On an Extremal Scale of Approximation Spaces

This paper is concerned with an extremal scale of approximation spaces involving logarithmic weights. We give equivalent norms and study the behavior of this scale under reiteration and interpolation. Some applications to Lorentz-Zygmund operator ideals and Besov spaces with logarithmic weights are given.     

正交各向异性弹性力学平面问题的样条虚边界元法

采用域外奇点技术并根据问题的边界条件,建立了正交各向异性弹性力学平面问题的非奇异虚边界积分方程,然后采用性态优越的B样条函数去逼近未知虚荷载函数,并采用性能稳定的最小二乘边界子段法去消除边界余量,据此获得积分方程的数值解.数值算例表明:该方法具有相当高的精度和良好的数值稳定性,且计算工作量少.文中引言部分还对域外奇点法的发展作了系统的评述.     

Polynomial interpolation in several variables

This is a survey of the main results on multivariate polynomial interpolation in the last twenty-five years, a period of time when the subject experienced its most rapid development. The problem is considered from two different points of view: the construction of data points which allow unique interpolation for given interpolation spaces as well as the converse. In addition, one section is devoted to error formulas and another to connections with computer algebra. An extensive list of references is also included. This revised version was published online in June 2006 with corrections to the Cover Date.     

Bipartite density of cubic graphs

We first obtain the exact value for bipartite density of a cubic line graph on n vertices. Then we give an upper bound for the bipartite density of cubic graphs in terms of the smallest eigenvalue of the adjacency matrix. In addition, we characterize, except in the case n=20, those graphs for which the upper bound is obtained.     

Infrared super-resolution imaging method based on retina micro-motion

With the wide application of infrared focal plane arrays (IRFPA), military, aerospace, public security and other applications have higher and higher requirements on the spatial resolution of infrared images. However, traditional super-resolution imaging methods have increasingly unable to meet this requirement in technology. In this paper, we adopt the achievement that the human retina micro-motion is the important reason why the human has the hyperacuity ability. Based on the achievement, we bring forward an infrared super-resolution imaging method based on retina micro-motion. In the method, we use the piezoelectric ceramic equipment to control the infrared detector moving variably within a plane parallel to the focal plane. The motion direction is toward each other into a direction of 90°. In the four directions of the movement, we get four sub-images and generate a high spatial resolution infrared image by image interpolation method. In the process of the shifting movement of the detector, we set the threshold of the detector response and record the response time difference when adjacent pixel responses are up to the threshold. By the method, we get the object’s edges, enhance them in the high resolution infrared image and get the super-resolution infrared image. The experimental results show that our proposed super-resolution imaging methods can improve the spatial resolution of the infrared image effectively. The method will offer a new idea for the super-resolution reconstruction of infrared images.     

地磁信息感应装定系统及其插值算法

为了向基于地磁场的弹体姿态角检测系统提供地磁场信息,根据地磁信息感应装定系统的工作原理,设计了基于GPS和ARM微处理器的地磁信息感应装定系统,GPS实时获取弹药发射地的地理位置信息,ARM微处理结合地磁场沿经线方向变化快和沿纬线方向变化慢的特点,采用线性周期样条组合插值算法计算地磁场强度矢量,然后以非接触电磁感应的方式装定地磁场强度矢量信息。插值分析表明,通过线性周期样条组合插值算法,地磁场总强度和水平分量的相对误差小于0.01%,磁偏角和磁倾角误差小于0.01o,并且实验结果与仿真计算一致,说明地磁信息感应装定系统能够快速准确地提供地磁场强度矢量信息。     

区域地磁测量实验及水下载体对周围磁场的影响分析

水下载体和磁力仪的匹配是水下地磁导航的关键技术之一.为了完成匹配实验,首先要选择地磁场平缓的局部区域,基于这一目的进行了局域地磁场的测量,并通过克里金插值法构建地磁图,给出基于克里金插值的局部二维和三维地磁图.从地磁图上可以找到磁异常区域和地磁平缓区域,并在地磁平缓区域进行有无水下载体的地磁空间测量.由于载体主要由铁磁物质组成,安装在载体上的传感器所测量的磁场除了地磁场以外,还有载体硬磁材料产生的固有磁场以及载体内机电设备产生的磁场.因此,如何从复杂的磁场环境中提取地磁场信息是实时测量的一大难题.基于载体的空间磁测,利用传感器测量值构建载体磁场的数学模型,分析了水下载体对周围磁场的影响,为水下载体与磁力仪的匹配和水下磁测提供了理论和实验依据.     

Error analysis for frequency-dependent interpolation formulas using first derivatives

We call attention to the entire errors which result when frequency-dependent interpolation formulas are utilized to approximate oscillatory functions f(x) at some x on the domain of interest with a frequency ω of the form,

f(x)=f₁(x)cos(ωx)+f₂(x)sin(ωx),     

Split-step orthogonal spline collocation methods for nonlinear Schrödinger equations in one, two, and three dimensions

Split-step orthogonal spline collocation (OSC) methods are proposed for one-, two-, and three-dimensional nonlinear Schrödinger (NLS) equations with time-dependent potentials. Firstly, the NLS equation is split into two nonlinear equations, and one or more one-dimensional linear equations. Commonly, the nonlinear subproblems could be integrated directly and accurately, but it fails when the time-dependent potential cannot be integrated exactly. In this case, we propose three approximations by using quadrature formulae, but the split order is not reduced. Discrete-time OSC schemes are applied for the linear subproblems. In numerical experiments, many tests are carried out to prove the reliability and efficiency of the split-step OSC (SSOSC) methods. Solitons in one, two, and three dimensions are well simulated, and conservative properties and convergence rates are demonstrated. We also apply the ways of solving the nonlinear subproblems to the split-step finite difference (SSFD) methods and the time-splitting spectral (TSSP) methods, and the approximate ways still work well. Finally, we apply the SSOSC methods to solve some problems of Bose-Einstein condensates.