再论生产函数的统计学问题——与余斌、程立茹先生商榷

生产函数有着相应的经济理论背景,是以科学的数据为样本,反复拟合、检验、修正后得到的,揭示产出量与生产要素资本和劳动之间内在的必然的统计相关关系,是科学的结论。本文就此与余斌、程立茹先生进行探讨和商榷。     

Structural characterisation of Sb-based heterostructures by X-ray scattering methods

Antimonide-based superlattices dedicated to the elaboration of opto-electronic devices have been studied by X-ray scattering techniques. In particular, specular and non-specular X-ray reflectometry experiments have been performed on two MBE-samples elaborated with different shutter sequences at the interfaces. The results have shown a limitation of the incorporation of Sb species in the subsequent InAs layer for one of the samples, as expected.Then, a study on a InGaAs-cap layer/(InGaAs/AlAsSb)_N superlattice grown on a InGaAs/InP buffer layer by both specular X-ray reflectometry and High resolution X-ray diffraction is reported. In particular, the results have revealed the presence of a highly disturbed thin-layer on top of the MOVPE-made GaInAs, whose presence has been explained by In-concentration modification during the desoxidation procedure at the surface of the MOVPE-made GaInAs.Beside the results on the Sb-based heterostructures, the use of X-ray scattering metrology as a routinely working non-destructive testing method has been emphasized.     

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.     

NONTRIVIAL SOLUTIONS OF HARDY-HENON TYPE ELLIPTIC SYSTEMS

In this article,the authors investigate the existence problem for Hardy Hénon type strongly indefinite elliptic systems.Existence results are obtained for such systems with superlinear suberitical nonlinearities.     

用力敏传感器测量液体表面张力系数

利用力敏传感器测量液体表面张力系数，既改进了传统的实验方法和仪器，提高了实验的准确度和稳定性，同时因实现了非电量电测，也有助于测量过程中学生对物理过程的观察和规律的理解。     

A class of Nevanlinna functions related to singular Sturm-Liouville problems

The class of Nevanlinna functions consists of functions which are holomorphic off the real axis, which are symmetric with respect to the real axis, and whose imaginary part is nonnegative in the upper halfplane. The Kac subclass of Nevanlinna functions is defined by an integrability condition on the imaginary part. In this note a further subclass of these Kac functions is introduced. It involves an integrability condition on the modulus of the Nevanlinna functions (instead of the imaginary part). The characteristic properties of this class are investigated. The definition of the new class is motivated by the fact that the Titchmarsh-Weyl coefficients of various classes of Sturm-Liouville problems (under mild conditions on the coefficients) actually belong to this class.

     

Generalized Solution of a Kind of Nonparametric Curvature Evolution with Boundary Condition

The existence and uniqueness of the generalized solution for a kind of nonparametric curvature flow problem are obtained. This kind of curvature flow problem describes the evolution of graphs with speed depending on the reciprocal of the Gauss curvature.     

An explicit characterization of Calogero-Moser systems

Combining theorems of Halphen, Floquet, and Picard and a Frobenius type analysis, we characterize rational, meromorphic simply periodic, and elliptic KdV potentials. In particular, we explicitly describe the proper extension of the Airault-McKean-Moser locus associated with these three classes of algebro-geometric solutions of the KdV hierarchy with special emphasis on the case of multiple collisions between the poles of solutions. This solves a problem left open since the mid-1970s.

     

关于艾森斯坦因判别法的间接应用

探讨了间接应用艾森斯坦因判别法判断整系数多项式在有理数域上不可约的两种途径.     

一类求解奇异延迟微分方程的两步连续Runge-Kutta方法的收敛性

本文给出了一类求解延迟落在当前积分步内延迟微分方程的两步连续Runge-Kutta方法。在一定条件下我们证明了方法收敛性,数值试验表明方法是有效的。