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…     

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 )　　…     

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…     

A note on a theorem of Tas, Telci and Fisher

I.IntroductionInarecentpaperTas,TelciandFisherlZ],obtainedthefollowingimprovedandgeneralizedversionofafixedpointtheoremofSharmaandSahulll:TheoremALet.A,B,SandTbeselfmappillgsonacompletemetricspace(X,ti,satisfyingA(X)GT(X)andB(X)GS(X)(l.l)[d(Ax,By)]2$Clmax{[d(Sx,Ax)]',[d(Ty,By)jZ,[d(Sx,Ty)]2} cd.max{d(Sx,Ax).d(Sx,By),d(Ax,Ty).d(By,Ty)} c,.d(Sx,By).d(Ty,As)(1.2)t'orallx,yinX,whereof,cZ,c3>0,of 2c2相似文献   

THE HOLDER CONTINUITY OF GENERALIZED SOLUTIONS OF A CLASS QUASILINEAR PARABOLIC EQUATIONS

I.IntroductionLetFbethen-dimensionalEuclideanspaceandGaboundeddomaininM,WI(C)andM(C)beusualSobolevspaces.Let0相似文献   

On the existence of periodic solutions for nonlinear system with multiple delays

IntroductionInthispaper,westudyT_periodicsolutionsofthefollowingnonlinearsystemwithmultipledelays x(t) =f(t,x(t) ,x(t-τ1(t) ) ,… ,x(t -τm(t) ) ) ,(1 )wherex(t) ∈C(R ,R) ,fiscontinuous,f(t+T ,·) =f(t,·) ,τi(t) (i=1 ,2 ,… ,m)arecontinuousperiodicfunctionsofperiodT .AlemmaisintroducedfordiscussingtheexistenceofT_periodicsolutionofsystem (1 ) .LetXbeaBanachSpace ,considerthefollowingoperatorequation :Lx =λNx　　 (λ∈ [0 ,1 ] ) ,whereL :DomL∩X→Xisalinearoperator,λ∈ [0 ,1 ]isapa…     

Problem of periodic solutions for neutral functional differential equation

ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＣ(ｋ- 1)2π =ｈ(ｔ) ｜ｈ :Ｒ →Ｒｉｓ (ｋ -1 )＿ｔｈｏｒｄｅｒｃｏｎｔｉｎｕｏｕｓｄｉｆｆｅｒｅｎｔｉａｂｌｅａｎｄｈ(ｔ+ 2π) ≡ｈ(ｔ) ,　　Ｃ2π =ｈ(ｔ) ｜ｈ :Ｒ →Ｒｉｓｃｏｎｔｉｎｕｏｕｓａｎｄｈ(ｔ+ 2π) ≡ｈ(ｔ) ,　　‖ｈ(ｔ)‖ =ｓｕｐｔ∈ [0 ,2π] ｜ｈ(ｔ) ｜ ,　　‖ｈ(ｔ)‖Ｐｋ- 1 =ｍａｘ‖ｈ(ｔ)‖ ,‖ｈ′(ｔ)‖ ,… ,‖ｈ(ｋ- 1) (ｔ)‖ ,　　ｘ(ｍ) (ｔ+ ·) (θ) =ｘ(ｍ) (ｔ+θ)　　θ∈Ｒ (ｍ =0 ,1 ,2 ,… ,ｋ-1 ) .Ｃｌｅａｒｌｙ ,ｘ(ｍ) (ｔ + ·) ∈Ｃ2π, …     

Oscillation criteria for second order nonlinear differential equation with damping

1IntroductionandProblem Thefollowingisthesecondordernonlineardifferentialequationwithdamping: [p(t)ψ(y)u(y′)]′ r(t)y′(t) q(t)f(y)g(y′)=0(t≥t0),(1) inwhich,p(t)∈C′([t0,∞),(0,∞)),r(t)∈C([t0,∞),(-∞,∞)),q(t)∈C([t0, ∞),[0,∞))withtheexistenceofT≥t0,q(t)≠0,t∈[T,∞),f(y),g(y),ψ(y),u(y) ∈C((-∞,∞),(-∞,∞)),andyf(y)>0,yu(y)>0,y≠0. Thesolutiony(t)ofEq.(1)iscallednormalsolutionify(t)isthenon_constantsolutionof Eq.(1)andsupt≥t0｜y(t)｜>0(refertoRef.[1]).Anormalsolutionisoscill…     

On (g, f)-factorizations of graphs

I.IntroductionLetGbeafinitegraph(withoutloops),V(G)andE(G)bethevenicessetandedgesset,respectively.Foreachxos(G),wedenotebydo(x)thedegreeofxinG.Letg,fbetwononnegativeinteger-valuedfunctionsdefinedonV(G)andg相似文献   

CONTROLLABILITY OF A CLASS OF HYBRID DYNAMIC SYSTEMS (Ⅲ)—MULTIPLE TIME_DELAY CASE

IntroductionConsidertheswitchedlinearsystemwithmultipletime_delaysincontrolfunctiongivenby x(t) =Ar(t) x(t) +Br(t) u(t) + Kk=1Dr(t) ,ku(t -τk) ,(1)wherex(t) ,u(t)andr(t)isdefinedasbefore ,(Ai,Bi,Di,1,… ,Di,K)｜i=1,… ,Nisafinitefamilyofsystemrealizations.Moreover,r(t) =iimplies (Ai,Bi,Di,1,… ,Di,K)ischosenasthesystemrealizationattimet.K <∞isthenumberoftime_delaysinthesystem .0<τ1<… <τKareKfixedtime_delays .Remark 1　Similarly ,wecandescribeswitchingpathbyintroducingswitchingsequ…     

