Approximate Method

It is possible to make a method approximately size-extensive by adding a correction to the final energy. This has been most widely used for correcting CISD energies. This is a valuable technique because a simple energy correction formula is easier to work with than full Cl calculations, which require an immense amount of computational resources. The most widely used correction is the Davidson correction ... 

Because the reverberation room test method approximates many real-world conditions, it is used to derive sound-absorption coefficients for evaluating the effect of most actual appHcations of sound-absorbing treatments. Sound-absorption coefficients pubflshed in acoustical textbooks and by manufacturers of acoustical materials are almost exclusively from reverberation room tests, and this may be assumed unless specified otherwise. 

This method approximates/(x) by a parabola on each subintei val. This rule is generally more accurate than the trapezoidal rule. It is the most widely used integration formula. 

Many gradient methods approximate the energy surface at step by a quadratic expression in terms of the coordinate vector the total energy the gradient and the Hessian... 

Empirical methods approximate methods, in which the resistance to heat transfer is considered to control the rate of condensation, and the mass transfer resistance is neglected. Design methods have been published by Silver (1947), Bell and Ghaly... 

In the calculations of Briddon and Jones (1988), the BC site was found to be the stable site of hydrogen for the H—Be (H-acceptor) pair. The H—As and H—Ga separations were found to be 1.54 A and 1.77 A, respectively. The Aj frequency was computed to be 2083 cm-1, very close to the experimentally determined value of 2037 cm-1. An E-mode was also calculated to have a frequency of (383, 346) cm-1. (This pair of computed results should be degenerate differences are artifacts of method approximations.)... 

In this method approximately 19 samples of marine sediment were oven dried at 110°C then digested with nitric acid-perchloric acid and hydrofluoric acid-hydrochloric acid. The digested solution is made up to 50ml of an equal volume mixture of 6M hydrochloric acid and 2M nitric acid. 0.1ml or less of the digest was pipetted into the hydride generator, followed by 1ml 2M acetic acid, diluted to 100ml with double distilled water and reacted with sodium borohydride. 

Demiralp E, Cagin T, Goddard WA(1999) Morse stretch potential charge equilibrium force field for ceramics Application to the quartz-stishovite phase transition and to silica glass. Phys Rev l tt 82 1708-1711 Dewar MJS (1977) Ground states of molecules. The MNDO method. Approximations and parameters. J Am Chem Soc 99 4899-4907... 

Method Approximate useful range of J. K Principal measured variables Relation of measured variables to T Remarks... 

Since the exact solution of the Hartree-Fock equation for molecules also proved to be impossible, numerical methods approximating the solution of the Schrodinger s equation at the HF limit have been developed. For example, in the Roothan-Hall SCF method, each SCF orbital is expressed in terms of a linear combination of fixed orbitals or basis sets ((Pi). These orbitals are fixed in the sense that they are not allowed to vary as the SCF calculation proceeds. From n basis functions, new SCF orbitals are generated by... 

The 1/r solution is in fact just an Euler s method approximation to the integral for the PFTR, in which one approximates the integral as a summation. The calculation is not very accurate because we used a 0.2 moles/liter step size to keep the spreadsheet small, but it illustrates the method and the identity between Euler s method and a spreadsheet solution. 

It is common to move adult zebrafish into breeding tanks when collections of embryos are desired. This type of breeding appears to be more stressful to the fish, but in most cases, zebrafish can be bred by this method approximately once per week. 

Method Approximate time scale (sec) Reference to protein studies... 

Method Approximate practical range (per cent by mass) Limitations... 

Yonezawa et al. in their CNDO level method approximate the penetration integral vab = (B ii) be setting them equal to the negative of the corresponding repulsion integral, thus... 

To measure elastic and viscous properties which are characteristic of the material under consideration and independent of the nature of the apparatus employed, the applied stress and the resulting deformation must be uniform throughout the sample. Concentric cylinder and cone and plate methods approximate these requirements. For materials which are self-supporting, measurements on, for example, the shearing of rectangular samples are ideal. 

Method Approximate size range (pm) Capability of technique ... 

The methods, approximations and assumptions employed in constructing Figure 6, similar to those used for Figure 5, are described in some detail by Reistad (19, 20). it is clear (20,22, 23) that the Second Law efficiencies shown in Figure 6, especially those for the Residential-Commercial and for the Industrial sectors, are conservatively high. The more recent estimates for the overall tijj of the Industrial sector (2 , 22) are about 8%... 

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