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Case P (case + p)
Selected AbstractsRare-event component importance for the consecutive- k systemNAVAL RESEARCH LOGISTICS: AN INTERNATIONAL JOURNAL, Issue 2 2002Hsun-Wen Chang Abstract Various indices of component importance with respect to system reliability have been proposed. The most popular one is the Birnbaum importance. In particular, a special case called uniform Birnbaum importance in which all components have the same reliability p has been widely studied for the consecutive- k system. Since it is not easy to compare uniform Birnbaum importance, the literature has looked into the case p = ½, p , 1, or p , ½. In this paper, we look into the case p , 0 to complete the spectrum of examining Birnbaum importance over the whole range of p. © 2002 Wiley Periodicals, Inc. Naval Research Logistics 49: 159,166, 2002; DOI 10.1002/nav.10001 [source] On L1 -minimization in optimal control and applications to roboticsOPTIMAL CONTROL APPLICATIONS AND METHODS, Issue 6 2006G. Vossen Abstract In this paper, we analyze optimal control problems with control variables appearing linearly in the dynamics. We discuss different cost functionals involving the Lp -norm of the control. The case p = 0 represents the time-optimal control, the case p > 1 yields a standard smooth optimal control problem, whereas the case p = 1 leads to a nonsmooth cost functional. Several techniques are developed to deal with the nonsmooth case p = 1. We present a thorough theoretical discussion of the necessary conditions. Two types of numerical methods are developed: either a regularization technique is used or an augmentation approach is applied in which the number of control variables is doubled. We show the precise relations between the L1 -minimal control and the bang,bang or singular controls in the augmented problem. Using second-order sufficient conditions (SSC) for bang,bang controls, we obtain SSC for L1 -minimal controls. The different techniques and results are illustrated with an example of the optimal control for a free-flying robot which is taken from Sakawa. Copyright © 2006 John Wiley & Sons, Ltd. [source] Reversible coagulation,fragmentation processes and random combinatorial structures: Asymptotics for the number of groupsRANDOM STRUCTURES AND ALGORITHMS, Issue 2 2004Michael M. Erlihson Abstract The equilibrium distribution of a reversible coagulation-fragmentation process (CFP) and the joint distribution of components of a random combinatorial structure (RCS) are given by the same probability measure on the set of partitions. We establish a central limit theorem for the number of groups (= components) in the case a(k) = qkp,1, k , 1, q, p > 0, where a(k), k , 1, is the parameter function that induces the invariant measure. The result obtained is compared with the ones for logarithmic RCS's and for RCS's, corresponding to the case p < 0. © 2004 Wiley Periodicals, Inc. Random Struct. Alg. 2004 [source] Exact and approximative algorithms for coloring G(n,p)RANDOM STRUCTURES AND ALGORITHMS, Issue 3 2004Amin Coja-Oghlan We investigate the problem of coloring random graphs G(n, p) in polynomial expected time. For the case p , 1.01/n, we present an algorithm that finds an optimal coloring in linear expected time. For p , ln6(n)/n, we give algorithms which approximate the chromatic number within a factor of O( ). We also obtain an O(/ln(np))-approximation algorithm for the independence number. As an application, we propose an algorithm for deciding satisfiability of random 2k -SAT formulas over n propositional variables with , ln7(n)nk clauses in polynomial expected time. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004 [source] | ||||||||||