Hyper-tubes consisting of hyper-cubes of n-dimensions were designed and formulas for substructures of vary dimensions established.

As the information acquisition and processing applications take greater roles in our everyday life, database management systems are growing in importance. Database management systems have traditionally exhibited poor cache performance and large memory footprints, therefore performing only at a fraction of their ideal execution and exhibiting low processor utilization. Previous research has stud...

In this paper we make an algebraic study of the variety of M V * –algebras introduced by C. C.Chang as an algebraic counterpart for a logic with positive and negative truth values. We build the algebraic theory of M V * –algebras within its own limits using a concept of ideal and of prime ideal that are very naturally related to the corresponding concepts in –groups. The main results are a subd...

Researchers from diverse disciplines are increasingly incorporating numeric highorder data, i.e., numeric tensors, within their practice. Just like the matrix-vector (MV) paradigm, the development of multi-purpose, but high-performance, sparse data structures and algorithms for arithmetic calculations, e.g., those found in Einstein-like notation, is crucial for the continued adoption of tensors...

In this paper we study rank one discrete valuations of the field k((X1, . . . ,Xn)) whose center in k[X1, . . . ,Xn] is the maximal ideal. In sections 2 to 6 we give a construction of a system of parametric equations describing such valuations. This amounts to finding a parameter and a field of coefficients. We devote section 2 to finding an element of value 1, that is, a parameter. The field o...