Stable solution

The second application of the CFTI approach described here involves calculations of the free energy differences between conformers of the linear form of the opioid pentapeptide DPDPE in aqueous solution [9, 10]. DPDPE (Tyr-D-Pen-Gly-Phe-D-Pen, where D-Pen is the D isomer of /3,/3-dimethylcysteine) and other opioids are an interesting class of biologically active peptides which exhibit a strong correlation between conformation and affinity and selectivity for different receptors. The cyclic form of DPDPE contains a disulfide bond constraint, and is a highly specific S opioid [llj. Our simulations provide information on the cost of pre-organizing the linear peptide from its stable solution structure to a cyclic-like precursor for disulfide bond formation. Such... 

Development of weighted residual finite element schemes that can yield stable solutions for hyperbolic partial differential equations has been the subject of a considerable amount of research. The most successful outcome of these attempts is the development of the streamline upwinding technique by Brooks and Hughes (1982). The basic concept in the streamline upwinding is to modify the weighting function in the Galerkin scheme as... 

The comparison between the finite element and analytical solutions for a relatively small value of a - 1 is shown in Figure 2.25. As can be seen the standard Galerkin method has yielded an accurate and stable solution for the differential Equation (2.80). The accuracy of this solution is expected to improve even further with mesh refinement. As Figmre 2.26 shows using a = 10 a stable result can still be obtained, however using the present mesh of 10 elements, for larger values of this coefficient the numerical solution produced by the standard... 

The integrals in Equation (3.32) are found using a quadrature over the element domain The viscoelastic constitutive equations used in the described model are hyperbolic equations and to obtain numerically stable solutions the convection terms in Equation (3.32) are weighted using streamline upwinding as (inconsistent upwinding)... 

The outlined scheme is shown to yield stable solutions for non-zero Weissenberg number flows in a number of benchmark problems (Swarbric and Nassehi, 1992b). However, the extension of this scheme to more complex problems may involve modifications such as increasing of elemental subdivisions for stress calculations from 3 x 3 to 9 x 9 and/or the discretization of the stress field by biquadratic rather than bi-linear sub-elements. It should also be noted that satisfaction of the BB condition in viscoelastic flow simulations that use mixed formulations is not as clear as the case of purely viscous regimes. 

Pectins are readily soluble in water to give viscous stable solutions. However, the importance of pectin to industry, in particular the food industry, is the abihty of its solutions to form gels with sugar (ca 65% soHds) and acid or calcium ion under suitable conditions (51). 

Locust bean gum is not completely soluble in cold water it must be heated to 80°C and cooled to attain a stable solution that has high viscosity at low concentrations. The gum is compatible with other plant gums and the viscosity of solutions is not appreciably affected by pH or salts. 

Aromatic Radical Anions. Many aromatic hydrocarbons react with alkaU metals in polar aprotic solvents to form stable solutions of the corresponding radical anions as shown in equation 8 (3,20). These solutions can be analyzed by uv-visible spectroscopy and stored for further use. The unpaired electron is added to the lowest unoccupied molecular orbital of the aromatic hydrocarbon and a... 

SolubiHty of the three commercial polysulfones foUows the order PSF > PES > PPSF. At room temperature, all three of these polysulfones as weU as the vast majority of other aromatic sulfone-based polymers can be readily dissolved in a few highly polar solvents to form stable solutions. These solvents include NMP, DMAc, pyridine, and aniline. 1,1,2-Trichloroethane and 1,1,2,2-tetrachloroethane are also suitable solvents but are less desirable because of their potentially harmful health effects. PSF is also readily soluble in a host of less polar solvents by virtue of its lower solubiHty parameter. 

Titanium Phosphates. Titanium(III) phosphate [24704-65-2] (titanous phosphate) is a purple soHd, soluble ia dilute acid, giving relatively stable solutions. It can be prepared by adding a soluble phosphate to titanous chloride or sulfate solution and raising the pH until precipitation occurs. 

With a high heat removal rate, corresponding to an almost vertical line, as was the case in the experiments in the CSTR, the full heat generation curve could be measured. An intersection could be achieved between the heat generation curve and the very steep heat removal line at the point where the non-existent middle point was, but this was just one of the many stable solutions possible and not an unstable point. ... 

