Iterative strategies

This represents a set of nonlinear algebraic equations that can he solved with the Newton-Raphson method. However, in this case, a viable iterative strategy is to evaluate the transport coefficients at the last value and then solve... 

A new iterative strategy for enantio- and diastereoselective syntheses of all possible stereoisomers of 1,3-polyol arrays has been described by Shibasaki. This strategy relies on a highly catalyst-controlled epoxidation of a, 3-unsaturated morpholi-nyl amides promoted by the Sm-BIN0L-Ph3As=0 complex, followed by the con-... 

Due to the rising interest in supramolecular structures and nanoarchitectures, as well as their broad applicability, including the field of combinatorial chemistry, iterative strategies will gain more and more importance in preparative organic chemistry [60]. 

The advantage of iterative strategies is based on the specific preparation of well defined structures and structurally perfect spacers of nanometer scale. This stepwise approach yields monodisperse material in contrast to other statistical routes. The use of the same reactants and the conversion of the same functional groups facilitates the synthetic effort compared with non-iterative methods. 

Certain special problems related to decomposition are also considered. One is whether the process model is determinate, that is, does the model have a solution. Section III indicates how decomposition can help in validating determinacy. Another problem is that of convergence of the iterative strategy. If certain of the equations are too sensitive to the values of the variables being iterated, convergence may not be obtained. Therefore, the decomposition procedure must be constrained so as to choose as iterates only those variables for which the system of equations has suitable sensitivity, as discussed in Section VI. 

The resulting compounds were evaluated by determination of their IC50 values (the inhibitor concentration causing 50% inhibition of PNP) and by x-ray diffraction analysis using difference Fourier maps. This iterative strategy—modeling, synthesis, and structural analysis—led us to a number of highly potent compounds that tested well in whole cells and in animals. 

Scheme 8.13. Astruc et all46 511 have investigated iterative strategies focused on Fe-activated arene chemistry.

The palladium-catalyzed formation of diarylamines has been used in several contexts to form molecules with biological relevance. The ability to prepare haloarenes selectively by an ortho-metallation halogenation sequence allows for the selective delivery of an amino group to a substituted aromatic structure. Snieckus has used directed metallation to form aryl halides that were subsequently reacted with anilines to prepare diarylamines (Eq. 34)) [156]. Frost and Mendon a have reported an iterative strategy to prepare (by palladium-catalyzed chemistry) amides and sulfonamides that may act as peptidomimetics. Diarylamine units are constructed using the DPPF-ligated palladium catalysts, and the products are then acylated or sulfo-nated with 4-bromo benzoyl or arylsulfonyl chlorides [157]. 

Blake J, Litzi-Davis L, Evaluation of peptide libraries An iterative strategy to analyze the reactivity of peptide mixtures with antibodies, Bioconjugate Chem., 3 510-513, 1992. 

Because of their structural and conformational complexity, polypeptides, proteins, and their feedstock contaminants thus represent an especially challenging case for the development of reliable adsorption models. Iterative simulation approaches, involving the application of several different isothermal representations8,367 369 enable an efficient strategy to be developed in terms of computational time and cost. Utilizing these iterative strategies, more reliable values of the relevant adsorption parameters, such as q, Kd, or the mass transfer coefficients (the latter often lumped into an apparent axial dispersion coefficient), can be derived, enabling the model simulations to more closely approximate the physical reality of the actual adsorption process. 

The process of research in chemical systems is one of developing and testing different models for process behavior. Whether empirical or mechanistic models are involved, the discipline of statistics provides data-based tools for discrimination between competing possible models, parameter estimation, and model verification for use in this enterprise. In the case where empirical models are used, techniques associated with linear regression (linear least squares) are used, whereas in mechanistic modeling contexts nonlinear regression (nonlinear least squares) techniques most often are needed. In either case, the statistical tools are applied most fruitfully in iterative strategies. 

Our iteration strategy here is much like that in Appendix J. It consists of finding the temperature at which a 2nd catalyst bed s ... 

Other approaches to the bryostatins have also used enantio- or diastereoselective aldol reactions. An interesting iterative strategy for the synthesis of the Cj-Cg polyacetate region 134 has been disclosed where each aldol addition proceeds with excellent stereocontrol (99 1) under the catalytic influence of oxazaborolidine 135 (Scheme 9-42) [60J. Finally, a moderately selective, auxiliary controlled, acetate aldol reaction has been used for the introduction of the C3 stereocenter of the bryostatins giving adduct 136 (84% d.s) [61]. 

S. Yamago, T. Yamada, O. Hara, H. Ito, Y. Mino, and J. Yoshida, A new, iterative strategy of oligosaccharide synthesis based on highly reactive /J-bromoglycosides derived from selenoglycosides, Org. Lett., 3 (2001) 3867-3870. 

Alternatively, closed-form model representations require a modular simulation approach, where each closed-form model is computed using the internal solver of the software tool the model is implemented in. The algorithm sets the model inputs, performs control over the simulation, and retrieves the outputs of each model through the commonly defined interface of the closed-form model representation, independently of the specific implementation. These outputs are propagated to the inputs of downstream units, and the simulation continues until all the units are computed. If the flowsheet contains recycles, an iterative strategy is performed until convergence of the flowsheet variables in tear streams is achieved. 

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