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1.
1 IntroductionInthispaper,weconsiderthefollowingperiodicinitialvalueproblemforthesystemofGinzburg LandauequationscoupledwithBBMequations:x∈Rεt+ με-(α1+iα2 )εxx+ (β1+iβ2 ) |ε|2 ε-iδnε=g1(x) ,(1 .1 )nt+ f(n) x+λn-αnxx-nxxt+ |ε|2 x =g2 (x) ,(1 .2 )ε(x+ 2π ,t) =ε(x ,t) ,n(x + 2π ,t) =n(x ,t) ,(1 .3)ε(x ,0 )…  相似文献   

2.
§ 1 IntroductionInthispaper ,wewillconsiderthesemilinearSchr dingerequationinonespacedimensionofthetypeut-iuxx =F(u) .  (x ,t)∈R×R+,( 1 )u(x ,0 ) =u0 , x ∈R ,( 2 )whereu =u(x ,t)iscomplex valuedfunction ,andFisasmoothfunctionofusuchthat|F(u) | =O( |u|α+1)for |u|sufficientlysmalland…  相似文献   

3.
Considerthefirstinitial boundaryvalueproblem u t=div q( u) ,  (x,t) ∈QT,(1 )u(x,t) =0 ,  (x,t) ∈ Ω× (0 ,T) ,(2 )u(x,0 ) =u0 (x) , x∈Ω ,(3 )whereΩisaboundeddomaininRNwithsmoothboundary Ω ,QT=Ω× (0 ,T) , q = φ ,φ∈C1(RN) ,and φ , qsatisfythestructureconditions(λ|ξ|1+δ-1 ) +≤ φ(ξ) ≤Λ|ξ|1+δ+ 1 ,  ξ∈RN,(4 )| q(ξ) …  相似文献   

4.
岳优兰  王月山 《数学季刊》1999,14(2):108-110
§1. IntroductionAlocallyintegrablefunctionf(x)belongstoLipα(Rn),ifthereisaconstantC,suchthatforeveryx,y∈Rn|f(x)-f(y)|≤C|x-y|α  ThesmallestconstantCsatisfiesaboveiscalledLipschitznormoffandisdenotedbyyfy∧α.By[1],f∈Lipα(Rn)equivalenttof∈εα,2,whereεα,2=…  相似文献   

5.
§ 1.Introduction Forthewell knownBernsteinpolynomialBn(f;x) = nk=0f kn pn,k(x) , pn ,k(x) =nk xk( 1 -x) n-k,BerensandLorentz[1]provedthatforf∈C[0 ,1 ] ,0 <α<2 ,onehas| (Bnf-f) (x) |=O x( 1 -x)nα/ 2 ω2 (f;t) =O(tα) . ( 1 .1 )Ontheotherhand ,DitzianandTotik[2 ]obtainedthatforf∈C[0 ,1 ] ,0 <α<2 ,onehas| (Bnf -f)…  相似文献   

6.
1 IntroductionForsolvingstiffinitialvalueproblemsforsystemsofODEsy′=f(y) ,y(t0 ) =y0 ,t0 <t≤T ,y0 ,y∈Rm,f :Ω Rm →Rm (1 .1 )manyparticularone blockmethodsoftheformYn+1= AYn+h( B0 F(Yn) + B1F(Yn+1) ) , A =A Im, Bi=Bi Im,A ,Bi∈Rr×r,Yn =(YTnr,… ,yT(n+1)r- 1) T,F(Yn) =(fT(ynr) ,… ,fT(y(n+1)r- 1) ) T,yj≈ y(tj) ,…  相似文献   

7.
高一年级1.设 f(t) =t3 +2 0 0 3t,易证 f(t)在R上是奇函数且递增函数 ,由题意可知 :f(x - 1) =- 1, f(y - 1) =1.即 f(x - 1) =-f( y - 1) =f( 1-y) .∴ x - 1=1-y ,故x +y =2 .2 .由条件知 :sinαcosβ2 0 0 2 ,sinβcosα2 0 0 2 中必有一个不大于 1,一个不小于 1.不妨设  sinαcosβ2 0 0 2 ≤ 1,  sinβcosα2 0 0 2 ≥ 1.∵ α ,β∈ ( 0 ,π2 ) ,又y=sinx在 ( 0 ,π2 )上递增 .∴ sinα≤cosβ且sinβ≥cosα .∴ sinα≤sin( π2 - β)且sinβ≥s…  相似文献   

8.
Periodic Solutions of Porous Medium Equations with Weakly Nonlinear Sources   总被引:1,自引:0,他引:1  
§ 1.Introduction ThispaperisconcernedwiththetimeperiodicsolutionsoftheporousmediumequationswithweaklynonlinearsourcesandwiththeDirichletboundaryvaluecondition ,namely ,theproblem u t =Δ(|u|m- 1u) +B(x ,t,u) +f(x ,t) inΩ×R ,(1 .1 )u(x ,t) =0 on Ω×R , (1 .2 )u(x ,t+ω) =u(x ,t) in Ω×R ,…  相似文献   

9.
1 IntroductionLetXbeacompactHausdorffspace ,withC(X)thespaceofcontinuousfunctionsdefinedonX ,andletM C(X)benonempty.LetF(x ,y) :X×R →Rbeanon negativefunction ,andconsiderthefollowingminimizationproblem :findy∈Mtominimize‖F(.,y )‖ ,(1)where‖F (.,y )‖ =supx∈XF(x ,y(x) ) .Them…  相似文献   

