Issues in Vendor/Library Relations -- Numbers

Integer Relations Among Algebraic Numbers

A vector m = (mx , ... , mn) eZ"\ {0} is called an integer relation for the real numbers a,, ... , an , if X)0,"1, = 0 holds. We present an algorithm that, when given algebraic numbers ax , ... , an and a parametere , either finds an integer relation for a,,... , an or proves that no relation of Euclidean length shorter than 1/e exists. Each algebraic number is assumed to be given by its minima...

Semantic Relations: Issues and Proposals

Semantic relations are an important element in the construction of ontology-based linguistic resources and models of problem domains. Nevertheless, they remain under-specified. This is a pervasive problem in both Software Engineering and Artificial Intelligence. Thus, we find semantic links that can have multiple interpretations, abstractions that are not enough to represent the relation richne...

Research Issues in Orchestra Labor Relations by

Congruences and relations for r-Fishburn numbers

Recently Andrews and Sellers proved some amazing congruences for the Fishburn numbers. We extend their results to a more general sequence of numbers. As a result we prove a new congruence mod 23 for the Fishburn numbers and prove their conjectured mod 5 congruence for a related sequence. We also extend and prove some unpublished conjectures of Garthwaite and Rhoades.

Representability of binary relations through fuzzy numbers

Weanalyse the representability of different classes of binary relations on a set bymeans of suitable fuzzy numbers. In particular, we show that symmetric triangular fuzzy numbers can be considered as the best codomain to represent interval orders. We also pay attention to the representability of other classes of acyclic binary relations. © 2005 Elsevier B.V. All rights reserved.