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by the concavity of the logarithm, it follows, by taking expectations, that W (b, F ) is concave in b. Finally, to prove the convexity of W (F ) as a function of F , let F1 and F2 be two distributions on the stock market and let the corresponding optimal portfolios be b (F1 ) and b (F2 ), respectively. Let the log-optimal portfolio corresponding to F1 + (1 )F2 be b ( F1 + (1 )F2 ). Then by linearity of W (b, F ) with respect to F , we have W ( F1 + (1 )F2 ) = W (b ( F1 + (1 )F2 ), F1 + (1 )F2 ) = W (b ( F1 + (1 )F2 ), F1 ) + (1 )W (b ( F1 + (1 )F2 ), F2 ) W (b (F1 ), F1 ) + (1 )W (b (F2 ), F2 ), (16.10) since b (F1 ) maximizes W (b, F1 ) and b (F2 ) maximizes W (b, F2 ). Lemma 16.1.2 The set of log-optimal portfolios with respect to a given distribution is convex. Proof: Suppose that b1 and b2 are log-optimal (i.e., W (b1 , F ) = W (b2 , F ) = W (F )). By the concavity of W (b, F ) in b, we have W ( b1 + (1 )b2 , F ) W (b1 , F ) + (1 )W (b2 , F ) = W (F ). (16.11) Thus, b1 + (1 )b2 is also log-optimal. In the next section we use these properties to characterize the logoptimal portfolio. (16.9)

18.6.3.3.1 AAL-1. AAL-1 is used to provide transport for synchronous bit streams. Its primary application is to adapt ATM cell transmission to typically E1/ DS1 and SDH/ SONET circuits. AAL-1 is speci cally used for voice communications (POTS; plain old telephone service). AAL-1 robs one octet from the payload and adds it to the header, leaving only a 47-octet payload. This additional octet in the header contains two major elds: (1) sequence number (SN), and (2) sequence number protection (SNP). The principal purpose of these two elds is to check that missequencing of information does not occur, by verifying a 3-bit sequence counter. It also allows for the original clock timing of the data received at the far end of the link. The SAR-PDU format of AAL-1 is shown in Figure 18.9.8 The 4-bit SN is broken down into a 1-bit CSI (convergence sublayer indicator) and a sequence count. The SNP contains a 3-bit CRC and a parity bit. End-to-end synchronization is an important function for the type of traf c carried on AAL-1. With one mode of operation, clock recovery is via a synchronous residual time stamp (SRTS) and common network clock by means of a 4-bit residual time

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On June 17, 1994, APA president Bob Resnick was formally recognized during the graduation ceremonies at the Walter Reed Army Medical Center for the rst two Department of Defense (DoD) Psychopharmacology Fellows, Navy Commander John Sexton and Lt Commander Morgan Sammons This program had been directed by the Fiscal Year 1989 Appropriations bill for the Department of Defense (PL 100 463) (US Department of Defense, 1988) and would ultimately graduate 10 fellows Upon their graduation, each of these courageous individuals became active within the practitioner community, demonstrating to their colleagues that psychologists can indeed readily learn to provide high-quality psychopharmacological care Several of the graduates have become particularly involved in providing consultation to evolving postdoctoral psychopharmacology training programs All of the external evaluations of the clinical care was provided by the DoD Fellows (ACNP, Summer, 2000)..

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