不动点集是Dold流形P(2m,2n+1)的带有对合T的流形

研究具有光滑对合T的4n 2m 2 K维闭流形M,如果对合的不动点集是F=P(2m,2n 1),其中m是4的倍数,证明了当n≥m>0时,(M,T)协边于零;当m>n≥0时,且m-n为偶数时,(M,T)协边于零.     

不动点集是Do1d流形P(2m+1,2n+1)的对合

本文证明了具有光滑对合T的(4n+2m+3+κ)-维闭流形,如果对合的不动点集为F=P(2m+1,2n+1),其中2m+2n=2+22+...+2b(2b为2n二幂展开式的最大二幂),m=4a或m=4a+3(a为非负整数),0＜κ≠2,则对合T协边于零.     

不动点集是Dold流形P(2m+1,2n+1)的对合

本文证明了具有光滑对合T的(4n+2m+3+k)-维闭流形,如果对合的不动点集为F=P(2m+1,2n+1),其中2m+2n=2+22+…+2b(2b为2n二幂展开式的最大二幂),m=4a或m=4a+3(a为非负整数),0相似文献   

On Jordan Biderivations of Triangular Matrix Rings

Let $R$ and $S$ be rings with identity, $M$ be a unitary $(R,S)$-bimodule and $T=\left(\begin{array}{cc}R & M \\ 0 & S\end{array}\right) $ be the upper triangular matrix ring determined by $R$, $S$ and $M$. In this paper we prove that under certain conditions a Jordan biderivation of an upper triangular matrix ring $T$ is a biderivation of $T$.     

ON THE DISTRIBUTION OF RANDOM LINES IN THE GENERAL CASE

$L$ is a line in a plane through the origin, with an angle $\[\alpha \]$ to the $x$-axis,$\[0 < \alpha < \pi \]$.$M$ is a point process on positive $x$-axis, Through the nth point of $M$ draw a line with a random angle $\[{\theta _n}\]$ to $x$-axis, $\[{\varphi ^ + }\]$ is the set of intersections of those lines with $\[{L^ + }\]$. Let $\[m = EM\]$. If, for every $\[c > 0\]$, then $\[{\varphi ^ + }\]$ is locally finite on $L$, and let $\[\tilde M\]$ be the point process constructed by $\[{\varphi ^ + }\]$ , then $\[E\tilde M\]$ exists. If, for all interval $\[L \subset {L^ + }\]$, $\[\int_0^\infty {r(I,x)M(dx)} = \infty \]$ then $\[{\varphi ^ + }\]$ is dense on $\[{L^ + }\]$. If $L$ is drawn parallel to $x$-axis,. the same results can be got，and this time $\[\tilde M\]$ is a cluster point process with cluster center $M$.     

Clifford 环面 Sm(\sqrt{\frac{m}{n}})×Sn-m(\sqrt{\frac{n-m}{n}})的刚性定理

\small\zihao{-5}\begin{quote}{\heiti 摘要:} 设$M$为$n+1$维单位球面$S^{n+1}(1)$中的一个极小闭超曲面，如果 $ n \le S \le n+\frac{2}{3}$, 则有 $S=n$ 且 $M$ 与某一Clifford 环面 $S^m(\sqrt{m/n}) \times S^{n-m}(\sqrt{(n-m)/n})$等距.     

一类具有奇异灵敏度的logistic趋化系统解的渐近行为

本文在无边界流的光滑有界区域$\Omega\subset\mathbb{R}^n~(n>2)$上研究了具有奇异灵敏度及logistic源的抛物-椭圆趋化系统$$\left\{\begin{array}{ll}u_t=\Delta u-\chi\nabla\cdot(\frac{u}{v}\nabla v)+r u-\mu u^k,&x\in\Omega,\,t>0,\\ 0=\Delta v-v+u,&x\in\Omega,\,t>0\end{array}\right.$$ 其中$\chi$, $r$, $\mu>0$, $k\geq2$. 证明了若当$r$适当大, 则当$t\rightarrow\infty$时该趋化系统全局有界解呈指数收敛于$((\frac{r}{\mu})^{\frac{1}{k-1}}, (\frac{r}{\mu})^{\frac{1}{k-1}})$.     

