An (n, a, b)-perfect double cube is a b × b × b sized n-ary periodic array containing all possible a × a × a sized n-ary array exactly once as subarray. A growing cube is an array whose cj × cj × cj sized prefix is an (nj, a, cj)-perfect double cube for j = 1, 2, . . ., where cj = n v/3 j , v = a 3 and n1 < n2 < · · ·. We construct the smallest possible perfect double cube (a 256×256×256 sized ...

The diierence among diierent topologies in interconnection networks is a debated issue among highly parallel machine designers, since opposing parameters innuence the network performance. This paper presents a new model, k-ary n-cube m-diags, which generalizes existing k-ary n-cube topologies to include hexagonal networks and their n-dimensional extensions. A performance analysis based on this ...

Polyvector-valued gauge field theories in noncommutative Clifford spaces are presented. The noncommutative binary star products are associative and require the use of the Baker-Campbell-Hausdorff formula. An important relationship among the n-ary commutators of noncommuting spacetime coordinates [X, X, ......, X] and the poly-vector valued coordinates X in noncommutative Clifford spaces is expl...

This paper presents three simple and efficient algorithms for generating, ranking and unranking t-ary trees in a lexicographic order. The simplest idea of encoding a t-ary tree with n nodes as a bit-string of length t*n is exploited to its full advantages. It is proved that the lexicographic order in the set of t-ary trees with n nodes is preserved in the set of bit-strings of length t*n, using...

Inspired by engineering of high-speed switching with quality of service, this paper introduces a new approach to classify finite lattices by the concept of cut-through coding. An n-ary cut-through code of a finite lattice encodes all lattice elements by distinct n-ary strings of a uniform length such that for all j, the initial j encoding symbols of any two elements x and y determine the initia...

The Semantic Web is a vision of the next generation Web, in which semantic markup will make Web resources more accessible to automatic processes. Description Logics (DLs) are of crucial importance to the development of the Semantic Web, where their role is to provide formal underpinnings and automated reasoning services for Semantic Web ontology languages such as DAML+OIL. In this paper, we sho...

The main purpose of this paper is to discuss the asymptotic behavior of the difference sq,k(P (n))−k(q−1)/2 where sq,k(n) denotes the sum of the first k digits in the q-ary digital expansion of n and P (x) is an integer polynomial. We prove that this difference can be approximated by a Brownian motion and obtain under special assumptions on P a Strassen’s type version of the law of the iterated...

The k-ary n-cube is one of the most popular interconnection networks for parallel computing. This paper addresses the size of a largest connected component of a faulty k-ary n-cube. We prove that, in a k-ary n-cube (k ≥ 4 and n ≥ 2) with up to 4n – 2 faulty vertices, all fault-free vertices but at most two constitute a connected component. Moreover, this assertion holds if and only if the set o...

In this paper, the cross-correlation distribution between a p-ary m-sequence s(t) and its p + 1 distinct decimated sequences s(dt + l) is derived. For an odd prime p, an even integer n, and d = pk + 1 with gcd(n, k) = 1, there are p + 1 distinct decimated sequences s(dt + l), 0 ≤ l < p + 1, for a p-ary m-sequence s(t) of period pn − 1 because gcd(d, pn − 1) = p + 1. The maximum magnitude of the...

This paper presents three simple and efficient algorithms for generating, ranking and unranking t-ary trees in a lexicographic order. The simplest idea of encoding a t-ary tree with n nodes as a bit-string of length t*n is exploited to its full advantages. It is proved that the lexicographic order in the set of t-ary trees with n nodes is preserved in the set of bit-strings of length t*n, using...