The inequality holds because u' > 0 and the integrand
In terms of the integral in (1), the variables of the integrands
are the two components [phi]' and z' of the source point.
This inconsistency is resolved with the creation of a new, equally-spaced sample by laying a grid of equally-spaced values of t' and interpolate the integrand
values onto that grid before the use of the discrete Fourier transform method.
In all these cases a normalized symmetric function is expressed as a contour integral with integrand
being the product of elementary factors.
13)] represents integrand
that is integrated over the interval [0,t]
The results of CHSINT algorithm are conducted from 30 independent runs for each integrand
, while the results of other techniques are found in Burden (2001) and Wang (2004).
Further the integrands
in (3) and (4) are products of polynomial functions with rational coefficients.
Really, each a summand of an integrand
in (14) proves to be an analytical function in that half-plane where the integration contour is closed, according to the Jordan's lemma.
Expansion of the integrand
expression (7) by Besel function gives:
If the buyer bids, the first part of the integrand
is independent of the seller's valuation.
where the integrand
depends on the stress state and is numerically equal to the probability of destroying the element of unit volume (Kassenti, B.
Using Equations (3b) and (6), the integrand
K/y may be expressed as follows.