notions of strongly regular, regular and left(right) regular $gamma$−semigroupsare introduced. equivalent conditions are obtained through fuzzy notion for a$gamma$−semigroup to be either strongly regular or regular or left regular.

This study develops and implements a computer-assisted learning (CAL) program with both multiplicative facts practices and the instruction of meaning behind these facts. The effectiveness of CAL on the development of multiplication abilities is also explored. Eight CAL activities are developed to teach multiplication to second grade elementary school students. The CAL program is comprised of th...

reactor core for nuclear power plant (1293 mwe) is of pressurized water reactor (pwr) type , with net electric output of 1200 mwe. the reactor is designed by a german company kwu (krafts werk :union:). in order to introduce the methods of calculation of the reactor core parameters to the students at the institute of nuclear science and technology, and in addition to provide them with the basic ...

Hierarchical ${\mathscr{H}}^{2}$ -matrices are asymptotically optimal representations for the discretizations of non-local operators such as those arising in integral equations or from kernel functions. Their O(N) complexity both memory and operator application makes them particularly suited large-scale problems. As a result, there is need software that provides support distributed operations o...

The Cohn-Umans group-theoretic approach to matrix multiplication suggests embedding matrix multiplication into group algebra multiplication, and bounding $\omega$ in terms of the representation theory of the host group. This framework is general enough to capture the best known upper bounds on $\omega$ and is conjectured to be powerful enough to prove $\omega = 2$, although finding a suitable g...

The human MxA protein is part of the antiviral state induced by alpha/beta interferon (IFN-alpha/beta). MxA inhibits the multiplication of several RNA viruses in cell culture. However, its antiviral potential in vivo has not yet been fully explored. We have generated MxA-transgenic mice that lack a functional IFN system by crossing MxA-transgenic mice constitutively expressing MxA with genetica...

let $r$ be a commutative ring with identity and $mathbb{a}(r)$ be the set   of ideals of $r$ with non-zero annihilators. in this paper, we first introduce and investigate the principal ideal subgraph of the annihilating-ideal graph of $r$, denoted by $mathbb{ag}_p(r)$. it is a (undirected) graph with vertices $mathbb{a}_p(r)=mathbb{a}(r)cap mathbb{p}(r)setminus {(0)}$, where   $mathbb{p}(r)$ is...