HIGHER ORDER MULTIVARIABLE NRLUND EULER-BERNOULLI POLYNOMIALS

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｋｔｈｏｒｄｅｒＮ ｒｌｕｎｄＥｕｌｅｒｐｏｌｙｎｏｍｉａｌｓＥ(ｋ)ｖ (ｘ｜ω1,… ,ωｋ)ａｎｄＢｅｒｎｏｕｌｌｉｐｏｌｙｎｏｍｉａｌｓＢ(ｋ)ｖ (ｘ｜ω1,… ,ωｋ)ａｒｅｇｉｖｅｎｂｙｔｈｅｆｏｌｌｏｗｉｎｇｅｘｐａｎｓｉｏｎｆｏｒｍｕｌａｒｅｓｐｅｃｔｉｖｅｌｙ[1]2 ｋｅｘｔ(ｅω1 ｔ+ 1 )… (ｅωｋｔ+ 1 ) = ∞ｖ=0Ｅ(ｋ)ｖ (ｘ｜ω1,… ,ωｋ) ｔｖｖ!,( 1 )ω1…ωｋｔｋｅｘｔ(ｅω1 ｔ-1 )… (ｅωｋｔ-1 ) = ∞ｖ=0Ｂ(ｋ)ｖ (ｘ｜ω1,… ,ωｋ) ｔｖｖ!. ( 2 )Ｃｌｅａｒｌｙｔ…     

EPSILON-ALGORITHM AND ETA-ALGORITHM OF GENERALIZED INVERSE FUNCTION-VALUED PAD APPROXIMANTS USING FOR SOLUTION OF INTEGRAL EQUATIONS

IntroductionLetf(x ,λ)beagivenpowerserieswithfunction_valuedcoefficients,i.e.,f(x ,λ) =c0 (x) +c1(x)λ+c2 (x)λ2 +… +cn(x)λn+… ,( 1 )wherecj(x)isarealorcomplexfunctionwithregardasxwhichisdefinedon (a ,b) .Supposethatf(x,λ)isanalyticasafunctionofλattheoriginλ=0 .ItisknownthatPad啨ａｐｐｒｏｘｉｍａｎｔｍｅｔｈｏｄｓａｒｅｕｓｅｄｆｏｒｏｂｔａｉｎｉｎｇｔｈｅｓｏｌｕｔｉｏｎｏｆａｗｋｗａｒｄｉｎｔｅｇｒａｌｅｑｕａｔｉｏｎｓ,andespeciallythosewhichpossessageneratingfunctionoftheform ( …     

GLOBAL DYNAMICS OF DELAYED BIDIRECTIONAL ASSOCIATIVE MEMORY （BAM） NEURAL NETWORKS

IntroductionConsiderthebidirectionalassociativememory (BAM )neuralnetworkswithconstanttransmissiondelaysdescribedbyasystemofdelaydifferentialequationsoftheform[1,2 ]:dxi(t)dt =-aixi(t) nj=1bijfj(yj(t-σij) ) Ii,　　i=1 ,2 ,… ,m ,dyj(t)dt =-cjyj(t) mi=1djigi(xi(t-τji) ) Jj,　　j=1 ,2 ,… ,n ,fort >0 .Thesystem ( 1 )consistsoftwosetsofneurons (orunits)arrangedontwolayers,namely ,I_layerandJ_layer.Inthesystem ( 1 ) ,xi( ·)andyj( ·)denotemembranepotentialoftheithneuronsfromtheI_laye…     

地震作用下高层钢结构的最优MTMD控制策略及设计

基于一般 MTMD,导出了 MTMD( )、MTMD( )和 TMD的动力放大系数 ( DMF)。以具有 MTMD( )、MTMD( )或 TMD结构的动力放大系数最大值中的最小值为优化准则。基于优化准则 ,列表显示了MTMD( )、MTMD( )和 TMD的最优参数。同时研究了最优参数对振型参与系数的敏感性。提出了 MTMD( )、MTMD( )和 TMD结构 -MTMD( )、MTMD( )和 TMD系统的优化设计方法。数值模拟表明 ,MTMD( )、MTMD( )和 TMD能有效地减小高层钢结构的地震反应     

