Optimization parameters

Fetisova Z G, Borisov A Y and Fok M V 1985 Analysis of structure-function correlations in light-harvesting photosynthetic antenna—structure optimization parameters J. Theoret. Biol. 112 41-75... 

In order to find optimal conditions for the soluble copper determination we examined the influence of electrolysis potential, electrolysis time, and the solution stirring rate on the accuracy and sensitivity of determination. We found that the optimal parameters for PSA determination of copper were electrolysis potential of -0.9 V vs. 3.5 mol/dm Ag/AgCl, electrolysis time of 300 s, and solution stirring rate of 4000 rpm. The soluble copper content in samples investigated in this study varied from 1.85 to 4.85 ppm. Very good correlation between the copper content determined by PSA and AAS indicated that PSA could be successfully applied for the soluble copper content determination in various dental materials. 

Empirical energy functions can fulfill the demands required by computational studies of biochemical and biophysical systems. The mathematical equations in empirical energy functions include relatively simple terms to describe the physical interactions that dictate the structure and dynamic properties of biological molecules. In addition, empirical force fields use atomistic models, in which atoms are the smallest particles in the system rather than the electrons and nuclei used in quantum mechanics. These two simplifications allow for the computational speed required to perform the required number of energy calculations on biomolecules in their environments to be attained, and, more important, via the use of properly optimized parameters in the mathematical models the required chemical accuracy can be achieved. The use of empirical energy functions was initially applied to small organic molecules, where it was referred to as molecular mechanics [4], and more recently to biological systems [2,3]. 

Proeess integration was developed initially as a means of optimizing the design of ehemieal and petroehemieal proeess plants. Proeess optimization is still only a pre-eonstruetion or pre-produetion exereise. This is surprising beeause many proeess plants are designed for bateh manufaeture of a range of produets, eaeh of whieh will require eontinuously ehanging optimization parameters. Proeess optimization and re-optimization on the fly ean enable eompanies to meet variations in market demand and maximize produetion effieieney and overall profitability. 

In the previous two chapters, equations were developed to provide the optimum column dimensions and operating conditions to achieve a particular separation in the minimum time for both packed columns and open tubular columns. In practice, the vast majority of LC separations are carried out on packed columns, whereas in GC, the greater part of all analyses are performed with open tubular columns. As a consequence, in this chapter the equations for packed LC columns will first be examined and the factors that have the major impact of each optimized parameter discussed. Subsequently open tubular GC columns will be considered in a similar manner. 

In order to obtain numeric values for the optimized parameters, it is necessary to define a given separation and the equipment by which the sample is to be analyzed. 

In a similar manner to the optimization of an LC column, in order to obtain numeric values for the optimized parameters, it is necessary to define a given separation and the equipment and materials by which the sample is to be analyzed. The data given in Table 2 are for a general GC separation using an open tubular column. 

The Optimized Parameters are the predicted bond lengths (named Rn), bond angles (An) and dihedral angles (Dn) for the optimized structure. The applicable atom numbers are in parentheses. Atoms in the molecule are numbered according to their order in the molecule specification section. These center numbers also appear in the Cartesian coordinates for the optimized strucmre expressed in the standard orientation which follows the listing of the optimized parameters. 

Our second example takes another member of the vinyl series, and considers the effect of replacing one of the hydrogens in ethylene with a fluorine. The fluoroethylene optimization converges at step 5. By looking at the optimized parameters for each job, we can compare the structures of the two molecules ... 

Typical normal-phase operations involved combinations of alcohols and hexane or heptane. In many cases, the addition of small amounts (< 0.1 %) of acid and/or base is necessary to improve peak efficiency and selectivity. Usually, the concentration of polar solvents such as alcohol determines the retention and selectivity (Fig. 2-18). Since flow rate has no impact on selectivity (see Fig. 2-11), the most productive flow rate was determined to be 2 mL miiT. Ethanol normally gives the best efficiency and resolution with reasonable back-pressures. It has been reported that halogenated solvents have also been used successfully on these stationary phases as well as acetonitrile, dioxane and methyl tert-butyl ether, or combinations of the these. The optimization parameters under three different mobile phase modes on glycopeptide CSPs are summarized in Table 2-7. 

