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where S is the support set of the random variable. As in the discrete case, the differential entropy depends only on the probability density of the random variable, and therefore the differential entropy is sometimes written as h(f ) rather than h(X). Remark As in every example involving an integral, or even a density, we should include the statement if it exists. It is easy to construct examples
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Conversely, given a set of codeword lengths that satisfy this inequality, it is possible to construct a uniquely decodable code with these codeword lengths. Proof: Consider C k , the kth extension of the code (i.e., the code formed by the concatenation of k repetitions of the given uniquely decodable code C). By the de nition of unique decodability, the kth extension of the code is nonsingular. Since there are only D n different D-ary strings of length n, unique decodability implies that the number of code sequences of length n in the kth extension of the code must be no greater than D n . We now use this observation to prove the Kraft inequality. Let the codeword lengths of the symbols x X be denoted by l(x). For the extension code, the length of the code sequence is
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The implementation of EISs has a huge potential for applications in the O&G industry at different stages of the process and management. Due to market pressure, they have to use better tools oriented to quality monitoring, prediction, and diagnosis. In the speci c case of re ning, our proposal is to identify the key applications that can be solved successfully using EISs and others that may be interesting to test in the near future. The oil re ning industry is very complex. Because of the nature of this complexity there are numerous opportunities for implementation of EIS. The information available in the oil re nery has several inherent characteristics: a high number of variables and a small range of variation, and highly collinear and noisy data. Most of the time, there is no clear relation between the data and type of feed. These factors increase uncertainty and noise. The tools that are most commonly used include soft analyzer, model building, and time-series predictors. The use of fuzzy rule-based systems is suitable for operator advisory systems in normal and emergency situations. An alarm management tool can be a special case of this application. Control engineering is one of the activities with the highest number of opportunities for implementation of EISs. It is very well suited for hybrid control, mixing between conventional control theory and fuzzy systems. Essentially, opportunities for application of EISs exist in nearly every department of the O&G industry, namely, in plant operations, process engineering, control engineering, predictive maintenance, price prediction, information management, and advanced intelligent sensors.
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code is employed, and it shows three characters transmitted sequentially.5 The vertical arrows are receiver sampling points, which are points in time. Receiving timing begins when the rst pulse is received. If there is a 5% timing difference between the transmitter and receiver, the rst sampling at the receiver will be 5% away from the center of the transmitted pulse. At the end of the tenth pulse or signal element, the receiver may sample in error. Here we mean that timing error accumulates at 5% per received signal element and when there is a 50% accumulated error, the sampling will now be done at an incorrect bit position. The eleventh signal element will indeed be sampled in error, and all subsequent elements will be errors. If the timing error between transmitting machine and receiving machine is 2%, the cumulative error in timing would cause the receiving device to receive all characters in error after the 25th element (bit).
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while maintaining the original aspect ratio of the movie. Borders may appear on two sides of the movie.
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Cells harvested at the end of the rst passage (or later passages if an insuf cient number of cells is available at the end of the rst passage) are used for the assays that are deemed appropriate. In our laboratory, highest priority is given to loading ceramic cubes for implantation. We do this for two reasons. First, as indicated above, we regard this as the de nitive assay for stem cells. The second reason is a practical matter relating to the length of the in vivo assay (6 weeks in vivo plus time for histologic processing and evaluation) and the time that companies that provide serum are willing to hold the product on reserve. Because we are usually pushing the limit of the reserve time, we try to get the cubes implanted as quickly as possible. Additional cell preparations may be needed to provide enough cells to complete all of the required assays, and because duplicate or triplicate data sets are desirable. Among the other assays that we routinely include in the testing of FBS for human MSCs are the in vitro assays for osteogenesis and chondrogenesis. For the former,
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The preceding command uses sed both to transform the input_file by executing (-e) the search and replace instructions in quotes and to put the results into the output_file. The execution instructions direct sed to substitute (s) all values of OLD with NEW and to do so globally (g). Table 5-1 shows a migration I did about a year ago when I moved web host providers.
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