分裂的$\delta$-Jordan 李三系

本文研究了任意分裂的$\delta$-Jordan李三系的结构,其为分裂的李三系的结构的推广. 利用这种三系的根连通, 得到了带有对称根系的分裂的 $\delta$-Jordan 李三系可以表示成 $T=U+\sum_{[\alpha]\in \Lambda^{1}/\sim} I_{[\alpha]}$,其中$U$是0根空间$T_{0}$的子空间,任意$I_{[\alpha]}$为$T$的理想, 并且满足 当$[\alpha]\neq [\beta]$时, $\{I_{[\alpha]},T,I_{[\beta]}\}=\{I_{[\alpha]},I_{[\beta]},T\}=\{T,I_{[\alpha]},I_{[\beta]}\}=0$.     

完备的$\nu$-广义度量空间上的不动点定理[英文]

本文对度量空间中$C$类函数的压缩映射进行推广. 在完备的$\nu$-广义度量空间上, 利用构造迭代序列的方法, 证明了关于($\psi$,$\phi$)-类型压缩映射的不动点定理. 并且证明了广义的$F$类型压缩和广义$\theta$类型压缩映射.     

具$w_0$-距离度量空间中$p$-逼近$\alpha$-$\eta$-$\beta$-拟压缩的最佳逼近点定理

本文提出了一类称为$p$-逼近$\alpha$-$\eta$-$\beta$-拟压缩的新的非自映射,并引进了关于$\eta$的$\alpha$-逼近可容许映射和关于$\eta$的$(\alpha,d)$正则映射的概念.基于这些新概念,在$w_0$-距离度量空间中研究了此类新压缩最佳逼近点的存在唯一性,并给出了一个新的定理,推广和补充了文[Ayari, M. I. et al. Fixed Point Theory Appl., 2017, 2017: 16]和[Ayari, M. I. et al. Fixed Point Theory Appl., 2019, 2019: 7]中的结果.给出了一个例子来说明主要结果的有效性.进一步地,作为推论得到关于两个映射的最佳逼近点和公共不动点定理.作为其中一个推论的应用,讨论了一类Volterra型积分方程组的求解问题.     

相对平坦模的$\aleph$-积

设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中设$M$是右$R$-模, $\aleph$是一个无穷基数. 称右$R$-模$N$是$\aleph$-$M$-凝聚的,如果对任意的$B/A\hookrightarrow mR$,其中$0\leq A相似文献   

严格凸赋范空间的$\lee^\beta$-

本文讨论了严格凸赋范空间的L~β-和(0<β≤1)上单位球面间非满等距算子的延拓问题,给出了此问题成立的充要条件．     

关于Ext代数生成次数的界的一个注记

为了研究分次代数的Yoneda代数的有限生成性,Green和Marcos于2005年引进了δ-Koszul代数的概念并提出了三个公开问题.本文通过讨论分段Koszul代数的相关性质,给出了第三个问题的答案.     

关于空间$S(\Omega,\Sigma,\mu)$与$L^\beta(\Omega,\Sigma,\mu)$上的次加上半连续$\alpha$-正齐性泛函

本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了$S(\Omega,\Sigma,\mu)$和$L^\beta(\Omega,\Sigma,\mu)$分别不存在非零的上半连续、次加、$\alpha$-正齐性泛函(分别有本文得到了S（Ω，∑，μ）与L^β（Ω，∑，μ）分别不存在非零的上半连续、次加、α-正齐性泛函（分别有0≤α≤1和β〈α≤1）的充要条件．     

条件样本函数极值中$\gamma^2$的估计方法

本文对条件样本函数极值中$\gamma^2$的估计进行了探讨,给出了$\gamma^2$估计的一种新方法------自助法,并对所得到的统计量的性质进行了分析.     

集值映射$\epsilon$-超次梯度的性质及应用[英文]

本文讨论集值映射$\epsilon$-超次梯度的性质，建立$\epsilon$-超次梯度意义下的Moreau-Rockafellar定理.作为应用， 借助$\epsilon$-超次梯度分别得到集值优化取得$\epsilon$-超有效元的充分和必要条件.     

$\widetilde{\rho}$混合序列的矩不等式与完全收敛性

给出一类较广泛的$\widetilde{\rho}$ 混合序列的矩不等式. 讨论了$\widetilde{\rho}$ 混合序列的完全收敛性, 所得的结果改进了相关文献中的结果,并得到了完全收敛速度与矩条件之间的等价关系.     

The Change-Base Issue for Ω-Categories

Let G ： Ω→Ω＇ be a closed unital map between commutative, unital quantales. G induces a functor G^- from the category of Ω-categories to that of Ω＇-categories. This paper is concerned with some basic properties of G^-. The main results are： （1） when Ω, Ω＇ are integral, G ： Ω→Ω＇ and F ： Ω＇→Ω are closed unital maps, F is a left adjoint of G^- if and only if F is a left adjoint of G; （2） G^- is an equivalence of categories if and only if G is an isomorphism in the category of commutative unital quantales and closed unital maps; and （3） a sufficient condition is obtained for G^- to preserve completeness in the sense that GA is a complete Ω＇-category whenever A is a complete Ω-category.     

