查询词典 extremal

Moreover, some subgroups of Aut are obtained, such asthe inner automorphism group, the central automorphism group, the involutional automorphism group, the first and the second extremal automorphism group.

证明了：当n=0时，Aut中每个元素都是内自同构，且Aut≌C(定理1.12)。n=1时，Aut中每个元素都是有限个内自同构，中心自同构，对合自同构和第一类外自同构的乘积(定理1.13)。

We also determine the extremal chain polygonal cacti with respect to the number of matchings and of independent sets.

另外，我们确定了关于k-匹配和k-独立集的多边形Cacti链的极值链。

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

It introduces normal families, including equicontinuity, Arzela's theorem, Montel's and Marty's theorems, Zalcman's lemma; univalent functions, including Koebe's and de Branges' theorems; quasiconformal mappings, including conformal length, extremal length, geometric, analytic and metric definitions, quasiconformal extension, distortion theorem, quasicircle; iteration of rational functions, including fixed points, the Fatou and Julia sets, periodic points, Siegel disks, the Hausdorff measure and dimension, etc.

具体为：正规族，包括等度连续性、Arzela定理、Montel和Marty正规定则、Zalcman引理；单叶函数，包括Koebe定理和de Branges定理；拟共形映照，包括共形模、极值长度、几何、分析和距离定义、拟共形延拓、偏差定理，拟圆周等；有理函数的迭代，包括不动点、Fatou集和Julia集、周期点、Siegel盘、Hausdorff测度和维数，等等。在教学内容上充分体现综合性、前沿性。

For example,a generalization of linear algebra is developed in which "convex bifunctions" are the analogues of linear transformations,and "inner products" of convex sets and functions are defined in terms of the extremal values in Fenchel's Duality Theorem.

例如，一类线性代数的推广形式在凸双重函数中发展起来，而凸双重函数是线性变换的类似情况，凸集和凸函数的内积是根据 Fenchel 对偶理论的极值定义的。

The use of genetic algorithms achieve about extremal function of problem solving, function has been give.

详细说明：使用遗传算法实现关于函数极值问题的求解，函数已给出。

The particle swarm optimization combined with the immune calculated extremal function optimization.

详细说明：将粒子群算法与免疫结合，计算函数的优化极值。

This article takes calibration data of assorted pressure gauge and jack of Qingfeng Bridge in Ningbo for example. According to that the quadratic sum of deviation in actual value and trend value has the minimum and extremal condition of the function,that is least square method.

本文以宁波市庆丰桥配套的千斤顶和压力表的标定数据为例，以实际值与趋势值的偏差的平方和最小为依据，根据函数存在的极值条件，求出线性方程，此为最小二乘法。

Baernstein[2] gave the conclusion by using Koebe function as the extremal function , Glenn Schober[6] studied the classes such as S, P, K, S* of H and represented these functions with integral formulations. Wang Jian[3] and others investigated the integral mean values. Our work is continuation of their work.

Baernstein首先在单位圆上讨论给出了以Koebe函数作为极值函数的结论，Glenn Schober对H中一些函数子类如S、P、K、S~*等作了研究，将这些子类上的函数用积分表达出来，王键结合Baernstein~*函数的定义及Glenn Schober的结论，定义了对称集的概念并得出了一些函数类在其上的积分平均。

In this paper, the author estimated the module of quasiconformal mapping in curved fan, by the expression of local maximal dilatation function of quasiconformal mapping, Riemann′ s existence theorem and extremal length method, the author obtained a result of moduler deviation on curved fan.

本文对曲边扇形内的拟共形映照的模进行估计。借助拟共形映照的局部最大伸张函数来表达，利用黎曼存在定理和极值长度方法，得到关于曲边扇形的一个模偏差定理。

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。