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The initial condition might be an initial temperature distribution, or chemical concentration. If u(x, t) is interpreted as temperature, then the boundary conditions (12.8a) state that the ends of the one-dimensional medium are held at a constant temperature of 0 (e.g., degrees Celsius). Equation (12.7) has the form of (12.3) with B = C = 0, and hence AC B 2 = 0, which is the criterion for a parabolic PDE. Finite-difference schemes analogous to the case for elliptic PDEs may be developed. Classically, perhaps the most popular choice is the Crank Nicolson method summarized by Burden and Faires [3], but given a more detailed treatment by Epperson [11]. Another popular numerical solution technique for PDEs is the nite-element (FEL) method. It applies to a broad class of PDEs, and there are many commercially available software packages that implement this approach for various applications such as structural vibration analysis, or electromagnetics. However, we will not consider the FEL method as it deserves its own textbook. The interested reader can see Strang and Fix [5] or Brenner and Scott [6] for details. A brief introduction appears in Burden and Faires [3]. As stated earlier, the emphasis in this book will be on wave propagation problems as modeled by hyperbolic PDEs. We now turn our attention to this class of PDEs.

in each pair is negligible if assigned t o the same channel. Using r a n d o m assignm e n t , as shown in the upper right assignment in Figure 5.14, u s e r 1 and user2 are assigned t o t h e same channel. Since the two users signatures have high correlation, t h e y cause strong interference t o each other, leading t o degraded performance. On the other hand, with judicious channel-aware assignment, as indicated in the bottom right assignment in Figure 5.14, the users with orthogonal spatial signatures are assigned t o the same channel, eliminating interference f r o m each other, It i s obvious that the channel-aware assignment yields better performance as less interference is introduced. I t has been proved that a n SDMA s y s t e m approaches its capacity using intelligent resource allocation strategies with a large number of users (15 1. T h i s i s achieved by packing as m a n y users as possible o n the same channel as long a s t h e y have orthogonal spatial signatures. It is obvious that, i f users are independent, their spatial signatures shall be randomly located in the spatial signature plane. A s a consequence, with the increase of users, the number of user tuples that have orthogonal spatial signatures increases too. B y intelligent resource allocation, the s y s t e m throughput can be improved by assigning these user tuples t o t h e same channel.

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They usually consist of a set of steps. Each step has a number. Follow the steps through with your copy of the database.

The second argument is still an array of objects. This time, the third argument specifies the field to use for the visual presentation of the list. The fourth argument is the actual value returned to the JavaScript code when one of the corresponding visual names is selected.

Figure 14-11: Using Point and Shoot from the In & Out Links view to switch one component with another

An important aspect of all of the CRUD components is speed. A well-designed database can create, read, update, and delete records quickly. There s no denying that a computerized database is a lot faster than a notebook or a ling cabinet. Instead of processing dozens of records per hour, a computerized database can process dozens or hundreds per second. (I once worked with a billing center that processed around 3 million accounts every three days.) Good design plays a critical role in database ef ciency. A poorly organized database may still be faster than the paper equivalent but it will be a lot slower than a well-designed database.

That is, you write the name of the variable storing the object, followed by an arrow symbol composed of a hyphen (-) and a greater-than symbol (>), followed by the property name. (Note that the property name doesn t have a $ symbol before it.)

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