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Gaussian integration

Because of the work involved in solving large systems of simultaneous linear equations it is desirable that only a small number of us be computed. Thus the gaussian integration formulas are useful because of the economy they offer. See references on numerical solutions of integral equations. [Pg.478]

A more vexing issue is that one of the e in (3.37) equals zero. To see this, note that the function Xins(t) [where Xjns is the instanton solution to (3.34)] can be readily shown to satisfy (3.37) with o = 0. Since the instanton trajectory is closed, it can be considered to start arbitrarily from one of its points. It is this zero mode which is responsible for the time-shift invariance of the instanton solution. Therefore, the non-Gaussian integration over Cq is expected to be the integration over... [Pg.45]

A similar expansion can be written in the vicinity of Q = 0. Path integration amounts to the Gaussian integration over the Q , whereas the integration over the unstable mode Qq is understood as described in section 3.3. In that section we also justified the correction factor (f) = T /T = X l2n which should multiply the Im F result in order to reproduce the correct high-temperature behavior. Direct use of the Im F formula finally yields... [Pg.83]

INPUFF is a Gaussian integrated puff model which is captible of addressing the accidental reletisc of a substance over several minutes or of modeling the more typical continuous plume from a stack. [Pg.385]

A more detailed calculation requires performing the Gaussian integration over the disorder realizations close to the saddle-point configuration Eq. (3.25). One then finds the following expression for the average density of electron states per unit length,... [Pg.366]

The integral can be further simplified using the following property of Gaussian integrals for any matrix A and B ... [Pg.164]

An alternative set of functions used to build up atomic orbitals are Gaussian functions that have a radical dependence expf-ftr2). A linear combination of these functions gives a reasonable representation of an atomic orbital. The functions are used for computational expediency in ab initio calculations, because four-center Gaussian integrals can be reduced to two-center integrals, which are relatively easy to calculate on a computer (21). [Pg.3]

With our model the evaluation of PtJ(r n) is an exercise in doing Gaussian integrals. (See Appendix A 3.3.) Wo only note here the results, leaving the explicit calculation to Sect. 3.3. We find... [Pg.22]

This again amounts to a Gaussian integral which yields... [Pg.22]

The r.h.s. of Eqs. (A3.10), (A3.12) are well defined also foT nonintegelr d and can be taken to give a meaning to the Gaussian integral in nonintegcr dimensions. It will turn out to be important to define the theory for arbitrary... [Pg.30]

In the functional integral (A 5.12) we may shift y (r) as in normal Gaussian integrals. Substituting... [Pg.87]

The Gaussian integral over is easily carried out. Using Stirling s formula to evaluate Mnl after a little calculation we find an expression for the density of the free energy in the large volume limit ... [Pg.92]

The (VS)2 term was transformed by partial integration, assuming S(r) to vanish at the boundaries of the integration volume. Equation (A 7.21) has the form of a functional Gaussian integral yielding... [Pg.121]

The integral over q is a gaussian integral that yields to the final result... [Pg.444]

Integral Evaluation. We here confine our attention to the evaluation of integrals over Cartesian Gaussians (V7.) A seen in Table IV, the essentially unmodified FORTRAN source of the ATMOL3 Gaussian Integrals program compiled on the CRAY runs at approximately 6.2 times faster than the IBM 370/165 (circa. 2.4 times... [Pg.13]

Figure 2. Orthodox procedure for evaluating Gaussian integrals. Figure 2. Orthodox procedure for evaluating Gaussian integrals.
In the CRAY-1 a Gaussian integrals program may be driven at 35 Mflops, a large closed shell SCF with a sparse list of integrals or Supermatrix at 10 Mflops, while a smaller SCF with a non-sparse Supermatrix may be driven at 135 Mflops. [Pg.41]


See other pages where Gaussian integration is mentioned: [Pg.2662]    [Pg.153]    [Pg.396]    [Pg.401]    [Pg.402]    [Pg.409]    [Pg.52]    [Pg.303]    [Pg.244]    [Pg.73]    [Pg.490]    [Pg.260]    [Pg.76]    [Pg.92]    [Pg.92]    [Pg.95]    [Pg.30]    [Pg.30]    [Pg.40]    [Pg.91]    [Pg.275]    [Pg.52]    [Pg.72]    [Pg.128]    [Pg.236]    [Pg.40]    [Pg.261]    [Pg.122]    [Pg.166]   
See also in sourсe #XX -- [ Pg.261 ]

See also in sourсe #XX -- [ Pg.195 ]




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Gaussian Integral Program System

Gaussian functional integrals

Gaussian integral evaluations

Gaussian integrals program

Gaussian integration, harmonic oscillators

Gaussian numerical integration

Gaussian quadrature weighted integrals

Gaussian-quadrature integration

Harmonic oscillator Gaussian integrals

Integral Gaussian

Integral Gaussian

Integrals over Gaussian-Type Functions

Numerical integration Gaussian quadrature

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