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1.
本文讨论Cauchy问题sub from i,j=0 to n aijuxixj+sub from i=0 to n biuxj+cu=0,x0>0,u(0,x1,…,xn)=ux0(0,x1,…,xn)=0的唯一性中的离散现象. 我们证明了,此问题在原点的一个邻域中只有平凡解的充要条件为b0(0)-sub from i=1 to n(2ai+1)λi≠0,其中λi>0是矩阵-(?2α00/?xi?xj(0))(i,j=1,…,n)与(aij(0))i,j=1,…,n)的乘积的特征根的平方根.αi是任意的非负整数.  相似文献   

2.
设Xi是无穷维复Banach空间, L(Xj,Xi)是Xj到Xi上的有界线性算子全体.考虑 n × n 上三角算子矩阵T=(Tij)1≤j≤n, 其中Tij L(Xj,Xi),1≤j≤n; Tij=0, i>j.本文研究了T的单值扩张性, 通过考察集合S(T)={λ∈C}: T在点λ没有SVEP},证明了S(T)在i=1 ? nS(Ti)中退化,进而给出等式S(T)=i=1 ? n S(Ti)成立的条件. 同时, 考察了T的单值扩张性扰动,得到了S(T)保持对角稳定时Ti所需的条件并予以证明, 同时举例说明这些条件的合理性.最后, 给出单值扩张性关于谱σ(T)和局部谱σT (x)的应用, 得到了谱扰动和局部谱扰动不变的新条件.  相似文献   

3.
关于切点单形的两个不等式   总被引:28,自引:3,他引:25  
Definition Let Ai(i=1,2,…,n+1) be the vertex of a simplex ΣA in n-dimen-sional Euclidean space En and Ai′ be the tangent points which the inscribed sphere of ΣA is tangent to the side face of ΣA, then the simplex with the tangent points as vertexes is called the tangent points simplex.  相似文献   

4.
对x = (x1, x2,···, xn) ∈ (0,1)n 和 r ∈ {1, 2,···, n} 定义对称函数 Fn(x, r) = Fn(x1, x2,···, xn; r) =∏1≤i1j=1r(1+xi3/1- xi3)1/r, 其中i1, i2, ···, ir 是整数. 该文证明了Fn(x, r) 是(0,1)n 上的Schur凸、Schur乘性凸和Schur调和凸函数. 作为应用,利用控制理论建立了若干不等式.  相似文献   

5.
In this paper, it is shown that., if x≡αi(mod ni)(i=1,…,k),112<…k,0≤αii is a covering sets of residue classes, there exist two distinct pairs of integer number ni,nj(is,nt(si,nj)>1, (ns,nt)>1, where (a,b) is the greatest common divisor of a,b.  相似文献   

6.
本文讨论P2(C)中全纯曲线相交处于次一般位置超平面的唯一性.设f1, f2, · · · , fλ为P2(C)中线性非退化的全纯曲线,H1, H1, · · · , Hq为P2(C)上处于m-次一般位置的超平面,满足Aj :f1-1(Hj) = · · · =fλ-1(Hj) (1 ≤ j ≤ q)且Ai ∩ Aj = ?(i = j).假设存在整数l (2 ≤ l ≤ λ),使得fj1(z) ∧ fj2(z) ∧ · · · ∧ fjl(z) = 0 (z ∈ Aj)对任意l个指标1 ≤ j1 < j2 < · · · < jl < λ成立.那么当 q > 2λ/λ-l+1 + 3/2 m时, f1 ∧ · · · ∧ fλ ≡ 0.关键技术是第二基本定理中不等式改进为: ∥(q - 3m/2)Tft(r)≤ Pjq=1N2(ft,Hj )(r, 0) + o(Tft(r))(1 ≤ t ≤ λ).  相似文献   

7.
Let CS*(α,ρ) and SBγ(β,σ) be the subclasses of close-to-starlike functions and Bazile-vic functions class respectively. It is proved that the integral operators is close-to-convex function under the same conditions, where fi∈CS*(aii,) and gj∈SBγjj, σj). In addition, we correct a mistake in [3].  相似文献   

8.
关于n维单形的一个不等式   总被引:9,自引:0,他引:9  
Let x1,x2… ,xn are vectors set out from any vertex of n-simplex. The ineluded angle of xi and xj is aij , and G=(?)aij, the volume of this simplex is V. In this paper, we prove the inequality as below:(?) When n=2, the equality holds in (*) , when n≥3, the equality holds in (*) if {xi} is orthogonal set.  相似文献   

9.
The homogeneous Dirichlet problem(1) for quasilinear elliptic system in a bounded domain Ω is investigated in this paper. The existence of generalized solutions in [H01(Ω)]N is obtained by using the contructive Galerkin method. For the case of aijlm=0 when i≠j, it is estatablished that such generalized solutions have bounded [L(Ω)]N norm and possess Holeler continuity. Even in the particular case that fi are independent of Du, our results have improved those of A. V. Lair [Ann. Mat. Pura Appl., 116(1978)], allowing bi1(x,u) and fi(x,u) to have a growth in u arbitrarily close to 1.  相似文献   

10.
In this paper, the authors discuss a generalization of Lappan’s theorem to higher dimensional complex projective space and get the following result: Let f be a holomorphic mapping of ? into Pn(C), and let H1, · · · , Hq be hyperplanes in general position in Pn(C).Assume that sup {(1 ? |z|2)f?(z) : z ∈ q[ j=1 f?1(Hj )o < ∞,if q ≥ 2n2 + 3, then f is normal.  相似文献   

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