Originating in Allen’s analysis of temporal relations, the notion of composition table has become a key technique in providing an efficient inference mechanism for a wide class of theories in the field artificial intelligence. This paper is mainly about the consistency-based composition table (RCC8 CT) of the Region Connection Calculus (RCC) raised by Randell, Cui and Cohn. First we show each R...

in this paper, we present a fourth order method for computing simple roots of nonlinear equations by using suitable taylor and weight function approximation. the method is based on weerakoon-fernando method [s. weerakoon, g.i. fernando, a variant of newton's method with third-order convergence, appl. math. lett. 17 (2000) 87-93]. the method is optimal, as it needs three evaluations per ite...

A composition of birational maps given by Laurent polynomials need not be given by Laurent polynomials; however, sometimes—quite unexpectedly—it does. We suggest a unified treatment of this phenomenon, which covers a large class of applications. In particular, we settle in the affirmative a conjecture of D. Gale and R. Robinson on integrality of generalized Somos sequences, and prove the Lauren...

We prove that every 4-Pfaffian that is not Pfaffian essentially has a unique signature matrix. We also give a simple composition Theorem of 2r-Pfaffian graphs from r Pfaffian spanning subgraphs. We apply these results and exhibit a graph that is 6-Pfaffian but not 4-Pfaffian. This is a counter-example to a conjecture of Norine [5], which states that if a graph G is k-Pfaffian but not (k − 1)-Pf...

A vector composition of a vector l is a matrix A whose rows sum to l. We define a weighted vector composition as a vector composition in which the column values of A may appear in different colors. We study vector compositions from different viewpoints: (1) We show how they are related to sums of random vectors and (2) how they allow to derive formulas for partial derivatives of composite funct...

We develop a theory of parafree augmented algebras similar to the groups and explore some questions related Parafree Conjecture. provide an example finitely generated algebra infinite cohomological dimension. Motivated by this example, we prove version Composition-Diamond lemma for complete give sufficient condition be residually nilpotent in terms its relations.

Differential privacy [DMNS06] is a strong definition of database privacy that provides individuals in a database with the guarantee that any particular person’s information has very little effect on the output of any analysis of the overall database. In order for this type of analysis to be practical, it must simultaneously preserve privacy and utility, where utility refers to how well the anal...

A new type of decomposition of graphs – the operator decomposition connected with the classical notion of homogeneous set (or module) is introduced. The properties of this decomposition are described. Using this decomposition we prove the following. Let P and Q be two hereditary graph classes such that P is closed with respect to the operation of join and Q is closed with respect to the operati...