General solution of A 2-D weak singular integral equation with constraint and its applications

Hertz'ssolutionTheProjectsupportedbytheNaturalScienceFoundationofGuangdongProvinceofChina[.IntroductionTheintegralequationsubjecttoconstraintp(s,te)=o,for(s,W)-(r,o)6Q={(r,O)lF(r,o)>c.}'(l.2)hasbeenstudiedin[l].Themultipleintegrationsimilartothelefthandsi…     

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅱ)—SINGLE TIME_DELAY CASE

IntroductionConsideraswitchedlinearsystemwithsingletime_delayinthecontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) +Dr(t) u(t -τ) ,(1)wherex(t) ∈Rnisthestate,u(t) ∈R mtheinput,thepiecewiseconstantscalarfunctionr(t) :R+ → 1,2 ,… ,Nistheswitchingpath ,(Ai,Bi,Di) ｜i =1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimpliesthat(Ai,Bi,Di)ischosenasthesystemrealizationattimet.τ >0isthefixedtimedelayincontrol.Inthispaper ,wewillstudythecontrollabilityofsystem (1) .Theone_per…     

GENERALIZED VECTOR QUASI-EQUILIBRIUM PROBLEMS IN LOCALLY G-CONVEX SPACES

IntroductionLetX ,YbetwotopologicalspacesandZbeanonemptyset.LetF∶X×X→ 2 Z,A∶X→ 2 XandC∶X→ 2 Zbeset_valuedmappingswhere2 ZdenotesthefamilyofallsubsetsofZ .　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅰ ) (inshort,GVQEP(Ⅰ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 1 )　　Thegeneralizedvectorquasi_equilibriumproblemofType (Ⅱ ) (inshort,GVQEP(Ⅱ ) )istofind ^x∈Xsuchthat^x∈A( ^x)andF( ^x ,z) C( ^x) ,　　 z∈A( ^x) . ( 2 )　　…     

THE ORTHOGONAL POLYNOMIALS AND THE PADE'APPROXIMATION

I.IntroductionThePade'approximationisatypeofrationalfractionapproximationtoafunction.LetfberepresentedbyapowerseriesthenUI(x)/Vm(x)issaidtobethei,mPade'approximanttof(x),denotedby[l/m],ifUI(x)isapolynomialofdegreeatmostl,Vin(x)isapolynomialofdegreeatmostnlandf(x)~UI(x)/Vm(x)=O(xl " ')(l.2)Ifl=m,thePade'approximantiscalledadiagonalone.APade'approximantisusefulinthatitmayapproximatelyrepresentafunctiononasetlargerthantheintervalofconvergenceofitsTaylorseries(l.l)if'31.Theorthogonalpolynom…     

EDITORIAL COMMITTEE OF “APPLIED MATHEMATICS AND MECHANICS”

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in-chief: Yeh, Kai-yuan (叶开沅) Standing Members:Guo Zhong-heng (郭仲衡) Yang Gui-tong (杨佳通) Chen Zhi-da (陈至达) Tan Hao-sheng (谈镐生) Zhou Heng (周恒) Li Hao (李灏) Chu Chao-hsiang (朱兆祥) Wu Xue-mou (吴学谋) Hsueh Dah-wei (薛大为) Loo Wen-da (卢文达) Ouyang Chang (欧阳鬯)     

EDITORIAL COMMITTEE OF “APPLIED MATHEMATICS AND MECHANICS”

Editor-in-chief: Chien, Wei-zang (钱伟长) Vice Editor-in-chief: Yeh, Kai-yuan (叶开沅) Standing Members:Guo Zhong-heng (郭仲衡) Yang Gui-tong (杨佳通) Chen Zhi-da (陈至达) Tan Hao-sheng (谈镐生) Zhou Heng (周恒) Li Hao (李灏) Chu Chao-hsiang (朱兆祥) Wu Xue-mou (吴学谋) Hsueh Dah-wei (薛大为) Loo Wen-da (卢文达) Ouyang Chang (欧阳鬯)