Model correlation

NONDESTRUCTIVE MAGNETIC METHID OF INSPECTION OF THE MECHANICAL PROPERTIES OF CAST STEELS. 1. CONSTRUCTION OF CORRELATION MODELS and II. PRACTICAL APPLICATION OF CORRELATION... 

For purposes of data correlation, model studies, and scale-up, it is useful to arrange variables into dimensionless groups. Table 6-7 lists many of the dimensionless groups commonly founa in fluid mechanics problems, along with their physical interpretations and areas of application. More extensive tabulations may oe found in Catchpole and Fulford (Ind. Eng. Chem., 58[3], 46-60 [1966]) and Fulford and Catchpole (Ind. Eng. Chem., 60[3], 71-78 [1968]). 

In his work Bicerano used only the zeroth and first order indices to develop his correlation model. However, various types of structural and correction parameters were used to correct for underestimation and/or overestimation of the contribution of several structural units. These corrections are cumbersome to use because of the many adjustable parameters that were utilized. Therefore, in this study a different approach was investi-... 

We assume that standard Coulomb-correlated models for luminescent polymers [11] properly described the intrachain electronic structure of m-LPPP. In this case intrachain photoexcitation generate singlet excitons with odd parity wavefunctions (Bu), which are responsible for the spontaneous and stimulated emission. Since the pump energy in our experiments is about 0.5 eV larger than the optical ran... 

Schubert K (1977) The Two-Correlations Model, a Valence Model for Metallic Phases. 33 139-177... 

Power Calculator provides sample size programs for various models, including normal, exponential, binomial, and correlation models http //home. stat.ucla.edu/ calculators/powercalc/... 

We are routinely screening compounds for ability to displace 1-125 DOI from frontal cortex homogenates. As far as the CNS stimulant effects, differentiating from psychostimulants, the present model we are using is substitution in amphetamine-trained rats, in drug discrimination. We have used synaptosomes and looked at their effect on dopamine release and reuptake. But basically they are correlative models. 

Halkier, A., Koch, H., Jprgensen, P., Christiansen, O., Nielsen, I. M. B., Helgaker, T., 1997, A Systematic Ab Initio Study of the Water Dimer in Hierarchies of Basis Sets and Correlation Models , Theor. Chem. Acc., 97, 150. 

A summary of the results of correlation models for smoke factor and smoke parameter is shown in Table X. For comparison purposes, correlation models for OSU and Cone calorimeter peak rates of heat release are also shown in Table X, together with one of the total heat release models. 

The logarithm for the capacity factor correlates well with known log P values obtained by the shake flask method. In practice, the k values are determined isocratically from 70 to 30% organic mobile phase and then extrapolated to 0%. Prior to determining the log P for an unknown compound, a set of structurally related molecules (standards) are analyzed to construct a correlation model between the logarithm of the retention factor and known log P values. The process is then repeated for the test compounds and their log P values determined from the mathematical relationship established for the standard compounds. 

In this paper we present a quantitative, correlative model for STDP based on simple, measured catalyst properties. 

It has also been shown that the selectivity features of para-selective catalysts can be readily understood from an interplay of catalytic reaction with mass transfer. This interaction is described by classical diffusion-reaction equations. Two catalyst properties, diffusion time and intrinsic activity, are sufficient to characterize the shape selectivity of a catalyst, both its primary product distribution and products at higher degrees of conversion. In the correlative model, the diffusion time used is that for o-xylene adsorption at... 

A paper by Kasprow et al.42 is important because it shows the realization that starting materials need to be analyzed on a routine basis just as with reaction products. Kasprow et al. discuss the correlation of fermentation yield with the yeast extract composition as seen by NIR. Using PLS for the correlations, models were constructed with a correlation of 0.996 and a standard error of 1.16 WSW. The authors used the models to predict yields, using different lots of yeast, and were quite satisfied with the results. 

According to this correlation model, in which the principles of steric control of asymmetric induction at carbon (40) are applied, the stereoselectivity of oxidation should depend on the balance between one transition state [Scheme 1(a)] and a more hindered transition state [Scheme 1(6)] in which the groups and R at sulfur face the moderately and least hindered regions of the peroxy acid, respectively. Based on this model and on the known absolute configuration of (+)-percamphoric acid and (+)-l-phenylperpropionic acid, the correct chirality at sulfur (+)-/ and (-)-5 was predicted for alkyl aryl sulfoxides, provided asymmetric oxidation is performed in chloroform or carbon tetrachloride solution. Although the correlation model for asymmetric oxidation of sulfides to sulfoxides is oversimplified and has been questioned by Mislow (41), it may be used in a tentative way for predicting the chirality at sulfur in simple sulfoxides. 

Many of the compositional parameters utilized as independent variables in the work cited above represented derived coal properties rather than fundamental chemical features. Further, variables traditionally used are often highly correlated with each other (for example volatile matter and hydrogen). As pointed out by Neavel (34) / this limits the utility of such parameters in correlational models. Instrumental techniques such as pyrolysis/mass spectrometry (35.36 C-n.m.r, FTIR, and... 

E. Other Correlation Models 1. Momentum-Exchange Model... 

This chapter reviews models based on quantum mechanics starting from the Schrodinger equation. Hartree-Fock models are addressed first, followed by models which account for electron correlation, with focus on density functional models, configuration interaction models and Moller-Plesset models. All-electron basis sets and pseudopotentials for use with Hartree-Fock and correlated models are described. Semi-empirical models are introduced next, followed by a discussion of models for solvation. 

Basis sets for use in practical Hartree-Fock, density functional, Moller-Plesset and configuration interaction calculations make use of Gaussian-type functions. Gaussian functions are closely related to exponential functions, which are of the form of exact solutions to the one-electron hydrogen atom, and comprise a polynomial in the Cartesian coordinates (x, y, z) followed by an exponential in r. Several series of Gaussian basis sets now have received widespread use and are thoroughly documented. A summary of all electron basis sets available in Spartan is provided in Table 3-1. Except for STO-3G and 3 -21G, any of these basis sets can be supplemented with additional polarization functions and/or with diffuse functions. It should be noted that minimal (STO-3G) and split-valence (3-2IG) basis sets, which lack polarization functions, are unsuitable for use with correlated models, in particular density functional, configuration interaction and Moller-Plesset models. Discussion is provided in Section II. 

For a recent thorough treatment of correlated models, see T. Helgaker, P. Jorgensen and J. Olsen, Molecular Electronic Structure Theory, Wiley, New York, 2000. 

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