Convergence domain

In the case of the quadratic equation, the convergence condition for the "thermodynamic branch" series is simply positive discriminant (Passare and Tsikh, 2004). For kinetic polynomial (48) this discriminant is always positive for feasible values of parameters (see Equation (49)). This explains the convergence pattern for this series, in which the addition of new terms extended the convergence domain. 

Figure 8 shows the convergence domain (75) (i.e. the rhomboid) and coefficients b2 — (k) 2)/(J ) and = (A fc3)/(fc ) as parametric function of parameter /2e[0,oo] at different values of /a (i.e. ovals). At lower values of parameter fs the whole loop is located within the convergence domain. This means that the series will converge for any/2e[0,oo]. At some value of/a, the ovals start intersecting the rhomboid boundary. In this case we can have (at least) two convergence intervals/2 e [0,/ ] and/2 e [f. ] separated by interval of non-convergence. 

Figure 9 shows the convergence domain as well as steady-state multiplicity domain on fi, h plane. We can see that steady-state multiplicity is not generally... 

Figure 8 A convergence domain (rhomboid) and coefficients of the kinetic polynomial (ovals). The ovals represent the coefficients b2 and b3 as parametric functions of parameter fj at different values of parameter Parameters f = 1.4, = 0.9 and = 0.4.

Figure 9 A convergence domain and steady-state multiplicity domain.

Figure 11 Dependencies from Figure 10 at = 0.23. Vertical dotted lines correspond to the boundaries of the convergence domain there is no convergence in the interval between these boundaries.

Figure 12 Dependencies from Figure 10 at f, = 0.24. There are four convergence boundaries in this case and three convergence domains (one of them is really narrow) separated by two non-convergence domains.

Ferraz-Mello, S. (1994), The convergence domain of the Laplacian expansion of the disturbing function. Cel. Mech. Dynam. Astron. 58, 37-52. 

Serine proteinases such as chymotrypsin and subtilisin catalyze the cleavage of peptide bonds. Four features essential for catalysis are present in the three-dimensional structures of all serine proteinases a catalytic triad, an oxyanion binding site, a substrate specificity pocket, and a nonspecific binding site for polypeptide substrates. These four features, in a very similar arrangement, are present in both chymotrypsin and subtilisin even though they are achieved in the two enzymes in completely different ways by quite different three-dimensional structures. Chymotrypsin is built up from two p-barrel domains, whereas the subtilisin structure is of the a/p type. These two enzymes provide an example of convergent evolution where completely different loop regions, attached to different framework structures, form similar active sites. 

BH3 domain) of the BH3-only proteins binds to other Bcl-2 family members thereby influencing their conformation. This interaction facilitates the release of cytochrome C and other mitochondrial proteins from the intermembrane space of mitochondria. Despite much effort the exact biochemical mechanism which governs this release is not yet fully understood. The release of cytochrome C facilitates the formation of the apoptosome, the second platform for apoptosis initiation besides the DISC. At the apoptosome which is also a multi-protein complex the initiator caspase-9 is activated. At this point the two pathways converge. 

Until now we spoke about convergence of a scheme and approximation on a fixed element u of the space However, if u belongs to the domain of a linear operator A from into B then Au = f, f B. Hence, u can be adopted as a solution to the equation... 

The proof of convergence of scheme (19) reduces to the estimation of a solution of problem (21) in terms of the approximation error. In the sequel we obtain such estimates using the maximum principle for domains of arbitrary shape and dimension. In an attempt to fill that gap, a non-equidistant grid... 

If the electron density partitioning results in subsystems without boundaries and with convergence properties which closely resemble the convergence properties of the complete system, then it is possible to avoid one of the conditions of the Holographic Electron Density Fragment Theorem , by generating fuzzy electron density fragments which do not have boundaries themselves, but then the actual subsystems considered cannot be confined to any finite domain D of the ordinary three-dimensional space E3. 

The discrete protonation states methods have been tested in pKa calculations for several small molecules and peptides, including succinic acid [4, 25], acetic acid [93], a heptapeptide derived from ovomucoid third domain [27], and decalysine [61], However, these methods have sofar been tested on only one protein, the hen egg lysozyme [16, 61, 71], While the method using explicit solvent for both MD and MC sampling did not give quantitative agreement with experiment due to convergence difficulty [16], the results using a GB model [71] and the mixed PB/explicit... 

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