The interesting part of the sum is the finite part, which is shape-dependent.
2.
Integral equations containing Hadamard finite part integrals ( with unknown ) are termed hypersingular integral equations.
3.
In these cases the Cauchy principal value ( finite part ) of the integrals may be of interest; these are
4.
In particular, divergences show up as poles in the analytically continued past this pole, to obtain a finite part at " s " = 0.
5.
"They have no domestic markets and suddenly they're competing for a finite part of ( the market in ) Europe, the United States, Africa ."
6.
Not every cavity configuration necessarily leads to a finite part ( the lack of a pole at " s " = 0 ) or shape-independent infinite parts.
7.
A M�bius transformation may be applied to move " into the finite part of the complex plane if required, see example on Bessel differential equation below.
8.
In theoretical physics, "'Pauli Villars regularization "'( "'P V "') is a procedure that isolates divergent terms from finite parts in loop calculations in renormalize the theory.
9.
Using the principle just discussed in the last paragraph, we know that if the non-returning portion is finite, then a finite part of the non-returning portion must return.
10.
In other words, we just packaged an infinite amount of space into a finite part of our geometry . talk ) 07 : 03, 17 August 2010 ( UTC)
मोबाइल