Oppositions defined

Note that Tsai and Pagano s angle of rotation is oppositely defined to that in Figure 2-10, so the sine terms in Equation (2.98) are also of opposite sign. 

Flere the subscripts and/refer to the initial and final states of the system and the work is defined as the work perfomied on the system (the opposite sign convention—with as work done by the system on the surroundings—is also in connnon use). Note that a cyclic process (one in which the system is returned to its initial state) is not introduced as will be seen later, a cyclic adiabatic process is possible only if every step is reversible. Equation (A2.1.9), i.e. the mtroduction of t/ as a state fiinction, is an expression of the law of conservation of energy. 

Then, the 3D coordinates of A are used for atom t, those of B forj, those ofC for h, and those of U for I. The first three atoms (in the order established by the ranking) define a plane if they are ordered clockwise and the fourth atom is behind the plane, the chirality signal, obtains a value of -rl for the opposite geometric arrangement, obtains a value of-1. 

What is significant about these reactions is that only two possibilities exist addition with the same configuration (D -> DD or L LL) or addition with th< opposite configuration (D DL or L LD). We shall designate these isotactic (subscript i) or syndiotactic (subscript s) additions, respectively, and shal define the rate constants for the two steps kj and k. Therefore the rates o isotactic and syndiotactic propagation become... 

If a molecule has a plane of symmetry, for which the symbol is a, reflection of all the nuclei through the plane to an equal distance on the opposite side produces a configuration indistinguishable from the initial one. Figure 4.3(a) shows the two planes of symmetry, (7 (xz) and (yfyz), of H2O using conventional axis notation. Just as theyz plane, the plane of the molecule, is a plane of symmetry so any planar molecule has at least one plane of symmetry. The subscript u stands for vertical and implies that the plane is vertical with respect to the highest-fold axis, C2 in this case, which defines the vertical direction. 

Now consider a domain fl containing a surface Tc, whose properties are described in Section 1.1.7. Denote Sc = Tc clTc, flc = fl Tg. Introduce the unit normal n to Tc and define the opposite faces T of the surface Tg. The signs fit positive and negative directions of n, respectively. Then we denote the boundary of flc by dflc = T U T. We assume that there exists a closed extension S of Tc dividing the domain fl into two subdomains Di, D2 with boundaries dfli,dfl2 and such that Tc C S. It is assumed that = S , 80,2 = S+ U r. We say that the boundary dOc belongs to the class if 80,1,80,2 belong to G . ... 

Dual solvent fractional extraction (Fig. 7b) makes use of the selectivity of two solvents (A and B) with respect to consolute components C and D, as defined in equation 7. The two solvents enter the extractor at opposite ends of the cascade and the two consolute components enter at some point within the cascade. Solvent recovery is usually an important feature of dual solvent fractional extraction and provision may also be made for reflux of part of the product streams containing C or D. Simplified graphical and analytical procedures for calculation of stages for dual solvent extraction are available (5) for the cases where is constant and the two solvents A and B are not significantly miscible. In general, the accurate calculation of stages is time-consuming (28) but a computer technique has been developed (56). 

Activators enhance the adsorption of collectors, eg, Ca " in the fatty acid flotation of siUcates at high pH or Cu " in the flotation of sphalerite, ZnS, by sulfohydryl collectors. Depressants, on the other hand, have the opposite effect they hinder the flotation of certain minerals, thus improving selectivity. For example, high pH as well as high sulfide ion concentrations can hinder the flotation of sulfide minerals such as galena (PbS) in the presence of xanthates (ROCSS ). Hence, for a given fixed collector concentration there is a fixed critical pH that defines the transition between flotation and no flotation. This is the basis of the Barsky relationship which can be expressed as [X ]j[OH ] = constant, where [A ] is the xanthate ion concentration in the pulp and [Oi/ ] is the hydroxyl ion concentration indicated by the pH. Similar relationships can be written for sulfide ion, cyanide, or thiocyanate, which act as typical depressants in sulfide flotation systems. 

Current flow through the frits is supported by ions. Cations and anions both support the virtual current by flowing in opposite directions, and the transference number of a particular ion is defined as the fraction of the total current it carries. The sum of all transference numbers then is necessarily unity. If the fraction of the virtual current carried by the cations equals the fraction carried by the anions then the solution is said to be equitransferent. 

Fig. 9. Voltammograms demonstrating a potentiometric titration using dual-polarized electrodes, where the dashed lines indicate the anodic and equal-but-opposite cathodic currents that must be carded by the two opposing electrodes during the titration. Terms are defined in text.

Re using the equivalent diameters defined in the following. This situation is, by arbitrary definition, opposite to that for the hydraulic diameter used for turbulent flow. 

A positive vane angle produees prewhirl in the direetion of the impeller rotation, and a negative vane angle produees prewhirl in the opposite direetion. The disadvantage of positive prewhirl is that a positive inlet whirl veloeity reduees the energy transfer. Sinee Vg is positive aeeording to the Euler equation defined by... 

Sometimes the terms erythro and threo are used to specify fee relative configuration of two adjacent stereogenic centers. The terms are derived fom fee sugars erythrose and threose. The terms were originally defined such feat a Fischer projection formula in which two adjacent substituents were on the same side was fee erythro isomer and feat in whidi the substituents were on opposite sides was the threo isomer. 

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