Complexity parameter

The analytic behavior of the wave function in a complex parameter plane is in several instances traceable to a physics-based equation of restriction. ... 

Orders with quotation marks mean that the rate constants given by the authors are complex parameters depending on the add concentration. (In this case see corresponding reference.) The overall reaction order does not indude the order with respect to catalyst. 

The most general formulation is in terms of real parameters, as any complex paramet -ization can always expanded into real and imaginary parts, while the converse construction (complex parameto S from combination of real... 

The variational procedure for the states xi can be implemented in many different ways a very general formalism introduces complex parameters z(t). 

Classic parameter estimation techniques involve using experimental data to estimate all parameters at once. This allows an estimate of central tendency and a confidence interval for each parameter, but it also allows determination of a matrix of covariances between parameters. To determine parameters and confidence intervals at some level, the requirements for data increase more than proportionally with the number of parameters in the model. Above some number of parameters, simultaneous estimation becomes impractical, and the experiments required to generate the data become impossible or unethical. For models at this level of complexity parameters and covariances can be estimated for each subsection of the model. This assumes that the covariance between parameters in different subsections is zero. This is unsatisfactory to some practitioners, and this (and the complexity of such models and the difficulty and cost of building them) has been a criticism of highly parameterized PBPK and PBPD models. An alternate view assumes that decisions will be made that should be informed by as much information about the system as possible, that the assumption of zero covariance between parameters in differ-... 

S.C. Rutan and S.D. Brown, Pulsed photoacoustic spectroscopy and spectral deconvolution with the Kalman filter for determination of metal complexation parameters. Anal. Chem., 55 (1983) 1707-1710. 

Oral availability is a complex parameter that involves several chemical and physiological processes such as solubility, chemical stability, permeability and first-pass metabolism, to mention a few. All of these subprocesses depend on two different types of factor (i) interaction of the drug compound with certain macromolecules, such as the metabolism mediated by the cytochromes P450 family and (ii) interaction of the drug molecule with a certain chemical or biological environment, that will determine the solubility or the passive permeability. 

Those involving complex parameter estimation that is, the relationship between a variable and a parameter can only be determined by numerical integration of one or more than one ordinary differential equation... 

The experimental results are fitted to the model described in Section 3 with f, g, and h as free complex parameters. Since we are only interested in the relative values of the coefficients, we finally normalize h = 1. This fit has been shown to be unique within an overall phase factor. The best fit is obtained for / = —(0.055 0.004) — (0.098 0.004)/, g = —(0.378 0.013) — (0.300 0.008)/, h = 1. Note that the coefficients / and g, which are only allowed by chirality, have significant out-of-phase parts with respect to the dominant coefficient h that does not rely on chirality. Such phase differences between the chiral and achiral coefficients are the origin of the circular-difference response evident in Figure 9.20. 

To investigate these two questions, a parametric model of the Jacobian of human erythrocytes was constructed, based on the earlier explicit kinetic model of Schuster and Holzhiitter [119]. The model consists of 30 metabolites and 31 reactions, thus representing a metabolic network of reasonable complexity. Parameters and intervals were defined as described in Section VIII, with approximately 90 saturation parameters encoding the (unknown) dependencies on substrates and products and 10 additional saturation parameters encoding the (unknown) allosteric regulation. The metabolic state is described by the concentration and fluxes given in Ref. [119] for standard conditions and is consistent with thermodynamic constraints. 

Solving these minimization problems results in the estimated regression coefficients Bridge and lasso. respectively. The parameters AR and AL are complexity parameters and they control the amount of shrinkage. They have to be chosen to be >0, the larger the complexity parameter the more penalty is on the regression coefficients and the more they are shmnk towards zero. If the complexity parameter is zero,... 

Sometimes it is useful to parameterize the complex parameter p by polar and azimuthal angles 9 and 2ti) ... 

Humulene complexes with silver, 12 343, 346 Hund s rule, 13 162 HupU protein, 47 289 HupUV proteins, 47 190 Hush model, 41 274-280 class II mixed-valence complexes, parameters, 41 293... 

This chapter gives an overview of microbiological biosensors on respiratory basis for the measurement of the following environmentally relevant compounds inorganic N-com-pounds, heavy metals, organic xenobiotics and the estimation of sum parameters or so-called complex parameters such as BOD, ADOC, N-BOD, and the inhibition of nitrification. 

Without doubt, the favored field of application of microbial sensors is the measurement of complex effects like sum parameters. The difficulties involved in analyzing the numerous substances that are present in wastewater samples make sum parameters an indispensable part of the wastewater monitoring systems. Additionally, sum parameters often allow a better evaluation of the status of the environment than the determination of the concentration of individual substances. Examples for complex parameters are the sum of biodegradable or bioavailable compounds and toxicity (BOD, ADOC). 

If At 6 E is a function of a real or complex parameter t, we can define differentiation and integration with respect to t, usual rules of operations being applicable to them. Also regularity (analyticity) of At can be defined and Cauchy s, Taylor s and Laurent s theorems are extended to these regular functions. 

As for this section, cf. Rellich [3] and Kato [2]. In the latter paper the subject is treated from a much wider point of view, and a perturbation theory is developed for general closed operators depending on a complex parameter. 

The specific activity of a debris sample will depend upon the thermal history experienced by the sample, the time after fission when the melted or heated soil was exposed to the fission product vapors, the time-temperature history of the exposure, and a number of undefined and complex parameters. 

The coefficients Rk that generate a unitary transformation of 10>, 10k> are complex parameters... 

More recently, Palais [17] showed that the generic cases of soliton—the Korteweg de Vries equation (KdV), the nonlinear Schrodinger equation (NLS), the sine-Gordon equation (SGE)—can be given an SU(2) formulation. In each of the three cases considered below, V is a one-dimensional space that is embedded in the space of off-diagonal complex matrices, ( ) and in each case L(u) at- I u, where u is a potential, i. is a complex parameter, and a is the constant, diagonal, trace zero matrix... 

The point P can then be labeled by a single complex parameter (, = X + iY. Using the definition... 

The first step consists in obtaining the conductance G. For that we need fr(x) and 0(x) (x varies between 0 and L), parameterizing respectively the fermion distribution and the superconducting correlations. 6 = 9 + i(>2 is a complex parameter that satisfies the equation... 

The complex parameter a = a + ia2 satisfies the following linear differential equation ... 

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