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Now let s move forward so we can see what the developments laid out thus far in the chapter really mean. We will see that the energy-momentum tensor can be expanded in a Laurent series, and that the Virasoro operators turn out to be the coef cients of the expansion. In other words, they describe the modes of the energymomentum tensor. In particular, the operator L0 is proportional to the energy operator or hamiltonian. As a speci c example, consider a closed string with worldsheet coordinates ( , ). The spatial dimension is compacti ed, that it is periodic with

multi-tiered applications are generally considered to be three-tiered applications because they are distributed across three different locations: client machines, JEE server machine, and the database or legacy machines at the back end. JEE applications consist of client components, web components, and business components.

= + 2

#import "EinSwitch01AppDelegate.h" #import "SwitchViewController.h" @implementation EinSwitch01AppDelegate @synthesize window, switchViewController; - (void)applicationDidFinishLaunching:(UIApplication *)application { // Override point for customization after application launch [window addSubview:switchViewController.view]; [window makeKeyAndVisible]; } - (void)dealloc { [window release]; [switchViewController release]; [super dealloc]; } @end

software units assembled into JEE applications with their related classes and files. These components communicate with other components.

(5.27)

development, because business logic is organized into reusable components, and the JEE server provides underlying services in the form of a container for every component type.

q A JEE application is usually assembled from two different types of modules:

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S to save your work. Holy implementation file, Batman! You re done!

The time coordinate satis es < < . We can describe the worldsheet of the closed string, which is an in nite cylinder, using conformal eld theory in the following way. We begin by making the following conformal transformation: z = e +i z = e i (5.28)

enterprise beans and web components. Both of these modules are reusable; therefore, new applications can be built from pre-existing enterprise beans and components. The modules are also portable, so the application that comprises them will be able to run on any JEE server conforming to the specifications.

The effect of this transformation is to map the cylinder to the complex plane. The radial coordinate plays the role of time, with the in nite past at the origin. With increasing radius, we move forward in time. Spatial integrals on the worldsheet are translated into contour integrals about the origin in the complex plane as the result of the conformal transformation [Eq. (5.28)]. A slice through the cylinder, which corresponds to a slice at constant time i , is transformed into a circle of radius ri in the complex plane. That is, radius in the z plane is a measure of Euclidean worldsheet time as R = z = e So, at time 1 a closed string is a circle of radius R1 = z = e 1 in the z plane, with the angular coordinate given by = . This is illustrated in Fig. 5.1. As time increases, from say 1 2 , 2 > 1 , the radius of the circle in the z plane increases from R1 to R2 > R1 . Let s recall the left-moving and right-moving modes described in Eq. (2.55) and (2.56). Given Eq. (5.28), it is clear that + ln z , and ln z . So we have

uses the following core patterns to enable flexible association of EJB classes with other components. The Proxy pattern provides a separate implementation of interface and working code for location transparency. The Decorator provides a similar contract for a class but with added functionality. The Factory Method provides ability to define a contract for creating an object but defers instantiation to subclasses. The Abstract Factory provides a contract for creating families of related or dependent objects without specifying concrete classes.

You have taken care of the EinSwitch01AppDelegate in terms of both its header and its implementation files. Referring back to Figure 6 10, we see that we have created the code for the einSwitchAppDelegate represented by the chess queen! Whew - time for a break!

XL (z ) =

architects. Successful architects and developers share their knowledge and pass on their proven techniques to others. The net result is productivity. The ultimate product is the implementation of solid applications.

2 x i s p ln z + i s n z n 2 2 2 n 0 n 2 x i s p ln z + i s n z n 2 2 2 n 0 n

peers in similar situations. It is applicable to a cross-section of scenarios with varying resources and sizes. It takes design requirements into consideration.

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