共查询到20条相似文献,搜索用时 609 毫秒
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设f:Rn→ Rn是一同胚,该文证明了 f 是拟共形映射的充要条件是 f 将 Rn 中的任一John域映成 Rn 中的John域. 相似文献
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褚玉明 《数学年刊A辑(中文版)》2004,(6)
设D是R2中的Jordan域,D*=R2\D是D的外部,本文证明了拟圆的下面三个充要条件:(1)D是拟圆当且仅当D和D*都是弱拟凸域;(2)D是拟圆当且仅当D和D*都是弱Cigar域;(3)D是拟圆当且仅当D是弱一致域. 相似文献
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定义了内部边界球可达域,利用曲线族的模证明了D是Rn中的有界Jordan域,f:Bn→D是K-拟共形映射,若D是内部边界球可达域,则f∈H1/K(Bn). 相似文献
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该文利用曲线族的模,得到了n维空间中的有界凸域 D 到单位球 Bn上的 K -拟共形映射f的全局Holder连续性, 且Holder指数α=K1/(1-n)是最佳的. 相似文献
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本文研究Cn里的单位球B到Cn里的K-拟共形全纯映射.证明的最后结果是:若f是B到Cn里的K-拟共形全纯映射,满足det(f'(0))=1,则f(B)包含一个半径至少是(CnK)1-n∫01(1+t)N-1/(1-t)2exp{-(n+1)t/1-t}dt的单叶球,其中Cn>1是只依赖于n的常数,当n→∞时,Cn→(10)~(1/2). 相似文献
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Ze Min Zhou 《数学学报(英文版)》2013,29(8):1543-1554
A homeomorphism w=f(z) of a domain D is called a locally quasiconformal mapping, if for each subdomain D' of D with 'D, the restriction of f(z) on D' is a quasiconformal mapping. We give some conditions for a measurable function μ(z) on the unit disc to be the complex dilatation of a locally quasiconformal mapping f which can be homeomorphically extended to the closed unit disc. 相似文献
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该文利用曲线族的模,得到了n维空间中的有界凸域D到单位球B^n上的K-拟共形映射f的全局Hoelder连续性,且Hoelder指数α=K^1/1-n是最佳的. 相似文献
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We investigate a system of delayed lattice differential system which is a model of pioneer-climax species distributed on one dimensional discrete space. We show that there exists a constant $c^*>0$, such that the model has traveling wave solutions connecting a boundary equilibrium to a co-existence equilibrium for $c\geq c^*$. We also argue that $c^*$ is the minimal wave speed and the delay is harmless. The Schauder's fixed point theorem combining with upper-lower solution technique is used for showing the existence of wave solution. 相似文献
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Banach空间中伪压缩映象不动点的迭代逼近 总被引:1,自引:0,他引:1
Let K be a nonempty closed convex subset of a real p-uniformly convex Banach space E and T be a Lipschitz pseudocontractive self-mapping of K with F(T) := {x ∈ K:Tx=x}≠φ. Let a sequence {xn} be generated from x1 ∈ K by xn+1 = anxn,+ bnTyn++ cnun, yn= a′nxn~ + b′nTx,+ c′n,un, for all integers n ≥ 1. Then ‖xn - Txn,‖ → 0 as n→∞. Moreover, if T is completely continuous, then {xn} converges strongly to a fixed point of T. 相似文献
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In this paper, we show that a multiplication operator on the Dirichlet space D is unitarily equivalent to Dirichlet shift of multiplicity n + 1 (n ≥ 0) if and only if its symbol is c zn+1 for some constant c. The result is very different from the cases of both the Bergman space and the Hardy space. 相似文献
