GM(1,N)模型的离散化结构解

针对灰色系统GM(1,N)模型是以差分方程为基础进行参数估计的,而其时间响应函数却是由微分方程的解得到的。从差分方程到微分方程的跨越,缺乏充分的科学基础和理论依据。通过对灰色系统模型建模机理进行深入剖析,利用采样定理和状态转移矩阵在差分方程和微分方程之间架起一座桥梁,通过算例仿真实验证明了该算法的有效性。     

关于荫度参数的Nordhaus－Gaddum定理

以ａ（Ｇ）ａ１（Ｇ）分别记图Ｇ的点荫度、边荫度，对任意Ｐ阶非平凡简单图Ｇ及其补图，本文得到以下Ｎｏｒｄｈａｕｓ－Ｇａｄｄｕｍ类型不等式：｜ｘ｜、｜ｘ｜分别表ｘ之上整数、下整数。而且，对于每一正整数ｐ，（ｉ）、（ｉｉ）、（ｉｖ）式下界和（ｉｉｉ）式上界均可达到。     

在数学分析中作辅助函数解题

以实例论述了辅助函数在数学分析中的应用，以及构作辅助函数的7种方法．     

应用Green定理解决渔业资源最优捕获问题

利用马尔萨斯生物种群理论中的鱼口模型和Verhulst方程，给出了时间和捕捞数量的关系，然后利用定理，得到了按照一定数量捕捞，才能使恰当时间捕捞的鱼口数量最多的最优方案。     

MINIMAX 问题解的稳定性和唯一性

本文研究了这类minimax问题：minx∈X max1≤i≤m{φi(x)}(X为紧集，φi(x)为连续函数，i=1，…，m)的解的通有稳定性和通有唯一性问题。     

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。     

信噪比的估计及其在参数设计中的作用

本文对SN比的估计进行了探讨,给出了另外两个估计公式——极大似然估计、一致最小方差无偏估计。文末以气动换向装置的参数设计为实例,用这两种不同的方法进行设计,所得结论基本上是一致的。     

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.