Colon notation

Sometimes it is helpful to specifically distinguish between row and column vectors. In such instances, we borrow Matlab s colon ( ) notation. A vector x... 

Recall the colon ( ) notation as introduced in Chapter 2.1, Matrices, Vectors, Scalars. The first column of F, fi, contains m ones, while the second... 

Matlab uses the colon notation, if you would like to address all columns or all rows, for example, 1 = ( , 1 2) means that matrix A1 has the same rows than matrixv4, the number of colums of A1 are only columns one to two of matrix. ... 

In order to form a vector as a sequence of numbers, one may use the colon notation, according to which s i e yields a sequence of numbers starting with s, and possibly ending with e in incremental steps of i. For example, 1 1 7 yields the following row vector ... 

A very common use of the colon notation is to refer to rows, columns, or a part of the matrix ... 

Bridging is indicated by the i prefix before the bridging ligand name, and unsymmetrical bridging by multiatom bridges is denoted by the ligating atom notation and central atom locant number separated by a colon x-(hydroxyamido)-2idV lK0-. For examples see Table 18. 

The use of the semi-colon in the notation y><(x R) is to denote the explicit dependence of y>i on the electronic space-spin co-ordinates x and its implicit dependence, along with Ei on the nuclear co-ordinates R. Clearly, the solution of equation (5) for all spatial arrangements of the nuclei will generate an energy (hyper)-surface, the... 

A number notation used widely for indicating the structure of a fatty acid is shown under the names of the fatty acids in Example 6.3. To the left of the colon is shown the number of C atoms in the acid to the right, the number of double bonds. The position of the double bond is shown by a superscript A followed by the number of carbons between the double bond and the end of the chain, with the carbon of the carboxylic acid group being called 1. 

The composition of a dilute solution is sometimes specified in terms of the volume of a more concentrated solution and the volume of solvent used in diluting it. The volume of the former is separated from that of the latter by a colon. Thus, a 1 4 HCl solution contains four volumes of water for each volume of concentrated hydrochloric acid. This method of notation is frequently ambiguous in that the concentration of the original solution is not always obvious to the reader. Moreover, under some circumstances 1 4 means dilute one volume with three volumes. Because of such uncertainties, you should avoid using solution-diluent ratios. 

The mode specific vibrational root mean squared displacement vector is thus replaced by the mean square displacement tensor of that atom in that specific mode, it has units of A. The tensor is represented in Eq. (A2.85) by a matrix, in more compact notation it is written, for a specific vibrational mode and atom Bi. The colon-operator ( ) or tensor contraction operation is found by taking the trace (Tr) of the product of the two tensors, see Eq. (2.50). Further we write the total mean square displacement tensor of an atom as the sum over all the individual vibrational contributions. 

The important attributes of a fatty acid are its carbon chain length, the number of double bonds present and their positions, which can be represented by a simple notation scheme. For example, oleic acid can be represented by c/s-18 1 co9, where cis refers to the stereochemistry about the C=C bond (see Fig. 2.2b and Box 2.3), 18 is the number of C atoms, the number of double bonds (1) is given after the colon, and the number following co is the position of the double bond from the opposite end to the acid group. As double bonds in polyunsaturated acids are usually conjugated (see Section 2.1.2), it is only necessary to give the position of the first double bond because all others follow on alternate carbon atoms. Hence... 

Figure 6.3 A SMIRKS notation specifying the conversion of a charge-separated nitro group to a representation with two double bonds and a 5-valent nitrogen atom. Corresponding atoms on each side have the same number (shown after the colon in the SMIRKS), and the atom attached to the nitro group is shown in the SMIRKS as indicating any atom .

Although this member function definition resembles an ordinary C procedure, there are some important differences that should be discussed. The definition starts with the notation Complex which is a way of reopening the context of the class declaration. The pair of colons, which is called the scope resolution operator, is placed after the name of a class to indicate a definition of something in the class. After the constructor header is a pair of initialization expressions. The first initialization expression is realpart(r), which states that the class member named realpart should have its initial value taken from the parenthesized expression, r. The second initialization expression sets the imagpart member to zero. The body of the constructor, like the body of all C procedures, is delimited by a pair of curly braces, but in this particular example there is nothing to do in the constructor body because all the work has been done in the initialization section of the constructor. 

More than 500 different fatty acids have been isolated from various cells and tissues. Given in Table 19.1 are common names and structural formulas for the most abundant of them. The number of carbons in a fatty acid and the number of carbon-carbon double bonds in its hydrocarbon chain are shown by two numbers separated by a colon. In this notation, linoleic acid, for example, is designated as an 18 2 fatty acid its 18-carbon chain contains two carbon-carbon double bonds. 

It provided an effective notation of the electronic structures of inorganic and organic molecules. Initially this was based on the representation of electron pairs as colons, but subsequently developed so that covalent bmids were represented by lines joining the atoms and non-bonding electrmi pairs as colons. 

A shorthand notation shows the number of carbon atoms in the molecule, followed by a colon and the number of double bonds. The position of the first double bond from the methyl group of the fatty acid is shown by n- or CO- (the CD-carbon is the furthest from the a-carbon, which is the one to which the carboxyl group is attached CD (omega) is the last letter of the Greek alphabet). 

Using the colon (range) notation (see Sec. 1.7.31 with semicolon ... 

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