简介：Inthispaperthederivativeanditsexceptionalsetaccordingtothealternativelyjumpingfunctionandself-similarfunctionrespectivelyarediscussed.Andintheappendix,aproofofthestatement1.2(2)of“CalculusonCantortriadicset(Ⅱ)—derivative”whichisimportanttothediscussionofexceptionalsetisgiven.

简介：Thispaperisconcernedwiththetopologicalstructureofefficientsetsforoptimizationproblemofset-valuedmapping.Itisprovedthatthesesetsareclosedorconnectedundersomeconditionsoncone-continuity,cone-convexityandcone-quasiconvexity.

简介：Inthisnote,itisshownthatifarationalfunctionfofdegree≥2hasanonemptysetofburiedpoints,thenforagenericchoiceofthepointzintheJuliaset,zisaburiedpoint,andiftheJuliasetisdisconnected,ithasuncountablymanyburiedcomponents.

简介：AlocallysemicompletedigraphisadigraphD=(V,A)satisfyingthefollowingcondi-tionforeveryvertexx∈VtheD[O(x)]andD[I(x)]aresemicompletedigraphs.Inthispaper,wegetsomepropertiesofcyclesanddeterminetheexponentsetofprimitivelocallysemicompleteddigraphs.

简介：Inthispaper,westudythehomogeneouspolynomialsorthogonalwiththeweightfunctionh(x(d))=x2k11green.Itissimplerthantheformulain[2],andcanberegardedasanextensionof[1]undertheweightedcase.

简介：定义一个线性领唱者设置了C是线性重申的功能系统f_j(x)=r_jx+b_j的引起注意的人(j=1,2，...，N)，在线上令人满意强壮的分开的条件。为关于C的失衡的措施，我们学习集中上面并且为φ(t的集中的更低的密度)有奇异选择并且与s的自然选择的=t~s。

简介：Basedonalevelsetmodelandthehomogenizationtheory,anoptimizationalgorithmforfindingtheoptimalconfigurationofthemicrostructurewithspecifiedpropertiesisproposed,whichextendscurrentresearchonthelevelsetmethodforstructuretopologyoptimization.ThemethodproposedemploysalevelsetmodeltoimplicitlydescribethematerialinterfacesofthemicrostructureandaHamilton-Jacobiequationtocontinuouslyevolvethematerialinterfacesuntilanoptimaldesignisachieved.Meanwhile,themovingvelocitiesoflevelsetareobtainedbyconductingsensitivityanalysisandgradientprojection.Besides,howtohandletheviolatedconstraintsisalsodiscussedinthelevelsetmethodfortopologicaloptimization,andareturn-mappingalgorithmisconstructed.Numericalexamplesshowthatthemethodexhibitsoutstandingflexibilityofhandlingtopologicalchangesandfidelityofmaterialinterfacerepresentationascomparedwithotherconventionalmethodsinliteratures.

简介：<正>SpecialgeneratorsoftheunorientedcobordismringMO*areconstructedtodeterminesomegroupsJn,kl1,l2,…,lmofcobordismclassesinMOncontainingarepresentativeMnadmittinga（Z2）k-actionwiththefixedpointsetof（n-li）-dimensionalsubmanifoldsofMn.

简介：LetFλ={x∈(0,1){2nx}≥1/2k,n∈z+},z++={0,1,2,3,...},k∈N;F=U∞k=1Fλbeadecimalsetin(0,1),where{2nx}isthefractionalpartofanumber2nx.Inthisnote,weprovethatdirnнF=1andН1(F)=0,wheredimнisHausdroffdimension,andН1(F)istheHausdorffmeasureofF.

简介：一场集合比赛，一个联盟的价值被一个集合在表示而不是一个实数，是合作游戏的一种新类型。一个限制F的集合游戏是分区系统限制的一个集合游戏。主要定理分别地显示出IM值，OIM值，SCM值和ICM值的结构，并且IM值的相等和OIM值formonotonic设置分区系统也限制的比赛。

简介：SupposethatCisthecomplexplaneandkisanon-negativeinteger.DefinefunctionsNk-(x)=|x|kifkisevenandNk(x)=x|x|k-1ifkisodd.SomeapproximationpropertiesofNk-(x)’sisdiscussedandanewexampleofaTchebycheffsystemisgivenout.

简介：Abstract.Usingthemethodofundeterminedfunction,asetof12parameterrectangularp|atedementwithdoub[esetparameterandgeometrysymmetryisconstructed.TheirconsistencyerrorareO(h2),oneorderhigherthantheusua[12parameterrectangu|arp[ateelements.

简介：ThispapeerstudiestheknowndensitytheoremofArrow-Barankin-Blackwell.Thefollowingmainresultisobtained:IfXisaHausdorfflocallyconvexTopologicalspaceandCbelongtoXisaclosedconvexconewithboundedbase,thenforeverynonemptyweaklycompactconvexsubsetA,thesetofpositiveproperefficientpointsofAisdenseinthesetofefficientpointsofA.

简介：LetGbeanonabelianfinitegroup.ThenIrr(G/G′)isanabeliangroupunderthemultiplicationofcharactersandactsonthesetofnon-linearirreduciblecharactersofGviathemultiplicationofcharacters.Thepurposeofthispaperistoestablishsomefactsabouttheactionoflinearcharactergrouponnon-linearirreduciblecharactersanddeterminethestructuresofgroupsGforwhicheitheralltheorbitkernelsaretrivialorthenumberoforbitsisatmosttwo.Usingtheestablishedresultsonthisaction,itisveryeasytoclassifygroupsGhavingatmostthreenomlinearirreduciblecharacters.

简介：ThepaperisacontributiontotheproblemofapproximatingrandomsetwithvaluesinaseparableBanachspace.Thisclassofset-valuedfunctioniswidelyusedinmanyareas.Weinvestigatethepropertiesofp-boundedintegrablerandomset.Basedonthisweendowitwith△pmetricwhichcanbeviewedasaintegraltypehausdorffmetricandpresentsomeapproximationtheoremofaclassofconvolutionoperatorswithrespectto△pmetric.Moreoverwealsocanestablishanalogoustheoremforotherintegraltypeoperatorin△pspace.

简介：Somepropertiesofconvexconesareobtainedandareusedtoderiveseveralequivalentconditionsaswellasanotherimportantpropertyfornearlycone-subconvexlikeset-valuedfunctions.Undertheassumptionsofnearlycone-subconvexlikeness,aLagrangianmultipliertheoremonBensonproperefficiencyispresented.Relatedresultsaregeneralized.

简介：InthispaperweconsidertheapproximationforfunctionsinsomesubspacesofL~2bysphericalmeansoftheirFourierintegralsandFourierseriesonsetoffullmeasure.Twomaintheoremsareobtained.

简介：Thesolvabilityofaclassofforward-backwardstochasticdifferentialequations(SDEsforshort)overanarbitrarilyprescribedtimedurationisstudied.Theauthorsdesignastochasticrelaxedcontrolproblem,withbothdriftanddifftusionallbeingcontrolled,sothatthesolvabilityproblemisconvertedtoaproblemoffindingthenodalsetoftheviscositysolutiontoacertainHamilton-Jacobi-Bellmanequation.ThismethodovercomesthefataldifficultyencounteredinthetraditionalcontractionmappingapproachtotheexistencetheoremofsuchSDEs.

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简介：Afeedbackvertexsetisasubsetofverticesinagraph,whosedeletionfromthegraphmakestheresultinggraphacyclic.Inthispaper,westudytheminimum-weightfeedbackvertexsetprobleminseriesparallelgraphsandpresentalinear-timeexactalgorithmtosolveit.