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Let(M~n, g)(n ≥ 3) be an n-dimensional complete Riemannian manifold with harmonic curvature and positive Yamabe constant. Denote by R and R?m the scalar curvature and the trace-free Riemannian curvature tensor of M, respectively. The main result of this paper states that R?m goes to zero uniformly at infinity if for p ≥ n, the L~p-norm of R?m is finite.As applications, we prove that(M~n, g) is compact if the L~p-norm of R?m is finite and R is positive, and(M~n, g) is scalar flat if(M~n, g) is a complete noncompact manifold with nonnegative scalar curvature and finite L~p-norm of R?m. We prove that(M~n, g) is isometric to a spherical space form if for p ≥n/2, the L~p-norm of R?m is sufficiently small and R is positive.In particular, we prove that(M~n, g) is isometric to a spherical space form if for p ≥ n, R is positive and the L~p-norm of R?m is pinched in [0, C), where C is an explicit positive constant depending only on n, p, R and the Yamabe constant. 相似文献
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Let P(G,λ) be the chromatic polynomial of a simple graph G. A graph G is chromatically unique if for any simple graph H, P(H,λ) = P(G,λ) implies that H is isomorphic to G. Many sufficient conditions guaranteeing that some certain complete tripartite graphs are chromatically unique were obtained by many scholars. Especially, in 2003, Zou Hui-wen showed that if n 31m2 + 31k2 + 31mk+ 31m? 31k+ 32√m2 + k2 + mk, where n,k and m are non-negative integers, then the complete tripartite graph K(n - m,n,n + k) is chromatically unique (or simply χ-unique). In this paper, we prove that for any non-negative integers n,m and k, where m ≥ 2 and k ≥ 0, if n ≥ 31m2 + 31k2 + 31mk + 31m - 31k + 43, then the complete tripartite graph K(n - m,n,n + k) is χ-unique, which is an improvement on Zou Hui-wen's result in the case m ≥ 2 and k ≥ 0. Furthermore, we present a related conjecture. 相似文献
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A *-ring is called *-clean if every element of the ring can be written as the sum of a projection and a unit. For an integer n ≥ 1, we call a *-ring R n-*-clean if for any a ∈ R,a = p + u1 + ··· + unwhere p is a projection and ui are units for all i. Basic properties of n-*-clean rings are considered, and a number of illustrative examples of 2-*-clean rings which are not *-clean are provided. In addition, extension properties of n-*-clean rings are discussed. 相似文献
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In this paper, a generalization of the class of semicommutative rings is investigated.A ring R is called left GWZI if for any a ∈ R, l(a) is a GW-ideal of R. We prove that a ring R is left GWZI if and only if S3(R) is left GWZI if and only if Vn(R) is left GWZI for any n ≥ 2. 相似文献
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令$k,\ell \geq 2$是正整数.令$A$是无限非负整数的集合.对$n\in \mathbb{N}$, 令$r_{1,k,\ldots,k^{\ell-1}}(A, n)$表示方程$n=a_0+ka_1+\cdots +k^{\ell-1}a_{\ell-1}$, $a_0, \ldots, a_{\ell-1}\in A$解的个数. 在本文中, 我们证明了对所有$n\geq 0$, $r_{1,k,\ldots,k^{\ell-1}}(A, n)=1$当且仅当$A$是$k^\ell$进制展开中数位小于$k$的所有非负整数的集合. 这个结果部分回答了S\''{a}rk\"{o}zy and S\''{o}s关于多维线性型表示的一个问题. 相似文献
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对任意的正整数与集合,令为解的个数.杨全会和陈永高证明了:若整数且,则不存在集合使得对所有充分大的整数成立,其中.对整数和,定义为满足对所有整数成立的集合的个数.杨全会和陈永高证明了是有限的,且.同时,他们问对任意整数,是否存在使得对所有整数成立.在本文中,我们给出了在时的准确公式.从而推出在时成立. 相似文献
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P(t,n)和C(t,n)分别表示在阶为n的路和圈中添加t条边后得到的图的最小直径;f(t,k)表示从直径为k的图中删去t条边后得到的连通图的最大直径.这篇文章证明了t≥4且n≥5时,P(t,n)≤(n-8)/(t 1) 3;若t为奇数,则C(t,n)≤(n-8)/(t 1) 3;若t为偶数,则C(t,n)≤(n-7)/(t 2) 3.特别地,「(n-1)/5」≤P(4,n)≤「(n 3)/5」,「n/4」-1≤C(3,n)≤「n/4」.最后,证明了:若k≥3且为奇数,则f(t,k)≥(t 1)k-2t 4.这些改进了某些已知结果. 相似文献