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Now 1 1 z z f + f =z+ +z + =z+z + + zz zz z z z+z z+z = zz + zz zz = So Re( f ) = f + f z 2 z + zz 2 + z + z = 2 2 zz z 2 z + zz 2 + z + z zz

Once you have finished your editing, you re almost ready to create your disc It s a good idea to run through the assembled clips a few times to make certain that everything flows the way you want before you burn your masterpiece to disc then you can go ahead and burn a sample Figure 1-8 shows that I m about to burn a copy of my ten-minute road trip movie to a VCD I m giving the movie one last run through before I click the Create Disc button As you may have noticed in Figure 1-8, creating a DVD or VCD copy of my movie isn t my only option In fact, Pinnacle Studio 8 (and most other video editing programs) gives me a number of different output options For example, if you want to send Grandma a copy of your movie and you know that she has a VCR but not a DVD player, you could choose to output the movie to tape Different types of output media have different sets of features, of course, so the videotape you send her won t have the menus you added for your DVD Still, it s good to know that you have enough options to suit pretty much any need

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It is important that security devices be able to recognize all fragments as members of the same datagram Some recent attacks exploit holes in firewall and router code that block the initial fragment of a data packet but allow the remaining fragments to pass through This attack takes advantage of the fact that the layer 4 header information is contained only in the first datagram fragment Once this fragment is blocked, if the blocking device does not keep a record of the discarded initial packet, it may mistakenly allow subsequent unauthorized fragments through Although an actual application connection cannot be established without the layer 4 header information in the initial fragment, an attacker might be able to create a denial of service attack by sending many fragmented datagrams to a particular host The host must hold the fragments in memory while it waits for all fragments to arrive, consuming valuable resources The specifics of this attack and its prevention will be covered in greater detail in later chapters

To get the imaginary part we calculate 1 1 z z f f = z + z + = z + z zz zz z z z+z z+z = zz zz zz = z 2 z + zz 2 z z zz

FIGURE 1-8

Consider an open region D in the complex plane and a function f : D If this function is continuous and if the partial derivatives f / x and f / y exist and are continuous, we say that f is continuously differentiable in D If f is k times continuously differentiable where k = 0,1, 2, (that is, k derivatives of f exist and are continuous) we say that f is C k If f is C 0 , this is a continuous function which is not differentiable Now, how do we determine if a function is analytic If f is a continuously differentiable function on some region D then it is analytic if it has no dependence on z That function is analytic in a domain D provided that df (314) =0 dz This condition must hold for all points in D Note that a function which is analytic is also called holomorphic Later we will see that we can form a local power series expansion of a holomorphic or analytic function Now let s go back to writing a function of a complex variable in terms of real and imaginary parts as in Eq (313) We want to think about how to compute the derivative d/dz in terms of derivatives with respect to the real variables x and y Let s go back to basics Remember that z = x + iy This tells us that z =1 x and z =i y (315)

Since z = x iy , it is the case that z =1 x and z = i y (316)

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