Cobalt naphthenate is generally supplied in solution in styrene, the solution commonly having a cobalt concentration of 0.5-1.0%. The cobalt solution is normally used in quantities of 0.5-4.0% based on the polyester. The accelerator solution is rather unstable as the styrene will tend to polymerise and thus although the accelerator may be metered from burettes, the latter will block up unless frequently cleaned. Cobalt naphthenate solutions in white spirit and dimethyl phthalate have proved unsatisfactory. In the first case dispersion is difficult and laminates remain highly coloured whilst with the latter inferior end-products are obtained and the solution is unstable. Stable solutions of cobalt octoate in dimethyl phthalate are possible and these are often preferred because they impart less colour to the laminate. 

Dihalodifluoromethanes react readily m OMF with activated cadmium or zinc powders to give a stable solution of trifluoromethylcadmium or -zinc,... 

Methylpyrrole gives only amorphous polymeric material with HCl or picric acid in ether.In contrast with the pyrroles just mentioned, 2,5- and 3,4-dimethyl-, 2-methyl-5-ethyl-, 3-methyl-4-ethyl-, and 2-methyl-4-ethyl-pyrrole do not form crystalline salts, either monomeric or dimeric, and 2,4-dimethyl- and 4-methyl-2-ethyl-pyrrole form only monomeric salts. The dialkylpyrroles in this latter group all dissolve in aqueous sulfuric acid to form relatively stable solutions (e.g., references 14 and 15). The various tri- and tetra-akylpyrroles are likewise soluble in aqueous mineral acid to form stable solutions, and either do not react with HCl or picric acid... 

The dried product is a reddish brown, amorphous solid presenting a glistening surface upon fracture. The dry product is somewhat hygroscopic and is freely soluble in water to give a stable solution. The following paragraph gives an alternative preparation. 

Chlorocyclopropene. on treatment with AgBF4, gives a precipitate of AgCl and a stable solution of a product that shows a single HNMR absorption at 11.04 8. What is a likely structure for the product, and what is its relation to Hiickel s rule ... 

Enolate ions are more useful than enols for two reasons. First, pure enols can t normally be isolated but are instead generated only as short-lived intermediates in low concentration. By contrast, stable solutions of pure enolate ions are easily prepared from most carbonyl compounds by reaction with a strong base. Second, enolate ions are more reactive than enols and undergo many reactions that enols don t. Whereas enols are neutral, enolate ions are negatively charged, making them much belter nucleophiles. As a result, enolate ions are more common than enols in both laboratory and biological chemistry. 

The chelatoborates LiB(C6H4 xFt 02)2 (x = 0, 1,4) are sufficiently soluble in various solvents and yield chemically stable solutions. Figure 14 shows the results of conductivity measurements at concentrations of about 1 mol L 1 in DME solvent, showing that a conductivity increase of about 440 percent at 35 °C and of about 240 percent at -45°C can be obtained with increasing fluorination of the salt. 

A stable solution is optimal if every man is at least as well off under it as under any other stable assignment. It can be shown by induction that the above procedure is optimal. 

Fig. 10.9 Diagram of steady states I and III are domains of existence of single solution, II is a domain of existence of three solutions (two stable and one unstable). Lines A and A2 correspond to two stable solutions. Reprinted from Yarin et al. (2002) with permission...

To solve Eq. 8 to obtain c(s) as a function of s requires Smin and Smax to be carefully chosen and adjusted accordingly inappropriate choice can be diagnosed by an increase of c(s) towards the limits of Smin or Smax- However, a stable solution can only be obtained if the contribution from diffusion broadening is dealt with. 

Certain solvents stabilize intermediates by strong solvation. The best known example is that of the electron itself which forms stable solutions in a number of solvents including liquid ammonia and hexamethyl-... 

Stable solutions at temperatures below — 150°C in SbFs—SO2 and FSO3H— SbFs—SO2, where the structure is static and hydride shifts are absent. Studies by H and NMR, as well as by laser Raman spectra and X-ray... 

In Chapter 3, it was mentioned that positive ions can form addition complexes with 7T systems. Since the initial step of electrophilic substitution involves attack by a positive ion on an aromatic ring, it has been suggested that such a complex, called a % complex (represented as 10), is formed first and then is converted to the arenium ion 11. Stable solutions of arenium ions or 7t complexes (e.g., with Br2, l2> picric... 

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