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homomorphic the donut has a hole but a sphere does not. The bottom line is there is no way to transform the donut into the sphere. If a geometric shape is homeomorphic to a sphere, then the Euler characteristic is (2.29) Many shapes have an Euler characteristic which vanishes. Some examples of this include a torus, a m bius strip, and a Klein bottle. Another example is a cylinder, which also has = 0 (see Fig. 2.2). Why is this interesting for us If the worldsheet of a string has a vanishing Euler characteristic, then it is possible to write the auxiliary eld h as a two-dimensional at space metric. That is, we take [using the choice of coordinates for the worldsheet as ( , )] 1 0 h = 0 1 (2.30)

can be reused on any tier in a multi-tiered client/server environment, offering an added level of reuse for XML documents. The same cannot be said of scripting environments or platform-specific binary executables.

Figure 2.2 Some surfaces with a vanishing Euler characteristic. When the Euler characteristic vanishes, we can de ne the auxiliary eld such that it has a representation of the at space Minkowski metric.

Given the industry s vast knowledge of communications, networking, and data processing, validating and processing data from other departments and/or enterprises should be a simple task. Unfortunately, that s not the case. Validating data formats and ensuring content correctness are still major hurdles to achieving simple, automated exchanges of data.

Figure 5 4. This is the image for the screen icon a lovely face!

Using XML technology as the format for data exchange can quickly remedy most of these problems for the following reasons:

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Now notice that with this choice, h = det h = 1. We also have h X X = X X + X X = X 2 + X 2 In this case, we are able to write the Polyakov action in the remarkably simple form SP = T 2 d ( X 2 X 2 ) 2 (2.31)

build proprietary parsers for each data format. XML technology eliminates this requirement by using a standard XML parser.

EXAMPLE 2.3 Find the equations of motion using the Polyakov action as written in Eq. (2.27) when the auxiliary eld takes the form of the at space metric. SOLUTION In this case we have SP = = = T 2 d h h X X 2 T 2 d ( X X + X X ) 2 T 2 d ( X X + X X ) 2

that all the required fields are provided and are in the correct order. This function, however, requires the availability of a DTD. Additional content validation is possible by developing applications using the W3C DOM. In addition, content and format validation can be completed outside of the processing application and perhaps even on a different machine. The effect of this approach is twofold: It reduces the resources used on the processing machine and speeds up the processing application s overall throughput because it does not need to first validate the data. In addition, the approach offers companies the opportunity to accept or deny the data at time of receipt instead of requiring them to handle exceptions during processing.

Recall that icons for the iPhone/iPad have a recommended size of 320 480 pixels. Make sure to be mindful of these dimensions. Once you have all three of these images the bottom layer, the top layer, and the icon save them onto your desktop.

So, we can write the lagrangian as L = X X + X X = X X + X X Therefore, L = X X + X X = X = X X X

Electronic Data Interchange (EDI)

The Euler-Lagrange equations are L L + =0 X X Hence, we nd that the equations of motion for the relativistic string are 2 X 2 2 X 2 =0

EDI is a special category of data exchange that nearly always uses a VAN (valueadded network) as the transmission medium. It relies on either the X12 or EDIFACT standards to describe the documents that are being exchanged. Currently, EDI is a very expensive environment to install and possibly requires customization, depending on the terms established by the exchanging parties. For this reason, a number of enterprises and independent groups are examining XML as a possible format for X12 and EDIFACT documents, although no decisions have been reached as of this writing.

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