查询词典 ramified algebraic function element

In the method, a optimization model of a ventilating network is put forward by taking the minimizing squared sum of algebraic sum of the ventilation pressure of all branches in a independent circuit about all independent circuits as object function, therefore a new algorithm of ventilation network optimization is obtained.

该方法通过使所有独立回路分支风压代数和的平方和最小化的方法，建立了通风网络解算优化模型，并用梯度法对该模型进行解算，获得了一种新的风网解算算法。

In the method, a optimization model of a ventilating network is put forward by taking the minimizing squared sum of algebraic sum of the ventilation pressure of all branches in a independent circuit shoot all independent circuits as object function, therefore a new algorithm of ventilation network optimization is obtained.

该方法通过使所有独立回路分支风压代数和的平方和最小化的方法，建立了通风网络解算优化模型，并用梯度法对该模型进行解算，获得了一种新的风网解算算法。

The main theory results includes:(1) Using the properties of Hilbert transform, perfectly reconstruction and new type of lifting scheme, a new type of dual-tree binary coefficients complex wavelet with linear phase is achieved.(2) For linear systems that can be diagonalized by GFT and DST-II matrices, an efficient MGM method is proposed, convergence is proved.(3) We discuss the algebraic structure when Toeplitz matrix is transformed by multi-band wavelet,show that Toeplitz matrix is composed of generating function is transformed to a band and sparse matrix when wavelet applied to this matrix, based on the above results, an efficient solution of Toeplitz equations is obtained, and the computational complex is O,where N is the order of matrix.

理论成果主要包括：(1)对于对偶树二进制系数复数小波，利用Hilbert变换对性质、完全重构条件并结合新的提升格式构造研究了含参系数多进制小波构造方法，作为特例得到具有线性相位的对偶树二进制系数复数小波构造方法；(2)对于广义离散傅立叶变换与正弦变换对角化系统，提出了高效、快速的多重网格算法，理论上证明了算法的收敛性；(3)研究了Toeplitz矩阵在多进制小波变换下的代数结构，验证了多项式生成函数构成的Toeplitz系统在小波变换下的稀疏带宽性质，从而建立基于小波变换求解Toeplitz系统的快速求解方法，运算量级控制在O，其中N为系统的阶。

Double angle formula can transform the circular function equation to a biquadratic algebraic equation,and the analysis solution can be solved by extract equation directly.

用倍角公式可将该三角函数方程转化成一个四次代数方程，然后用求根公式直接求出解析解。

In the fourth chapter, firstly it introduces the Boolean functions algebraic expressions of the 2-value clock-controlled stop-and-go generator and Gunther generator. It reveals the balanced property of the two kinds of Boolean functions, and studies the Walsh cycle spectrum and the autocorrelation function. It also obtains the coincidence rate of their output sequences with affine sum of some bits of input sequences, and analyzes their ability of resisting the best affine approximation cryptanalysis and differential cryptanalysis. Secondly, we properly present a new definition of the Best Affine Approximation, namely BAA on the Boolean vector functions, followed by the spectral characteristic of such defined BAA attacks through using the decomposition formula of the union distribution for random variables. A lower bound of such BAA attacks is proposed. Finally, we also study the spectral characteristic of the second kind of nonlinearity of Boolean vector functions, followed by a higher bound of such nonlinearity. Furthermore, the limited relationship between the second kind of nonlinearity of Boolean vector functions and the linear structure of the linear combination of every component is analyzed.

在第四章中，首先给出了2值密钥流"停走生成器"和"衮特生成器"中实际存在的布尔函数的代数表示，揭示了这两类布尔函数的平衡性，随后研究了它们的Walsh循环谱和自相关函数等，得到了它们的输出序列与输入序列中的某些bit的仿射项的符合率，分析了它们抵抗最佳仿射逼近攻击和差分攻击的能力；其次，我们合理地给出了布尔向量函数最佳仿射逼近的新定义，利用布尔随机变量联合分布的分解式考察了相应的谱特征，并给出了布尔向量函数与其最佳仿射逼近的符合率的一个下界；最后，我们还考察了布尔向量函数第二类非线性度的谱特征，给出了布尔向量函数第二类非线性度的一个上界，并揭示了布尔向量函数第二类非线性度与其各个分量的线性和的线性结构之间存在的制约关系。

PartⅡ,Applying the developed and extended direct algebraic methods that presented in recent years and based on the 2+1 dimensional variable separation solutions,abundant Jacobi elliptic function doubly periodic waves and periodic propagating wave patterns for many 2+1 dimensional nonlinear wave models are obtained,and in long wave limit solitary waves are derived as well.

第二部分，本文拓展和推广(来源：a2AB7aC论文网www.abclunwen.com)了新近发展的几种典型的直接代数方法和基于分离变量解的间接方法，获得多个2+1维非线性波动模型丰富的雅克比椭圆函数双周期波解和周期传播波模式，并得到长波极限情形下存在的非线性孤立波。

Using algebraic methods which include extended Tanh-method,some new solitary solutions to the DBM and Log-DBM equation,such as singular solitary solutions,double singular peakon solitary wave solutions,double solitary wave solution with peakon and singular periodic solitary wave solutions are obtained..With the aid of an auxilitary function combined with the elliptic integral of the first kind,periodic solitary solution,singular and periodic singular solitary solutions can be obtained.

第三章利用扩展的Jacobi椭圆函数展开法研究了方程，并给出ZK-MEW方程的Jacobi椭圆函数解，特别的，当模数m→0和m→1时，其中一部分解退化为三角函数解和孤立波解；其次使用sn-cn拟设法，研究了K(k，s，1)方程，得到了k=s=3时的新的精确解，并在模数m→0和m→1时得到了丰富的三角函数和孤立波解。

Focus on the origin of Weierstrass\' Complex Analysis, considering to external and internal causes are the development of complex function in 19~ century reviewed, and three basic approaches lead to complex analysis, namely, algebraic analysis, integral and geometry are introduced.

指出了德国数学组合分析与古德曼的级数工作以及分析严格化要求的共同影响，构成了魏尔斯特拉斯发展复变函数理论的动机。2。

In addition, when calculating the products of various terms of equations, this paper uses the principle that the integrated function of highest order term meets algebraic precision as the one of determining the number of integral points.

另外，在计算方程各项的内积时，本文以具有最高次项的被积函数满足代数精度为积分点数目的选取原则。

This data visualization system in this thesis has an extensive function, including calculus operation, solving the algebraic equation and differential equation, the operation of series and the transform of integral and so on.

本设计开发的数据可视化系统具有强大的运算功能，包括微积分运算、代数方程与微分方程的求解、级数运算、积分变换等。

I'm not an actor. I'm a professor of paleontology.

我不是演员，我是古生物学教授

Spider Network Web site that is a very image of the name.

网络蜘蛛即Web Spider，是一个非常形象的名字。