不动点集为RP(2)∪L~1(p)的对合

(M3+ k,T)是在光滑闭流形上的一个非平凡光滑对合 ,它的不动点集为 RP(2 )∪ L 1 (p ) .本文给出了带对合的流形 (M3+ k,T)的协边类     

有限uM,D-正交指数函数系的一个充分条件

设$\mu_{M,D}$是由仿射迭代函数系$\{\phi_{d}(x)=M^{-1}(x+d)\}_{d\in D}$唯一确定的自仿测度, 它的谱与非谱性质与Hilbert空间$L^{2}(\mu_{M,D})$中正交指数函数系的有限性和无限性有着直接的关系. 本文将利用矩阵的初等变换给出$\mu_{M,D}$\,{-}\!\!正交指数函数系有限性的一个充分条件. 由于这个条件只与 矩阵$M$的行列式有关, 因此, 它在$\mu_{M,D}$的非谱性的判断方面便于直接验证.     

复射影空间CP(2n+1)上保持定向的光滑对合

记[l]为非负实数 l 的整数部分.设 n 为非负整数,8(n)=0,1,分别在 n 为偶数和奇数时.本文证明了,CP(2n+1)作为2(2n+1)维光滑闭流形,其上保持定向的光滑对合,在协边的意义下仅为[n+2/2]+s(n)种;而且这种对合的不动点集,或者为 CP(2n+1)的一个偶维光滑闭子流形,或者为 CP(2n+1)的两个偶维光滑闭子流形 F~(2k_1)和 F~(2k_2)的不交并,k_1≠k_2,k_1+k_2=2n;特别地,这样的对合的协边类不为0当且仅当其不动点集为 CP(2n+1)的两个偶维闭子流形 F~(4k_1)和 F~(4k_2)的不交并,k_1≠k_2,2k_1+2k_2=2n,H(F~(4k_4);Z_2)含多项式子环 Z_2[x|x~(2k_4+1)=0],i=1,2,x 为 F~(4k_4)的二阶 Stiefel-Whitney 类.在视 CP(2n+1)为具有稳定复结构的复流形时,由于屎持复结构的对合一定保持定向.最后指出,此种情况下也有类似的结果.     

不动点集为$RP(2^m)\sqcup P(2^m,\,2n-1)$的对合

Let （M^2m＋4n＋k-2, T） be a smooth closed manifold with a smooth involution T whose fixed point set is RP（2^m） ∪ P（2^m, 2n - 1） （m 〉 3, n 〉 0）. For 2n ≥ 2^m, （M^2m＋4n＋k-2, T） is bordant to （P（2^m, RP（2n））, To）.     

ON A MULTILINEAR OSCILLATORY SINGULAR INTEGRAL OPERATOR （I）

ＯＮＡＭＵＬＴＩＬＩＮＥＡＲＯＳＣＩＬＬＡＴＯＲＹＳＩＮＧＵＬＡＲＩＮＴＥＧＲＡＬＯＰＥＲＡＴＯＲ（Ｉ）ＣＨＥＮＷＥＮＧＵＨＵＧＵＯＥＮＬＵＳＨＡＮＺＨＥＮＭａｎｕｓｃｒｉｐｔｒｅｃｅｉｖｅｄＯｃｔｏｂｅｒ１８，１９９４．ＲｅｖｉｓｅｄＤｅｃｅ...     

具误差隐格式迭代逼近严格伪压缩映像族公共不动点 (英)

设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设$K$是实Banach空间$E$中非空闭凸集, $\{T_i\}_i=1^{N}$是$N$个具公共不动点集$F$的严格伪压缩映像, $\{\alpha_n\}\subset [0,1]$是实数列, $\{u_n\}\subset K$是序列, 且满足下面条件 (i)\ 设K是实Banach空间E中非空闭凸集，{Ti}i=1^N是N个具公共不动点集F的严格伪压缩映像，{αn}包括于[0,1]是实数例，{un}包括于K是序列，且满足下面条件（i）0〈α≤αn≤1;（ii）∑n=1∞（1-αn）=＋∞.（iii）∑n=1∞ ‖un‖〈＋∞.设x0∈K,{xn}由正式定义xn=αnxn-1＋（1-αn）Tnxn＋un-1,n≥1,其中Tn=Tnmodn，则下面结论（i）limn→∞‖xn-p‖存在，对所有p∈F；（ii）limn→∞d（xn,F）存在，当d（xn,F）=infp∈F‖xn-p‖；（iii）lim infn→∞‖xn-Tnxn‖=0.文中另一个结果是，如果{xn}包括于[1-2^-n,1]，则{xn}收敛，文中结果改进与扩展了Osilike（2004）最近的结果，证明方法也不同。     

