ON THE ASYMPTOTIC BEHAVIOUR OF THE STEADY SUPERSONIC FLOWS AT INFINITY

This paper studies the asymptotic behaviour of steady supersonic flow past a piece-wise smooth corner or bend. Under the hypothese that both vertex angle and the total variation of tangent along the boundary are small, it is shown that the solution can be obtained by a modified Glimm scheme, and that the asymptotic behaviour of the solution is determined by the velocity of incoming flow and the limit of the tangent of the boundary at infinity.     

BOUNDEDNESS OF MAXIMAL SINGULAR INTEGRALS

The authors study the singular integrals under the Hormander condition and the measure not satisfying the doubling condition. At first, if the corresponding singular integral is bounded from L2 to itself, it is proved that the maximal singular integral is bounded from L∞to RBMO except that it is infinite μ-a.e. on Rd. A sufficient condition and a necessary condition such that the maximal singular integral is bounded from L2 to itself are also obtained. There is a small gap between the two conditions.     

综合题新编选登：题136

函数f(x)对一切实数x，y均有f(x y)-f(Y)=x(x 2y 1)成立，且f(1)=0．     

Structural Characteristics of Liquid Sn

We investigate the structural properties of liquid Sn. With the help of the internal friction (tanФ) method, it is found that a peak appears in the tan Ф - T curve, suggesting that an anomalous discontinuous temperatureinduced structure change may take place in liquid Sn. From the experimental data of pair distribution functions, we calculate the viscosity η and the excess entropy S and it is found that there are a peak of viscosity in the η-T curve and a bend of excess entropy in the S - T curve, which give a positive support to the appearance of the internal-friction peak in the tan Ф- T curve.     

对求解非线性方程方法的探索

BaiCL在2001年提出了双曲函数法，并把解设成具体的双曲函数，即sinhw和coshw的线性组合．本文把解设成是由2个函数f(ξ)和g(ξ)组成的线性组合，它们可以有多种取法，从而使方程更直接、更有效．借助数学软件Maple，用改进后的方法和吴文俊消元法，求解Bai C L文中的一个例子，获得了包含Bai文结果在内的更为丰富、精确的行波解．     

矩阵损失下回归系数的线性估计的可容许性

针对广义的Gauss-Markoff模型Y=Xβ+θ,E(θ)=0,Cov(θ)=σ2V,其中X和V＞0是已知的n×p和n×n矩阵;β∈Rp和σ2＞0是未知参数,给出了矩阵损失条件下,Sβ的估计LY+a在非齐次线性估计类中可容许的充要条件.     

一类非线性规划问题的等价性证明

给出了非线性规划问题中目标函数单调变换前后的一个等价性证明.     

双无限随机环境中马氏链的瞬时性与不变函数

在随机环境中马氏链的研究领域,引入了一类π-不可约、常返和瞬时性的概念,给出了π-不可约链是瞬时链的一个充要条件,引入了双无限随机环境中马氏链不变函数的概念,讨论了它们的存在性及基本性质。最后,利用不变函数的性质,给出了π-不可约链是瞬时链的一个判别准则,此准则与不变函数有关。