INDEX time-dependent

Multichannel time-resolved spectral data are best analysed in a global fashion using nonlinear least squares algoritlims, e.g., a simplex search, to fit multiple first order processes to all wavelengtli data simultaneously. The goal in tliis case is to find tire time-dependent spectral contributions of all reactant, intennediate and final product species present. In matrix fonn tliis is A(X, t) = BC, where A is tire data matrix, rows indexed by wavelengtli and columns by time, B contains spectra as columns and C contains time-dependent concentrations of all species arranged in rows. 

Fig. 14. Time dependence of key indexes during en2ymatic hydrolysis (a) degree of hydrolysis (DH) (b) peptide chain length (PCL) (soluble peptides) (c)...

Table 26 Transportation lane index sets depending on transportation time...

Pharmacodynamic tolerance, probably on the basis of down-regulation of receptors, develops more rapidly to the effects of barbiturates on mood and sedation than to the anticonvulsant and lethal action. This results in a marked decrease in therapeutic index and the ratio of LD50 and ED50 can approach 1. Furthermore, barbiturates induce P450 enzymes and thus increase their own metabolism resulting in time dependent pharmacokinetic behavior. 

Accordingly pragmatic individuals have long been interested in the evolution of a universal explanation for fluid behavior of all kinds and the establishment of quantitative relationships with which to correlate and extrapolate the flow curves of all fluids, Newtonian and non-Newtonian alike. Progress toward the former of these two objectives appears to be too limited to warrant presentation at this stage, but recently a method has been proposed (F2, Mil, W4) by means of which the flow behavior of all fluids which are not time dependent may be compared. Two indexes are necessary to accomplish this ... 

In general, the time dependence of the perturbation with index n is... 

The relaxation of a local mode is characterized by the time-dependent anomalous correlations the rate of the relaxation is expressed through the non-stationary displacement correlation function. The non-linear integral equations for this function has been derived and solved numerically. In the physical meaning, the equation is the self-consistency condition of the time-dependent phonon subsystem. We found that the relaxation rate exhibits a critical behavior it is sharply increased near a specific (critical) value(s) of the interaction the corresponding dependence is characterized by the critical index k — 1, where k is the number of the created phonons. In the close vicinity of the critical point(s) the rate attains a very high value comparable to the frequency of phonons. 

Comparison between Experimental Results and Model Predictions. As will be shown later, the important parameter e which represents the mechanism of radical entry into the micelles and particles in the water phase does not affect the steady-state values of monomer conversion and the number of polymer particles when the first reactor is operated at comparatively shorter or longer mean residence times, while the transient kinetic behavior at the start of polymerization or the steady-state values of monomer conversion and particle number at intermediate value of mean residence time depend on the form of e. However, the form of e influences significantly the polydispersity index M /M of the polymers produced at steady state. It is, therefore, preferable to determine the form of e from the examination of the experimental values of Mw/Mn The effect of radical capture mechanism on the value of M /M can be predicted theoretically as shown in Table II, provided that the polymers produced by chain transfer reaction to monomer molecules can be neglected compared to those formed by mutual termination. Degraff and Poehlein(2) reported that experimental values of M /M were between 2 and 3, rather close to 2, as shown in Figure 2. Comparing their experimental values with the theoretical values in Table II, it seems that the radicals in the water phase are not captured in proportion to the surface area of a micelle and a particle but are captured rather in proportion to the first power of the diameters of a micelle and a particle or less than the first power. This indicates that the form of e would be Case A or Case B. In this discussion, therefore, Case A will be used as the form of e for simplicity. 

The time-dependent wavepacket constructed in Section 4.1 is not the wavepacket that a laser with finite duration creates in the excited electronic state. It represents the wavepacket created by a pulse with infinitely narrow width in time. In order to construct the real wavefunction of the molecular system we must go back to Section 2.1. For simplicity of presentation, let us consider a diatomic molecule with internuclear separation R. We assume that the excitation takes place from the electronic ground state (index 0) to a bound upper state (index 1). The extension to a dissociative state, several coupled excited states, or several degrees of freedom is formally straightforward. 

Fig. E5.1 Parameter reflecting thermal degradation of unplasticized PVC, Geon 101 EP-F24, as indicated by the time dependence of the consistency index m of the Power Law fluid model. [Reprinted by permission from E. A. Collins, B. F. Goodrich Chemical Co., Avon Lake, Ohio. Paper presented at the 1965 Society of Plastics Engineers Annual National Technical Conference, March 1966.]...

The relationship between the depolarized time-dependent transmitted intensity l(t) and the refractive index difference in two orthogonal directions x and y, in which one is in the direction of the applied electric field and both are perpendicular to the direction of propagation of the incident light, is given by (2)... 

Here the index s runs over the relevant saddle points, those that are visited by an appropriate deformation of the real integration contour, which is the real five-dimensional (t,t, k) space, to complex values, and Sp(t,t, k) s denotes the five-dimensional matrix of the second derivatives of the action (4.5) with respect to t,t and fc, evaluated at the saddle points. The time dependence of the form factors (4.6) and (4.7) is considered as slow, unless stated otherwise (see Sect. 4.5 and [27]). 

---