Banach空间中伪压缩映象不动点的迭代逼近

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.     

Existence of solutions for a degenerate auasilinear elliptic system in bounded domain

Using variational methods, we study the existence of weak solutions forthe degenerate quasilinear elliptic system$$\left\{\begin{array}{ll}- \mathrm{div}\Big(h_1(x)|\nabla u|^{p-2}\nabla u\Big) = F_{u}(x,u,v) &\text{ in } \Omega,\\-\mathrm{div}\Big(h_2(x)|\nabla v|^{q-2}\nabla v\Big) = F_{v}(x,u,v) &\text{ in } \Omega,\\u=v=0 & \textrm{ on } \partial\Omega,\end{array}\right.$$where $\Omega\subset \mathbb R^N$ is a smooth bounded domain, $\nabla F= (F_u,F_v)$ stands for the gradient of $C^1$-function $F:\Omega\times\mathbb R^2 \to \mathbb R$, the weights $h_i$, $i=1,2$ are allowed to vanish somewhere,the primitive $F(x,u,v)$ is intimately related to the first eigenvalue of acorresponding quasilinear system.     

ERGODIC THEOREMS FOR NON-LIPSCHITZIAN SEMIGROUPS WITHOUT CONVEXITY

§１．ＩｎｔｒｏｄｕｃｔｉｏｎＬｅｔＨｂｅａＨｉｌｂｅｒｔｓｐａｃｅｗｉｔｈｎｏｒｍ‖·‖ａｎｄｉｎｎｅｒｐｒｏｄｕｃｔ（·，·）ａｎｄｌｅｔＣｂｅａｎｏｎｅｍｐｔｙｓｕｂｓｅｔｏｆＨ．ＡｍａｐｐｉｎｇＴ：Ｃ｜→ＣｉｓｓａｉｄｔｏｂｅＬｉｐｓｃｈｉｔ...     

Co-commuting Mappings of Generalized Matrix Algebras

Let G be a generalized matrix algebra over a commutative ring R and Z(G)be the center of G.Suppose that F,T:G→G are two co-commuting R-linear mappings,i.e.,F(x)x=xT(x) for all x∈G.In this note,we study the question of when co-commuting mappings on G are proper.     

多尺度分析生成元的刻画

本文将给出多尺度分析生成元的一种完全刻画.将证明:函数φ∈L~2(R)是二进多尺度分析生成元的充要条件是(1)存在{a_k}∈l~2,φ(x)=∑_(k∈Z)a_kφ(2x-k);(2)存在正数A相似文献   

Embedded Surfaces for Symplectic Circle Actions

The purpose of this article is to characterize symplectic and Hamiltonian circle actions on symplectic manifolds in terms of symplectic embeddings of Riemann surfaces.More precisely, it is shown that(1) if(M, ω) admits a Hamiltonian S~1-action, then there exists a two-sphere S in M with positive symplectic area satisfying c1(M, ω), [S] 0,and(2) if the action is non-Hamiltonian, then there exists an S~1-invariant symplectic2-torus T in(M, ω) such that c1(M, ω), [T] = 0. As applications, the authors give a very simple proof of the following well-known theorem which was proved by Atiyah-Bott,Lupton-Oprea, and Ono: Suppose that(M, ω) is a smooth closed symplectic manifold satisfying c1(M, ω) = λ· [ω] for some λ∈ R and G is a compact connected Lie group acting effectively on M preserving ω. Then(1) if λ 0, then G must be trivial,(2) if λ = 0, then the G-action is non-Hamiltonian, and(3) if λ 0, then the G-action is Hamiltonian.