UGD property of Musielak-Orlicz sequence spaces

LetXbeaBanachspace,S(X)andB(X)betheunitsphereandunitballofX ,respectively.ByX ,X denotethedualandtwicedualspaceofX ,respectively .Ifthereexistsafunctiong( · ,·) :S(X) ×S(X) →Rwhichsatisfiesanyε >0 ,x,y∈S(X)thereexistsδ(ε,x,y) >0 ,whenh <δ(ε,x,y)(‖x+hy‖ -‖x‖h -g(x ,y) <ε ,wesaythatXisGateauxdifferential (GD) ;ifinf‖y‖=1δ(ε ,x ,y) >0XisFrechetdifferential(FD) ;ifinf‖x‖ =1δ(ε,x,y) >0XisuniformGateauxdifferential (UGD)andif inf‖x‖ =‖y‖ =1δ(ε,x,y) >0Xisunif…     

Proximal point algorithm with errors for generalized strongly nonlinear quasivariational inclusions

I.IntroductionLetHbeaHibertspaceendowedwithanorm11'11andaninnerproduct',.)andC(H)bethefamilyofallnonemptycompactsubsetsofH.LetT,A:H~C(H)besetvaluedmappings,g:H~Hbeasingle-valuedmappingand9:HxH~RU{ ac}besuchthatforeachfixedyeH,9.,y):H~RUt co}isaproperconvexlowersemicontinuousfunctiononHandg(H)ndomag'Y)#oforeachyeH,ThentheproblemoffindingxeH,ueT(x)andveA(x)suchthatg(x)edomag',x)and(u~v,y~g(x))39(g(x)'x)~9(y'x)(VYeH)(l.l)iscalledthegeneralizedstronglynonlinearquasivariationalinclusio…     

Singular perturbation of nonlinear vector boundary value problem

In this paper we study the perturbed boundary value problem of the form dx/dt=f(x,y,t;ε), εdy/dt=g(x,y,t;ε), a_1(ε)x(0,ε)+a_2(ε)y(0,ε)=a(ε) b_1(ε)x(1,ε)+εb_2(ε)y(1,ε)=β(ε)in whichx,f,β∈E~m, y,g,a∈E~n, 0<ε(?)1and a_1(ε), a_2(ε), b_2(ε)and b_2(ε) are matrices of the appropriate size. Under the condition that g_y(t) is nonsingular and other suitable restrictions, the existence of the solution is proved, the asymptotic expansion of solution of order n is constructed, and the remainder term is estimated.     

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…     

《实验力学》2003年(第18卷)作者索引

白象忠 (BAI Xiang- zhong)　　　 2 (193) ,3(393)　邴歧大 (BING Qi- da) 2 (15 6 )　蔡继红 (CAI Ji- hong) 2 (16 6 )　曹正元 (CAO Zheng- yuan) 2 (16 1)　常江 (CHANG Jiang) 3(338)　陈继光 (CHEN Ji- guang) 3(389)　陈金龙 (CHEN Jin- long) 2 (199)　陈金龙 (CHEN Jin- long) 2 (2 2 9)　陈岭丽 (CHEN L ing- li) 4 (5 49)　陈骝 (CHEN L iu) 1(12 3) ,2 (2 39)　陈维善 (CHEN Wei- shan) 1(73)　陈晓宏 (CHEN Xiao- hong) 1(39)　陈学东 (CHEN Xue- dong) 4 (5 2 0 )　陈占清 (CHEN Zhan- qing) 1(…     

EDITORAL 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)     

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 ( …     

Fixed Points on Two Complete and Compact Metric Spaces

ＩｎｔｒｏｄｕｃｔｉｏｎＴｈｅｆｏｌｌｏｗｉｎｇｒｅｌａｔｅｄｆｉｘｅｄｐｏｉｎｔｔｈｅｏｒｅｍｗａｓｐｒｏｖｅｄｉｎ [1 ] .Ｔｈｅｏｒｅｍ 1　Ｌｅｔ(Ｘ ,ｄ)ａｎｄ (Ｙ ,ρ)ｂｅｃｏｍｐｌｅｔｅｍｅｔｒｉｃｓｐａｃｅｓ,ｌｅｔＴｂｅａｍａｐｐｉｎｇｏｆＸｉｎｔｏＹａｎｄｌｅｔＳｂｅａｍａｐｐｉｎｇｏｆＹｉｎｔｏＸｓａｔｉｓｆｙｉｎｇｔｈｅｉｎｅｑｕａｌｉｔｉｅｓρ(Ｔｘ,ＴＳｙ) ≤ｃｍａｘ ｄ(ｘ ,Ｓｙ) ,ρ(ｙ,Ｔｘ) ,ρ(ｙ,ＴＳｙ) ,ｄ(Ｓｙ ,ＳＴｘ) ≤ｃｍａｘ ρ(ｙ ,Ｔｘ) ,ｄ(ｘ,Ｓｙ) ,ｄ(ｘ ,ＳＴｘ)…     

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)