This study discussed the performance of FPSO deck modules under loads exerted on the hull of the ship. Modeling of the studied module was executed by SACS software and the effect of support using neoprene in the function o...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

book social media are reading communities primarily developed as online social networks. this study aims to find precise criteria and indicators for evaluation of book social network and examine and rank the most popular book social networks. the sample population included 10 english and two persian book/reading social networks publicly available on the web. a checklist containing 9 main criter...