To my knowledge all definitions of interval arithmetic start with real endpoints and prove properties. Then, for practical use, the definition is specialized to finitely many endpoints, where many of the mathematical properties are no longer valid. There seems no treatment how to choose this finite set of endpoints to preserve as many mathematical properties as possible. Here we define interval...

In the present document, we present some aspects of what a standard for the implementation of the elementary functions could be. We do not claim that we always suggest the right choices, or that we have thought about all relevant issues. The mere goal of this paper is to raise questions and to launch the discussion towards a standard. 1 Introductory discussion We take the opportunity of the cur...

Vlasov equations can be formally derived from $N$-body dynamics in the mean-field limit. In some suitable singular limits, they may themselves converge to fluid equations. Motivated by this heuristic, we introduce natural scalings under which incompressible Euler rigorously with repulsive Coulomb interaction. Our analysis is based on modulated energy methods of Brenier and [Comm. Partial Differ...

many e-commerce transactions via e-payment systems is carried out. the aim of this study is that the theory of structures, an empirical analysis about the importance and ranking key factors that may be on customer satisfaction in electronic payment systems affect the iranian banks.9 specific topics of the factors in e-payment systems, customer satisfaction and affect are more key, were selected...

We give the results of our search for the worst cases for correct rounding of themajor elementary functions in double precision floating-point arithmetic. These results allow the design of reasonably fast routines that will compute these functions with correct rounding, at least in some interval, for any of the four rounding modes specified by the IEEE-754 standard. They will also allow one to ...

Barry W. Boehm, Ph.D. Christopher M. Abts, M.S. Elizabeth K. Bailey, Ph.D. Center for Software Engineering Center for Software Engineering University of Southern California University of Southern California Software Metrics, Inc. 941 W. 37 Place, SAL 328 941 W. 37 Place, SAL 328 4345 High Ridge Road Los Angeles, CA 90089-0781 Los Angeles, CA 90089-0781 Haymarket, Virginia 20169 +1-213-740-5703 ...