Separating Cases

The choice of room airflow pattern and air supply method is subject to study in each separate case. Table 8.9 presents, however, some guidelines for air distribution methods most commonly applied for various cases. 

Large generator designs incorporate two or three separate casings. The turbine is broken down into three areas high-pressure (HP)... 

Numerical calculations were carried out in order to test the whole numerical algorithm and accuracy of the rate calculation. The potential system employed is a nonlinearly transformed model of the separable case [31]. That is... 

For the case of Zone-Melting to form a single crystal, we can distinguish between two separate cases, i.e.- horizontal and vertical zone melting. This is shown as follows ... 

K. Note that we have assumed that I is a cation impurity in the crystal, MX. We can differentiate between 2 separate cases, as shown in the following diagram, given as 6.8.4. on the next page. 

When an acid in solution is exactly neutralized with a base the resulting solution corresponds to a solution of the salt of the acid-base pair. This is a situation which frequently arises in analytical procedures and the calculation of the exact pH of such a solution may be of considerable importance. The neutralization point or end point in an acid-base titration is a particular example (Chapter 5). Salts may in all cases be regarded as strong electrolytes so that a salt AB derived from acid AH and base B will dissociate completely in solution. If the acid and base are strong, no further reaction is likely and the solution pH remains unaffected by the salt. However if either or both acid and base are weak a more complex situation will develop. It is convenient to consider three separate cases, (a) weak acid-strong base, (b) strong acid-weak base and (c) weak acid-weak base. 

A log-log plot using K Km, /ccat and Acuncat data from the 18 separate cases of antibody catalysis exhibited a linear, albeit scattered, correlation over four orders of magnitude and with a gradient of 0.86 (Fig. 16).4 Considering the assumptions made, this value is sufficiently close to unity to suggest that the antibodies do stabilize the transition state for their respective reactions. However, even the highest A cat/A uncat value of 106 in this series (Tramontano et al., 1988) barely compares with enhancement ratios seen for weaker enzyme catalysts (Lienhard, 1973). 

Equation (111) is reported to be applicable up to flow rates of about 0.05 cm3/sec, for liquids having viscosity up to 185 cp. But apart from the approach being semiempirical, the flow rates studied are in too low a range to be of any practical importance. The problem is further complicated by the treatment of each angle as a separate case. 

Several schools of thought then arose. Members of one school treated each structure as a separate case, more or less succumbing to the thesis of an almost infinite variety of structural parameters. A second school took the view that although carborane structures were complex in nature, such structures could eventually be categorized or collated by improved theoretical treatments which could be expected to become ever more accurate because of constantly improving computer systems. A third school considered the complexity of carborane structures to be not as severe as had appeared at first view, arguing that when a sufficient number of structures would eventually be determined, the fundamental structural precepts would become decipherable and, consequently, amenable to a simplistic empirical organizational format. 

The breakthrough was the Li-Al/LiCl-KCl eut./FeS system intermediate ED, good cycle life proven at >60% dod. There are probably many other systems just as good or better. Interesting chemistry includes appearance of new crystalline complexes as intermediates bewildering stability problems with separators, cases, seals and very fast charge-transfer processes. 

Ethylene hydroformylation was treated as a separate case, as difSculties arise from dramatic changes in the IR spectrum of dissolved ethylene as a function of its partial pressure. This was overcome using the method of band-target entropy minimisation (BTEM, see Chapter 4) to recover the pure component spectra of all observable species and their concentrations [72]. As well as the conventional acyl tetra-carbonyl, [Rh(C(0)Et)(C0)4], evidence was obtained for [Rh(C(0)Et)(C0)3(C2H4)], containing coordinated ethylene. The presence of this species indicates that ethylene can compete with H2 for the unsaturated [Rh(C(0)Et)(C0)3]. The ketone and polyketone side products of Rh-catalysed ethylene hydroformylation arise from insertion of coordinated ethylene into the Rh-acyl bond in [Rh(C(0)Et)(C0)3(C2H4) ... 

Since, in general, factors which influence the adhesion of metal/epoxy resin structural joints also influence adhesion in metal/epoxy resin protective coating systems, these two separate cases will often be combined and referred to simply as metal/epoxy adhesion systems. 

