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...

a modular $k$-coloring, $kge 2,$ of a graph $g$ without isolated vertices is a coloring of the vertices of $g$ with the elements in $mathbb{z}_k$ having the property that for every two adjacent vertices of $g,$ the sums of the colors of the neighbors are different in $mathbb{z}_k.$ the minimum $k$ for which $g$ has a modular $k-$coloring is the modular chromatic number of $g.$ except for some s...

in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i & ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i & ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

We report a new illusion of elasticity in a rigid surface. A square frame is presented behind a concentric occluding cross. When the two surfaces are rotated rigidly, the square frame appears “rubbery”, that is, it appears to contract or expand during the rotation. The rubber square illusion is related to a number of other illusory phenomena involving motion and surface stratification. It is ge...