Table 2-7. Summary of optimization parameters on glyeopeptide CSPs. ...

The optimal parameters of tantalum extraction with 2-octanol are as follows ... 

Optimal parameters for the extraction, washing and stripping of niobium were determined to be number of stages for all three processes - 4, volumetric ratios Vorg Vaqu are 1 1, 20 1 and 8 1, respectively. Additional fine purification of the extractant was recommended by stripping of tantalum and niobium remainders using a 0.5% wt. ammonia solution. This additional stripping leads to final concentrations of both tantalum and niobium in the extractant that are < 0.001 g/1. Table 62 shows the purity of niobium oxide prepared by the described method. 

Table 63. Optimal parameters of tantalum and niobium extraction with 2-octanol.

To determine the optimal parameters, traditional methods, such as conjugate gradient and simplex are often not adequate, because they tend to get trapped in local minima. To overcome this difficulty, higher-order methods, such as the genetic algorithm (GA) can be employed [31,32]. The GA is a general purpose functional minimization procedure that requires as input an evaluation, or test function to express how well a particular laser pulse achieves the target. Tests have shown that several thousand evaluations of the test function may be required to determine the parameters of the optimal fields [17]. This presents no difficulty in the simple, pure-state model discussed above. 

Old or current value for optimization parameter App. 6 Concentration of product P at the external surface of 10.8 the catalyst... 

A solution of such a problem is already known and so it remains only to write the final expressions for optimal parameters and in question. Having stipulated the conditions a = (3 = i] for A(Ai) =, A(Aa) =... 

Plumb AP, Rowe RC, York P, Doherty C. Effect of varying optimization parameters in optimization by guided evolutionary simulated annealing (GESA) using... 

We determined the reaction parameters using the optimal parameter estimation technique with the experimentally obtained copolymer yield and norbomene composition data. Based on the literature report, we assume that k = 3 [5]. Fig. 1 shows that the estimated rate constant values depend on the norbomene block length. Note that the reaction rate constant... 

Figure 3. Determination of the optimal parameters of PelZ activity. A pectate lyase activity in a reaction medium containing PGA 0.05%, CaCl2 0.2 mM and Tris-HCl 50 mM at various pH. B pectate lyase activity in a reaction medium containing PGA 0.05%, Tris-HCl 50 mM pH 8.5 and increasing concentrations of CaCl2- C pectate lyase activity in a reaction medium containing CaCl2 0.2 mM, Tris-HCl 50 mM pH 8.5 and as substrate either PGA 0.05% or pectins 0.05%, with different degrees of methylation (from Copenhagen Pectin).

The Veillard basis set [23] (1 ls,9p) has been used for A1 and Si, and the (1 ls,6p) basis of the same author has been retained for Mg. However, three p orbitals have been added to this last basis set, their exponents beeing calculated by downward extrapolation. The basis sets for Al, Si and Mg have been contracted in a triple-zeta type. For the hydrogen atom, the Dunning [24] triple-zeta basis set has been used. We have extended these basis sets by mean of a s-type bond function. We have optimized the exponents a and locations d of these eccentric polarization functions, and the internuclear distance R of each of the studied molecules. These optimized parameters are given in Table 3. 

Parameter estimates should not differ by orders of magnitude from those evaluated using well established methods of thermodynamics or known from the literature several rules concerning adsorption phenomena have been worked out by Boudart et al. (1967) the optimal parameter estimates should not differ very much from the initial guesses if the latter were determined in well designed separate dedicated experiments. 

Our task was to develop a feasible synthesis for diamino resorcinol. From several possibilities [1-4] the resorcinol and anihne were chosen as starting materials. The diazotated aniline was coupled with resorcinol among basic conditions giving 4,6-bisphenylazo resorcinol. Hydrogenation of the latter resulted in diamino resorcinol and aniline, which could be recycled (scheme 14.2). This chemistry is well known [5-13] therefore, the research work focused on finding the optimal parameters and catalyst and finally on elaborating a process for scale-up. 

The necessary conditions for k to be the optimal parameter values corresponding to a minimum of the augmented objective function SLo(k,a)) are given by Edgar and Himmelblau (1988) and Gill et al. (1981) and are briefly presented here. 

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