不定Sturm—Liouville算子的特征函数的振荡问题

研究了定义在有限区间（0，l）上的具有一般分离型边条件的不定Sturm—Liouville算子的特征函数的振荡问题．利用Prufer变换，给出了上述Sturm-Liouville算子特征值的符号指标的具体形式；得到了特征值的符号指标与Weyl函数以及Prufer角在该特征值处的罗朗展式（泰勒展式）的首项系数的符号之间的关系；最后，在上述两个结果的基础上给出了上述Sturm—Liouville算子的第n个正特征值所对应的特征函数在[0，l]内的零点个数的计算公式．     

Asymptotics of optimal control in the problem of harmonic wave scattering by an obstacle

Optimal impedance control for the Helmholtz equation in an unbounded domain is studied. Asymptotics of the optimal control with respect to a regularization parameter are constructed.     

On Selecting k Balls from an N-circle Without Unit Separation

Ｏｎ　Ｓｅｌｅｃｔｉｎｇ　ｋ　Ｂａｌｌｓ　ｆｒｏｍ　ａｎ　Ｎ－ｃｉｒｃｌｅ　Ｗｉｔｈｏｕｔ　Ｕｎｉｔ　ＳｅｐａｒａｔｉｏｎＣａｉＴｉａｎｘｉｎ（蔡天新）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｃｍａｔｉｃｓ，ＨａｎｇｚｈｏｎＵｎｉｖｅｒｓｉｔｙ，Ｈａｎｇｚ...     

算子点态遍历定理

本文证明了关于Ｌ^P（１≤Ｐ≤∞）空间中线性算子与非线性算子的几个点态遍历定理，还推广了Ｙｏｓｉｄａ与ＫａＫｕｔａｎｉ关于拟紧算子的一致遍历定理。     

提高大学物理实验教学质量的措施与设想

本提出了提高大学物理实验教学质量的一些措施与设想。并加以简要论述。     

Numerical simulation of the unsteady aerodynamic interaction of two plane airfoil cascades

A method for the calculation of unsteady aerodynamic interaction of two plane airfoil cascades that are in relative motion in a subsonic flow of ideal gas is developed. This interaction provides a two-dimensional approximation of the flow in a stage of an axial turbomachine. The method is based on the reduction of the problem to the calculation of the unsteady flow in a single interblade passage of each of the cascades. The calculation uses generalized space-time periodicity relations corresponding to the unsteady process of interest. The calculation is based on the direct numerical integration of the non-stationary gas dynamics equations with the use of the finite difference Godunov-Kolgan-Rodionov scheme of the second approximation order with respect to time and space. The calculation procedure includes the determination of the acoustic fields that are generated by the stage in the incident flow and in the flow behind it. The results of the calculations that illustrate the accuracy of the numerical solution and the capabilities of the method are presented.     

Bending of elastic plates with a physically nonlinear inclusion

An infinite elastic isotropic plate with an elliptical, physically nonlinear inclusion loaded at infinity by uniformly distributed moments is considered. Surface loads are absent. The problem of the stress-strain state of the plate is solved in a closed form. It is shown that, for reasonably general stress-strain relations for the inclusion, the bending-moment field (and the corresponding curvatures) in the inclusion is homogeneous. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 6, pp. 152–157, November–December, 2006.     

高频感应炉燃烧–红外吸收法测定银杏及银杏叶中的硫含量

采用高频感应炉燃烧–红外吸收法测定银杏叶、银杏果肉、银杏壳和银杏仁中的硫含量。样品以艾士卡试剂为熔融剂,在800℃马弗炉内熔融1 h,冷却后测定硫含量。硫的质量分数在0.40%~4.00%范围内与吸收峰面积呈良好的线性关系,线性相关系数为0.990 4,检出限为0.000 9%。测定结果的相对标准偏差为4.04%(n=11),平均加标回收率为101.03%。将红外吸收法与电感耦合等离子体原子发射光谱法及硫酸钡重量法进行比对试验,3种方法测定结果相一致。利用该方法测定了不同区域银杏叶中硫的含量,结果表明,风景区和居民区银杏叶干燥基全硫的含量较低,重工业区硫含量较高。对同一地区的银杏果肉、银杏壳、银杏仁中干燥基全硫的含量进行比较,结果表明银杏果肉硫含量最高,银杏壳次之,银杏仁最低。该方法灵敏度高,重现性好,可用于银杏及银杏叶中硫含量的准确测定。