Amplitude parameters

Final detennination of the structure was made by proposing a structural model with Cu sitting in threefold hollow sites and O atoms on atop sites with respect to the Cu atoms (Fig. 27.16). A program, FEFFIT, was used to analyze the data (Stem et al., 1995). This calculates the phase and amplitude parameters for the various backscatters. The EXAFS for the parallel polarization could be fitted six Cu-Cu interactions at a bond distance of 2.67 A and three Cu-Pt interactions at 2.6 A. For the perpendicular polarization, the data could be fitted one Cu-0 interaction at 1.96 A and three Cu-Pt interactions at 2.6 A. The Cu-Pt bond length is shorter than the sum of the metallic radii of Cu and Pt, which is 2.66 A. This indicates a Cu oxidation state different from zero, which agrees with the XANES results. 

The theoretical half amplitude parameters defining the width of the absorption band of each chromophore are not... 

Figure 3.8 Contour plot of the yield of Bi- ( Piy2) (percentage of Br as product) in the. photodissociation of IBr from an initial bound state in X Sq with v — 0, Jj = 1, M,- = 0. I Results arise from simultaneous (wl,co3) excitation (co3 = 3cO ) with to, = 6657.5 cm-1. Abscissa is labeled by the amplitude parameter s = x2/(l +x2) and ordinate by the relative phase parameter d3 — 3 0], equivalent to 3 — 3 j of the text. (Taken from Fig. 4, Ref. [63],) ...

The variable projection (VARPRO) method was devised by Golub and Pereyra.91 Subsequent authors have given less rigorous but more readable accounts.92 94 Essentially, this is a nonlinear method, but the amplitude parameters, which appear in a linear fashion, are treated separately with a subsequent reduction in the dimensionality of the least-squares fitting problem. 

VARPRO T N Y Y Y N Amplitude parameters appear linearly. Nonlinear least-squares fit Good... 

The amplitude parameter selection rules for the discrete and continuum exci-ton contributions were found concordant with those of the Eq transitions. 

The parameter t]0 is the limiting viscosity at low co. The reciprocal (t-1) of relaxation time % marks the midpoint co for the transition from a power-law exponent of 0 at low co to - 1 at high co. Interpretation of these low strain amplitude parameters in nonlinear fabrication shear flows is enabled by the Cox-Merz rule [43]. 

Add a column of noise, as well as space for a noise amplitude parameter na. Fill the column with Gaussian noise of zero mean and unit standard deviation. 

The spectral density function, J(co0), is modeled as a constant, a, plus a sum of Lorentzian terms, each characterized by an amplitude parameter, / , and a correlation time, rc ... 

Gor kov (G2), in 1957, and Malkus and Veronis (Ml), in 1958, succeeded in calculating the steady-state amplitude, as a function of the Rayleigh number, for a given cellular pattern and wavelength using the time-independent Boussinesq equations. A perturbation technique was employed in which the variables were expanded in terms of an amplitude parameter, e, such as... 

Kuo (K2) has recently obtained a solution to the nonlinear equations of cellular convection by expanding the dependent variables in series of orthogonal functions and by expanding the coefficients of these functions in a power series of an amplitude parameter. His solution also predicts a heat transfer rate proportional to the 5/4 power of the temperature difference. 

A surface can be characterized by many, many parameters. In fact it is easier to define a new parameter than to come with a thorough analysis of the usefulness of the already existing parameters. Parameters are defined in many ISO standards (see references). They can be separated in 2-D and 3-D parameters, and further separation is possible in amplitude parameters, spacing parameters, hybrid parameters, parameters derived from integrated probability density curves, and topological parameters. 

Ellipsometiy, which is the measurement of the change in the reflected light intensity and the polarization state of the elliptically polarized light, provides useful information on nucleation and growth processes, as well as the fllm thickness [11,190,282-291]. Two parameters are determined the relative amplitude parameter Q ) and the relative phase parameter (A) ... 

Two basic methods of EXAFS data analysis have been developed, one based primarily on theoretical principles [9] and the other based on transferable phase and amplitude parameters derived from the study of structurally defined model compounds [1, 13]. Both methods have been successfully applied to the... 

The more empirical approach suffers from the requirement for model compounds to develop the phase and amplitude parameters. Model systems for this type of EXAFS analysis are defined in a broader sense than is commonly used for other bioinorganic and biophysical methods. EXAFS models consist of compounds having the appropriate absorber/backscatterer atoms (e.g., metal/ligand or metal/metal) present at a known distance. For this reason, it becomes possible to determine metal-ligand bond distances in enzyme states for which direct structural analogs do not exist. 

Figure 2 Contour plot of the yield of I (i.e. percent of I as product) in the photodissociation of CH3 I from a linear superposition of a) [ 2 > and Eg >, b) Eg > and IE5 >. The abscissa is labelled by the relative amplitude parameter...

Two-dimensional (2-D) surface roughness parameters are often divided into three groups based on the characteristics of the surface that they quantify [1-3] (Table 1). (1) Amplitude parameters these are solely height descriptive, for examples R, R, R or Spacing parame-... 

Surface roughness is generally expressed by three types of conventional roughness parameters, namely amplitude parameters, spacing parameters and hybrid parameters. Amplitude parameters are the vertical characteristics of... 

The free surface pressure condition (2.18a) is (asymptotically) consistent with the Boussinesq limit process (3.1), only for a small free surface amplitude parameter 6, such that ... 

---