Convergent method

There are quite a number of ways to effectively change the equation in an SCF calculation. These include switching computation methods, using level shifting, and using forced convergence methods. 

Use a forced convergence method. Give the calculation an extra thousand iterations or more along with this. The wave function obtained by these methods should be tested to make sure it is a minimum and not just a stationary point. This is called a stability test. 

Conventional crude oils Conventional petroleum Convergence methods Conversion processes Convertal... 

The calculation of (DCFRR) usually requires a trial-and-error solution of Eq. (9-57), hut rapidly convergent methods are avadahle [N. H. Wild, Chem. Eng, 83, 15.3-154 (Apr. 12, 1976)]. For simplicity linear interpolation is often used. 

Dendrimers produced by divergent or convergent methods are nearly perfectly branched with great structural precision. However, the multistep synthesis of dendrimers can be expensive and time consuming. The treelike structure of dendrimers can be approached through a one-step synthetic methodology.31 The step-growth polymerization of ABx-type monomers, particularly AB2, results in a randomly branched macromolecule referred to as hyperbranch polymers. 

Continuous polymerization processes, 167 Convergent method, 8 COOH-terminated poly(ethylene adipate), 95-96... 

If we consider the limiting case where p=0 and q O, i.e., the case where there are no unknown parameters and only some of the initial states are to be estimated, the previously outlined procedure represents a quadratically convergent method for the solution of two-point boundary value problems. Obviously in this case, we need to compute only the sensitivity matrix P(t). It can be shown that under these conditions the Gauss-Newton method is a typical quadratically convergent "shooting method." As such it can be used to solve optimal control problems using the Boundary Condition Iteration approach (Kalogerakis, 1983). 

We became interested in a disconnection between the pyrrolidine and the aryl group (Approach D) as the most convergent method for enantioselective construction of 12 [10]. Although (-)-sparteine mediated enantioselective lithiation of N-Boc pyrrolidine 19 is well established by Beak [11], arylation of the resulting chiral... 

Two series of triazine-based dendrons were efficiently prepared by a convergent method and their properties studied <06OL1541>. A practical syntheis of [l,3,5]triazine dendritic... 

C. Ozawa, H. Hojo, Y. Nakahara, H. Katayama, K. Nabeshima, T. Akahane, and Y. Nakahara, Synthesis of glycopeptide dendrimer by a convergent method, Tetrahedron, 63 (2007) 9685-9690. 

In general, convergent methods produce the most nearly isomolecular dendrimers. This is because the convergent growth process allows purification at each step of the synthesis and therefore no cumulative effects of failed couplings are found [85, 89]. Appropriately purified convergent dendrimers are probably the most precise synthetic macromolecules that exist today. 

Perhaps the three most significant features [5] of the convergent method are ... 

Figure 5 Schematics of dendrimer growth by the divergent and the convergent methods...

For this reason, the simple convergence methods are usually quite adequate for dynamic simulations. 

This method is probably the most popular convergence method. It is somewhat more complicated since it requires the evaluation of a derivative. It also can lead to stability problems if the initial guess is poor and if the function is highly... 

Moreover, if the average yield per step decreases only slightly, let us say down to 85%, the overall yield of the convergent synthesis is still quite acceptable -37%-, but now the overall yield of the linear synthesis would be only 0.004%. It is clear, therefore, that for polypeptides of any complexity and for proteins, linear syntheses in solution are not practicable even if the yields of each step are kept high. However, solid-phase peptide synthesis can be quite efficient. This is because solid-phase synthesis represents an improvement in linear methodology which has, as yet, not found an equivalent in convergent methods [17]. 

Like the divergent approach, the convergent method also involves repetition of several basic chemical reactions. However, the reaction cycles are used to synthesize individual dendrons (dendrimer branches) instead of complete dendrimers. The dendrons have a protected focal point which can be activated in the last synthetic step and linked to two or more attachment points of a core molecule. Dendrimers synthesized by either method contain defects, but the problem is less pronounced for materials prepared by the convergent method. 

In the divergent method (Fig. 4), the molecule is assembled from the core to the periphery, while in the convergent method, the molecule is synthesized from the periphery to the core. In either method, the synthesis requires a stepwise process, attaching each layer to the previous one, purifying and then changing functional groups for the next stage of reaction. 

See Double-Reciprocal Plot Hanes Plot Direct Linear Plot Dixon Plot Dixon-Webb Plot Eadie-Hofstee Plot Substrate Concentration Range Frieden Protocol Fromm Protocol Point-of-Convergence Method Dal-ziel Phi Relationships Scatchard Plots Hill Plots... 

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