In this paper, by using Gröbner-Shirshov bases, we show that in the following classes, each (resp. countably generated) algebra can be embedded into a simple (resp. two-generated) algebra: associative differential algebras, associative Ω-algebras, associative λ-differential algebras. We show that in the following classes, each countably generated algebra over a countable field k can be embedded...

Let Vn be the number of equivalence classes of invertible maps from {0,1}n to {0,1}n, under action of permutation of variables on domain and range. So far, the values Vn have been known for n 6 6. This paper describes the procedure by which the values of Vn are calculated for n 6 30.

we consider the fundamental relation  on a semihypergroup  to interpret the lower and upper approximations as subsets of the fundamental semigroup  and we give some results in this connection. also, we introduce the notion of a bi-hyperideal to study the relationship between approximations and bi-hyperideals.

Recently different approaches have been developed in the field of sensor fault diagnostics based on Auto-Associative Neural Network (AANN). In this paper we present a novel algorithm called Self reconstructing Auto-Associative Neural Network (S-AANN) which is able to detect and isolate single faulty sensor via reconstruction. We have also extended the algorithm to be applicable in multiple faul...

The submodules with the property of the title ( a submodule $N$ of an $R$-module $M$ is called strongly dense in $M$, denoted by $Nleq_{sd}M$, if for any index set $I$, $prod _{I}Nleq_{d}prod _{I}M$) are introduced and fully investigated. It is shown that for each submodule $N$ of $M$ there exists the smallest subset $D'subseteq M$ such that $N+D'$ is a strongly dense submodule of $M$ and $D'bi...