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While the exact phrase carrier wave may not be referenced on the CWTS exam, it is an important concept in wireless communications Wireless engineers and technicians must deal with many different wireless technologies In the 80211 standard (as amended) alone, you are dealing with four or more different modulation methods, and this does not include the newest 80211n modulation techniques provided by the High Throughput PHY Therefore, a brief summary of carrier waves and why they are important is in order Tom Standage s exceptional book The Victorian Internet (Walker & Company, 2007) documents the many signaling techniques we as humans have used throughout the recent centuries For example, the book documents how Claude Chappe and his brother communicated over great distances with time-bound audio signals The signal was unary in nature in that there was only one signal: the clanging of a pot However, the brothers had synchronized their clocks so that a clang was linked to a second on the clock and each number was linked to a letter; thus a message could be sent If the transmitting brother clanged the pot when the second hand was pointing to 12, the listening (receiving) brother knew to translate the number 12 into the appropriate message As you can imagine, this system would not allow for rapid communications, but it did allow for communications over a short distance Eventually, the brothers realized that sound waves were not good carriers of signals (since they attenuate so quickly and they take so long to arrive at the destination), so they developed a new system based on visual cues Using a simple black-and-white two-sided panel (black on one side and white on the other) and a telescope, the brothers successfully communicated over a distance of approximately ten miles What did both of these communications devices have in common They both used waves to carry a signal The first used sound waves, and the second used light waves Since light waves travel much faster than sound waves, the latter device worked much better and over greater distances However, a dilemma remained Both of these early devices required a human interpreter on the other end at all times The instrument of the human ear and the instrument of the human eye were used to interpret the data that was carried on the sound and light waves, respectively In order to send information without a human interpreter, scientists and engineers had to develop concepts and tools related to electricity Today s carrier waves are almost always electromagnetic waves Mechanical devices can be formed that transmit the waves and also receive the waves This means that data can be sent and received by modulating the data onto the waves For example, the frequency can be modified to represent a binary 1 or a binary 0 The wave is generated, but it is manipulated in such a way that it carries binary data, and this makes it a carrier wave.



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EXAMPLE 97 Let G be the 3 3 matrices with real entries and nonvanishing determinant a b c d e f g h i Let the group law be matrix multiplication As we noted in Example 94, this is a group Let H be the subset of G consisting of those matrices with nonzero entries on the main diagonal and zero entries off the diagonal a 0 0 0 e 0 0 0 i Then H is a subgroup Let G be a group and H a subgroup Let us de ne a relation R on G as follows: (x, y) R provided that x 1 y H If x is any element of G then of course x 1 x = e H so the relation is re exive Notice that x 1 y H if and only if y 1 x H , for these elements are multiplicative inverses of each other, and H is a group Thus the relation is symmetric Finally, suppose that x, y, z G, that x is related to y, and that y is related to z Then x 1 y H and y 1 z H As a result, [x 1 y] [y 1 z] = x 1 z H So we may conclude that x is related to z, and the relation is transitive Therefore we have an equivalence relation The equivalence relation partitions the group G into pairwise disjoint subsets What do these subsets look like If x G then de ne x H = {x h : h H } The set x H is called a coset of H Notice the following properties: (1) Elements of x H are distinct: If h, k H then xh = xk implies x 1 (xh) = x 1 (xk) hence h = k So the elements of x H are distinct (2) If a, b x H then aRb: If a, b x H then a = xh and b = xk for some h, k H But then a 1 b = (xh) 1 (xk) = h 1 x 1 xk = h 1 k H Thus a and b are related under R (3) If a x H and aRb then b x H: Now let a x H and assume that (a, b) R Thus a 1 b H So there is an element h H such that a = xh and there is another element k H such that a 1 b = k But then b = ak = (xh)k = x(hk) x H.





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PDF Viewer component allows the developers to show pdf documents in a WPF application.

 

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Fill PDF forms in C# with iTextSharp | Fun Projects of Various Types
26 Aug 2011 ... Fill PDF forms in C# with iTextSharp ..... (609mm x 508mm - for the rest of the world); Our implementation uses free and open source software ...

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