Approximate Lie $\ast$-Derivations on $\rho$-complete Convex Modular algebras

In this paper, we obtain generalized Hyers--Ulam stability results of a $(m,n)$-Cauchy-Jensen functional equation associated with approximate Lie $*$-derivations on $\rho$-complete convex modular $*$-algebras $\chi_\rho$ with $\Delta_\mu$-condition on the convex modular $\rho$.     

关于$\omega$-Smash余积Hopf代数的$(f,\omega)$相容对$(B,,H)$

In this paper we introduce the notion of （f,ω）-compatible pair （B,H）, by which we construct a Hopf algebra in the category HHYD of Yetter-Drinfeld H-modules by twisting the comultiplication of B. We also study the property of ω-smash coproduct Hopf algebras Bω H.     

α-TRANSIENCE AND α-RECURRENCE FOR RANDOM WALKS AND LEVY PROCESSES

The authors investigate the α-transience and α-recurrence for random walks and Levy processes by means of the associated moment generating function, give a dichotomy theorem for not one-sided processes and prove that the process X is quasi-symmetric if and only if X is not α-recurrent for all α< 0 which gives a probabilistic explanation of quasi-symmetry, a concept originated from C. J. Stone.     

Compactness of the Canonical Solution Operator of $ \bar \partial $ on Bounded Pseudoconvex Domains

On bounded pseudoconvex domains Ω the orthogonal projection P_q : L²_(p,q) (Ω) → ker _q is given by P_q = Id – S_{q+1 q} = Id – ^*_q+1N_{q+1 q}, where S_q is the canonical solution operator of the ‐equation and N_q is the ‐Neumann operator. We prove a formula for the solution operator S_q restricted on (0, q)‐forms with holomorphic coefficients. And as an application we get a characterization of compactness of the solution operator restricted on (0, q)‐forms with holomorphic coefficients. On general (0, q)‐forms we show that this condition is necessary for compactness of the solution operator.     

Generalized Hankel operators and the generalized solution operator to $ \bar \partial $ on the Fock space and on the Bergman space of the unit disc

In this paper we consider Hankel operators = (Id – P ₁) from A ²(?, |z |²) to A ^2,1(?, |z |²)^⊥. Here A ²(?, |z |²) denotes the Fock space A ²(?, |z |²) = {f: f is entire and ‖f ‖² = ∫_? |f (z)|² exp (–|z |²) dλ (z) < ∞}. Furthermore A ^2,1(?, |z |²) denotes the closure of the linear span of the monomials { z ⁿ : n, l ∈ ?, l ≤ 1} and the corresponding orthogonal projection is denoted by P ₁. Note that we call these operators generalized Hankel operators because the projection P ₁ is not the usual Bergman projection. In the introduction we give a motivation for replacing the Bergman projection by P ₁. The paper analyzes boundedness and compactness of the mentioned operators. On the Fock space we show that is bounded, but not compact, and for k ≥ 3 that is not bounded. Afterwards we also consider the same situation on the Bergman space of the unit disc. Here a completely different situation appears: we have compactness for all k ≥ 1. Finally we will also consider an analogous situation in the case of several complex variables. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cn中单位球上$mu$-Bloch函数的等价刻画

设$\mu$是$[0,1)$上的正规函数, 给出了${\bf C}^{\it n}$中单位球$B$上$\mu$-Bloch空间$\beta_{\mu}$中函数的几种刻画. 证明了下列条件是等价的: (1) $f\in \beta_{\mu}$; \ (2) $f\in H(B)$且函数$\mu(|z|)(1-|z|^{2})^{\gamma-1}R^{\alpha,\gamma}f(z)$ 在$B$上有界; (3) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{1}-1}\frac{\partial^{M_{1}} f}{\partial z^{m}}(z)}$ 在$B$上有界, 其中$|m|=M_{1}$; (4) $f\in H(B)$ 且函数${\mu(|z|)(1-|z|^{2})^{M_{2}-1}R^{(M_{2})}f(z)}$ 在$B$上有界.     

赋$\beta$-范空间中的最佳逼近问题

本文讨论赋$\beta$-范空间中的最佳逼近问题.以[1]引进的共轭锥为工具,借助[2]中关于$\beta$-次半范的Hahn-Banach延拓定理,第二节给出赋$\beta$-范空间的闭子空间中最佳逼近元的特征,第三节得到赋$\beta$-范空间中任何凸子集或子空间均为半Chebyshev集的充要条件是空间本身严格凸,文章最后证明了严格凸的赋$\beta$-范空间中任何有限维子空间都是Chebyshev集.