Efficient Implementation of a Spectral-Tau Method for a Class of Two-Point Boundary-Value and Initial-Boundary-Value Problems

A simple and efficient spectral method for solving the second, third order and fourth order elliptic equations with variable coefficients and nonlinear differential equations is presented. It is different from spectral-collocation method which leads to dense, ill-conditioned matrices. The spectral method in this paper solves for the coefficients of the solution in a Chebyshev series, leads to discrete systems with special structured matrices which can be factorized and solved efficiently. We also extend the method to boundary value problems in two space dimensions and solve 2-D separable equation with variable coefficients. As an application, we solve Cahn-Hilliard equation iteratively via first-order implicit time discretization scheme. Ample numerical results indicate that the proposed method is extremely accurate and efficient.     

Trace theorems for functions of bounded variation in metric spaces

In this paper we show existence of traces of functions of bounded variation on the boundary of a certain class of domains in metric measure spaces equipped with a doubling measure supporting a 1-Poincaré inequality, and obtain $L^1$ estimates of the trace functions. In contrast with the treatment of traces given in other papers on this subject, the traces we consider do not require knowledge of the function in the exterior of the domain. We also establish a Maz'ya-type inequality for functions of bounded variation that vanish on a set of positive capacity.     

A backward Euler alternating direction implicit difference scheme for the three‐dimensional fractional evolution equation

A backward Euler alternating direction implicit (ADI) difference scheme is formulated and analyzed for the three‐dimensional fractional evolution equation. In our method, the Riemann‐Liouville fractional integral term is treated by means of first order convolution quadrature suggested by Lubich. Meanwhile, an ADI technique is adopted to reduce the multidimensional problem to a series of one‐dimensional problems. A fully discrete difference scheme is constructed with space discretization by finite difference method. Two new inner products and corresponding norms are defined to analyze the scheme. The verification of stability and convergence is based on the nonnegative character of the real quadratic form associated with the convolution quadrature. Numerical experiments are reported to demonstrate the efficiency of our scheme.     

On convolutions of harmonic univalent mappings convex in the direction of the real axis

In this paper, we show that convolutions of some planar harmonic mappings which convex in the direction of the real axis are also convex in the same direction. Furthermore, by means of the \textit{Mathematica} software, we present an example to illuminate the main result.     

局部可分度量空间的伪序列覆盖映射

指出了文[1]中的一个问题,并给出了局部可分度量空间的伪序列覆盖s映象和局部可分度量空间的伪序列覆盖紧映象的刻划。     

断层扫描分析法用于联用色谱二维数据的解析Ⅱ. 定量分析:原理与应用

提出了一种全新的色谱一光谱二维数据信息处理手段——断层扫描分析法。本研究介绍断层扫描分析法的定量分析原理：在重叠色谱峰簇中,每个色谱保留时间处都可得到一条光谱“断层”;针对不同的光谱“断层”,可结合褶合曲线分析法进行定量分析,并最终获得重叠色谱峰簇中待测组分的定量信息。用断层扫描分析法对一实验体系进行了定量分析,结果满意。     

基于滑模理论的水下机器人定深控制算法研究

水下机器人操控性能指标中对定深控制性能有较高要求,而水下机器人的运动具有强的非线性和耦合性,使得不同航速下的定深控制成为难点。建立了水下航行器的运动学模型,基于滑模理论设计了深度控制器和纵倾控制器,在MATLAB SIMULINK环境下搭建了深度控制仿真系统,数值仿真结果表明：滑模变结构控制器对于不同航行条件具有较强的适应性,同时深度的控制效果明显优于PID控制器。     

Elemental and chemical state depth analysis by combined use of a polycapillary and a thin wire in a synchrotron X‐ray microprobe

A simple method is proposed to improve the depth resolution of a conventional X‐ray confocal microscopy system by adding a thin wire close to the sample surface and upstream of the polycapillary in the exit channel. A depth resolution of around 10 μm is easily obtained. The detection efficiency is improved by a factor of two to three times, compared with the thin wire technique previously proposed. It is also shown that not only the elemental distribution but also the X‐ray absorption near‐edge structure (XANES) spectrum from locations below the sample surface can be obtained. Copyright © 2017 John Wiley & Sons, Ltd.     

右半平面调和映照的卷积

研究右半平面调和映照卷积的单叶性判别和几何特征的刻画问题.证明第二复伸张为w(z)=-z×(z-a)/(1-az)(0≤a≤1)的右半平面调和映照f(z),其与典范右半平面调和映照f₀(z)的卷积映照f*f₀不仅属于S⁰_H,而且是沿实轴方向上是凸的.