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15-2.1.3 Textured (Segregated) Mixtures. The most troublesome mixtures are those that exhibit long scale texture (i.e., segregation), complicating description of mixture distributions and characterization. Textured mixtures form when a characteristic of one or more particle species causes that component to separate into speci c regions of the mixture, depending on the type of agitation applied to the bulk mixture. Also, dead zones or incomplete agitation of the powder can lead to segregated regions in blenders. In general, more free- owing mixtures exhibit more extreme segregated states. Cohesivity acts to inhibit mixture segregation, as individual particles have trouble moving independently of the bulk mixture. Determining mixture quality of textured mixtures depends on accurately determining the size, location, and severity of the segregated regions. Figure 15-3 shows two types of segregated mixtures, one for free- owing materials and the other for a cohesive mixture. In the free- owing case, if the particles do not differ in any particle characteristic other than color, long scale texturing of the mixture will not occur for a suf ciently agitated system. But when there are differences in particle characteristics (size, shape, density, etc.), a situation like that shown in Figure 15-3a can arise, where individual particle species are preferentially found in speci c regions of the mixture (left to right in this case). For more cohesive systems, a partially randomized mixture can

Fig. 13.10 (a) Two paths that can be continuously deformed one into the other. (b) The paths Q and \k belong to different homotopy classes since they cannot be continuously deformed into each other.

You can also create Date objects that represent specific times other than the current time. There are two basic ways to accomplish this with the Date constructor. Let s first look at how you can create a new Date object based on Epoch milliseconds. Recall from the earlier discussion that the Epoch milliseconds are the number of milliseconds from midnight of January 1, 1970 to the time and date you are referencing. Now, of course, it is not common for humans to think in terms of Epoch milliseconds, and if we asked you the Epoch millisecond value for your birthday it is doubtful that you would know. But computers do tend to think in terms of Epoch time be it milliseconds or, in some cases, seconds. For this reason, it is a convenient way for your Flash application to communicate with other applications. This is especially true if you are using server-side scripts and databases with your Flash application, and you are using either a LoadVars or an XML object to load and send your data. To create a Date object based on Epoch milliseconds, use the following syntax:

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Equation (4.5) states that the limiting vector of ciphertext letter frequencies bj( yi) in the f ith ciphertext sub le yi is the left-circular-shift ski p of p where ki is the unknown key. As the limiting vector of ciphertext letter frequencies b( yi) is observed, the recovery fj of the unknown key ki requires us to nd the left-shift of p that most closely matches the measured vector of ciphertext letter frequencies. The nearness can be measured in terms of the Euclidean distance between the vectors bj( yi) and the unknown left-circular-shift of p. f f The square of the Euclidean distance between the vectors sk p and bj( yi) ski p is D2 (sk p, b ( yi )) ksk p, sk pl 2kb( yi ), b( y i )l 2ksk p, b(y i )l fi fi fi fi 2 fi 2 p 2rk (b( y ))

FIGURE 5-20