高功率全固态绿光激光技术研究进展

 报道了高功率全固态腔内和腔外倍频两种绿光激光器研究进展。腔内倍频绿光激光器采用L型腔双棒串接结构,在重复频率10 kHz时,用三硼酸锂晶体倍频获得绿光功率186 W,光-光效率达15.8%。腔外倍频绿光激光器采用主振荡和功率放大器,在重复频率400 Hz时,获得基频激光单脉冲能量1.2 J,采用Ⅱ类相位匹配KTP晶体腔外倍频,获得525 mJ的绿光输出,倍频效率为43.7%。采用偏振合成技术获得了单脉冲能量大于1 J的绿光输出。在该激光放大器实验装置上,进行了双模块热效应补偿技术和受激布里渊散射相位共轭技术实验研究,改善了激光光束质量。     

高功率激光整形脉冲波形控制技术

 针对神光-Ⅲ原型装置物理实验要求的三台阶整形脉冲（三个台阶的脉冲宽度比为1.5∶1.0∶0.5,强度比为1∶4∶16,脉冲总能量为500 J）,并根据该装置的系统构成和具备任意脉冲整形技术,开展了高功率激光整形脉冲波形控制技术研究,通过对基频光段的增益饱和效应和三倍频光的频率转换过程的分析,获得了脉冲时间波形在传输、放大及频率转换过程中的一些变化特点,在此基础上建立了一套简单的预测模型。经过反复迭代计算和多次全系统联机实验获得了实验结果,并在物理实验中得到了应用,初步形成了高功率激光整形脉冲波形的控制方法。     

GENERALIZED FRACTIONAL TRACE VARIATIONAL IDENTITY AND A NEW FRACTIONAL INTEGRABLE COUPLINGS OF SOLITON HIERARCHY

Based on fractional isospectral problems and general bilinear forms, the gener-alized fractional trace identity is presented. Then, a new explicit Lie algebra is introduced for which the new fractional integrable couplings of a fractional soliton hierarchy are derived from a fractional zero-curvature equation. Finally, we obtain the fractional Hamiltonian structures of the fractional integrable couplings of the soliton hierarchy.     

STABILITY RESULTS OF RANDOM IMPULSIVE SEMILINEAR DIFFERENTIAL EQUATIONS

In this paper, we study the existence, uniqueness, continuous dependence, Ulam stabilities and exponential stability of random impulsive semilineax differential equations under sufficient condition. The results are obtained by using the contraction mapping principle. Finally an example is given to illustrate the applications of the abstract results.     

ON SOLVABILITY AND WAVEFORM RELAXATION METHODS FOR LINEAR VARIABLE-COEFFICIENT DIFFERENTIAL-ALGEBRAIC EQUATIONS

This paper is concerned with the solvability and waveform relaxation methods of linear variable-coefficient differential-algebraic equations （DAEs）. Most of the previous works have been focused on linear variable-coefficient DAEs with smooth coefficients and data, yet no results related to the convergence rate of the corresponding waveform relaxation methods has been obtained. In this paper, we develope the solvability theory for the linear variable-coefficient DAEs on Legesgue square-integrable function space in both traditional and least squares senses, and determine the convergence rate of the waveform relaxation methods for solving linear variable-coefficient DAEs.     

关于可数点集的盒维数的一些探讨

本文研究了一类可数点集的盒维数的计算问题.通过构造双Lipschitz映射,把原可数点集的盒维数的求解问题转化为求解一类相对简单的可数点集的盒维数.获得了两个单调的可数点集在具有同阶间隔时具有相同的上盒维数和下盒维数的结论.该结论为计算一类可数点集的盒维数提供了方便.     

粗糙有限状态机的分解

利用代数的方法研究了粗糙有限状态机的可恢复性、连通性与可分离性等代数性质,得到了一个粗糙有限状态机是可恢复的当且仅当它的每一个准素粗糙子有限状态机都是强连通的当且仅当其每一个单生成粗糙子有限状态机都是准素的当且仅当其每一个非空连通粗糙子有限状态机都是准素的,给出了粗糙有限状态机不是连通的的充分必要条件,讨论了粗糙有限状态机的一些分解性质。     

THE FRACTIONAL QUADRATIC-FORM IDENTITY AND BI-HAMILTONIAN STRUCTURES OF AN INTEGRABLE COUPLING OF THE FRACTIONAL COUPLED BURGERS HIERARCHY

Based on a general isospectral problem of fractional order and the fractional quadratic-form identity by Yue and Xia, the new integrable coupling of fractional coupled Burgers hierarchy and its fractional bi-Hamiltonian structures are obtained.     

算子代数上的Lie可导映射

设A为有单位且包含一非平凡幂等元的环,M为A双模.称δ:A→M为Lie可导映射(无可加或连续假设),若δ([A,B])=[δ(A),B]+[A,δ(B)],(?)A,B∈A.在一定条件下该文证明了Lie可导映射δ具有形式δ(A)=τ(A)+f(A),其中r:A→M是可加导子,f是从A到M的中心且满足f([A,B])=0,(?)A,B∈A的映射.由此刻画了因子von Neuamnn代数和套代数上的Lie可导映射.     

超Li系统的Bargmann对称约束和双非线性化

给出超Li系统的一个显式对称约束和关于其Lax对的双非线性化.在此对称约束下,超Li系统的时间部分和空间部分分别被约化为有限维Liouville可积超Li系统.