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简介：Inthispaper,weanalyzethefuzzyreliabilityofparallelingsystem,focusingonthesituationoftheearlyfailuremode.TheearlyfailuremodeoffuzzyreliabilitymainlyobeystheWeibulldistribution.Basedonthis,weobtainthedistributionfunction,densityfunction,failurefunction,reliabilityfunctionandtheformulaofthemeantimetofailure.Fortheparallelingsystemcomposedofmultiplecomponents,C1,C2,???,Cn,especiallywhenη=1,wealsoobtainthecorrespondingformulas.Finally,weciteanexampletoverifytheformulaanddeepentheunderstanding.

简介：LongtimebehaviorofdegenerateequationswiththenonlinearityofpolynomialgrowthofarbitraryorderonthewholespaceRNisconsidered.Byusing-trajectoriesmethods,weprovedthatweaksolutionsgeneratedbydegenerateequationspossessan(L2U(RN),L2loc(RN))-globalattractor.Moreover,theupperboundsoftheKolmogorovε-entropyforsuchglobalattractorarealsoobtained.

简介：Generalizedcase-cohortdesignhasbeenprovedtobeacost-effectivewaytoenhancetheefficiencyoflargeepidemiologicalcohort.Inthisarticle,weproposeaninferenceprocedureforestimatingtheunknownparametersinCox’sproportionalhazardsmodelingeneralizedcase-cohortdesignandestablishanoptimalsamplesizeallocationtoachievethemaximumpoweratagivenbudget.Thefinitesampleperformanceoftheproposedmethodisevaluatedthroughsimulationstudies.TheproposedmethodisappliedtoarealdatasetfromtheNationalWilm’sTumorStudyGroup.

简介：Tow-phaseflowmixedvariationalformulationsofevolutionfiltrationproblemswithseawaterintrusionareanalyzed.Adualmixedfractionalflowvelocity-pressuremodelisconsideredwithanair-freshwaterandafreshwater-seawatercharacterization.Foranalysisandcomputationalpurposes,spatialdecompositionsbasedonnonoverlappingmultidomains,aboveandbelowthesealevel,arevariationallyintroducedwithinternalboundaryfluxesdualizedasweaktransmissionconstraints.Further,parallelaugmentedandexactlypenalizeddualityalgorithms,andproximationsemi-implicittimemarchingschemes,areestablishedandanalyzed.