共查询到20条相似文献,搜索用时 78 毫秒
1.
Li Xunjing 《数学年刊B辑(英文版)》1982,3(5):655-662
Let X and Z be two reflexive Banach spaces, U\in Z and b(\cdot,\cdot):[t_0,T]*U\rightarrow X continuous. Suppose $x(t)\equiv x(t,u(\cdot))$ is a function from [t_0, T] into X , satisfying the distrbnted parameter system
$dx(t)\dt=A(t)x(t)+b(t,u(t)),t_0+\int_t_0^T {
+r(t,u(t))dt}$. We have proved the following theorem. Theorem. Suppose u^*(\cdot) is the optimal control function, $x^*(t)=x(t,u^*(\cdot))$ and $\psi (t)=-U'(T,t)Q_1x^*(T)-\int_t^T{U'(\sigma,t)Q(\sigma)x^*(\sigma)d\sigma}$, then the maximum principle $<\psi(t),b(t,u^*(t))>-1/2r(t,u^*(t))=\mathop {\max }\limits_{u \in U} {\psi (t),b(t,u)>-1/2r(t,u)}$ (16) holds for almost all t on [t_0, T ]. 相似文献
2.
Let T 1 be an integer, T = {0, 1, 2,..., T- 1}. This paper is concerned with the existence of periodic solutions of the discrete first-order periodic boundary value problems△u(t)- a(t)u(t) = λu(t) + f(u(t- τ(t)))- h(t), t ∈ T,u(0) = u(T),where △u(t) = u(t + 1)- u(t), a : T → R and satisfies∏T-1t=0(1 + a(t)) = 1, τ : T → Z t- τ(t) ∈ T for t ∈ T, f : R → R is continuous and satisfies Landesman-Lazer type condition and h : T → R. The proofs of our main results are based on the Rabinowitz's global bifurcation theorem and Leray-Schauder degree. 相似文献
3.
Trudinger和Gilbarg—Trudinger对椭园型方程的广义解推广了古典的最大值原理,唯一性定理也有新发展。现在我们把结果推广到一致抛物型方程的第一边值问题。 设Ω是n维欧氏空间E~n中的有界域,Ω为其边界,Q=Ω×(O,T),T是有限值。用(Q)记空间W_2~1(Q)的子空间,其函数在意义下满足如下边界条件: u(x,0)=0,x∈Ω和u(x,t)=0,x∈Ω,t∈(0,T)。 在Q考虑下面形状的方程 相似文献
4.
讨论如下抛物型方程模型问题: 这里Ω为具充分光滑边界(?)Ω的平面有界区域.假设对于讨论的f和A,(1.1)的解存在唯一,且具有所需要的正则性.引进q=-grad u,V=H(div,Ω),W=L~2(Ω),则(1.1)的变分形式如下:求{q,u}:t∈[0,T]→V×W,使 相似文献
5.
积分微分方程有限元逼近的强超收敛性 总被引:3,自引:0,他引:3
考虑下面的抛物型积分微分方程初边值问题: (a) ut+A(t)u+∫0tB(t,s)u(s)ds=f, (x,t)∈Q=Ω×J,J=(0,T] (b) u=0,(x,t)∈ Ω×J,(1) (c) u(x,0)=u0,x∈Ω,其中Ω为Rd(d≤4)中具有分片光滑边界 Ω的有界域,A(t)是一致正定的二阶椭圆微分算子 相似文献
6.
包立平 《高校应用数学学报(A辑)》2003,18(4):423-430
在空间H1,pg(Ω,Rn)中讨论如下一类变系数Ginzburg-Landau型泛函Eε(Ω)=∫Ωa(x)p|Δu|p+14εpb(x)(|u|2-β2(x))2dx的极小元列的渐近性质.这里2≤p0,m≤a(x),b(x),β(x)≤M,且a(x),b(x),β(x)是光滑函数.研究了当ε→0时极小元的渐近性态,证明了极小元列在H1,pg(Ω,Rn)中强收敛于某个元素,且得到了该元素所满足的微分方程边值问题. 相似文献
7.
