轭点

The results also show that subtituent position on the benzene ring has a great influence on the transfer volume. The trends of change of δ〓ΔΦ〓〓 for mand p-isometers with the composition of the mixed solvent are similar. However, the position and amplitude of the limit valve are different from each other. These are discussed according to the inductive effect and the resonance effect.

研究发现：取代基在苯环上的取代位置对迁移偏摩尔体积有明显影响，间、对位取代的异构体在DMF-水混合溶剂中的δ〓Δφ〓〓随混合溶剂的组成变化规律相似，但极值点的位置及幅度有所不同，根据诱导效应和共轭效应对此进行了讨论。

In this paper,some properties of automorphisms of classical Lie algebras was given first and then a classification of conjugacy automorphisms using only the matrix theory was presented.

首先给出了典型李代数自同构的一些性质，接着用矩阵的形式具体给出典型李代数自同构共轭的充要条件，并计算了任意阶自同构的不动点集。

In this thesis, we will mainly do research on the novel scheme for Digital image Steganography, Digital Image Secret Transmission in network and the development of the information hiding device for application. The main contributions of this thesis are as following: The novel conversion method for mapping image to complex number is proposed, and the plus, minus, multiply and complex conjugate operation of image are defined based on Positional number systems and complex number system. Following new results have been gotten: 1 The suitable complex number basis to be used to express integers is a big set. 2 Any image can be mapping into a one-to-one point. 3 Lots of image processing problem can be considered based on geometric theory.

在本论文中，研究工作集中在数字图像伪装算法的新模型、图像在网络中的加密传输的新方案和信息伪装设备的研发等三个方面，主要包括：基于位值制记数法和复数系理论，提出利用复数作为基底的数字图像新的表示方法，用复数运算定义了图像和图像间的"加"、"减"、"乘"、"共轭"等运算关系；得到理论结果： 1、能表示任何整数的复数基是很大的一个集合。2、任何一幅图像，都能和复平面上的一个点一一对应。3、可以将图像问题化归为平面几何问题处理。4、复数系下的图像表示适合用于信息伪装。

Utilizing the symmetric property of the hyperbolic complex space-time, we may explain the correspondence relations of time inversions, energy inversions and complex conjugate transformations.

利用双曲复时空间的对称性，可以解释时间反演、能量反演与复共轭变换的对应关系，能够找出正、反粒子的时空对应点。

In terms of the minimum question of a positive definite quadratic function,a set of Newton directions in minimum points derived with an accurate single dimensional search are used to produce a set of conjugate direction ,and a proof of convergence is presented.

对正定二次函数极小问题，利用精确一维搜索所得极小点处的牛顿方向来生成一组共轭方向，并给出收敛性证明

It has been deduced that the search direction remains the same but that the step length decreases in optimizing the improved cost function with the conjugate gradient algorithm from the gradient of the cost function that the FIR filter apporaches the contrary point spread function more, and that the estimated image is closer to the original one.

从代价函数的梯度入手推导出共轭梯度算法，其搜索方向保持不变而搜索步长变小，使滤波系数更加逼近于点扩展函数逆算子，从而使估计图像与原始图像更加接近。

Suppose C is a Graph with k loops andf: G 梸- G is a continuous map with at least a peri- odic point. We prove the following three conditions are equivalent:(1) f is equicontinuous;(2) One of the following End + 2k + 1 conditions holds: in FJm.~0(E~+2L!= flJ1,m = l,2,挃,End J=1 + 2k; 1 0 = flf is a ioop on Gandf I~:0?- 0 is conjugate j=1 to a rational rotation;(3) One of the following End + 2k + 1 conditions holds: k m Lfl.m/~oE~(G+2i!~ is uniformly convergent, m = 1,2,,End+2k; n There is a poistive integer number n,~~~ is uniformly convergent.

假设G是含有k个圈的图，f是G到自身上的连续映射，并且至少有一个周期点，我们证明了下列三条陈述是等价的：（1）f是等度连续的；（2）下列End+2k+1个条件之一成立： m）F l）O=是G的一个圈，且fl_o：O→O共轭于一个有理旋转；（3）下列End+2k+1个条件之一成立： m）是一致收敛的，m=1，2，…，End+2k； l）存在某个正整数n，是一致收敛的。

Since the B-spline is a locally supported function, the smoothing formula can be strictly limited in a neighborhood of each point. The smoothing surface defined by the smoothing formula has the same convexity as that of the original image. Secondly, the edge points are detected by either computing the local extremum points of the directional derivative or computing zero-crossing of the second-order directional derivative of the smoothing surface. Finally, an example of an edge detector is given.

针对反卷积视觉模型的病态性，增加了适当的约束，给出了基于低松弛迭代格式的快速自适应滤波算法，对于一个N×N输入图象，由于变换核的局部支撑性质以及低松弛迭代格式的引入，使得快速自适应滤波算法的计算复杂度降为象素个数N〓的线性量阶N〓，就最小二乘算法的复杂性而言，优于不动点迭代算法的O以及基于FFT的预处理共轭梯度算法的O。

First the topological relations between the unknown points and known points are built as a linear constrain, then the DSI equation group is formulated by combining Laplace equation with the linear constrain equation.

首先由待插值点与已知点之间的拓扑关系建立线性约束，进一步结合位元场满足Laplace方程，建立离散光滑插值联立方程组，采用预条件共轭梯度求解该方程组。

The main results are:(1) the L1 boundedness of the Cesaro means operator of the harmonic expansions on the unit sphere with reflection-invariant measures is proved, and the characterization of the convergence index is given; for the points not in the planes with singularities, the pointwise convergence is also proved; these results are the generalizations of those both for the classical spherical harmonic expansions and for the Jacobi expansions;(2) Using the differential-reflection operators of Dunkl type, the uncertainty principle of a class of Sturm-Liouville operators is established, and as consequences, the uncertainty principles of some well-known classical orthogonal expansions such as Jacobi, Hermite and Laguerre expansions are obtained;(3) by introducing the Cauchy-Riemann equations in terms of the differential-reflection operators of two variables, the harmonic analysis of the extended Jacobi expansions is studied; the results include the Lp boundedness and the weak-L1 boundedness of the conjugate extended Jacobi expansions; specially, for some indexes p smaller than 1, the basic theory of the related Hardy spaces is established.

主要成果有：（1）证明了带有反射不变测度的球面调和展开蔡沙罗平均算子的L1有界性，给出了收敛指标的特征刻划，对不在奇性平面上的点，还证明了点态收敛性，这些成果同时推广了经典球面调和展开和雅可比展开的结果；（2）利用Dunkl型的微分-反射算子建立了一类斯特姆-刘威尔算子的测不准原理，并由此得到一些著名的经典正交展开如雅克比展开、赫米特展开和拉盖尔展开的测不准原理；（3）利用由两个变量的微分-反射算子定义的柯西-黎曼方程组来研究扩展雅克比展开的调和分析，证明了共轭扩展雅克比展开的Lp有界性和弱L1有界性，特别是对小于1的一些指标p，建立了相应的哈代空间的基本理论。

In the United States, chronic alcoholism and hepatitis C are the most common ones.

在美国，慢性酒精中毒，肝炎是最常见的。

If you have any questions, you can contact me anytime.

如果有任何问题，你可以随时联系我。