查询词典 affine

To be specific, its generalized characteristic polynomial has positive double roots, which we proved further has only a double, root by using the affine transformation and inverse affine transformation, his easy to detect interference accurately between two ellipses using NFB analytic equation.

根据该解析方程不仅可以直接对任意两个椭圆之间的干涉性做出精确判断，并且可由此绘出NFB的轨迹图，同时使用可视化方法给出了快速粗略的判断。

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。

By using implicit function theorem, Taylor's formula and mean theorem, the form of the non-affine nonlinear systems is transformed into the form of affine nonlinear systems.

利用隐函数定理和泰勒公式及中值定理，将非仿射非线性系统转变为仿射型非线性系统。

An international advanced target tacking algorithm, which is an analytical trackingprocess based on the affine transformation model by simulating biological vision machinery, isalso introduced. And the mathematical denotation for the infinitesimal generator of affine Liegroup is deduced in this paper.

论文的主要工作包括： 1、介绍了靶场测量中火箭三维姿态的光学测量方法及其理论基础，着重对单相机测量滚转角的四区域轮廓螺旋线法进行了深入探讨和研究，对该算法进行了编程实现，利用仿真图和靶场某型火箭的数字图像对该算法进行了检测，对测量结果进行了精度分析。

The inverse polynomial and the invertible affine transformation exist by the finite field, linear algebra and matrix theory. The invertible affine transformation and the inversion in are easily realized by using lookup table. An algorithm can be used to get the inverse element of modulo .

本文运用有限域、线性代数和矩阵理论，论证了逆多项式和逆仿射的存在性，并且应用查表法简捷地实现了中元素的求逆和逆仿射变换；设计了一个易于在在计算机上实现的算法，来求形如的多项式模时的逆元，该多项式的系数在上。

The experimental results show that the affine model works best in the test area. The accuracy can reach to 0.6~0.8 m in planimetry and about 1.0 m in elevation based on the affine model by using 5~6 well distributed control points.

实验结果表明，在该区域使用一阶仿射变换模型进行补偿，在5~6个均匀分布的控制点支持下，即可达到0.6~0.8m的平面精度和1.0m左右的高程精度。

This result is a generalization of the Chevalley basis in case a simply-laced complex simple Lie algebra. Meanwhile, it generalizes also the corresponding Chevalley forms in case affine Lie algebras and 2- extended affine Lie algebras.

该结果是simply-laced复半单李代数情形下Chevalley基的推广，同时也是仿射李代数和2-扩大仿射李代数的相应Chevalley结构形式的推广。

The projecting directions of three affine pictures form affine coordinate system , and they also form a triangular pyramid at the same time.

用 3 个仿射图的投射方向构成 1 个仿射坐标系，同时也构成 1 个三棱锥，在此仿射坐标系中用球面三角重新研究由两个仿射图求第 3 个仿射图的投影作图理论——平行线束法。

This paper introduces an affine invariant of trapezia, and the explicit constraint equation between the intrinsic matrix of a camera and the similarity invariants of a trapezium are established using the affine invariant.

引入了梯形的一个仿射不变量，并利用这个不变量，建立了梯形的相似不变量与摄像机内参数之间的约束关系。

Let G be the domain whose inverse image is the cross section of u definedin (H1) where the mapping is affine,g and ψ are smooth functions and g＞0,thenthere is a unique smooth convex-monotone function which satisfies the followingproblem 〓Furthermore,if 〓 where C is a constant,ψis an affine function,〓 is astrictly interior sub-domain of G in the sense of"parabolic distance",then

若G为按（H1）中定义的u的截影经仿射变换而得的区域，g和〓为光滑函数且〓，则〓存在惟一的凸单调光滑解。若〓常数，〓仿射函数，〓为G在&抛物距离&下的严格内子域，则

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失