In this paper we introduce new models of random graphs, arising from Latin squares which include random Cayley graphs as a special case. We investigate some properties of these graphs including their clique, independence and chromatic numbers, their expansion properties as well as their connectivity and Hamiltonicity. The results obtained are compared with other models of random graphs and seve...

Let A be a matrix over the integers, and let p be a positive integer. A submatrix B of A is zero-sum mod p if the sum of each row of B and the sum of each column of B is a multiple of p. Let M(p, k) denote the least integer m for which every square matrix of order at least m has a square submatrix of order k which is zero-sum mod p. In this paper we supply upper and lower bounds for M(p, k). In...

The information inequality has been shown to be an effective tool for providing lower bounds for the minimax risk. Bounds based on the chisquare distance can sometimes offer a considerable improvement especially when applied iteratively. This paper compares these two methods in four examples including the bounded normal mean problem as well as obervations from a Poisson distribution.

Geometries and geometric systems are not architecture, though architecture is geometric. Geometries and geometric systems, because of their autonomous nature, are generally understandable and can serve as the basis of communicable patterns expressed in architectural form, even though they are not necessarily at the base of man's structural understanding of environmental order. As a method of il...

The objective of the present work is to develop a numerical model to analyze melting solidification process considering the natural convection phenomena to an alloy metal in a square section. Physical medium is taken as incompressible Newtonian fluid with isotropy thermal properties where the heat is transferred by conduction and convection, including de thermal phase change phenomenon. The las...

The Chi square test is a statistical test which measures the association between two categorical variables. A working knowledge of tests of this nature are important for the chiropractor and osteopath in order to be able to critically appraise the literature.

Chess has evolved over a span of about 2300 years. The game was not always the “packaged game” that it is today. Its origins are traceable to Indian ashtapada boards commonly used among diceplaying games of that time. This game spread from culture to culture via several different means, periodically undergoing revision. Most chess players are aware of the radical reforms that shaped the game of...

An abelian square is the concatenation of two words that are anagrams of one another. A word of length n can contain at most Θ(n) distinct factors, and there exist words of length n containing Θ(n) distinct abelian-square factors, that is, distinct factors that are abelian squares. This motivates us to study infinite words such that the number of distinct abelian-square factors of length n grow...

Embedded exponentiation techniques have become a key concern for security and efficiency in hardware devices using public key cryptography. An exponentiation is basically a sequence of multiplications and squarings, but this sequence may reveal exponent bits to an attacker on an unprotected implementation. Although this subject has been covered for years, we present in this paper new exponentia...

The main topic of this contribution is the problem of counting square-free numbers not exceeding n. Before this work we were able to do it in time Õ( √ n). Here, the algorithm with time complexity Õ(n) and with memory complexity Õ(n) is presented. Additionally, a parallel version is shown, which achieves full scalability. As of now the highest computed value was for n = 10. Using our implementa...