Let P_n={Z=(Z_1,…,Z_n)|Z_iZ_i^n<1, Z_i are 2×2 complex matrices},H_n={W=(W_1,…, W_n)|W_i=Z_iB,(Z_1,…,Z_n)∈P_n,B∈SL(2,C)}, D_n={W=(W_1,…,W_n)| W_i=AZ_iB,(Z_1,…,Z_n)∈P_n,A, B∈SL(2, C)}. Are H_n,D_n doma...Let P_n={Z=(Z_1,…,Z_n)|Z_iZ_i^n<1, Z_i are 2×2 complex matrices},H_n={W=(W_1,…, W_n)|W_i=Z_iB,(Z_1,…,Z_n)∈P_n,B∈SL(2,C)}, D_n={W=(W_1,…,W_n)| W_i=AZ_iB,(Z_1,…,Z_n)∈P_n,A, B∈SL(2, C)}. Are H_n,D_n domains of holomorphy? In the present paper, we prove that H_2, D_2 are domains of holomorphy by using the follow-ing proposition: H_2={W∈C^2[2×2]|W_1W_2~*∈P_1, |detW_1|<1, |detW_2|<1}.展开更多
Shuowen J iezi (《说文解字 》)is one of the richest sources of linguistic data for Ancient Chinese.However,unlike edited primary texts like Shijing(《诗经》)or compilations of individual glosses like Erya (《《尔雅》)...Shuowen J iezi (《说文解字 》)is one of the richest sources of linguistic data for Ancient Chinese.However,unlike edited primary texts like Shijing(《诗经》)or compilations of individual glosses like Erya (《《尔雅》),the Shuowen is a work through and through shaped by the novel intention and method of its author.Consequently,without understanding Xu Shen's(许慎)purpose and how it motivates his individual explanations one risks misconstruing the data.By inclination an intellectual historian rather than a linguist,I am primarily interested in the vision that shaped this unique collection of language facts rather than in using the information contained therein toward a reconstruction of the Chinese it reflects.My own goal,however,is not opposed to the later,quite on the contrary,by uncovering the motivation behind Shuowen glosses I hope to disentangle them from the intricate mesh of interrelations into which they had been woven by their author so that they can be safely utilized by the linguist.展开更多
This paper analyzes two extended finite element methods(XFEMs)for linear quadratic optimal control problems governed by Poisson equation in non-convex domains.We follow the variational discretization concept to discre...This paper analyzes two extended finite element methods(XFEMs)for linear quadratic optimal control problems governed by Poisson equation in non-convex domains.We follow the variational discretization concept to discretize the continuous problems,and apply an XFEM with a cut-off function and a classic XFEM with a fixed enrichment area to discretize the state and co-state equations.Optimal error estimates are derived for the state,co-state and control.Numerical results confirm our theoretical results.展开更多
针对一类非线性不确定系统,构造了一种多变量线性扩张状态观测器(Multi-variable linear extended state observer,MVLESO),用于实时估计非线性系统的不确定动态.采用频域分析方法,剖析了所构造的MVLESO在非线性系统不确定动态估计方面...针对一类非线性不确定系统,构造了一种多变量线性扩张状态观测器(Multi-variable linear extended state observer,MVLESO),用于实时估计非线性系统的不确定动态.采用频域分析方法,剖析了所构造的MVLESO在非线性系统不确定动态估计方面的收敛性,并推导出不确定动态的频域估计误差模型.仿真结果表明,所设计的MVLESO可以较为精准地估计出非线性系统当前的不确定动态,该特性为基于MVLESO鲁棒控制方案的有效实施奠定了基础.展开更多
文摘Let P_n={Z=(Z_1,…,Z_n)|Z_iZ_i^n<1, Z_i are 2×2 complex matrices},H_n={W=(W_1,…, W_n)|W_i=Z_iB,(Z_1,…,Z_n)∈P_n,B∈SL(2,C)}, D_n={W=(W_1,…,W_n)| W_i=AZ_iB,(Z_1,…,Z_n)∈P_n,A, B∈SL(2, C)}. Are H_n,D_n domains of holomorphy? In the present paper, we prove that H_2, D_2 are domains of holomorphy by using the follow-ing proposition: H_2={W∈C^2[2×2]|W_1W_2~*∈P_1, |detW_1|<1, |detW_2|<1}.
文摘Shuowen J iezi (《说文解字 》)is one of the richest sources of linguistic data for Ancient Chinese.However,unlike edited primary texts like Shijing(《诗经》)or compilations of individual glosses like Erya (《《尔雅》),the Shuowen is a work through and through shaped by the novel intention and method of its author.Consequently,without understanding Xu Shen's(许慎)purpose and how it motivates his individual explanations one risks misconstruing the data.By inclination an intellectual historian rather than a linguist,I am primarily interested in the vision that shaped this unique collection of language facts rather than in using the information contained therein toward a reconstruction of the Chinese it reflects.My own goal,however,is not opposed to the later,quite on the contrary,by uncovering the motivation behind Shuowen glosses I hope to disentangle them from the intricate mesh of interrelations into which they had been woven by their author so that they can be safely utilized by the linguist.
基金supported by National Natural Science Foundation of China(Grant No.11771312)。
文摘This paper analyzes two extended finite element methods(XFEMs)for linear quadratic optimal control problems governed by Poisson equation in non-convex domains.We follow the variational discretization concept to discretize the continuous problems,and apply an XFEM with a cut-off function and a classic XFEM with a fixed enrichment area to discretize the state and co-state equations.Optimal error estimates are derived for the state,co-state and control.Numerical results confirm our theoretical results.
文摘针对一类非线性不确定系统,构造了一种多变量线性扩张状态观测器(Multi-variable linear extended state observer,MVLESO),用于实时估计非线性系统的不确定动态.采用频域分析方法,剖析了所构造的MVLESO在非线性系统不确定动态估计方面的收敛性,并推导出不确定动态的频域估计误差模型.仿真结果表明,所设计的MVLESO可以较为精准地估计出非线性系统当前的不确定动态,该特性为基于MVLESO鲁棒控制方案的有效实施奠定了基础.
