2×2阶上三角型算子矩阵的Moore-Penrose谱

设$H_{1}$和$H_{2}$是无穷维可分Hilbert空间. 用$M_{C}$表示$H_{1}\oplusH_{2}$上的2$\times$2阶上三角型算子矩阵$\left(\begin{array}{cc} A & C \\ 0 & B \\\end{array}\right)$. 对给定的算子$A\in{\mathcal{B}}(H_{1})$和$B\in{\mathcal{B}}(H_{2})$,描述了集合$\bigcap\limits_{C\in{\mathcal{B}}(H_{2},H_{1})}\!\!\!\sigma_{M}(M_{C})$与$\bigcup\limits_{C\in{\mathcal{B}}(H_{2},H_{1})}\!\!\!\sigma_{M}(M_{C})$,其中$\sigma_{M}(\cdot)$表示Moore-Penrose谱.     

由H\"{o}rmander向量场构成的抛物方程的 $W_{\ast}^{1,p}$ 正则性

设 $X_{1},\cdots ,X_{q}\ (q相似文献   

算子代数的性质∏σ和张量积

本文引入算子代数的性质${\Pi}_\sigma$这一概念,证明了任一 vonNeumann代数中的套子代数和有限宽度CSL子代数都具有性质$\Pi_\sigma.$最后得到张量积公式$\mbox{alg}_{\cal M}{\cal L}_1\overline{\otimes}\mbox{alg}_{\cal N}{\cal L}_2= \mbox{alg}_{{\cal M}\overline{\otimes}{\cal N}}({\cal L}_1\otimes{\cal L}_2)$成立,这里${\cal L}_1$和 ${\cal L}_2$分别是von Neumann代数${\cal M}$和${\cal N}$中的有限宽度CSL.     

三角Banach代数的Lie弱顺从性

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辫子Hopf代数的积分(英)

本文引进了无限维辫子Hopf代数$H$的忠实拟对偶$H^d$和严格拟对偶$H^{d'}$.证明了每个严格拟对偶$H^{d'}$是一个$H$-Hopf 模. 发现了$H^{d}$的极大有理$H^{d}$-子模$H^{d {\rm rat} }$ 与积分的关系, 即: $H^{d {\rm rat}}\cong \int ^l_{H^d} \otimes H$.给出了在Yetter-Drinfeld范畴$(^B_B{\cal YD},C)$中的辫子Hopf代数的积分的存在性和唯一性.     

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$((\frac{r}{\mu})^{\frac{1}{k-1}}, (\frac{r}{\mu})^{\frac{1}{k-1}})$.     

混合径角$\lambda$中心有界平均振荡空间的一个特征

在这篇文章中,我们通过Hardy算子交换子$\mathrm{H}_b$与它的对偶算子交换子$\mathrm{H}^*_b$, 其中$b\in {\mathrm{CMOL}^{p_2, \lambda}_{\rm rad}L^{p_1}_{\rm ang}(\mathbb R^n)}$,建立了混合径角$\lambda$中心有界平均振荡空间的一个特征.     

EXISTENCE OF DISCONTINUOUS SOLUTIONS FOR A DOUBLY DEGENERATE ELLIPTIC EQUATIONS ON $R^N$

It is demonstrated that under the hypotheses I—III the problem $\[\left\{ {\begin{array}{*{20}{c}} {div((k(U) + \varepsilon )|DU{|^{M - 1}}DU) = f(|x|,U) + \varepsilon U{\text{ }}in{\text{ }}{R^N},N > 1,{\text{ (1}}{\text{.1}}{{\text{)}}_\varepsilon }} \ {U(0) > 0,U(x) \geqslant 0{\text{ on }}{R^N},U(x) \to 0{\text{ as }}|x| \to + \infty {\text{ }}(1.2)} \end{array}} \right.\]$ for each fixed $\epsilon >0$ has infinitely many distinct radially symmetric solutions $U_\epsilon=V_\epsilon(|x|)$ such that $V_\epsilon(s),s^{N-1}(k(V_\epsilon(s))+\epsilon)|V''(s)|^{M-1}V''_\epsilon(s)\in C[0,+\infinity)\capC^1(0,+\infinity)$, $\[\left\{ {\begin{array}{*{20}{c}} {({s^{N - 1}}(k({V_\varepsilon }(s)) + \varepsilon )|V''(s){|^{M - 1}}V''(s)) = {\varepsilon ^{N - 1}}(f(s,{V_\varepsilon }(s)) + \varepsilon {V_\varepsilon }(s))for{\text{ }}s > 0,{{(1.3)}_\varepsilon }} \ {{V_\varepsilon }(0) = B > 0,{V_\varepsilon }(s) \geqslant 0{\text{ for }}s > 0,and{\text{ }}{V_\varepsilon }( + \infty ) = 0,(1.4)} \end{array}} \right.\]$ where B is a positive number chosen arbitrarily, which extends the result in [3]. In particular, the author proves that $U_0(x)=V_0(|x|)$ is a weak solution of the problem $(l.l)_0-(1.2)$.     

