简介：ＡＮＥＦＦＥＣＴＩＶＥＩＭＰＲＯＶＥＭＥＮＴＯＦＲＥＭＥＳＡＬＧＯＲＩＴＨＭＸｉｏｎｇｇｕｉｊｉｎｇ；（熊规景）Ｘｉｅｓｉｑｉｎｇ（谢四清）（Ｉｎｓｔ．ｏｆＭａｔｈ．Ｓｃｉ．，ＣｈｉｎｅｓｅＡｃａｄｅｍｙｏｆＳｃｉｅｎｃｅｓ，４３００７１Ｗｕｈａｎ，...

简介：Inthispaper,anewgloballyconvergentalgorithmfornonlinearoptimizationproblemswithequalityandinequalityconstraintsispresented.ThenewalgorithmisofSQPtypewhichdeterminesasearchdirectionbysolvingaquadraticprogrammingsubproblemperiteration.Somerevisionsonthequadraticprogrammingsubproblemhavebeenmadeinsuchawaythattheassociatedconstraintregionisnonemptyforeachpointxgeneratedbythealgorithm,i.e.,thesubproblemsalwayshaveoptimalsolutions.Thenewalgorithmhastwoimportantproperties.Thecomputationofrevisionparameterforguaranteeingtheconsistencyofquadraticsubproblemandthecomputationofthesecondordercorrectionstepforsuperlinearconvergenceusethesameinverseofamatrixperiteration,sothecomputationamountofthenewalgorithmwillnotbeincreasedmuchmorethanotherSQPtypealgorithms;Anotheristhatthenewalgorithmcangiveautomaticallyafeasiblepointasastartingpointforthequadraticsubproblemsperiteration,thiswillobivouslysimplifythecomputationprocedureofthesubproblems.Somenumericalresultsarereported.

简介：Inthispaperweconsidertheeffectivereducibilityofthefollowinglineardifferentialequation:x=(A+∈Q(t,∈))x,|∈|≤∈0,whereAisaconstantmatrix,Q(t,e)isquasiperiodicint,andeisasmallperturbationparameter.WeprovethatiftheeigenvaluesofAandthebasicfrequenciesofQsatisfysomenon-resonantconditions,thelineardifferentialequationcanbereducedtoy=(A^*(∈)+R^*(t,∈))y,|∈|≤∈o,whereR^*isexponentiallysmallin∈.

简介：复杂系统除了受到不确定性的影响以外,还常常演化为多重时间尺度和(或)多重空间尺度。因此,相应的随机偏微分方程模型包含了时间空间上的多尺度。段金桥与王伟的新书《EffectiveDynamicsofStochasticPartialDifferentialEquations(随机偏微分方程的有效动力学)》重点研究具有快慢时间尺度及大小空间尺度的随机偏微分方程,将平均、慢流形、均匀化等基本技巧发展到随机偏微分方程中,从中萃取出有效动力学。这本书之所以提出有效动力学的原因有二:一方面,有效动力学正