A method to approximate derivatives of real functions using complex variables which avoids the subtractive cancellation errors inherent in the classical derivative approximations is described. Numerical examples illustrating the power of the approximation are presented. 1. Overview. A standard method to approximate the derivative of a real valued function F… (More)
Algebraic conditions and algorithmic procedures are given to determine whether an mn rectangular connguration of switches can be transformed so that all switches are in the oo position, regardless of initial connguration. However, when any switch is toggled, it and its rectilinearly adjacent neighbors change state. Using linear algebra, a nite eld… (More)
BACKGROUND Alzheimer's disease (AD) has been associated with both oxidative stress and excessive glutamate activity. A clinical trial was designed to compare the effectiveness of (i) alpha-tocopherol, a vitamin E antioxidant; (ii) memantine (Namenda), an N-methyl-D-aspartate antagonist; (iii) their combination; and (iv) placebo in delaying clinical… (More)
ACKNOWLEDGEMENT: This effort has been sponsored by Defense Advance Research Projects Agency (DARPA), under contract No. MDA972-91-J-1022 for DARPA Initiative in Concurrent Engineering (DICE).
We dedicate this paper (and the rhombus) to Professor Henry Gould on the occasion of his 70th birthday and in appreciation of his work on recurrences such as the rhombus Abstract Pascal's rhombus is a variation of Pascal's triangle in which values are computed as the sum of four terms, rather than two. It is shown that the limiting ratio of the number of… (More)
A new international standard, called STEP, is in final draft form. STEP defines a neutral computer readable format for product data exchange, sharing and archiving. STEP deals with all product data throughout the product's life-cycle. In the electronics domain, STEP seeks to harmonize and generalize many of the existing data exchange standards. The STEP… (More)