Cauchy principal value

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Cauchy principal value

[kō·shē ¦prin·sə·pəl ¦val·yü]
(mathematics)
Also known as principal value.
The Cauchy principal value of provided the limit exists.
If a function ƒ is bounded on an interval (a,b) except in the neighborhood of a point c, the Cauchy principal value of provided the limit exists.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
If we are not turning to an all-powerful deity as a higher authority, he says, we must "acknowledge that we are essentially dependent on--and answerable to--other persons who cannot be mastered or controlled, since we are all free, finite beings." It's this last part, the finite part, that I found most interesting in his thesis.
The finite part of (21) and (22) is equal to [delta]m/m at E = 10m in the relevant temperature range.
The cross on the integral of (15) and (16) means the hypersingular, and it must be interpreted as a Hadamard finite part integral [31, 33, 34].
The technique of neglecting appropriately defined infinite quantities was devised by Hadamard, and the resulting finite value extracted from a divergent integral is referred to as the Hadamard finite part. In fact, his method can be regarded as a particular application of the neutrix calculus developed by van der Corput (see [1]).
This underlines a major advantage of deep drawing TWBs, namely the significant reduction of the finite part's weight, by replacing the monoblock blank with a constant thickness of 1.5 mm (which would provide the required strength) with a TWB that allows using the 1.5 mm sheet only in the most stressed area.
Using this capability in conjunction with advanced probing routines eliminates the need for time-consuming finite part alignment, resulting in a substantial reduction in part set-up time.
"They have no domestic markets and suddenly they're competing for a finite part of the market in Europe, the United States, Africa."
This is what director of rugby John White calls the finite part of their season.
This method distributes the cross- sections of elements of the structure into several finite parts and analyzes them individually on work-energy principle.
Ross provides the following general definitions of the latter terms: "An organic relation describes a set of objects integrated in such a way that they are all bound together by a common teleology, each animated by the desire to take part in a whole that has a continuity that transcends that of the finite parts. A mechanism, by contrast, is a set of objects organized by external force, atomistic individuals that only cohere together in order to preserve themselves, while remaining indifferent to the broader context of their relations" (p.
He mentioned that whatever nature divides stays in it endlessly in actuality, and that bodies are composed of compounded finite parts. If otherwise, infinity would exist in a time limited in actuality, which is impossible.
Also the finite parts of the radiative corrections are fixed.