Camassa-Holm方程的Cauchy问题

在一定条件下讨论了L^p框架下Camassa-Holm方程的整体存在性，同时考虑了Camassa-Holm方程当线性色散系数k→0的收敛性.     

分布式协作虚拟样机可视化框架

基于微型计算机的分布式协作虚拟样机可视化框架具有低成本、体系结构开放的特点。通过模型对象的层次化设计，利用全局场景和本地场景的概念，不仅能够保证虚拟样机对象分布式渲染的实时性，同时也能够实现分布式系统中对象的同步处理。在可视化框架中，Microsoft DirectX提供了优秀的渲染引擎，CORBA技术在分布式环境中构成系统软总线。实验原型系统验证了DirectX能够在微型机算机上满足虚拟样机的3D渲染需求。     

Optimal design study of high order FIR digital filters based on neural network algorithm

An optimal design approach of high order FIR digital filter is developed based on the algorithm of neural networks with cosine basis function . The main idea is to minimize the sum of the square errors between the amplitude response of the desired FIR filter and that of the designed by training the weights of neural networks, then obtains the impulse response of FIR digital filter . The convergence theorem of the neural networks algorithm is presented and proved, and the optimal design method is introduced by designing four kinds of FIR digital filters , i.e., low-pass, high-pass, bandpass , and band-stop FIR digital filter. The results of the amplitude responses show that attenuation in stop-bands is more than 60 dB with no ripple and pulse existing in pass-bands, and cutoff frequency of passband and stop-band is easily controlled precisely .The presented optimal design approach of high order FIR digital filter is significantly effective.     

层次分析法中逆序问题与其决策环境的研究

本文研究了层次分析法中的逆序问题与其决策环境的关系,并对产生逆序现象的机理做了数学上的分析和定性的解释。文中还给出了多准则下排序的强保序定理。     

社会学本土化及其在中国的表现——中国特色社会学理论探索的梳理和回顾之三

社会学本土化理论是从新的视角 ,通过社会学本土化从地区性向世界性发展的历史进程 ,以及社会学在世界各国经历的本土化过程的更为开阔的眼界 ,对社会学中国化所作的新的深入研究。这一理论对社会学本土化的内涵和目的、社会学本土化的主要类型和特征、社会学本土化与社会学西方化、国际化、全球化的关系等等 ,进行了阐述 ,指出了中国社会学的发展前景 ,这就是“建构本土特色”与“超越本土特色”的道路     

Hilbert空间方法在半线性方程上的应用

运用Sobolev嵌入定律和Schauder不动点定理,在一个比文[2]更宽松的条件下,建立了Hilbert空间方法,并有效地解决了如下方程解的存在性Lu-C(u,0)u=f(u).其中L是线性自伴算子,C(u,0)是非线性的并满足与L的谱有关的一系列条件,同时突破了文[1]中非共振条件中两个常数p,q的限制及文[2]中类似的限制条件,从而推广了文[1,2]的结论.     

Robustness Proof on A United Watermarking Based on CRT Theorem

A new method of embedding and detecting a joint watermarking is proposed. It applies the asmuth-bloom secret sharing scheme, which is based on CRT (Chinese remainder theorem) theorem, to the digital watermarking technology. On the base of describing the watermarking embedding proceeding and analyzing the watermarking detection proceeding, a series of experiments is done. The experiments emphasize on the method‘s robust proving and security analysis. And the experiments show that the method can resist the attacks of JPEG compress, geometry, noise and gray adjusting. The results of the experiments show that the method has a nice recognition of copyright for joint ownership.     

脉冲微分系统解的右边整体存在性问题

研究了脉冲微分系统解的右边整体存在性问题，利用比较原理推广了Ｌａｋｓｈｍｉｋａｎｔｈａｍ等的有关结论，并以其为本文的特例。     

测定气轨的粘性阻尼常量的一种方法

利用功能原理，设计了测定气轨粘性阻尼常量的实验方法。