10.
20 0 2年全国高中数学联赛试题第 15题 :设二次函数 f(x) =ax2 +bx +c  (a ,b ,c∈R ,a≠ 0 )满足条件 :(1)当x∈R时 ,f(x -4 ) =f(2 -x) ,且f(x)≥x ;(2 )当x∈ (0 ,2 )时 ,f(x)≤ (x + 12 ) 2 ;(3)f(x)在R上的最小值为 0 .求最大的m(m >1) ,使得存在t∈R ,只要x∈ [1,m ] ,就有 f(x +t)≤x .解 f(x -4 ) =f(2 -x) ,∴ 函数 f(x)的图象关于直线x =-1对称 ,∴  -b2a=-1,即b =2a①令 g(x) =(x + 12 ) 2 ,则直线 y =x与抛物线 g(x) =(x + 12 ) 2图 1相切于点A(1,1) .又当x∈…  相似文献   

11.
12.
We present a unified approach to compute the number of connected components in the group of real points of adjoint almost simple real algebraic groups.  相似文献   

13.
本文在LF拓扑空间中建立了L-fuzzy集网的弱收敛(R-收敛)概念,应用文[4]中的R-闭包,系统讨论了它们的性质,证明了等式RlimA_n=∧(∨A_m)_R和RlimA_n=A_n=∧(∨A_m)_R并且给出了L-fuzzy集网与其子网之间的关系。  相似文献   

14.
Let G be a graph and let Pm(G) denote the number of perfect matchings of G.We denote the path with m vertices by Pm and the Cartesian product of graphs G and H by G×H. In this paper, as the continuance of our paper [W. Yan, F. Zhang, Enumeration of perfect matchings of graphs with reflective symmetry by Pfaffians, Adv. Appl. Math. 32 (2004) 175-188], we enumerate perfect matchings in a type of Cartesian products of graphs by the Pfaffian method, which was discovered by Kasteleyn. Here are some of our results:1. Let T be a tree and let Cn denote the cycle with n vertices. Then Pm(C4×T)=∏(2+α2), where the product ranges over all eigenvalues α of T. Moreover, we prove that Pm(C4×T) is always a square or double a square.2. Let T be a tree. Then Pm(P4×T)=∏(1+3α2+α4), where the product ranges over all non-negative eigenvalues α of T.3. Let T be a tree with a perfect matching. Then Pm(P3×T)=∏(2+α2), where the product ranges over all positive eigenvalues α of T. Moreover, we prove that Pm(C4×T)=[Pm(P3×T)]2.  相似文献   

15.
Let R(A) denote the row space of a Boolean matrix A of order n. We show that if n 7, then the cardinality |R(A)| (2n–1 - 2n–5, 2n–1 - 2n–6) U (2n–1 - 2n–6, 2n–1). This result confirms a conjecture in [1].AMS Subject Classification (1991): 05B20 06E05 15A36Support partially by the Postdoctoral Science Foundation of China.Dedicated to Professor Chao Ko on the occasion of his 90th birthday  相似文献   

16.
An estimator of the number of components of a finite mixture ofk-dimensional distributions is given on the basis of a one-dimensional independent random sample obtained by a transformation of ak-dimensional independent random sample. A consistency of the estimator is shown. Some simulation results are given in a case of finite mixtures of two-dimensional normal distributions.  相似文献   

17.
Let A be a UFD of characteristic p > 0, let 𝒵 be a set of some eigenvectors of a derivation of A. We prove, under some additional assumptions, a necessary and sufficient condition for 𝒵 to be a p-basis of the minimal ring of constants containing 𝒵. The main preparatory result is the unique decomposition theorem with respect to a factor from a given subalgebra containing Ap.  相似文献   

18.
N/Kbe a Galois extension of number fields with finite Galois group G.We describe a new approach for constructing invariants of the G-module structure of the K groups of the ring of integers of N in the Grothendieck group of finitely generated projective Z[G]modules. In various cases we can relate these classes, and their function field counterparts, to the root number class of Fröhlich and Cassou-Noguès.  相似文献   

19.
马海成 《数学研究》2003,36(2):215-218
设P1,P2,……,Pt是几乎覆盖图G的l条不相交的路,s是没有被这些路覆盖的孤立点数.本证明:(i)匹配多项式μ(G,x)的非零根的重数最多是l,零根的重数最多l s。(ii)对于不含三角形的n阶图G,伴随多项式h(G,x)的非零根的重数最多是l,零根的重数最多是1/2(n l s).(iii)对一种含三角形的所谓A型图,(ii)也成立.  相似文献   

20.
任意矩阵的特征值的扰动估计   总被引:1,自引:0,他引:1  
宋永忠 《应用数学》1992,5(4):19-25
设A和B是两个任意的n阶方阵,其特征值分别为{λ_1,…,λ_n}和{μ_1,…,μ_n}.本文对此两组特征值的如下“距离”的界给出了若干估计: B对于A的谱改变量 A与B的特征值的改变量这里的结果包含了Bauer-Fike定理,并且优于Kahan-Parlett/Jiang定理及Chu,施和肖所得出的结果.  相似文献   

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