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Scientific Software Design: The Object-Oriented Way - Pagina 158
11 12 inline integrand::ptr_t operator*(integrand::ptr_t a, 13 real_t b) 14 { 15 integrand::ptr_t tmp = a->clone(); 16 *tmp *= b; 17 return tmp; 18 } 19 20 #endif //! _H_MODEL_OPS_ Figure 7.3(e):integrand.cpp 1 #include "integrand.h" 2 #include ...
Damian Rouson, Jim Xia, Xiaofeng Xu, 2011
2
Numerical Methods for Scientists and Engineers
Before attempting numerical evaluation of any integral, it is necessary to analyse the integrand to check for any singularity or near singularity, discontinuity, as well as possible sources of roundoff error in evaluating the integrand. It should be ...
3
Minimal Surfaces, Stratified Multivarifolds, and the ... - Pagina 248
Integrands. Definition 6.3.1 1. Let / be an arbitrary continuous function on GkM . For any multivarifold V of order k on M we set J.(V)=V'(l), 0<i<k. (3.13) The functional Jt denned by (3.13) (resp. the collection of functionals (J0, ... , Jk)) is called an ...
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Selected Papers of Abdus Salam: (with Commentary) - Pagina 10
V of D II and merely count the powers of the relevant 1 in the numerator and the denominator of the integrand. An n-fold integral, 1, will be absolutely convergent if, besides the final integration, the subintegrations over all of the smaller sets of ...
Abdus Salam, Ahmed Ali, 1994
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Variational Analysis - Pagina 670
(a) If f : T × IR” – IR is given by f(t, x) = g(t, F(t, x)) for a normal integrand g : T × IR” – IR and a Carathéodory mapping F : T × IR” – IR", then f is a normal integrand. (b) If f : T × IR” – IR is given by f(t, x) = 0(t, g(t, x)) for a normal integrand g : T × IR” ...
R. Tyrrell Rockafellar, Roger J.-B. Wets, 2009
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Mathematics for Physical Chemistry - Pagina 105
If this did not work, manipulate the integrand into a product of two factors and try the method of partial integration. 6. If all these things have failed, or if they could not be attempted, do a numerical approximation to the integral. This is discussed ...
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Symbolic Integration I: Transcendental Functions - Pagina 132
The only obstruction to a complete algorithm for Liouvillian integrands is the case where t is a nonelementary primitive over k: even though we can reduce the problem to an integrand in k, the problem becomes however to determine whether f ...
8
Computer Algebra Recipes for Mathematical Physics - Pagina 202
sin(theta):=(z-1/z)/(2*I); cos(theta):=(z+1/z)/2; sin(θ) := −1 2 I(z − 1 z ) cos(θ) := z2+ 1 2z Using the Integrand command to extract the integrand of J and using the fact > integrand:=simplify(Integrand(J)/(I*z)); 1 4 I (z2 − 1)2 integrand ...
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Current Topics in Quantum Field Theory Research - Pagina 146
We recall I'(p, m, 6,e)= I dx ln{m2 - x(l - x){92p20 - |p|2) - ie) (84) The analyticity properties of the integrand above, for a given p depend upon x and 9. For a real s = p2 < 4m2 and a 9 €[0,1], s' = p'2 < 4m2 also; and hence for all a; €[0,1] and all 9 ...
10
Random and Quasi-Random Point Sets - Pagina 155
The condition that the 3, tend to zero fast enough means that the integrand varies less and less with respect to ac, as j tends to infinity. 8.2 The Effective Dimension of an Integrand Figures 6.1–6.4 show the dependence of the discrepancy or Po ...
Peter Hellekalek, Gerhard Larcher, 2012
