Calculations and significant

The Crystal Field Splitting Parameter Dq Calculation and Significance... 

The programm structure just described speeds up the calculation and significantly reduces the computer capacity requirement with respect to the previous approach. At the moment, we are working on a procedure where the only matrices to be stored are the 1- and 2-RDM s which should greatly improve the applicability of the method. 

Application of the exact continuum analysis of dispersion forces requires significant calculations and the knowledge of the frequency spectmm of the material dielectric response over wavelengths X = 2irc/j/ around 10-10 nm. Because of these complications, it is common to assume that a primary absorption peak at one frequency in the ultraviolet, j/uv. dominates the dielectric spectrum of most materials. This leads to an expression for the dielectric response... 

This value of fexp is compared with the critical value for f(a, v), where the significance level is the same as that used in the ANOVA calculation, and the degrees of freedom is the same as that for the within-sample variance. Because we are interested in whether the larger of the two means is significantly greater than the other mean, the value of f(a, v) is that for a one-tail significance test. 

These multidimensional analyses do not necessarily predict overall generator performance or operating characteristics significantly more accurately than do the qua si-one-dimensional analyses, which are more economical to mn. Thus the latter are used for general channel design calculations, and the more sophisticated codes mainly to deal with more detailed aspects of channel operation. For example, current concentrations at electrode edges can be predicted by use of the more sophisticated codes. This allows appropriate electrode design for the condition. 

The effect of the specific values of the B j can be readily calculated for some simple laminates and can be calculated without significant difficulty for many more complex laminates. The influence of bending-extension coupling can be evaluated by use of the reduced bending stiffness approximation suggested by Ashton [7-20]. If you examine the matrix manipulations for the inversion of the force-strain-curvature and moment-strain-curvature relations (see Section 4.4), you will find a definition that relates to the reduced bending stiffness approximation. You will find that you could use as the bending stiffness of the entire structure,... 

Significant figures provide an indication of the precision with which a quantity is measured or known. The last digit represents, in a quantitative sense, some degree of doubt. For example, a measurement of 8.12 inches implies tliat Uie actual quantity is somewhere between 8.315 and 8.325 inches. This applies to calculated and measured quantihes quantities tliat are known exactly (e.g., pure integers) have an infinite number of significant figures. 

Both the MP2 Onsager calculation and the IPCM calculaton are in good agreement with experiment. The SCI-PCM and Hartree-Fock Onsager SCRF calculations perform significantly less well for this problem. ... 

Summarizing, in order to calculate rate and equilibrium constants, we need to calculate and AGq. This can be done if the geometry, energy and force constants are known for the reactant, TS and product. The translational and rotational contributions are trivial to calculate, while the vibrational frequencies require the ftill force constant matrix (i.e. all energy second derivatives), which may involve a significant computational effort. 

A preliminary study of the above equilibrium, using 4-31G//MNDO calculations and including thermal and solvation energies [82JPR(324)827], was significantly improved by subsequent calculations. Enchev increased the level of the calculations to 4-31G//STO-3G and considered four other... 

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