A Hypothesis Testing Problem in the Linear Model (in English)

本文讨论了多元线性模型中的一个假设检验问题。假定 $\[{E(Y) = A\theta + B\eta }\]$ $Y的各行独立、正太、同协差阵V$ 现在要检验假设H_0:存在矩阵C使$\theta= C\eta$ 是否成立。首先可将问题化为法式的形式，对法式分两种情况进行讨论： （一）$[V = {\sigma ^2}I,{\sigma ^2}\]$未知，此时可求出 \theta,C，\sigma ^2的最大似然估计（当 H^0成立时）是 $[\left\{ {\begin{array}{*{20}{c}} {\hat \theta = {{({I_p} + \hat C'\hat C)}^{ - 1}}({y_1} + \hat C'{y_2})}\{\hat C = - {{({{T'}_{22}})}^{ - 1}}{{T'}_{12}}}\{{{\hat \sigma }^2} = \frac{1}{{nk}}(\sum\limits_{j = p + 1}^{p + q} {\lambda _j^* + \sum\limits_{j = 1}^k {{d_j})} } } \end{array}} \right.\]$ 其中y_1,y_2是法式 $[E\left( {\begin{array}{*{20}{c}} {{y_1}}\{{y_2}}\{{y_3}} \end{array}} \right) = \left( {\begin{array}{*{20}{c}} \theta \\eta \0 \end{array}} \right)\begin{array}{*{20}{c}} p\q\{n - (p + q)} \end{array}\]$ 中的资料阵y_1,y_2,d_1,\cdots，d_k是y^'_3y_3的全部特征根，$[\lambda _1^* \ge \cdots \lambda _{p + q}^*\]$是$[\left( {\begin{array}{*{20}{c}} {{y_1}}\{{y_2}} \end{array}} \right)\left( {\begin{array}{*{20}{c}} {{{y'}_1}}&{{{y'}_2}} \end{array}} \right)\]$的全部特征根，相应特征向量依$\lambda^*_i$的大小顺序从左到右排成矩阵T，T的分块子阵是T_ij，即 $[T = \left( {\begin{array}{*{20}{c}} {{T_{11}}}&{{T_{12}}}\{{T_{21}}}&{{T_{22}}} \end{array}} \right)\begin{array}{*{20}{c}} p\q \end{array}\]$ 对H_0的广义似然比检验是 $[\Lambda = \sum\limits_{j = p + 1}^k {{\lambda _j}/\sum\limits_{j = 1}^k {{d_j}} } \]$ $=lambda_1 \geq \lambda_2 \geq \cdots \geq \lambda_k$是$y_1^'y_1+y_2^'y_2$的全部特征根。 （二）一般情形V未知，此时 \theta,C的估计量同前，可求出 $[\hat V = \frac{1}{n}({y_2}^\prime {T_{22}}{T_{22}}^\prime {y_2} + {y_2}^\prime {y_2})\]$ H_0相应的Lawley不变检验是 $[\sum\limits_{j = p + 1}^k {{\beta _j}} \ge {\alpha _1}\]$ 其中 $\beta_1 \geq \beta_2 \geq \cdots \beta_k$是$y'_1y_1+y'_2y_2$的相应于$y'_sy_s$的全部特征根。 有关$\Lambda \$的以及$[\sum\limits_{j = p + 1}^k {{\beta _j}} \]$的极限分布将在另外的文章中讨论。     

一类非线性分数阶薛定谔-泊松系统非零解的存在性

本文研究了分数阶薛定谔-泊松系统$$\left\{\begin{array}{l}(-\Delta)^su+u+\phi u=\lambda f(u)\ \text {in} \ \mathbb {R}^3, \\ (-\Delta)^{\alpha}\phi =u^2\ \text {in} \ \mathbb {R}^3\emph{},\end{array}\right. $$ 非零解的存在性, 其中$s\in (\frac{3}{4},1), \alpha\in(0,1),\lambda$ 是正参数, $(-\Delta)^s,(-\Delta)^{\alpha}$是分数阶拉普拉斯算子. 在一定的假设条件下, 利用扰动法和Morse迭代法, 得到了系统至少一个非平凡解.     

