查询词典 algebraic function

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。

By using the techniques of an explicit criterion to determine the number of real roots of a univariate polynomial in ( [13] , [73] ); B-net form of bivariate splines function; discriminant sequence of polynomial (cf. [13] , [73] ) and the number of sign changes in the sequence of coefficients of the highest degree terms of sturm sequence, this paper determines the number of real intersection points two piecewise algebraic curves whose common points are finite.

3：利用杨路，张景中，侯晓荣在文献（[13]，[73]）中关于一元多项式实根的显式判准，以及二元样条函数的B-网形式，多项式的判别序列和Sturm序列的最高次数项系数序列的变号数，本文给出了两个分片代数曲线的实交点数的计算公式。

Function to calculate the Jacobian matrix for a set of nonlinear algebraic equations.

calc_Jac.m 用来计算一套非线性代数方程的雅可比矩阵。

Firstly, the generalization of Fan-Ha section theorem and a general vector variational inequality without convexity assumption and minimax theorem of vector-valued function are obtained. Then, the quasi-montone vector variational inequality problem is concerned. Cx-quasi-monotone operator is defined in topological vector space, inner point of a closed convex set K is introduced, the relation between inner point and relative algebraic interior point is given, an existence result for quasi-monotone vector variational inequality is obtained.

第三章主要研究了向量变分不等式和极小极大定理(来源：3282AB83C论文网www.abclunwen.com)，建立了广义的Fan-Ha截口定理、新的向量变分不等式与极小极大定理，并在拓扑向量空间中定义了C_x-拟单调算子，引入了闭凸集K的inner点，给出了inner点与相对代数内点的关系，利用innK_c代替K的拓扑内部，建立了新的拟单调向量变分不等式。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。