多项式

From the ultrashort pulsed Gaussian beams, based on the properties of Laguerre polynomial, a family of solutions are found in theory, which represents a new family of ultrashort pulsed beams called ultrashort pulsed elegant Laguerre-Gaussian beams.

从超短高斯脉冲光束出发，根据拉盖尔多项式的性质，用理论解析推导的方法，给出了一组新的超短脉冲光束的解析解，称为超短复宗量拉盖尔高斯脉冲光束。

The main contributions of the second part of this dissertation are focused on the cryptographic properties of logical functions over finite field, with the help of the properties of trace functions, and that of p-polynomials, as well as the permutation theory over finite field: The new definition of Chrestenson linear spectrum is given and the relation between the new Chrestenson linear spectrum and the Chrestenson cyclic spectrum is presented, followed by the inverse formula of logical function over finite field; The distribution for linear structures of the logical functions over finite field is discussed and the complete construction of logical functions taking on all vectors as linear structures is suggested, which leads to the conception of the extended affine functions over finite field, whose cryptographic properties is similar to that of the affine functions over field GF (2) and prime field F〓; The relationship between the degeneration of logical functions and the linear structures, the degeneration of logical functions and the support of Chrestenson spectrum, as well as the relation between the nonlinearity and the linear structures are discussed; Using the relation of the logical functions over finite field and the vector logical functions over its prime field, we reveal the relationship between the perfect nonlinear functions over finite field and the vector generalized Bent functions over its prime field; The existence or not of the perfect nonlinear functions with any variables over any finite fields is offered, and some methods are proposed to construct the perfect nonlinear functions by using the balanced p-polynomials over finite field.

重新定义了有限域上逻辑函数的Chrestenson线性谱，考察了新定义的Chrestenson线性谱和原来的Chrestenson循环谱的关系，并利用一组对偶基给出了有限域上逻辑函数的反演公式；给出了有限域上随机变量联合分布的分解式，并利用随机变量联合分布的分解式对有限域上逻辑函数的密码性质进行了研究；给出了有限域上逻辑函数与相应素域上向量逻辑函数的关系，探讨了它们之间密码性质的联系，如平衡性，相关免疫性，扩散性，线性结构以及非线性度等；讨论了有限域上逻辑函数各类线性结构之间的关系，并给出了任意点都是线性结构的逻辑函数的全部构造，由此引出了有限域上的"泛仿射函数"的概念；考察了有限域上逻辑函数的退化性与线性结构的关系、退化性与Chrestenson谱支集的关系；给出了有限域逻辑函数非线性度的定义，利用有限域上逻辑函数的非线性度与相应素域上向量逻辑函数非线性度的关系，考察了有限域上逻辑函数的非线性度与线性结构的关系；利用有限域上逻辑函数与相应素域上向量逻辑函数的关系，揭示了有限域上的广义Bent函数与相应素域上的广义Bent函数的关系，以及有限域上的完全非线性函数与相应素域上向量广义Bent函数之间的关系；给出了任意有限域上任意n元完全非线性函数存在性与否的完整证明，并利用有限域上平衡的p-多项式的性质给出了有限域上完全非线性函数的一些基本构造方法。

The conjugates of an element are the roots of the irreducible polynormial of which the given element is a root. The conjugates of 根号（根号3+1） over the field of rational numbers are

a。题目中的'over the rational numbers'是不是指四次多项式的系数是有理数，怎么能这么表达呢，为什么要强调有理数，系数应是整理罢。

And they got somecodes with better parameters, In [12], San Ling, Harald Niederreiter and Chaoping Xing have constructed a kind of linear codes using elements from any finite extension F_q~s(s≥3) of F_q. The rational functions are linearly combinations of the product ofsymmetric polynomial power.

San Ling，Harald Niederreiter以及Chaoping Xing在[12]中利用F_(s≥3)中元来构造一类线性码，有理函数取对称多项式的幂的乘积的线性组合，这就使码的长度可以任意大。

I have to factor a univariate polynomial over a finite field.

我必须在有穷界内分解单项多项式

The content is : theory of polynomials and finite field; psudo-random sequence and stream cipher; textbook cryptography and modern cryptography.

主要的内容有：多项式理论与有限域理论；伪随机序列与流密码；教科书密码与现代密码。

Based on a kind of orthogonal complete functions in L2[0,1], another one (called V-system) which has equivalence relation with U-system is created. It is a kind of new and effective mathematical tool on signal multi-resolution analysis. Besides that V-system keeps the favorable properties of U-system and can accurately reconstruct geometry information which expressed in piecewise polynomials by finite sum of functions in V-system, it has more special properties, such as simple construction, abundant levels, convenience of application, quick calculation, local support, and so on. V-system is the generalization of Haar orthogonal functions, and to be a class of wavelet base. It has a good future for some applications in the fields of wavelet analysis and signal processing.

从L2[0，1]空间的一类正交完备函数系U系统出发，构造了另一类与之等价的正交完备函数系，称之为V系统，它是信号多分辨分析方面的一种新型的、有效的数学工具。V系统不仅保持了U系统的优良特性，对多项式表达的几何信息能够做到有限项精确重构，并且较之U系统，它更有结构简单、层次分明、计算快捷、局部支集等特点，应用起来将更加灵活方便。V系统可以看作是Haar函数系的推广，是一类小波基，在某些数字信号处理及小波分析问题中有良好的应用前景。

We give a polynomial algorithm for the first problem and an approximation algorithm for the second one.

对于一类具有离散资源约束的排序问题当机器数目固定时本文给出了一个多项式时间算法，对于一类加工时间依赖资源的排序问题给出了近似算法。

In this article, method of Fixed Point Frequency Analysis was used to extract Fundamental Frequency ( F0) as well as establish the normalized Liner Polynomial Tone Model.

该文利用固定点频率分析提取基音频率(0)建立归一化线性多项式声调模型。

First, to optimize imprecise polynomial circuits using arithmetic transformation, implement the design under different error precision bound and considering the case of fixed point and floating point representation., to search the optimized circuits with branch and bound algorithm.

方法首先利用算术变换进行非精确多项式电路优化，给出电路在不同精度界限下的实现，考虑电路的定点和浮点设计表示，然后应用分枝定界方法求解出最终的优化结构。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。