Parenthesizing

UNIQUAC interaction parameters were not determined, but were assumed to be zero for this system. Quantities in parentheses refer to adiabatic flash. 

In addition to fundamental units from the SI system, i.e., m, kg, s, mol, K, A, and cd, multiples and sub-multiples of these units as well as derived or combined units are also used and indicated in parentheses. 

A complication now arises. The surface tensions of A and B in Eq. IV-2 are those for the pure liquids. However, when two substances are in contact, they will become mutually saturated, so that 7a will change to 7a(B) and 7b to 7B(A). That is, the convention will be used that a given phase is saturated with respect to that substance or phase whose symbol follows in parentheses. The corresponding spreading coefficient is then written 5b(A)/a(B)-... 

Gilman [124] and Westwood and Hitch [135] have applied the cleavage technique to a variety of crystals. The salts studied (with cleavage plane and best surface tension value in parentheses) were LiF (100, 340), MgO (100, 1200), CaFa (111, 450), BaFj (111, 280), CaCOa (001, 230), Si (111, 1240), Zn (0001, 105), Fe (3% Si) (100, about 1360), and NaCl (100, 110). Both authors note that their values are in much better agreement with a very simple estimate of surface energy by Bom and Stem in 1919, which used only Coulomb terms and a hard-sphere repulsion. In more recent work, however, Becher and Freiman [126] have reported distinctly higher values of y, the critical fracture energy. ... 

Here, fisAB denotes the angle as measured in liquid A, and the phases in parentheses have saturated the immediately preceding phase. A strictly rigorous nomenclature would be yet more complicated we simply assume that A and B are saturated by the solid and further take it for granted that the two phases at a particular interface are mutually saturated. mutual saturation effects are neglected, then the combination of Eqs. X-23 and X-21 gives... 

In each case we have indicated the doorway stage using parentheses. We note how in each of the two groups ((i) and... 

The upper sign is for anti-Stokes scattering, the lower for Stokes scattering. The factor in the parentheses is... 

Table Bl.5.1 Independent non-vanishing elements of the nonlinear susceptibility, for an interface in the Ay-plane for various syimnetry classes. When mirror planes are present, at least one of them is perpendicular to they-axis. For SFIG, elements related by the pennutation of the last two elements are omitted. For SFG, these elements are generally distinct any syimnetry constraints are indicated in parentheses. The temis enclosed in parentheses are antisymmetric elements present only for SFG. (After [71])...

The symbol M represents the masses of the nuclei in the molecule, which for simplicity are taken to be equal. The symbol is the Kionecker delta. The tensor notation is used in this section and the summation convention is assumed for all repeated indexes not placed in parentheses. In Eq. (91) the NACT appears (this being a matrix in the electronic Hilbert space, whose components are denoted by labels k, m, and a vector with respect to the b component of the nuclear coordinate R). It is given by an integral over the electron coordinates... 

Notice, all terms in the curled parentheses are of O(fi ) curl condition becomes... 

Recalling that the summation within the round parentheses can be written as [1 <2m]) where Qm is the projection operator for Q subspace, we obtain... 

If we assume again that all relevant functions are smooth enough, the expression in the curled parentheses can be evaluated further to become... 

Numbers in parentheses are reference numbers and indicate that the author s work is referred to although his name is not mentioned in the text, Numbers in italic show the pages on which the complete references are listed,... 

Values given in parentheses in Phenylhydrazone column are B.ps. Di-deriv. f Mono dcriv. Two forms. 

Values in parentheses in the columns for Methyl, Ethyl, and Phenyl Esters and for Anhydrides and Nitriles are M.ps. 

Alternative procedure Mathcad. Follow the procedure above except that where QMOBAS is indicated, use Mathcad instead. Enter the Huckel molecular orbital matrix, modified by subtracting xl, with some letter name. For example, call the modified matrix A. Type the command eigenvals(A) = with the name of the modified HMO matrix in parentheses. Mathcad prints the eigenvalues. The command eigenvecs(A) yields the eigenvectors, which are useful in ordering the energy spectrum. 

The following liquids may be used (boiling points are given in parentheses) — chlorobenzene (132-3°) bromobenzene (155°) p cymene (176°) o-dichloro-benzene (180°) aniline (184°) methyl benzoate (200°) teti-alin (207°) ethyl benzoate (212°) 1 2 4-trichlorobenzene (213°) iaopropyl benzoate (218°) methyl salicylate (223°) n-propyl benzoate (231°) diethyleneglycol (244°) n-butyl benzoate (250°) diphenyl (255°) diphenyl ether (259°) dimethyl phth ate (282°) diethyl phthalate (296°) diphenylamine (302°) benzophenone (305)° benzyl benzoate (316°). 

Repeat the boiling point determination with the following pure liquids (a) carbon tetrachloride, A.R. (77°) (6) ethylene dibromide (132°) or chlorobenzene (132°) (c) aniline, A.R. (184-6°) and (d) nitrobenzene, A.R. (211°). An air condenser should be used for (c) and (d). Correct the observed boiling points for any appreciable deviation from the normal pressure of 760 mm. Compare the observed boiling points with the values given in parentheses and construct a calibration curve for the thermometer. Compare the latter with the curve obtained from melting point determinations (Section 111,1). 

All new information on chemical matters or original presentations and discussions of known material are published in scientific journals. The most important of these dealing with organic compounds are (the abbreviated names are given in parentheses) ... 

As the Pople basis sets have further expanded to include several sets of polarization functions, / functions and so on, there has been a need for a new notation. In recent years, the types of functions being added have been indicated in parentheses. An example of this notation is 6—31G(dp,p) which means that extra sets of p and d functions have been added to nonhydrogens and an extra set of p functions have been added to hydrogens. Thus, this example is synonymous with 6—31+G. ... 

In order to describe the number of primitives and contractions more directly, the notation (6s,5p) (ls,3p) or (6s,5p)/(ls,3p) is sometimes used. This example indicates that six s primitives and hve p primitives are contracted into one s contraction and three p contractions. Thus, this might be a description of the 6—311G basis set. However, this notation is not precise enough to tell whether the three p contractions consist of three, one, and one primitives or two, two, and one primitives. The notation (6,311) or (6,221) is used to distinguish these cases. Some authors use round parentheses ( ) to denote the number of primitives and square brackets [ ] to denote the number of contractions. 

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