查询词典 combinatorial sphere

By the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proof is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity.

恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

Moreover, by the combinatorial proof or combinatorial interpretation, the identity is equipped with certain count meaning. The most general way in the combinatorial proofs is to count two sides of the identity by two different methods. Generaly, through building a bijection from one set to another one, the number of the two sets respectively represents the two sides of the identity. Because of the 1-1 property of bijection, the identity is proved.

此外，恒等式的组合证明或组合解释赋予了恒等式一定的计数意义，组合证明最常用的方法是分别用两种不同的方法对恒等式的两端进行计数，一般通过构造两个集合之间的双射，这两个集合的个数分别表示恒等式的两端，从而根据双射的一一对应性证明恒等式。

In the thesis some vital identities with binomial coefficient are given with their combinatorial proof, and the q-analogues of some identities are offered with corresponding combinatorial proofs on the subspace-lattice. Especially, one remarkable result is that a new q-analogue of the cube-sums identity is obtained with its combinatorial proof over the vector space.

本文给出了一些重要的二项式系数恒等式的组合证明或组合解释，并从向量空间角度给出了一些恒等式的q-模拟及组合证明，其中突出的成果是给出了立方和恒等式的一个新的q-模拟及组合证明。

In the thesis , we give combinatorial proof of some q-identities using integer partition.In the thesis some vital identities with binomial coefficient are given with their combinatorial proof, and the q-analogues of some identities are offered with corresponding combinatorial proof using integer partition.

本文给出了一些重要的二项式系数恒等式的组合证明或组合解释，并从分拆的角度给出了一些q-恒等式的组合证明，其中突出的成果是给出了平方和恒等式的一个直接的组合证明并给出了偶数平方和与奇数平方和的q-模拟及组合证明。

If the power series ∑anxn an ∑anxn and ∑bnxn satisfy the condition r =∑bn xn, we obtain the twin combinatorial identity theorem between the sequences {an} and bn}.We also obtain some specific twin combinatorial identities by using the expansion on the binomial expression formula, including two expansions of combinatorial number(rsn and ...

如果幂级数∑anxn与∑bnxn满足条件r＝∑bnxn 时，获得数列｛an｝与｛bn｝之间孪生组合恒等式的定理，应用在二项式定理等展开式上得出具体的多组孪生组合恒等式，其中包含组合数的两种展开法，Bernoulli数直接表达式的新证等结果。

The chapter 3 investigates the constructive method which means that many combinatorial numbers, such as Stirling number, Bell number, harmonic number, Fibonacci number and the number of derangement, are represented to moments of some random variables. This method is used in the computation of combinatorial sums, discovery and proof of combinatorial identities.

第三章研究了构造性概率方法，即一些常见组合变量(以后统称组合数为组合变量)的概率表示，诸如Stirling数、Bell数、调和数、Fibonacci数、错排数都可以表示为一些随机变量的矩，这些概率表示可以用来研究组合和式的计算与恒等式的证明。

In inertia system K,geometric sphere is changed to elliptic sphere in K system by Lorentz transformation ,and the pre-sphere of optical wave in K system is changed to sphere in K system.

对惯性系K中的几何球面施以洛仑兹变换，在K′系得到扁椭球面；对K中的光波前球面，在K′系则得到球面；两者皆源于时空的基本属性，但前者是由于物体长度的相对性，后者则是由于光速的不变。

In this chapter, three kinds of target recognition methods are performed, which are:①Target recognition method based on the description of polarization parameter plane. The echo polarization states of target are projected onto the polarization state plane described by the ellipticity ε and the tilt angle τ of the polarization ellipse, the change of parameter following ferquency becomes the chart. According to the changing trait of the chart, the multidimensional polarization feature space of target has been contructed. Furthermore, a series of polarization feature parameters used in designing the structure of target recognition device are extracted, and they are insensible to the posture of target.②Target recognition method based on the description of Poincare polarization sphere. The echo polarization states of target expressed by Stokes vector are projected onto the Poincare polarization sphere. The conception of polarization ferquency stability, which is used in describing the dynamic distribution characteristics of the target echo polarization states on Poincare polarization sphere, has been defined. A group of polarization feature parameters used in designing the structure of target recognition device are extracted, and they are insensible to the posture of target.③Target recognition method based on the description of frequency sensitivity. In accordance with the conception of the polarization state distance defined on Poincare polarization sphere, the frequency sensibility of the physical structure property of target has been investigated, the frequency distribution feature curves in PSD domain are obtained, and targets'features are extracted by means of the curve-fitting method with Least Square Criterion.

这章具体研究了基于三种极化散射特性描述的相应的目标识别方法：①基于极化参数平面描述的目标识别方法，将目标回波极化状态投影到以极化椭圆参数，即椭圆率角ε和倾角τ表征的极化状态平面上，参数随观测频率的变化就形成了图，根据图的变化特点构造了目标的多维极化特征空间，并提取了不敏感目标姿态变化的极化特征参数组来设计目标的识别器结构；②基于Poincare极化球面描述的目标识别方法，采用Stokes矢量表征目标回波的极化状态，并将其投影到描述极化状态的Poincare极化球面上，定义了极化频率稳定度的概念用以刻画目标回波极化状态在Poincare极化球面上的动态分布信息，提取了准方位不变性的目标极化特征，最后设计了目标的识别器结构；③基于频率敏感性描述的目标识别方法，通过在Poincare极化球面上所定义的极化状态距离的概念，研究的是复杂目标物理结构特性对探测信号频率的敏感程度问题，获得了在极化状态距离下的频率分布特性曲线，采用最小二乘估计曲线拟合方法，它既用于极化特征的降维，同时又直接将拟合参数作为目标的分类特征。

This work is a research-level monograph whose goal is to develop a general combination, decomposition, and structure theory for branched coverings of the two-sphere to itself, regarded as the combinatorial and topological objects which arise in the classification of certain holomorphic dynamical systems on the Riemann sphere.

Combinations of Complex Dynamical Systems|复杂的动态系统的结合復雑なダイナミカルシステムの結合这工作那个目标是发展一一般结合，分解，和结构理论分开包括二领域给它自己的一研究水平专题著作，认为是组合和在Riemann 领域上在一定holomorphic动态系统的分类过程中出现的拓扑对象。

In order to reduce the effect of imaging recognition error, the recognition location of projection is extended and refined, and the projection edge of sphere centre is implanted. So a pyramid is formed by radial line between the camera optical centre and the implanted point. A curved face is formed by the two pyramids and barbette sphere. To calculate the shape centre of the common section of the curved face, the shape centre is the coordinate of sphere centre.

为了降低图像识别误差的影响，对投影的识别位置进行拓展和细化，并对球心投影边界进行插值，摄像机光心与插值点连线射线形成了一个锥体，两摄像机的锥体分别与炮台球面相交形成曲面，计算两曲面公共部分的形心，即为球心位置。

More direct, directer ; most direct, directest

径直的，笔直的

Do you know how to use a chain saw?

你知道如何使用链锯吗？