Showing papers on "Algebraic expression published in 1974"
CERN1
TL;DR: An elaborate set of substitutions and commands is provided which allows one to perform most of the commonly required algebraic manipulations, and many special operations which are used in high-energy physics calculations, are built in.
250 citations
Journal Article•
101 citations
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01 Jan 1974
TL;DR: The procedure to be used for constructing fault trees, the application of Boolean Algebra and the use of probability values in the final algebraic expressions are described.
Abstract: : The report describes the procedure to be used for constructing fault trees, the application of Boolean Algebra and the use of probability values in the final algebraic expressions. While not the only method which can be used, the fault tree technique is considered to be a very effective analytical tool in assessing system safety.
13 citations
TL;DR: The algebraic independence of three values of the exponential function has been proved in this paper for algebraic and algebraic numbers of degree 7 and α ≥ 0, 1, respectively, and the proof employs a method due to A. O. Gel'fond and N. I. Fel'dman.
Abstract: We prove general results concerning the algebraic independence of three values of the exponential function. Forβ algebraic and of degree 7 andα algebraic and ≠ 0, 1 there exist among the numbers αβ,...,\(\alpha ^{\beta ^6 } \) three which are algebraically independent. The proof employs a method due to A. O. Gel'fond and N. I. Fel'dman.
7 citations
6 citations
01 Jan 1974
01 May 1974
TL;DR: REDUCE 2 as mentioned in this paper is a FORMAC program which symbolically calculates the transfer function(s) of any linear-block-diagram output variable to any or all input variables.
Abstract: REDUCE 2 is reported as a FORMAC program which symbolically calculates the transfer function(s) of any linear-block-diagram output variable to any or all input variables. The program requires as input a set of algebraic expressions representing the block diagram, the desired transfer function(s), and a string of variables indicating the desired order of reduction. The solution is presented in the compact form of a set of nested functions (super G's). The program can handle systems as large as 600 equations and is intended as a tool for the analysis of complex control and dynamic systems. A companion FORTRAN program, EVAL 2, which numerically evaluates the solution set to obtain amplitude ratio and phase angle as functions of frequency is also presented.