高斯光束计算平板波导自由传输区远场分布及其修正

对近轴近似条件下求解亥姆霍兹方程得到的高斯光束显式传播公式做了分析，同时，基于基尔霍夫衍射理论，在菲涅耳近似的条件下给出了相应的高斯光束在远场的传播公式，在此基础上，对近轴近似条件做出了定量分析，给出了这个近似条件引入的误差，提出了一种计算高斯光束远场分布的修正方法，并采用有限差分-光束传播方法(FD-BPM)来检验各种方法的准确性。把这种修正方法应用到平面光集成波导器件，如阵列波导光栅(AWG)、蚀刻衍射光栅(EDG)等器件的设计和模拟中，可以大大降低工作的复杂性，同时可以得到精确的结果。     

Variational conclusions of set-valued bifunctions on convex subsets of Banach spaces with applications

In this paper, variational conclusions of set-valued bifunctions on convex subsets of Banach spaces are investigated and several new results are obtained. The results are applied to the fixed point theory and variational inequalities. We obtain two fixed point theorems and existence theorems of solutions of variational inequalities.     

硫酰胺的快速分析（Ⅱ） 

硫酰胺生产过程中副产的大量氯化铵要干扰硫酰胺的测定，采用四苯硼钠将全部氯化铵呈沉淀析出，再用次溴酸钠把滤液中的硫酰胺分解成氮气，测其体积，计算出硫酰胺的含量。对样品进行测定的结果表明，该法重现性好、准确度高、分析周期在３５ｍｉｎ内，相对误差在±１％以内。     

用于留数算术中的数值／留数／数值的转换

介绍用光学方法完成留数算术中的数值/留数/数值的转换,并附有实验结果。     

Superconvergence of discontinuous Galerkin finite element method for the stationary Navier‐Stokes equations

This article focuses on discontinuous Galerkin method for the two‐ or three‐dimensional stationary incompressible Navier‐Stokes equations. The velocity field is approximated by discontinuous locally solenoidal finite element, and the pressure is approximated by the standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least‐squares surface fitting for the stationary Navier‐Stokes equations. The method ameliorates the two noticeable disadvantages about the given finite element pair. Finally, the superconvergence result is provided under some regular assumptions. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 421–436, 2007     

Generalization of a sharp Hölder's inequality and its application

In this paper, we generalize Hu Ke's sharpness of Hölder's inequality. As application, the obtained result is used to improve the well-known Opial-Olech inequality.     

Runge–Kutta Methods for Itô Stochastic Differential Equations with Scalar Noise

A general class of stochastic Runge–Kutta methods for Itô stochastic differential equation systems w.r.t. a one-dimensional Wiener process is introduced. The colored rooted tree analysis is applied to derive conditions for the coefficients of the stochastic Runge–Kutta method assuring convergence in the weak sense with a prescribed order. Some coefficients for new stochastic Runge–Kutta schemes of order two are calculated explicitly and a simulation study reveals their good performance.     

Effects of SnO2 addition on the magnetic properties of manganese zinc ferrites

SnO₂ was added to high-permeability MnZn ferrites and MnZn ferrites for high-frequency power supplies. The effects of the SnO₂ addition were studied. Sn⁴⁺ ions can dissolve into the spinel lattice and form stable Fe²⁺–Sn⁴⁺ pairs and hence can compensate the magneto-crystalline anisotropy constant K₁ and improve the initial permeability effectively. The initial permeability of ferrites is also improved as abnormal grain growth caused by ion vacancy is controlled with SnO₂ doping. In addition, the SnO₂ doping also leads to a decrease in the relative loss factor and an increase in density. The power loss and minimum power loss temperature decrease with SnO₂ doping.     

Hydrothermal synthesis of FeS2 for lithium batteries

Nanocrystalline FeS₂ cathode material of lithium cell was synthesized from cheap materials of FeSO₄, Na₂S₂O₃, and sulfur by a hydrothermal process. The scanning electron microscopy analysis showed the obtained material was nano-sized, about 500 nm. The X-ray powder diffraction analysis showed that the synthetic FeS₂ material had two phases of the crystalline structure, pyrite and marcasite. The phase of marcasite seems to have no negative effect on the electrochemical performance of the material. The synthetic FeS₂ showed a significant improvement of electrochemical performance for Li/FeS₂ cells.