Functional determinant

Fig. 6.2 Radial distribution function determined from a lOOps molecular dynamics simulation of liquid argon at a temperature of 100K and a density of 1.396gcm. ...

Since the composition of the unknown appears in each of the correction factors, it is necessary to make an initial estimate of the composition (taken as the measured lvalue normalized by the sum of all lvalues), predict new lvalues from the composition and the ZAF correction factors, and iterate, testing the measured lvalues and the calculated lvalues for convergence. A closely related procedure to the ZAF method is the so-called ())(pz) method, which uses an analytic description of the X-ray depth distribution function determined from experimental measurements to provide a basis for calculating matrix correction factors. 

Mac Beath G, Schreiber SL (2000) Printing proteins as microarrays for high throughput function determination. Science 289 1760-1763... 

Fig. 10. Comparison of the measured refractive indices for PET film with values calculated from the orientation functions determined from n.m.r. assuming transversely isotropic structural units. I, Experimental points predicted values. Reproduced from Polymer by permission of the publishers, Butterworth Co (Publishers) Ltd. (C)...

N.D. Lang, and A.R. Williams, Theory of local-work-function determination by photoemission from rate-gas adsorbates, Physics Review B 25(4), 2940-2942 (1982). 

Kemmel V, Taleb O, Andriamampandry C, et al Gamma-hydroxybutyrate receptor function determined stimulation of rubidium and calcium movements from NCB-20 neurons. Neuroscience 116 1021—1031,2003... 

The mapping (7) introduces the unknown interface shape explicitly into the equation set and fixes the boundary shapes. The shape function h(x,t) is viewed as an auxiliary function determined by an added condition at the melt/crystal interface. The Gibbs-Thomson condition is distinguished as this condition. This approach is similar to methods used for liquid/fluid interface problems that include interfacial tension (30) and preserves the inherent accuracy of the finite element approximation to the field equation (27)... 

Figure 24. Shown is the derivative of the first-order spherical Bessel function determining the effective decrease in the elastic field gradient produced by a phonon of wavelength k (x = kR).

Ifourth(fd, 2 Q) was multiplied with a window function and then converted to a frequency-domain spectrum via Fourier transformation. The window function determined the wavenumber resolution of the transformed spectrum. Figure 6.3c presents the spectrum transformed with a resolution of 6cm as the fwhm. Negative, symmetrically shaped bands are present at 534, 558, 594, 620, and 683 cm in the real part, together with dispersive shaped bands in the imaginary part at the corresponding wavenumbers. The band shapes indicate the phase of the fourth-order field c() to be n. Cosine-like coherence was generated in the five vibrational modes by an impulsive stimulated Raman transition resonant to an electronic excitation. 

PERIOD = 1 is the heating period using a steam mass flow rate of Fs. The mass balance on the steam jacket determines the steam density ps, which together with a steam table function determines the temperature of the jacket Tj. 

Conditional control using the control variables Z and X and the ISIM "COMP" comparater function determines the end of the free surface drying and the start of the diffusional drying. 

Ratio of polymeryl chains to total aluminum alkyl functionality determined by 2H NMR Determined using NMR gCopolymerizations with 40 g 1-hexene added... 

Another approach that provides a good desciption of the band structure of the host crystal is based on the Green s function determined for the perfect crystal. This function is then used to calculate changes induced by the presence of the defect (e.g., Rodriguez et al., 1979 Katayama-Yoshida and Shindo, 1983). The Green s function approach seems to be more cumbersome and less physically transparent that the supercell technique. 

Figure 4 Examples of classes of pharmaceutical compounds with amine functionality, determined by Ru(bpy)32+ ECL.

The relation between microbial diversity and soil functions is poorly understood because we cannot measure easily the microbial diversity, even if we can detect unculturable microorganisms by molecular techniques (Nannipieri et al. 2003). In addition, the present assays for measuring microbial functions determine the overall rate of entire metabolic processes, such as respiration, or specific enzyme activities, without identifying the active microbial species involved. The recent advances in RNA extraction from soil might permit us to determine active species in soil (Griffiths et al. 2000 Hurt et al. 2001). Further advances in understanding require us to determine the composition of microbial communities and microbial functions in microhabitats. 

The sign of the Gibbs function determines reaction spontaneity, so a reaction will occur if AG is negative and will not occur if AG is positive. When the reaction is poised at 7)cntlcai between spontaneity and non-spontaneity, the value of AG = 0. 

A short-term memory function determines how long a tabu restriction remains active. This can be expressed as the number of iterations a tabu condition is enforced once it is imposed. 

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