Computer optimization

Whether the optimum phase system is arrived at by a computer system, or by trial and error experiments (which are often carried out, even after computer optimization), the basic chromatographic data needed in column design will be... 

The first step in the analysis was to assess the effect of mass velocity for the 1000 psia data. By plotting and cross-plotting and finally by computer optimization it was found that 15 of the different geometries conformed very... 

The analysis given in Macbeth (M4) continues by assuming that the term dh effectively represents the cross-sectional geometry of the normal rod-bundle data. If this assumption is correct, then the general correlation [Eq. (18)], may be applied by representing A and C as functions of G and dh for a given pressure. It was found that simple power functions were adequate, and a correlation was obtained by computer optimization which predicted 97% of the vertical-upflow normal data (Nos. 6-15 inclusive in Table V) to within 12%. 

The result of the computer optimization on the 1000 psia normal data with vertical-upflow is as follows ... 

The computer-optimized y values obtained for a number of conditions are given in Table VI. It can be seen that the first condition assumes simple power functions only and a value for B strictly in compliance with Eq. (18). The rms error achieved is good, but marked improvements are obtained by relaxing the equations for A and B in stages, as shown, the final result giving a much better rms error. It was not necessary in the analysis to separate the data into low- and high-velocity regimes, as was the case for round-tube data, since the lowest mass velocity is not so low as to cause difficulty. 

A general methodology has been developed for the treatment of NMR data of polymer mixtures. The methodology is based on reaction probability models and computer optimization methods, resulting in a family of computer programs called MIXCO. The use of MIXCO programs enabled three components to be resolved from NMR tacticity data of fractionated polybutylene. 

Conceptually, therefore, if one has a good algorithm, computer optimization methods can be used to fit observed versus theoretical intensities to obtain wj and Pj. ... 

The COMPACT (computer-optimized molecular parametric analysis of chemical toxicity) procedure, developed by Lewis and co-workers [92], uses a form of discriminant analysis based on two descriptors, namely, molecular planarity and electronic activation energy (the difference between the energies of the highest occupied and lowest unoccupied molecular orbitals), which predict the potential of a compound to act as a substrate for one of the cytochromes P450. Lewis et al. [93] found 64% correct predictions for 100 compounds tested by the NTP for mutagenicity. 

Given an EoS, the objective of the parameter estimation problem is to compute optimal values for the interaction parameter vector, k, in a statistically correct and computationally efficient manner. Those values are expected to enhance the correlational ability of the EoS without compromising its ability to predict the correct phase behavior. 

The key to successful application of the experimental optimization techniques is based on adequate experimental design. A system based on this experimental design (see Table 4), but utilizing a special analog computer for analysis, was presented by Clax-ton [19] as the Firestone Computer/Optimizer. 

Convex hull formulations of MILPs and MINLPs lead to relaxed problems that have much tighter lower bounds. This leads to the examination of far fewer nodes in the branch and bound tree. See Grossmann and Lee, Comput. Optim. Applic. 26 83 (2003) for more details. 

In an effort to prepare bidentate boranes as colorimetric anion sensors, the incorporation of chromophoric boron moieties has also received attention. Reaction of lO-bromo-9-thia-lO-boranthracene 33 with dimesityl-1,8-naphthalenediylborate 26 affords diborane 34 (Scheme 14). This bright yellow diborane is soluble in chloroform, THF and pyridine. It has been fully characterized but its X-ray crystal structure could not be determined experimentally. Its structure was computationally optimized using DFT methods (B3LYP, 6-31 + G for the boron and sulfur... 

The sample average approximation method applied to stochastic routing problems A computational study. Computational Optimization e[ Applications, 24, 289. 

Since ca. 1985 in particular, a great deal of practical experience has been accumulated related to the characteristics of different RPC systems, their use in computer-optimized method development, and the physicochemical origin of the retention and kinetic phenomena that peptides manifest in these systems. Peptide retention in RPC is largely due to the docking of certain amino acid side-chain and main-chain functional groups of the peptide... 

Whether the optimum phase system is arrived at by a computer system, or by trial and error experiments (which are often carried out, even after computer optimization), the basic chromatographic data needed in column design will be identified. The phase system will define the separation ratio of the critical pair, the capacity ratio of the first eluted peak of the critical pair and the capacity ratio of the last eluted peak. It will also define the viscosity of the mobile phase and the diffusivity of the solute in the mobile phase. 

J.B. Schwartz, J.R. Flamholz, R.H. Press, Computer optimization of pharmaceutical formulations I General procedure. Journal of Pharmaceutical Sciences, 62(1973) 1165. 

Since each nucleus has three parameters, 8,

overall structure of the complex ab initio. However, uncertainty between alternative structures of substrates is capable of being resolved, as is uncertainty in alternative assignments of the NMR resonances, or uncertainty in the orientation or position of coordination of substrates of known structure. A computer optimization of agreement between observed shifts and coordination orientation (or whatever other uncertain features are to be investigated) is the normal procedure, as first demonstrated for the [Pr(dpm)3(bomeol)] adduct.546... 

The effect of this equation is that the ratios of the paramagnetic contributions to the relaxation rates of a set of, for example, H nuclei belonging to the same complex are determined by the lanthanide 3H distance only. Hence a similar type of computer optimization as for the paramagnetic shifts may be used to test compatibility with hypothetical structures which incorporate distance-dependent parameters such as the orientation or conformation of an organic ligand. 

Compute optimal t to minimize r3.Then compute new values... 

This is, however, an illustration of the importance of taking adsorbate deformations into account, and the usefulness of theoretical modelling for doing so. A computationally optimized 1 shifted adsorption geometry is shown in figure 5 (right), and this has an adsorbate orientation very close to the desired 45°, and not the simplistically expected 60°. Instead, the deformed 2 shift structure does not have a 45° orientation, but rather one of 35°. 

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