Character set, alternate

There is another way to enter some useful characters. From the keyboard, you can enter symbols that are in the so-called alternate character set. In Excel for the Macintosh these characters are obtained by pressing OPTION+(key) or OPTION-i-SHIFT-i-(key). The characters produced may be different for each different font. The ones shown in Figure 1-26 are obtained with the Geneva font, the default font for Excel for the Macintosh. 

The general problem to construct basis functions, as linear combinations of local orbitals, for irreducible representation, is managed most conveniently if the reducible characters on decorated orbits are built using the alternative local sets of harmonic functions sketched in Figure 3.2, Figure 3.3 and Figure 3.5. 

Regular expression patterns are delimited by forward slashes. The simplest ones contain a sequence of normal characters that must match somewhere within the body of a string. The EcoR I-site detector is one such example. Regular expressions are much more powerful than this, however. For example, square brackets can be used to specify a set of alternative characters in the manner shown here ... 

An alternative is to define a completely different set of symbols. A common approach in speech technology is to use one or more ascii characters for each phoneme, so that the consonant at the start of shoe is /sh/, the vowel is /uw/ and so on. Note that the use of ascii characters is relatively easy when our task is to represent 50 or less phonemes coming up with a unique ascii representation for each hundreds phones is much more difficult. For now we will use the modified limit ascii character set, defined for general American English a full description and justification of this will be given in Chapter 8. In addition to any practical, computer benefit, the use of a... 

As should have been made plausible by the above discussion, symbolic dynamics provides an intuitive conceptual bridge between continuous and discrete dynamical systems. On the one hand, except for the fact that the coarse-grained discrete dynamics of symbolic systems is typically nonlocal in character (see the following section), symbolic dynamical systems are essentially CA-in-disguise. On the other hand, by exploiting the fundamental CA property of continuity in the Cantor-set topology under the metric defined by equation 4.49, real-valued representations of CA dynamics may be readily obtained. We discuss these two alternative points of... 

Polymer products synthesized in laboratories and in industry represent a set of individual chemical compounds whose number is practically infinite. Macro-molecules of such products can differ in their degree of polymerization, tactici-ty, number of branchings and the lengths that connect their polymer chains, as well as in other characteristics which describe the configuration of the macromolecule. In the case of copolymers their macromolecules are known to also vary in composition and the character of the alternation of monomeric units of different types. As a rule, it is impossible to provide an exhaustive quantitative description of such a polymer system, i.e. to indicate concentrations of all individual compounds with a particular chemical (primary) structure. However, for many practical purposes it is often enough to define a polymer specimen only in terms of partial distributions of molecules for some of their main characteristics (such as, for instance, molecular weight or composition) avoiding completely a... 

This wording may be considered as duplication, because one can hardly think of continuous titration without automation however, the intention is simply to stress its character as an alternative to automated discontinuous titrations. The principle of continuous titration can be illustrated best by Fig. 5.151 it applies to a steady stream of sample (C). Now, let us assume at first that the analyte concentration is on specification, i.e., it agrees with the analyte concentration of the standard (B). If, when one mixes the titrant (A) with the sample stream (C), the mass flow (equiv./s) of titrant precisely matches the mass flow of analyte, then the resulting mixture is on set-point. However, when the analyte concentration fluctuates, the fluctuations are registered by the sensor it is clear that the continuous measurement by mixing A and C is only occasionally interrupted by alternatively mixing A and B in order to check the titrant for its constancy. 

The characters Xj for the examples in the previous section were calculated following the method described in Section 8.9, that is, on the basis of Cartesian displacement coordinates. Alternatively, it is often desirable to employ a set of internal coordinates as the basis. However, they must be well chosen so that they are sufficient to describe the vibrational degrees of freedom of the molecule and that they are linearly independent The latter condition is necessary to avoid the problem of redundancy. Even when properly chosen, the internal coordinates still do not usually transform following the symmetry of the molecule. Once again, the water molecule provides a very simple example of this problem. 

Duncan s latest novel launches a new series set in an alternate Venice and filled with the author s customary touches of humor, light satire, and fast-paced action. [Duncan] shows his mastery of both storytelling and character building. ... 

---