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.

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...

Today power consumption is considered to be one of the important issues. Therefore, its reduction plays a considerable role in developing systems. Previous studies have shown that approximately 50% of total power consumption is used in cache memories. There is a direct relationship between power consumption and replacement quantity made in cache. The less the number of replacements is, the less...

Let R be an associative ring with identity, C(R) be the category of com-plexes of R-modules and Flat(C(R)) be the class of all at complexes of R-modules. We show that the at cotorsion theory (Flat(C(R)); Flat(C(R))−)have enough injectives in C(R). As an application, we prove that for each atcomplex F and each complex Y of R-modules, Exti (F,X)= 0, whenever Ris n-perfect and i > n.

Let $R$ be an associative ring and let $M$ be a left $R$-module.Let $Spec_{R}(M)$ be the collection of all prime submodules of $M$ (equipped with classical Zariski topology). There is a conjecture which says that every irreducible closed subset of $Spec_{R}(M)$ has a generic point. In this article we give an affirmative answer to this conjecture and show that if $M$ has a Noetherian spectrum, t...

Abstract We prove a hom-associative version of Hilbert’s basis theorem, which includes as special cases both non-associative and the classical theorem for associative Ore extensions. Along way, we develop hom-module theory. conclude with some examples extensions are all noetherian by our theorem.