The main aim of this work is to introduce and study the notions ideal direct product d-algebras, d-ideal sub-direct edge positive implicative d-algebras investigate their characterizations.

Let α(G) denote the independence number of a graph G and let G ×H be the direct product of graphs G and H. Set α(G ×H) = max{α(G) · |H|, α(H) · |G|}. If G is a path or a cycle and H is a path or a cycle then α(G×H) = α(G×H). Moreover, this equality holds also in the case when G is a bipartite graph with a perfect matching and H is a traceable graph. However, for any graph G with at least one ed...

This paper is concerned with finite primitive permutation groups G which are subgroups of wreath products W in product action and are such that the socles of G and W are the same. The aim is to explore how the study of such groups may be reduced to the study of smaller groups. The O'Nan-Scott Theorem (see Liebeck, Praeger, Saxl [12] for the most recent and detailed treatment) sorts finite primi...

We introduce and study the direct product of a family of fuzzy hyperalgebras of the same type and present some properties of it.

The input to the freeform fabrication process is essentially geometric data, raw material, material data and process parameters. Optimal process parameters depend upon current material and the part geometry. This paper describes an research approach in which all necessary input including process parameters are obtained or derived from the product model. The part geometry with its process parame...

In this paper, we define a new type of product of association schemes (and of the related objects, permutation groups and orthogonal block structures), which generalizes the direct and wreath products (which are referred to as “crossing” and “nesting” in the statistical literature.) Given two association schemes Qr for r = 1, 2, each having an inherent partition Fr (that is, a partition whose e...

In this paper we investigate the monodromy groups of the truncated simplices of all possible ranks and investigate related structures. In particular, we demonstrate that the monodromy group of a truncated simplex is the direct product of symmetric groups.

We calculate the minimal degree for a class of finite complex reflection groups G(p, p, q), for p and q primes and establish relationships between minimal degrees when these groups are taken in a direct product.

It is proved that the automorphism group of a semigroup being an inflation of its proper subsemigroup decomposes into a semidirect product of two groups one of which is a direct sum of full symmetric groups.