γ-LiAlO2晶体生长、改性和热学性质研究

采用快速提拉法生长出了透明、完整的γ-LiAlO2晶体,但是晶体的高熔点和易挥发性限制了γ-LiAlO2晶体质量.采用气相传输平衡法(vapor transport equilibration technique,VTE)工艺对晶体改性,半高宽(FWHM)值从116.9arcsec降至44.2arcsec,继续升高VTE处理温度至1300℃,FWHM值反而升高至55.2arcsec.快速提拉法生长出来晶体,[100]方向和[001]方向的热膨胀系数分别为17.2398×10-6/K,10.7664×10-6/K.经过三步VTE处理后[100]和[001]方向热膨胀系数降至16.6539×10-6/K和10.1784×10-6/K.     

Application of N,N‐bis(diphenylphosphino)aniline palladium(II) complexes as pre‐catalysts in Heck coupling reactions

Palladium(II) complexes with N,N‐bis(diphenylphosphino)aniline ligands catalyse the Heck reaction between styrene and aryl bromides, affording stilbenes in good yield. The structures of two of the complexes used as pre‐catalysts have been determined by single‐crystal X‐ray diffraction. Copyright © 2007 John Wiley & Sons, Ltd.     

Theoretical and numerical analysis on multispectral bioluminescence tomography

Recently, molecular imaging has been rapidly developed to studyphysiological and pathological processes in vivo at the cellularand molecular levels. Among molecular imaging modalities, opticalimaging has attracted a major attention for its unique advantages.In this paper, we establish a mathematical framework for multispectralbioluminescence tomography (BLT) that allows simultaneous studiesof multiple optical reporters. We show solution existence, uniquenessand continuous dependence on data as well as the limiting behaviourswhen the regularization parameter approaches zero or when thepenalty parameter approaches infinity. Then, we propose twonumerical schemes for multispectral BLT and derive error estimatesfor the corresponding solutions.     

A note on model diagnostics in longitudinal data analysis

Longitudinal study has become one of the most commonly adopted designs in medical research. The generalized estimating equations (GEE) method and/or mixed effects models are employed very often in causal inferences. The related model diagnostic procedures are not yet fully formalized, and perhaps never will be. The potential causes of major problems are the high variety of the dependence within subjects and/or the number of repeated measurements. A single testing procedure, e.g., run test, is not possible to resolve all model diagnostics problems in longitudinal data analysis. Multiple quantitative indexes for model diagnostics are needed to take into account this variety. We propose eight testing procedures for randomness accompanied with some conventional and/or non-conventional plots to remedy model diagnostics in longitudinal data analysis. The proposed issue in this paper is well illustrated with four clinical studies in Taiwan.     

On the limit cycles of a quintic planar vector field

This paper concerns the number and distributions of limit cycles in a Z_2-equivariant quintic planar vector field.25 limit cycles are found in this special planar polynomial system and four different configurations of these limit cycles are also given by using the methods of the bifurcation theory and the qualitative analysis of the differential equation.It can be concluded that H(5)≥25=5~2, where H(5)is the Hilbert number for quintic polynomial systems.The results obtained are useful to study the weakened 16th Hilbert problem.     

聚能射流的断裂时间

从描述聚能射流失稳的一维近似方程出发，导出了聚能射流断裂时间的近似公式。这个近似公式定量显示了屈服应力、本构关系、粘度和径向收缩效应等对射流断裂时间的影响，在４个不同的特殊近似下，可以自然演化为近１０年来所发表的几个半经验解析公式，并且在合理的参数范围内，公式给出的断裂时间曲线覆盖了射流断裂时间的全部实验点。     

OnM-ideals and best approximation

In this paper we will prove some theorems on theM-ideals of compact operators and the best approximation of quasitriangular operator algebras. These results improve and extend the known results in [4, 5, 7].This work is supported in part by the National Natural Science Foundation of China.     

A posteriori error analysis for linearization of nonlinear elliptic problems and their discretizations

The paper is devoted to a posteriori quantitative analysis for errors caused by linearization of non-linear elliptic boundary value problems and their finite element realizations. We employ duality theory in convex analysis to derive computable bounds on the difference between the solution of a non-linear problem and the solution of the linearized problem, by using the solution of the linearized problem only. We also derive computable bounds on differences between finite element solutions of the nonlinear problem and finite element solutions of the linearized problem, by using finite element solutions of the linearized problem only. Numerical experiments show that our a posteriori error bounds are efficient.     

On meromorphic functions that share three values of finite weights

A uniqueness theorem for two distinct non-constant meromorphic functions that share three values of finite weights is proved, which generalizes two previous results by H.X. Yi, and X.M. Li and H.X. Yi. As applications of it, many known results by H.X. Yi and P. Li, etc. could be improved. Furthermore, with the concept of finite-weight sharing, extensions on Osgood-Yang's conjecture and Mues' conjecture, and a generalization of some prevenient results by M. Ozawa and H. Ueda, ect. could be obtained.