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A new approach is presented in this paper for expending a rational fraction which is ratio of polynomials to linear combination of simpler terms of the same type. It is very useful to determine analytic solutions of linear time-invariant systems with higher-order multiple poles. Compared to traditional method, this approach is simple and efficient for both manual computation and computer programming...
0-1 programming was used widely. The implicit enumeration method for 0-1 programming is onerous. In the paper the implicit enumeration method for 0-1 programming was improved. The condition of element in the R sets was enacted over again. The pruning condition was clarified farther. In order to validate the improved arithmetic an example was given in the paper.
It is shown that floating point (or integer) multiplication can be reduced to the evalution of a very large class of functions including most of the nontrivial functions used in practice. That means that whenever any such function can be evaluated by boolean circuits of size S(n), then multiplication can be done with circuits of size O(S(n)). as well.
A finite precision rational number system provides for representation of a collection of rational numbers subject to limitations on numerator and denominator magnitude. In fixed-point and floatingpoint radix number systems only rationals of the form i/βj, where β is the base, can be realized. In contrast, a finite precision rational number system will allow representation of practically all simple...
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