Titlebook: Encyclopedia of Marine Sciences; Hanneke J. G. Baretta-Bekker,Egbert K. Duursma,Bou Book 1998Latest edition Springer-Verlag Berlin Heidelb

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Applications of Stochastic Dominance Rules,Stochastic dominance rules are employed in numerous research fields, particularly in the following research areas: finance, economics, insurance, statistics, agriculture, and medicine. Due to space constraints, we will mention only a few such applications in this chapter.

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Inequalities,The manipulation of simple algebraic inequalities. The function |.|. The solution of inequalities reducible to the form f(.) > 0, where f(.) can then be expressed in factors: sketches of the graphs of . = f(.) in these cases.

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Partial Fractions,Partial fractions, to include denominators such as (. + .) (. + .) (. + .), (. + .) (. + .). and (. + .) (. + .).

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Averaging of the Iterates,The difficulty of selecting a good step size sequence {ε.} has been a serious handicap in applications. In a fundamental paper, Polyak and Juditsky [142] showed that (loosely speaking) if ε. goes to zero slower than .(1/.), the averaged sequence . converges to its limit at an optimum rate.

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Partial Fractions,Partial fractions, to include denominators such as (. + .) (. + .) (. + .), (. + .) (. + .). and (. + .) (. + .).

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Applications of Statistics and Probability to Seismic Disaster Mitigation Researches,There are many sources of uncertainties in the problems of earthquake engineering. These sources may be classified into three groups. They are (a) uncertainties In earthquake occurrences, (b).uncertainties In earthquake ground motions, and (c) uncertainties in structural response and seismic damage.