Global exponential stability of neural networks with discrete and distributed delays and general activation functions on time scales

By employing time scale calculus theory, free weighting matrix method and linear matrix inequality (LMI) approach, several delay-dependent sufficient conditions are obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the neural networks with both infinite distributed delays and general activation functions on time scales. Both continuous-time and discrete-time neural networks are described under the same framework by the reported method. Illustrated numerical examples are given to show the effectiveness of the theoretical analysis. It is noteworthy that the activation functions are assumed to be neither bounded nor monotone.     

Necessary conditions of optimality for a class of optimal control problems on time scales

A class of optimal control problems of a system governed by linear dynamic equations on time scales with quadratic cost functional is considered. By the Lebesgue Δ-integral theory and the Sobolev-type space H¹ on time scales the weak solution of linear dynamic equations on time scales for both initial value problem and backward problem are introduced, therefore the necessary conditions of optimality are presented. Some typical examples are given for demonstration.     

Model reduction of multi-scale chemical Langevin equations

This paper addresses the model reduction problem for a class of stiff chemical Langevin equations that arise as models of biomolecular networks with fast and slow reactions and can be described as continuous Markov processes. Initially, a coordinate transformation is sought that allows the decoupling of fast and slow variables in the model equations. Necessary and sufficient conditions are derived for such a linear transformation to exist, along with an explicit change of variables which achieves the desired decoupling. For the systems for which this step is applicable, the method of adiabatic elimination is applied to determine a representation of the slow dynamics. Theoretical concepts and results are illustrated with simple examples.     

Stability radius of implicit dynamic equations with constant coefficients on time scales

This paper deals with the stability radii of implicit dynamic equations on time scales when the structured perturbations act on both the coefficient of derivative and the right-hand side. Formulas of the stability radii are derived as a unification and generalization of some previous results. A special case where the real stability radius and the complex stability radius are equal is studied. Examples are derived to illustrate results.     

斜拉索主参数共振的稳定性分析

研究轴向激励下斜拉索的主参数共振的稳定性问题．考虑拉索垂度和几何非线性的影响,导出了拉索在轴向激励下的非线性参数振动方程．利用多尺度方法研究了斜拉索的主参数共振问题,并对其稳态解的稳定性作了较详细的分析．对斜拉索的主参数共振进行了数值模拟,得到了不同阻尼、初始条件及激励幅值作用下拉索的时程曲线．结果表明：斜拉索的固有频率与外激励参数对斜拉索稳态解的个数及其稳定性都存在直接影响,从而对斜拉索的参数设计起到了指导作用．     

GIS在公共气象服务网站的应用

给出以GIS分析为核心的公共气象服务网站框架。阐述GIS与多时空尺度气象要素间的相互关系,GIS在系统逻辑分层中的位置,一维、二维、三维分析图的网页功能。同时对GIS应用中所面对的一些关键技术进行了深入分析。如含权地理边界预剪裁气象要素插值算法、netCDF文件产生、二维和三维可视化技术等等。该套系统已经在中国天气网、四川气象网、成都公共气象服务网等网站中得到应用。     

料斗秤自动监控系统的开发

传统的料斗秤其称重传感器直接与称重显示仪表连接,称重数据直接在显示仪表上显示,操作人员靠眼睛观察,手工打铃通知放料工人放料,操作效率低下,很容易出错,甚至会直接导致贸易纠纷.     

多尺度法的设解形式之探讨

当采用多尺度法研究非线性振动问题时，经常会遇到不同情形下系统响应的设解形式不同的问题．文中针对一类具有平方和立方非线性项的单自由度和多自由度非线性系统，得到不同设解形式下的一次近似解和二次近似解，并与数值解相比较，发现2种设解形式的近似解与数值仿真解的解曲线吻合很好，表明传统的各种设解形式在研究弱非线性系统时都有很好的近似性．     

Forest visualization at multiple scales for management and planning

In this study forests were visualized at various scales by placing individual trees into a forest with realistic sizes and densities. Tree images were used from two sources: high quality field photos and images created using graphic design software. The terrain, species composition, and tree sizes and density from forest inventory were all represented in GIS data format. In addition, non-tree objects and features that are essential for close-to-reality visualization were combined with the tree images in a 3-D visualization software package. We further portrayed stand level effects by animating a simulated fly-through of a forest. To visualize temporal change, a case study of four different forest patches was animated. The advantages of this approach comparing to other visualization approaches are: (1) it represents the forests with realistic individual tree images; and (2) it maintains both visual and informational realism in a forest viewable from within-stand to landscape scales. Thus, this approach is realistic in two aspects. First, it is almost as realistic as a photograph, and secondly, its information content is actual forest composition, density, and height.