递归方程

Firstly, based on natural gradient and nonlinear principal component analysis, a matrix equation is obtained by block recursive updating,and then the matrix equation is solved using QR factorization and back substitution to obtain the optimal separating matrix.

此外，结合自然梯度和非线性主分量分析提出了一种块递归的盲源分离方法，构造出按块递归更新的矩阵方程，然后用QR分解和回代法求解该矩阵方程得到最优分离矩阵。

Presents the study of second order linear constant coefficient progressive regression equation with the latest achievements in the "greatest common divisor" theory to give the great significance of Fibonacci combination series equation, Fermat Number , and Mersenne Number, and a only exceptional value each.

用"最大公约数"理论的最新结果，研究二阶线性常系数齐次递归方程，给出斐波那契数列组合式、费马数、梅森数在组合数学上的重要意义和它各自有一个且唯一例外

In this paper a recursion equation of butterfly FFT is represented according to which a program is given.

实际应用中全部点的FFT算法是冗余的，为解决少数点的FFT算法，文章导出了蝶形FFT的递归方程，给出实现少数点应用程序，进而提出直接多项式方法，较全部点迭代FFT算法具有更高的效

Recursion algorithms are composed of initialization condition and recursion part, so they can he figured out with recursion equation.

递归算法由初始情况和递归部分组成，一般可以采用递归方程表示。

Methods to seek the result of the recursion equation are analyzed in the article, and the difference and application range of the methods are compared, then how to express algorithm complexity and its adjacent rank are analyzed.

分析了递归方程常用解法，比较了各个解法的区别及使用范围，并研究了如何表示递归方程对应的算法复杂度的渐进阶。

It is shown that two-component Wadati-Konno-Ichikawa equation, i.e. a generalization of the wellknown WKI equation is obtained from the motion of space curves in Euclidean geometry, and it is exactly a system for the graph of the curves when the curve motion is governed by the two-component modified Korteweg-de Vries flow. At the same time, a n-component generalization to the WKI equation is obtained. Also, starting from the motion of curves, mKdV and its symmetry recursion operator is exhibited explicitly; two- and n-component mKdV systems are obtained. It is shown that WKI systems are gauge equivalent to mKdV systems. The two-component WKI equation admits an infinity number of conservation laws and a recursion formula for the conserved densities is given by considering an eigenvalue problem together with introducing an appropriate transformation.

在二维和三维欧氏空间上，我们从空间曲线运动出发，推导出了mKdV方程以及它的用以生成高阶对称的递归算子；推导出了多元mKdV方程以及二元和多元WKI方程，并证明了WKI系统和mKdV系统的规范等价性；尔后，通过考虑特征值问题，并引入一个恰当变换，给出了二元WKI方程的用以计算无穷多守恒密度的递归公式，从而证明了二元WKI方程的守恒可积性；系统地分析了两种mKdV方程的Painleve性质，并分别给出了两种不同形式的二元和n元mKdV方程的共振点出现的规律。

For the simple network with several routers, we propose a discrete time feedback control system model and a set of recursive equations to describe it. The numerical examples about the bifurcation of average and instantaneous queue size along with the variety of exponential averaging weight w, RED control parameter qmax, pmax and system parameter K are shown.

对拥有多个路由器的简单网络，提出了离散时间反馈控制系统模型，推导出可以研究网络非线性本质的递归方程，针对指数平均权值w，RED控制参数qmax， pmax和系统参数K的变化，进行了平均和瞬时队列长度的分岔数值实验。

To prepare studying hierarchical intelligent control system of material flows in mineral processing plant further, picturing, transition rulers, analytic methods, relevance matrix and dynamic equation, defect in applying of Petri network, fall short of orient object models applying are discussed after technology of formalization model built, non-formalization built and compound model. And Petri network system with time attribute is expanded opening network system with interface of input and output. The network system expanded with all attributes of basic Petri network model has hierarchy and recursiveness, can be analyzed with mathematical tools of network system and can deal with concurrent and asynchronously also.

为了对选矿厂生产物流递阶智能控制系统的进一步研究奠定基础，本文在讨论了形式化建模技术、非形式化建模技术和复合模型的基础上，研究和分析了Petri网的图形表示、变迁规则、分析方法、关联矩阵与动态方程、Petri网模型应用中的缺陷、面向对象模型应用中的不足，并把采用赋时的Petri网系统扩展成为对外界有输入和输出接口的开放网系统，扩展后的Petri网具有递阶性和递归性，同时保持基本Petri网的所有性质，使模型仍可采用网系统数学工具进行分析，并可处理生产物流系统中的并发性和异步性。

As it can be expressed easily by argument equations, we use the conicoid as the criteria of points" classification. Based on the point"s normal and the adjacent field, corresponding to the conicoid equation such as plane, ball and cylinder, we search the points that fit the equation along the adjacent field. Using this method, we realized the automatic classification of unorganized points.The experiments using the algoritlim and criteria approved from this thesis are also carried out.

本文采用了可以比较方便地用参数方程表示的二次曲面作为数据点的分类标准，根据点的法向量以及其邻域结点的各种属性，对应于平面、球面、柱面等二次曲面，依据曲面方程的特点，从起始点开始沿邻域深度优先递归寻找符合方程的数据点，实现了散乱数据点的自动分类。

Also it presents the assumptions and the recursions of every kind of tracking algorithms.

给出了每种跟踪算法应满足的假设条件及其递归方程。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。