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.     

Weak and Strong Solutions for the Stokes Approximation of Non-homogeneous Incompressible Navier-Stokes Equations

In this paper,the Dirichlet problem of Stokes approximate of non-homogeneous incompressibleNavier-Stokes equations is studied.It is shown that there exist global weak solutions as well as global andunique strong solution for this problem,under the assumption that initial density ρ_0(x)is bounded away from0 and other appropriate assumptions(see Theorem 1 and Theorem 2).The semi-Galerkin method is applied toconstruct the approximate solutions and a prior estimates are made to elaborate upon the compactness of theapproximate solutions.     

Semilinear Differential Inclusions in Separable Banach Spaces

Ｓｅｍｉｌｉｎｅａｒ　Ｄｉｆｆｅｒｅｎｔｉａｌ　Ｉｎｃｌｕｓｉｏｎｓ　ｉｎ　Ｓｅｐａｒａｂｌｅ　Ｂａｎａｃｈ　ＳｐａｃｅｓＸｕｅＸｉｎｇｍｅｉ（薛星美）ａｎｄＳｏｎｇＧｕｏｚｈｕ（宋国柱）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，Ｎａｎｊｉｎ...     

Synthesis and Structural Characterization of Adduct [La(NO_3)_3·4H_2O]·2(BQEB)

Differentkindsofopenchaincrownethershavebeensynthesizedasthemodelcompoundsofionophoresandtheirinteractionswithsodium,potassiumandrareearthionshavealsobeenstudiedl'z.PanshowedCe(III)yieldedalf1complexwithl,8-bis(8'-quinolyloxy)-3,6-dioxaandtheCe(IIl)ioncoordinatedbothtoetheroxygenandquinolinenitrogenatoms3.TUmInleridentifiedtwolanthanidenitratecomplexeshavingastoichiometryof3:2(3RE:2L)'.InordertostUdythefunctionsofbothquinolineandbenzenering,introducedintothepolyetherchain,a1inearpolyether…     

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．     

The measurements of correlation times of molecules adsorbed on silica gel,alumina and charcoal using NOESY and MAS NMR

The correlation times (τ_c) and cross relaxation rates of toluene, dimethylformamide, tetrahydrofuran, water-acetone and water-dioxane adsorbed on silica gel, alumina and charcoal were obtained by measurements of the integrated intensities of cross and diagonal peaks in their NOESY spectra. The (τ_c) of the above mentioned systems is in the range of 10^?6?10^?9 s, much longer than that in the liquid (10^?12?10^?14 s). It was found that intramolecular rotation of toluene adsorbed on charcoal is slower than that on SiO₂, Al₂O₃ and the inversion of α and β protons in tetrahydrofuran is very fast (τ_c = 1.76×10^?9 s). The cross relaxation plays an important role in the relaxation of molecules adsorbed on solid surfaces with low electron densities.