用泰勒级数求解非线性代数和微分方程组

提出一种求解非线性代数方程和非线性常微分方程的新方法。所论方程组被转换成增量形式，而解被表示成泰勒级数。在代数方程（多项式形式）的情况下，此算法归结为求解一系列线性方程组，而且在每一增量步中系数矩阵是不变的；在常微分方程组的情况下，此算法归结为一组递归算式，并不要求解方程组。此方法固有的自动走步功能，可保证得到收敛的解，从而大大节省计算时间。     

离散H∞全信息控制器临界参数计算

 离散H∞全信息控制器存在的临界条件取决于相关的Riccati方程解的存在性,因此控制器的存在条件可以由Riccati方程的临界参数γ-2opt与Hamilton差分系统一阶特征值之间的对应关系,opt确定。建立了γ-2并基于这一对应关系结合特征值计数方法给出了确定γ-2opt的算法。     

公共治理视域下的廊坊城市软环境建设上水平研究

近年来,廊坊市城市公共治理取得了一定的成效,主要呈现以下特征：一是治理主体逐步多元化;二是部门联动逐步完善化;三是城市管理日渐开放化。面对新的形势实现城市发展由传统治理向公共治理转变必须重塑政府,增强政府治理能力;实现政府理念再造;重新定位政府角色;增强政府回应性;激发城市主体参与意识。     

RBFs-MSA Hybrid Method for Mesh Deformation

Simulating unsteady flow phenomena involving moving boundaries is a challenging task,one key requirement of which is a reliable and fast algorithm to deform the computational mesh.Radial basis functions(RBFs) interpolation is a very simple and robust method to deform the mesh.However,the number of operations and the requirement of memory storage will be increased rapidly as the number of grid nodes increases,which limits the application of RBFs to three-dimensional(3D) moving mesh.Moving submesh approach(MSA) is an efficient method,but its robustness depends on the method used to deform the background mesh.A hybrid method which combines the benefits of MSA and RBFs interpolation,which is called RBFs-MSA,has been presented.This hybrid method is proved to be robust and efficient via several numerical examples.From the aspect of the quality of deforming meshes,this hybrid method is comparable with the RBFs interpolation;from the aspect of computing efficiency,one test case shows that RBFs-MSA is about two orders of magnitude faster than RBFs interpolation.For these benefits of RBFs-MSA,the new method is suitable for unsteady flow simulation which refers to boundaries movement.     

Regional 4-D modeling of the ionospheric electron density

The knowledge of the electron density is the key point in correcting ionospheric delays of electromagnetic measurements and in studying the ionosphere. During the last decade GNSS, in particular GPS, has become a promising tool for monitoring the total electron content (TEC), i.e., the integral of the electron density along the ray-path between the transmitting satellite and the receiver. Hence, geometry-free GNSS measurements provide informations on the electron density, which is basically a four-dimensional function depending on spatial position and time. In addition, these GNSS measurements can be combined with other available data including nadir, over-ocean TEC observations from dual-frequency radar altimetry (T/P, JASON, ENVISAT), and TECs from GPS-LEO occultation systems (e.g., FORMOSAT-3/COSMIC, CHAMP) with heterogeneous sampling and accuracy.     

带通椭圆球面波函数能量聚集性分析

针对带通椭圆球面波函数的能量聚集性及其在通信系统中应用的有效性问题,对带通椭圆球面波函数的能量聚集性进行了理论分析,提出了带通椭圆球面波函数是具有最佳能量聚集性的时限带通函数形式,并与基带椭圆球面波函数、类椭圆球面波函数进行了比较分析,采用基于特征值分解的数值算法对函数进行了仿真分析。理论分析和仿真结果均表明,带通椭圆球面波函数可以应用于大多数现有的传输系统,并能有效地提高系统的功率利用率。     

辛算法的纠飘研究

辛算法较RK(Runge-Kutta)方法,保持辛结构不变或保持哈密顿系统规律性不变是突出的优点,但点态数值精度并不理想.推导出了三阶、四阶辛算法的漂移量计算公式,通过补偿漂移量就能提高点态数值精度,既保辛结构又保证点态数值高精度,适合于工程应用.建立了分数步对称辛算法(即FSJS算法)的纠漂公式,制定了漂移的约束标准.相关算例的数值结果表明:三阶FSJS算法漂移量最小,点态数值精度更高.     

基于低通等效的带通PSWF脉冲产生方法

椭圆球面波函数不存在闭式解,带通 PSWF脉冲信号的实时求解产生限制了 PSWF的应用。针对这一问题,从带通信号低通等效的基本原理出发,分析了带通 PSWF脉冲信号的低通等效形式；在此基础上,反向运用低通等效原理,给出了一种带通 PSWF脉冲重构产生方法,并用 FPGA对该方法进行了设计实现。这一方法将带通 PSWF脉冲信号的产生转化为其低通等效形式的产生,可有效降低信号产生的复杂度,该方法引入了正余弦变换,建立了非正弦 PSWF脉冲产生与正余弦变换技术之间的联系,为 PSWF脉冲的工程应用奠定了基础。     

A partition of unity level set method with moving knot CS-RBFs for optimizing variable stiffness composites

A partition of unity level set method with moving knot Compactly Supported Radial Basis Functions (CS-RBFs) is proposed for optimizing variable stiffness composite structures. The iso-contours of a level set function are utilized to represent the curved fiber paths, and the tangent vector of the iso-contour defines the orientation of fiber. The level set function of the full design domain is constructed according to the Partition of Unity (POU) method by a set of local level set functions defined on an array of overlapping subdomains, and they are constructed by using the CS-RBFs. The positions of knots are iteratively changed during the optimization to improve the performance of composite structures. Several examples of compliance minimization are presented.