3$\times$3阶上三角型算子矩阵的可能谱

Let H1, H2 and H3 be infinite dimensional separable complex Hilbert spaces. We denote by M（D,V,F） a 3×3 upper triangular operator matrix acting on Hi ＋H2＋ H3 of theform M（D,E,F）=（A D F 0 B F 0 0 C）.For given A ∈ B（H1）, B ∈ B（H2） and C ∈ B（H3）, the sets ∪D,E,F^σp（M（D,E,F））,∪D,E,F ^σr（M（D,E,F））,∪D,E,F ^σc（M（D,E,F）） and ∪D,E,F σ（M（D,E,F）） are characterized, where D ∈ B（H2,H1）, E ∈B（H3, H1）, F ∈ B（H3,H2） and σ（·）, σp（·）, σr（·）, σc（·） denote the spectrum, the point spectrum, the residual spectrum and the continuous spectrum, respectively.     

缺项算子矩阵的本性谱

Let =(A C X B)be a 2×2 operator matrix acting on the Hilbert space н( )κ.For given A ∈B (H),B ∈B(K)and C ∈B(K,H)the set Ux∈B(H,к)σe(Mx)is determined,where σe(T)denotes the essential spectrum.     

形式三角矩阵环的PS性质和CESS性质

设$R$是环. 称右$R$-模$M$是PS-模,如果$M$具有投射的socle. 称$R$是PS-环,如果$R_R$是PS-模. 称$M$是CESS-模,如果$M$的任意具有基本socle的子模是$M$的某个直和因子的基本子模.本文给出了形式三角矩阵环 $T=\left( \begin{array}{cc} A & 0 \\     

$2\times 2$阶上三角算子矩阵的谱扰动

研究了Hilbert空间H(?)K上的2×2阶上三角算子矩阵Mc=(AO CB)当A,B 给定,C为任意有界线性算子时,对Mc的点谱、剩余谱、连续谱的扰动分别给出了描述．     

一类缺项算子矩阵的四类点谱的扰动

有界线性算子的点谱可进一步细分为4类,分别为$\sigma_{p1}$, $\sigma_{p2}$, $\sigma_{p3}$ 和$\sigma_{p4}$.设 $H, K$为无穷维可分的Hilbert空间,用$M_C$表示$2\times 2$上三角算子矩阵$\left(\begin{array}{cc} A & C \\ 0 & B \\ \end{array} \right)$,对于给定的 $A\in B(H),~B\in B(K)$,描述了集合$\bigcap\limits_{C\in B(K,H)}\sigma_{p1}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p2}(M_C)$, $\bigcap\limits_{C\in B(K,H)}\sigma_{p3}(M_C)$和$\bigcap\limits_{C\in B(K,H)}\sigma_{p4}(M_C)$.     

Forward dynamical problem for the Timoshenko beam

The initial boundary value problem

A modified Brauer algebra as centralizer algebra of the unitary group

The centralizer algebra of the action of on the real tensor powers of its natural module, , is described by means of a modification in the multiplication of the signed Brauer algebras. The relationships of this algebra with the invariants for and with the decomposition of into irreducible submodules is considered.

     

Extensions of hereditary algebras

Let be a triangular matrix algebra, uhere k is an algebraically closed field, B is the path algebra of an oriented Dynkin diagram of type E₆ or E₇ or E₈ and M is a finite dimensional k-B-bimodule. The aim of this paper is to determine the representation type of A for any orientation of the Dynkin diagram and for any indecomposable B-module M. This classification is obtained by comparing the representation types of the algebras and using the theory of tilting modules.     

依赖于一阶导数的二阶脉冲微分方程边值问题的正解(英)

本文研究一类二阶脉冲微分方程：■的正解存在性．其中,0＜η＜1,0＜α＜1,f：[0,1]×[0,∞)×R→[0,∞),I_i：[0,∞)×R→R,J_i：[0,∞)×R→R,(i=1,2,…,k)均为连续函数．本文所用方法是文献[5]推广的Krasnoselskii不动点定理,此定理为解决依赖于一阶导数的边值问题提供了理论依据．基于此定理,获得了问题正解存在性定理．特别地,我们获得此类问题的Green函数,使问题的解决更直观和简单．