The Lagrangian Globalization Method for Nonsmooth Constrained Equations

The difficulty suffered in optimization-based algorithms for the solution of nonlinear equations lies in that the traditional methods for solving the optimization problem have been mainly concerned with finding a stationary point or a local minimizer of the underlying optimization problem, which is not necessarily a solution of the equations. One method to overcome this difficulty is the Lagrangian globalization (LG for simplicity) method. This paper extends the LG method to nonsmooth equations with bound constraints. The absolute system of equations is introduced. A so-called Projected Generalized-Gradient Direction (PGGD) is constructed and proved to be a descent direction of the reformulated nonsmooth optimization problem. This projected approach keeps the feasibility of the iterates. The convergence of the new algorithm is established by specializing the PGGD. Numerical tests are given. This author's work was done when she was visiting The Hong Kong Polytechnic University. His work is also supported by the Research Grant Council of Hong Kong.     

Chemoselective Catalytic Hydrogenation of α,β-Unsaturated Ketones and α,β-Unsaturated Carboxylic Esters

ＣｈｅｍｏｓｅｌｅｃｔｉｖｅＣａｔａｌｙｔｉｃＨｙｄｒｏｇｅｎａｔｉｏｎｏｆα，β┐ＵｎｓａｔｕｒａｔｅｄＫｅｔｏｎｅｓａｎｄα，β┐ＵｎｓａｔｕｒａｔｅｄＣａｒｂｏｘｙｌｉｃＥｓｔｅｒｓＺＨＡＮＧＪｉｎｇ－ｗｅｎ＊，ＺＨＡＯＪｉａｎ－ｚｈａｎｇ，Ｚ...     

激光二极管泵浦的高重复频率Nd：YAG激光器

报道两个１．５Ｗ连续激光二极管端面泵浦的声光调ＱＮｄ：ＹＡＧ激光器，输出激光脉冲的最高重复频率为３０ｋＨｚ重复频率１ｋＨｚ时，最窄脉宽为１２ｎｓ，最高峰值功率为１２．１ｋＷ。     

1．5GHz锯材超导腔的研制

介绍铌材超导腔的研制进展，重点讨论了国产铌腔的材料改性，以及相应的超导腔性能的改进．叙述了１．５ＧＨｚ铌腔的腔形设计，分析了铌材的射频性能和机械性能，制定了铌腔制作与后处理的特定工艺．最后给出了１．５ＧＨｚ铌材超导腔的低温实验结果．     

Renormalization group calculation of the critical temperature dependence on longitudinal magnetic field for a disordered superconductor model

We describe a calculation ofT _c (P, H) in a model of a disordered superconductor which is based on the de Gennes-Skal-Shklovskii (dGSS) picture of the large cluster in a percolation system. The calculation is done by carrying out successive decimations on the Landau-Ginzburg Hamiltonian describing the links in the model. We calculateT _c (P, H) in the presence of longitudinal magnetic field by evaluating the renormalized Landau-Ginzburg coupling when the renormalized Landau-Ginzburg length equals the percolation link length in the dGSS picture and obtain the approximate analytic form ofT _c (P, H).Work supported by China Natural Science Foundation     

Thermodynamic properties of aqueous mixtures of LiCl and Li2SO4 at different temperatures

Emf measurements were made on the cell without liquid junction: Li?ISE LiCl(m₁), Li₂SO₄(m₂) Ag/AgCl. The performances of the electrode pairs constructed in our laboratory were tested and exhibited near-Nernstian behavior. The mean activity coefficients of LiCl for the system Li⁺?Cl^??SO ₄ ^2? ?H₂O have been investigated by the emf values at temperatures of 0, 15, 35°C and constant total ionic strengths of 0.05, 0.1, 0.5, 1.0, 2.0, 3.0 and 5.0 mol·kg^?1. The activity coefficients decrease with increasing temperature and the ionic strength fraction of Li₂SO₄ in the mixtures. The thermodynamic properties are interpreted by use of Harned's empirical equations and Pitzer's ion interaction approach including the contribution of higher order electrostatic terms. The experimental results obey Harned's rule and are described by using Pitzer equations satisfactorily. The activity coefficients of Li₂SO₄, the osmotic coefficients and the excess free energies of mixing for the system in the experimental temperature range were reported.