Added accuracy

The main disadvantage of this algorithm is that it is computationally a little more expensive than the simpler Verlet or leap-frog algorithms (though the added accuracy often outweighs this slight overhead). 

Li and Wang described a convenient linear plotting protocol that permits one to evaluate stability constants for the formation of reversible metal hgand complexes. Added accuracy is achieved over classical approaches, because their generalized equations quantitatively account for side-reactions of metal ion and/or ligand as well as the difference between the total and free ligand concentration. 

A subsequent, more complete treatment of the band-structure problem for the lanthanides by Skriver (1983b, 1985) confirmed the essence of the Duthie-Pettifor (Duthie and Pettifor 1977) theory, at the same time adding accuracy to the computed structural energy differences. By using full LMTO calculations Skriver was also able to obtain the correct partial occupation numbers - the same as those subsequently calculated by Eriksson et al. (1990c), and shown in fig. 15. By calculating the partial occupation numbers at the pressures required to induce the structural transitions in La, Sm and Gd, Skriver (1983b) was able to associate = 2.0, 1.85 and 1.75 with the dhcp->fcc, Sm-type -> dhep and hep -> Sm-type transition, respectively. Then, calculation of the partial d occupation numbers as function of the pressure, led to fig. 30, which predicts the pressure-induced transitions for the lanthanides. 

The potential fiinctions for the mteractions between pairs of rare-gas atoms are known to a high degree of accuracy [125]. Flowever, many of them use ad hoc fiinctional fonns parametrized to give the best possible fit to a wide range of experimental data. They will not be considered because it is more instmctive to consider representations that are more finnly rooted in theory and could be used for a wide range of interactions with confidence. 

The simplest use of an NMR spectnim, as with many other branches of spectroscopy, is for quantitative analysis. Furthennore, in NMR all nuclei of a given type have the same transition probability, so that their resonances may be readily compared. The area underneath each isolated peak in an NMR spectnim is proportional to the number of nuclei giving rise to that peak alone. It may be measured to 1% accuracy by digital integration of the NMR spectnim, followed by comparison with the area of a peak from an added standard. 

Sodium Hypochi ite. zM- This may be prepared with sufficient accuracy by dissolving 100 g. of NaOH in 200 ml. of water in a large beaker, cooling the solution, and then adding about 500 g. of crushed ice. Now counterpoise the beaker on a rough set of scales, and pass in chlorine from a cylinder until an increase in weight of 72 g. is obtained. Make up the solution to i litre and stir well. The solution must be kept in a cool dark place, but even then slowly decomposes. 

G3. G3 theory (Curtiss et al., 1998) is very similar to G2 except that certain refinements have been added to improve accuracy and computational efficiency. The Pople group has devised a new basis function for the largest calculation called, appropriately enough, GSlarge. 

Correlation can be added as a perturbation from the Hartree-Fock wave function. This is called Moller-Plesset perturbation theory. In mapping the HF wave function onto a perturbation theory formulation, HF becomes a hrst-order perturbation. Thus, a minimal amount of correlation is added by using the second-order MP2 method. Third-order (MP3) and fourth-order (MP4) calculations are also common. The accuracy of an MP4 calculation is roughly equivalent to the accuracy of a CISD calculation. MP5 and higher calculations are seldom done due to the high computational cost (A time complexity or worse). 

Interpolation is facilitated and accuracy is maximized if the % transmittance is between 1 and 10, by multiplying its value by 10, finding the absorbance corresponding to the result, and adding 1. For example, to find the absorbance corresponding to 8.45% transmittance, note that 84.5% transmittance corresponds to an absorbance of 0.0731, so that 8.45% transmittance corresponds to an absorbance of 1.0731. For % transmittance values between 0.1 and 1, multiply by 100, find the absorbance corresponding to the result, and add 2. 

Internal standards at a known concentration are added to the sample after its preparation but prior to analysis to check for GC retention-time accuracy and response stability. If the internal standard responses are in error by more than a factor of two, the analysis must be stopped and the initial calibration repeated. Only if all the criteria have been met can sample analysis begin. 

Procedures for determining drilling fluid properties ate available (21,22,166). Tests and test methods ate constantly reviewed by API committees to ensure acceptable accuracy when performed under field conditions as well as in the laboratory. API pubHcations ate tepubUshed as new tests ate added or existing tests ate modified. 

Virtuady ad new pdot plants wid be computer controded and heavdy automated due to the high cost of operating labor, need for high accuracy and repeatabdity, and ease of data gathering and work-up. Stand-alone computer and programmable logic controder systems wid continue to dominate the market because of their low cost and ease of use. 

Proofing materials have many of the same sources of variability as film, plus the added problem of registering, ie, accurately overlaying, the different colored layers. The printing plate must be exposed precisely to hold all that is discernible in the films. The accuracy of the exposure is critical because the plate must retain all the information contained in the films for faithful reproduction on the press. 

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