Second order parabolic equations in Banach spaces with dynamic boundary conditions

In this paper, we exhibit a unified treatment of the mixed initial boundary value problem for second order (in time) parabolic linear differential equations in Banach spaces, whose boundary conditions are of a dynamical nature. Results regarding existence, uniqueness, continuous dependence (on initial data) and regularity of classical and strict solutions are established. Moreover, several examples are given as samples for possible applications.

     

An Improved Synthesis of Retinoic Acid from β-Ionone

A convenient and large-scale preparation of retinoic acid 1 from β-ionone in five steps with 38% overall yield is described.The key steps are the epoxidization of 2 with a new methylated agent and the condensation 4 with tetraethyl methylenediphophonate in one-pot procedure to prepare 6.     

Crystallographic report: Bis(norfloxacin)dilead(II) tetranitrate, [Pb2(H‐Norf)2(ONO2)4]

The centrosymmetric binuclear structure of [Pb₂(H‐Norf)₂(ONO₂)₄]shows the geometry around each lead(II) atom to be distorted trigonal bipyramidal with Pb–O distances ranging from 2.357(3) to 2.769(4) Å. Copyright © 2003 John Wiley & Sons, Ltd.     

电感耦合等离子体原子发射光谱法测定化妆品中砷、铅、汞

本文采用五氧化二钒作催化剂，HNO3－H2SO4消解法对化妆品前处理后，用电感耦合等离子体发射光谱仪同时测定砷，铅，汞，方法简便，快速，回收率在95％－103．5％之间，相对标准偏差不大于3％。     

MgO在Mg-hBN体系中对合成cBN晶体的影响

 以金属镁粉为触媒，以六角氮化硼为原料，其中加入适量比例的氧化镁，在国产六面顶压机上，在约5.0 GPa压力、1 500～1 800 K温度条件下，合成出了颜色均匀、晶形完整的黄色立方氮化硼单晶体。实验结果表明，在Mg-hBN体系中，氧化镁对合成cBN晶体的颜色及合成温度有很大的影响。     

Optimizing the optical field distribution of solid immersion lens system by a continuous phase filter

In solid immersion lens (SIL) microscopy systems with high numerical aperture (NA), there always exists the aberration produced by Fresnel effects at the interface between SIL and the sample. This aberration may cause the degradation of the image of sample. We design a continuous phase filter and optimize the optical field distribution of SIL system. The numerical results show that when the continuous phase filter is used, the field distribution of SIL system can be optimized, and the focal depth and intensity of transmitted light can be increased. At the same time, the intensity of side-lobe and the resolution are kept almost unchanged.     

独立不同分布随机变盆序列的部分和的增量有多小

关于独立同分布随机变量部分和的增量有多小问题，目前已有了著名的结果.本文通过与独立同分布情形时完全不同的途径，讨论了独立不同分布情形时相应的问题.在矩母函数存在的条件下，获得了与同分布情形相近的结论.     

界面反射偏振象差分析

在光学没计中,一般认为在同一光波面上,光束具有相同的振幅和偏振状态。事实上,光束经过许多光学元件后,偏振状态会发生变化,特别是入射角和光程的不同,会导致出射光波面上偏振分布不再均匀,形成偏振象差。本文主要就轴上物点发出的光束经过界面反射后的偏振象差方面进行了分析。     

Two differential equation systems for equality-constrained optimization

This paper presents two differential systems, involving first and second order derivatives of problem functions, respectively, for solving equality-constrained optimization problems. Local minimizers to the optimization problems are proved to be asymptotically stable equilibrium points of the two differential systems. First, the Euler discrete schemes with constant stepsizes for the two differential systems are presented and their convergence theorems are demonstrated. Second, we construct algorithms in which directions are computed by these two systems and the stepsizes are generated by Armijo line search to solve the original equality-constrained optimization problem. The constructed algorithms and the Runge–Kutta method are employed to solve the Euler discrete schemes and the differential equation systems, respectively. We prove that the discrete scheme based on the differential equation system with the second order information has the locally quadratic convergence rate under the local Lipschitz condition. The numerical results given here show that Runge–Kutta method has better stability and higher precision and the numerical method based on the differential equation system with the second information is faster than the other one.