Analytical representation

The corresponding states approach suggested by Pitzer et al. requires only the critical temperature and acentric factor of the compound. For a close approximation, an analytical representation of this method proposed by Reid et al. " for 0.6 [Pg.394]

I. P. Perdew and Y. Wang, Accurate and Simple Analytic Representation of the Electron Gas Correlation Energy, Phys. Rev. B, 45,13244 (1992). 

There are possible different forms of analytic representation of the t versus j dependence with an allowance made for non-Newtonian effects. To expose the decisive factors of this dependence an approach suggested in [19] deserves much attent-... 

R. W. G. Wyckoff, The Analytical Representation of the Results of the Theory of Space Groups Publications Carnegie Institution No. 318 (1922). 

Perdew, J.P. and Wang, Y. (1992) Accurate and simple analytic representation of the electron-gas correlation energy. Physical Review B - Condensed Matter, 45, 13244-13249. 

To conclude this section, it could be helpful to make a connection between the pictorial discussion we have just given and the type of computation that one can carry out in quantum chemistry. The double cone topology shown in Figure 9.3 can be represented mathematically by Eqs 9.3a and 9.3b. Qx, Qx, are the branching space coordinates. This equation is valid close to the apex of the cone. (A full discussion of the analytical representation of conical intersections can be found in references 9 and 10.)... 

For the analytical representation the signals have to be transformed from time functions into conventional measuring functions. These are characterized by analytical quantities on abscissa and ordinate axes where the values of them may be relativized in some cases (e.g. MS). Such a transformation of quantities is mostly carried out on the basis of instrument-internal adjustment and calibration. 

For the case that both Rouse and Zimm relaxation are present, the coherent dynamic structure factor is also available [40]. For completeness, its analytical representation is included in Table 1. 

Fig. 16. Three dimensional conformational map of cyclohexane. The representation is analogous to that of Fig. 15 the third (vertical) coordinate is the potential energy. The given calculated potential energy differences (kcal mole-1) of the minima and transition states are drawn to scale. The interconnecting curves are drawn qualitatively they are merely meant to indicate the absence of intermediate further minima and maxima. See ref. 106 for details of analytical representations of conformational maps of cyclohexane...

Analytic representation of dependence of albedo on daily average zenith angle... 

Up to this point, GIPF expressions have been formulated for only one type of biological activity - the inhibition of reverse transcriptase (RT), the enzyme that promotes the reverse transcription of genomic RNA into double-stranded DNA, a key step in the replication of the human immunodeficiency virus, HIV [82, 87]. Analytical representations were obtained for the anti-HIV potencies of three families of RT inhibitors the correlation coefficients are between 0.930 and 0.952. We are currently investigating the effects of applying the GIPF approach to certain portions of the molecules rather than their entireties. This might reveal the source of the activity, or alternatively, indicate it to be delocalized. 

The thermodynamic properties of single-component condensed phases are traditionally given in tabulated form in large data monographs. Separate tables are given for each solid phase as well as for the liquid and for the gas. In recent years analytical representations have been increasingly used to ease the implementation of the data in computations. These polynomial representations typically describe the thermodynamic properties above room temperature (or 200 K) only. 

We can see that the different positions along the chain show distinct temperature-dependent relaxation curves. To further analyze these relaxation functions, we must Fourier transform them to determine their spectral density, which is best done employing an analytic representation of the data that... 

W. Byers Brown, /. Chem. Phys., 87, 566 (1987). Analytical Representation of the Excess... 

Equations (59) and (62) ensure that the analytical representations of jly, have the correct transformation properties under the inversion operation E. Since the appropriate symmetry group for NH3, can be written as the direct... 

The parameterized, analytical representations of fi, ., fiy, fifi determined in the fitting are in a form suitable for the calculation of the vibronic transition moments V fi V") (a—O, +1), that enter into the expression for the line strength in equation (21). These matrix elements are computed in a manner analogous to that employed for the matrix elements of the potential energy function in Ref. [1]. 

In a more or less complex fashion, equations 1.97, 1.103, and 1.107 describe the response of the crystal, in terms of energy, to modification of the intensive variable P. We note that, in all cases, the differential forms combine internal energy and volume and are thus analytical representations of the potential diagram seen above for Ni2Si04 in figure 1.12. 

The analytical representation of closure temperature for a geochronological system (Dodson, 1973) is... 

Applying "kinetic polynomial" approach we found the analytical representation for the "thermodynamic branch" of the overall reaction rate of the complex reaction with no traditional assumptions on the rate limiting and "fast" equilibrium of steps. 

One might suspect that the discrepancy between the thermal rigidity factors of Eqs. (24) and (36) is due to inadequacies of the SACM treatment in general or of the pure harmonic oscillator model. However, after having corrected the analytical representation of the trajectory results through Eqs. (28)—(31), for x 11, Eq. (28) leads to... 

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