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Our description of the fascinating topic of D-branes in this chapter barely scratches the surface, but it should help prepare you for more detailed and/or more advanced treatments. We have followed the development by Zweibach in this chapter, so you can see his book for a more detailed analysis, in particular including his discussion of intersecting D6-branes and his accessible discussion of string charge and electromagnetic elds on D-branes (see References). Another good book to consult is the Szabo text listed in the References. For a really detailed (and advanced) description of D-branes, see Clifford V. Johnson s D-Brane Primer Johnson s.

a shift toward the longer wavelength, blue end of the spectrum. The trailing edge, on the other hand, decreases the refractive index of the core, causing a shift toward the shorter wavelength, red end of the spectrum. This causes an overall spreading or smearing of the transmitted signal a phenomenon known as chirp. It occurs in fiber systems that transmit a single pulse down the fiber and is proportional to the amount of chromatic dispersion in the fiber: the more chromatic dispersion, the more SPM. It is counteracted with the use of large effective area fibers.

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A 1. Consider a potential given by V ( ) = ( 2 1)2 . What are the critical 6 points A 2. Consider V ( ) = ( 2 1)2 and expand to second order. Then identify the 6 mass in the case of each critical point found in Prob. 1. Are any of these related to a tachyon 3. What are the critical points 4. Which critical point corresponds to a tachyon 5. If a string is stretched between two parallel D-branes, the ground state acquires mass. Why is that

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Cross-Phase Modulation (XPM)

Black holes, the collapsed remnants of large stars or the massive central cores of many galaxies, represent an arena where a quantum theory of gravity becomes important. The possibility of the existence of black holes was recognized long ago by the great physicist and mathematician Laplace, but it wasn t until the Schwarzschild solution in general relativity was put forward that these objects and their truly bizarre properties really came into their own. In recent decades the existence of black holes has been established without doubt from observational evidence. Classically, black holes are remarkably simple objects that can be described by just three properties: Mass Charge Angular momentum Then Stephen Hawking made a remarkable discovery. In a result that is now famous and is without a doubt known by most readers of this book, Hawking found out that black holes radiate. But this was only the beginning of the story. Black holes have remarkable characteristics that connect them directly it turns out to the science

When multiple optical signals travel down the same fiber core, they both change the refractive index in direct proportion to their individual power levels. If the signals happen to cross, they will distort each other. While XPM is similar to SPM, there is one significant difference: While selfphase modulation is directly affected by chromatic dispersion, crossphase modulation is only minimally affected by it. Large effective area fibers can reduce the impact of XPM.

I don t think any persistence implementation is complete without some discussion of migrating from one version of a database schema to another. I try to keep migrations simple. I rely on a new table, which I usually call ApplicationProperties, that stores the current version of the schema and any other properties I want to store for the entire application. I then check that version number on launch, and if an old version is detected, I run the necessary SQL to do the migrations. I stay away from using the actual model classes during the migration, because that can cause compatibility issues if you ever delete or rename a model class that would prevent the migrations from running. First, create a subclass of ISDatabase called ExampleDatabase. This will contain all the application-specific database handling and migration code. Add ISModel to the import statements for ExampleDatabase.m, and add the following init method:

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