Brackets, square

The terms before the square brackets give the nonrelativistic part of the Hamilton-Jacobi equation and the continuity equation shown in Eqs. (142) and (141), while the term with the squaie brackets contribute relativistic corrections. All terms from are of the nonmixing type between components. There are further relativistic terms, to which we now turn. 

The square brackets denote a vector, and [ ] a transposed vector. The exact expression for the Onsager-Machlup action is now approximated by... 

In empirical formulas of inorganic compounds, electropositive elements are listed first [3]. The stoichiometry of the element symbols is indicated at the lower right-hand side by index numbers. If necessary, the charges of ions are placed at the top right-hand side next to the element symbol (e.g., S "). In ions of complexes, the central atom is specified before the ligands are listed in alphabetical order, the complex ion is set in square brackets (e.g., Na2[Sn(OH)+]). 

Atoms Atoms a e represented by their atomic symbols. Ambiguous two-letter symbols (e.g., Nb is not NB) have to be written in square brackets. Otherwise, no further letters are used. Free valences are saturated with hydrogen atoms. 

Cyclic structures Ring dosures are described by a bond to a previously defined atom which is specified by a unique ID number. The ID is a positive integer placed in square brackets behind the atom. An " " indicates a ring closure. 

But also at this limit, D, and the first term in square brackets... 

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. 

Isomers are distinguished by lettering the peripheral sides of the parent beginning with a for the side 1,2, and so on, lettering every side around the periphery. If necessary for clarity, the numbers of the attached position (1,2, for example) of the substituent ring are also denoted. The prefixes are cited in alphabetical order. The numbers and letters are enclosed in square brackets and placed immediately after the designation of the attached component. Examples are... 

Free Radicals. In the formula of a polyatomic radical an unpaired electron(s) is(are) indicated by a dot placed as a right superscript to the parentheses (or square bracket for coordination compounds). In radical ions the dot precedes the charge. In structural formulas, the dot may be placed to indicate the location of the unpaired electron(s). 

Enclosing Marks. Where it is necessary in an inorganic formula, enclosing marks (parentheses, braces, and brackets) are nested within square brackets as follows ... 

Molar concentrations are used so frequently that a symbolic notation is often used to simplify its expression in equations and writing. The use of square brackets around a species indicates that we are referring to that species molar concentration. Thus, [Na ] is read as the molar concentration of sodium ions. ... 

The rate of a process is expressed by the derivative of a concentration (square brackets) with respect to time, d[ ]/dt. If the concentration of a reaction product is used, this quantity is positive if a reactant is used, it is negative and a minus sign must be included. Also, each derivative d[ ]/dt should be divided by the coefficient of that component in the chemical equation which describes the reaction so that a single rate is described, whichever component in the reaction is used to monitor it. A rate law describes the rate of a reaction as the product of a constant k, called the rate constant, and various concentrations, each raised to specific powers. The power of an individual concentration term in a rate law is called the order with respect to that component, and the sum of the exponents of all concentration terms gives the overall order of the reaction. Thus in the rate law Rate = k[X] [Y], the reaction is first order in X, second order in Y, and third order overall. 

Fig. 4. Example of international patent classification (stmctured, hierarchical), where numbers ia square brackets identify edition of IPC ia which class was first used. In C07c 45/50, the first four characters iadicate section C (chemistry). Class 07 (organic chemistry), and subclass c (acycHc compounds) the number 45 /00 iadicates the preparation of compounds having carbonyl groups bound only to carbon or hydrogen atoms by any method and 45 /50...

Here and elsewhere, locants enclosed in square brackets do not correspond to the numbering of the complete skeleton, only to that of a component part. 

For bicyclic structures the von Baeyer name consists of the prefix bicyclo-, followed in square brackets by the numbers of carbon atoms separating the bridgeheads on the three possible routes from one bridgehead to the other, followed in turn by the name of the alkane (or other homogeneous hydride, or repeating unit hydride) containing the same number of atoms in the chain as the whole bicyclic skeleton (examples 55-57). Replacement nomenclature can be applied to hydrocarbon names (example 58). 

When ring fusions and/or bridges are present in addition to spiro linkages, the fused or bridged units are first named individually (by any of the available methods) and the names are then cited (in square brackets and in alphabetical order) with the prefix spiro- or dispiro-, etc. Points of spiro attachment are indicated between the names of the components, with primes as necessary (examples 64-66). This method is also applicable to structures like (62) and (63) but is more cumbersome. 

The relative contributions of each type of interaction to the total van der Waals interaction has been determined by Israelachvili [95] for pairs of similar and dissimilar molecules theoretically by comparing the magnitudes of the terms within the square brackets, using reported values for the polarizability and the ionization potential of these molecules. These results are summarized in Table 1. 

Commands in Mathematica are given in natural language form such as "Solve" or "Simplify" etc. The format of a command is the word starting with a capital letter and enclosing the argument in square brackets ... 

In the square brackets are given the exact values found in the literature. Surface area S, in the table, is the normalized per face of the unit cube L, surface area S of the interface in the unit cell, S = S/1, L = N - )h. The energy is given per unit volume. 

Optional items appear in square brackets (which are not themselves typed when the item is included). 

The terms in square brackets are to do with the nuclear motion the first two of these represent the kinetic energy of the nuclei labelled A and B (each of mass M), and the third term in the square brackets is the Coulomb repulsion between the two nuclei. The fourth and fifth terms give the kinetic energy of the two electrons. The next four negative terms give the mutual Coulomb attraction between the two nuclei A, B and the two eleetrons labelled 1, 2. The final term is the Coulomb repulsion between electrons 1 and 2, with rn the distance between them. As in Chapter 3, I have used the subscript tot to mean nuclear plus electron. 

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