汪更生 《数学物理学报(B辑英文版)》2001,21(4)
1 IntroductionThroughout this paPer, we denote n an opell bounded domain in Rn with smooth boulldary0fl, let Q = fl x (0,T) and r = 0n x (0,T). Let H = L'(n).We shall study the optimal control problems governed by the following system:y'(t) Ay(t) p(y(t) -- rk(t)) 9 B1u(t) I1(t), (1.1)y(0) = u0,rk'(t) Aop(f) 7(op(f)) = B2u(t) f2(f), (1.2)op(0) = op0with the state constrchtF(y) C W' (1.3)The pay-off functional is given byJ(y, u) = l"[,(,, y) h(u)]dt. (1.4)JoNote that y' and… 相似文献
8.
《数学物理学报(A辑)》2010,(6)
设B=(Ω,F,(F_t)_(t≥0),(B_t)_(t≥0),(P_x)_(x∈R~d))为L~2(R~d,m)上经典的布朗运动,(ε,D(ε))为其联系的对称狄氏型.设u∈D(ε),u(B_t)-u(B_0)=M_t~u+N_t~u为u(B_t)的Fukushima分解.该文主要研究由上鞅可乘泛函L_t~(-u):=e~(M_t~(-u)-1/2〈M~(-u〉t)对(B_t)_(t≥0)进行变换所得到的新过程(B_t)_(t≥0)的一些性质;同时还研究了由N_t~u产生的布朗运动可加泛函渐近性问题,并得到了新的结果:如果u有界,▽u∈K_(d-1),且L_t~(-u)是鞅,||E.(e~(M_t~-u))||_q∞,那么对任意的x∈R~d有 相似文献
9.
10.
设C是Banach空间X的非空有界闭凸子集,T:C →C既是一致L-Lipschitz映象, L≥1,又是渐近伪压缩映象,具有序列{kn}(?)[1,∞),limn→kn=1.固定u∈C.对每个n≥1,xn是压缩映象Sn(x)=(1-(tn)/(Lkn))u (tn)/(Lkn)Tnx, (?)x∈C的唯一不动点,其中,{tn}(?) [0,1). 在适当的条件下,本文表征了序列{xn}强收敛到T的不动点. 相似文献
11.
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
12.
Jogi Henna 《Annals of the Institute of Statistical Mathematics》2005,57(4):655-664
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
13.
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
14.
Piotr Je¸drzejewicz 《代数通讯》2013,41(4):1500-1508
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
15.
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
16.
任意矩阵的特征值的扰动估计 总被引:1,自引:0,他引:1
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
17.
有资格限制的指派问题的求解方法 总被引:3,自引:0,他引:3
在实际的指派工作中,常会遇到某个人有没有资格去承担某项工作的问题,因此,本建立了有资格限制的指派问题的数学模型。在此数学模型中,将效益矩阵转化为判定矩阵,由此给出了判定此种指派问题是否有解的方法;在有解的情况下,进一步将效益矩阵转化为求解矩阵,从而将有资格限制的指派问题化为传统的指派问题来求解。最后给出了一个数值例子来说明这样的处理方法是有效的。 相似文献
18.
We study the nilpotency of the sums of all coefficients of some sorts of products of polynomials over reversible, IFP, and NI rings, and introduce an SCN ring as a generalization. We characterize SCN rings in relation with related ring properties, and also provide several useful properties and ring extensions of SCN rings. 相似文献
19.
This note deals with the R-order of convergence of Weierstrass-Durand-Kerner-Dochev type single-step methods for the simultaneous determination of only a part of all roots of algebraic polynomials. 相似文献
20.
Rodney Y. Sharp 《Proceedings of the American Mathematical Society》2003,131(10):3009-3017
It is a well-known result of M. Brodmann that if is an ideal of a commutative Noetherian ring , then the set of associated primes of the -th power of is constant for all large . This paper is concerned with the following question: given a prime ideal of which is known to be in for all large integers , can one identify a term of the sequence beyond which will subsequently be an ever-present? This paper presents some results about convergence of sequences of sets of associated primes of graded components of finitely generated graded modules over a standard positively graded commutative Noetherian ring; those results are then applied to the above question.