The value of W is intermediate to the values obtained for the separate cases and fits a geometric combining rule. 

The heating cylinder of the mixer is normally made up of separate casing elements... 

It is well recognized that antithyroid drugs, and especially propylthiouracil, can be associated with development of anti-neutrophil cytoplasmic antibody (ANCA)-positive vasculitis, often manifesting as renal disease. Atypical presentations, with pyoderma gangrenosum (49) and progressive bilateral sensorineural hearing loss (50), have been described in separate case reports of subjects taking propylthiouracil. 

Note that the recoveries in the optimal solution shown in Figure 9.6 are at their lower bounds for r 2 and r fc2, and at the upper bound for. A comparison between sharp and nonsharp sequences Aggarwal and Floudas (1990) shows that significant savings can result from optimizing the degree of nonsharp separation. In particular, in example 2 of their paper, which corresponds to the same optimization model presented in the illustrative example but with different product compositions, the optimal solution consists of a single column with a by-pass stream. This corresponds to 70% cost reduction versus the sharp separation case. 

The division of total cohesive energy into multicomponents has been successfully studied by Hansen (1967) and has been extended for solubility prediction for different compounds in separate cases (Martin etal., 1981 Bustamante etal., 1991 Richardson etal., 1992). 

The isolated proteinaceous surfactants, obtained from commercial agarose powder and forest soil extract, were found to have extremely similar total amino acid compositions. Table 4.2 summarizes the amino acid values obtained from four determinations for each of the two surfactant preparations it can be seen that the rather unusual amino acid ratios obtained (among 17 different amino acids) for the two separate cases closely resemble one another. Specifically, in both of these cases the relative amounts of the different amino acids identified (excluding tryptophan which is completely destroyed during acid hydrolysis) were as follows glycine serine > aspartic acid (and/or aspara-... 

C) In many experimental studies, all of the intensive variables are determined, giving a redundancy of experimental data. However, Equations (10.70) and (10.73) afford a means of checking the thermodynamic consistency of the data at each experimental point for the separate cases. Thus, for Equation (10.70), the required slope of the curve of P versus ylt consistent with the thermodynamic requirements of the Gibbs-Duhem equations, can be calculated at each experimental point from the measured values of P, xt, and at the experimental temperature. This slope must agree within the experimental error with the slope, at the same composition, of the best curve... 

It is convenient to represent the ratio k/x by the symbol m. It is then found necessary to consider two separate cases, namely, the general case for which m p 0, and the special case for which m = 0. The former corresponds to a reaction system in which radicals can be lost from reaction loci by first-order processes the latter effectively corresponds to a reaction system in which radicals cannot be lost from reaction loci by first-order processes, although theoretically the case m = 0 also includes reaction systems for which % is truly infinite (and therefore k. is truly infinite) and k may or may not be zero. For the case m 0, the behaviour of the reaction system during the decay period is characterised by the locus-population generating function... 

This theoretical example may serve to illustrate the importance of preparation and implementation of the sampling to both the accuracy and the reproducibility of the analytical results reflecting the environmental problem. It is, furthermore, obvious that the sampling process must be adapted and optimized for each separate case. This requires a very sensitive balance between environmental knowledge and experience on the one hand and statistical requirements on the other. 

I. The study of various types of conjugated reactions and classification of separate cases as belonging to one type or another. 

It should be pointed out that in many cases it seems uncertain which substance it is that constitutes the veritable catalyst. Particularly for metallic and oxidic catalysts each separate case must be investigated for formation of a monomolecular layer of compounds or adsorbates, for instance, sulfides, carbides, hydrides, etc., which constitutes the real catalyst after an individual activation period of the metal or the oxide. In such cases the electron exchange between the film and the substrate will, of course, be the decisive factor 13). 

In addition to the simple cycle without any form of recuperation (Base Case) that was analyzed in the previous section, we will consider five separate cases with thermal and/or chemical recuperation. In the interest of maintaining uniformity, we will assume a constant temperature of 800F as the exit temperature of any stream undergoing such recuperation. A description of the five cases is as follows ... 

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