因子定理

In this paper, firstly, the embeddability of near-triangular graphs on the orientable surface is studied. By using Petersen's Theorem about 1-factor, we first prove that for a near-triangulation on the orientable surface, its geometry dual graph has a 1-factor; then after a procedure of operation leaded by the 1-factor, we show that if a graph G triangulates some orientable surface S_g, then G has a near-triangular embedding in S_h for h = g,g + 1,...,β(G/2」, where β is the Betti number of G. Hence we obtain a conclusion: A near-triangulation of the orientable surface is upper-embeddable. As a generalization, a class of near-quadrangulation is studied, and similar results are obtained.

本文首先研究了近三角剖分图的可定向曲面嵌入性质，通过运用Petersen关于1-因子的定理，首先证明了对于可定向曲面上的三角剖分图，其几何对偶图具有1-因子；然后在1-因子的导向下，通过做一系列增加亏格的手术，证明了如果一个图G三角剖分可定向曲面S_g，那么G可以近三角剖分可定向曲面S_h，这里h=g，g+1，…，「β(G／2」，β是指图G的Betti数，从而得出推论：可定向曲面上的三角剖分图是上可嵌入的，作为推广，又研究了一类近四角剖分图的可定向曲面嵌入性质，并得到类似的结论。

A fast algorithm for calculating the inverse and Moore-Penrose inverse of the permutation factor circulant matrix is presented. Then, a fast algorithm for the product of the permutation factor circulant matrix is given. Finally, The least-square solutions of inverse problems and the optimal approximation problems for the permutation factor circulant matrix are discussed.

首先给出了一种求n阶置换因子循环矩阵的逆阵、自反g-逆、群逆、Moore-Penrose逆的快速算法，然后给出了计算两n阶置换因子循环矩阵之乘积阵的一种快速算法，最后给出了其反问题的最小二乘解的存在性定理及它的一般表示，并证明了逼近矩阵的存在唯一性且给出它的具体表达式。

Theorem factor calculated using the same order of 200% for all types of groups. and the non-abelian group of 15 bands within the structure.

本文利用不变因子定理计算确定出了200阶以内所有可换群的类型，并介绍了15阶以内非可换群的结构。

In this paper, we study the foundation of the constructing in CDT, and get the theorem of CDT factorization.

文章对范畴数据类型构造的基本原理作了深入探讨，并采用了一种新的方法实现了CDT同态的因子分解定理，得到了CDT构造中某些重要的性质和CDT因子分解定理。

The main work and innovation1 In general , a image compression method has different effect to different image . Some are fit for image which has much high frequency . Some are fit for image which has much low frequency .This paper analysis the applicability of fractal algorithm . In this dissertation , an improved algorithum is given . The basic algorithum without eight change and the joint use of quantitative coding , The compression ratio and PSNR can be adjusted , and it can get more quickly speed of coding .2 To a group of exact fractal code , the decoding image can be any resolution .With this characteristic ,choose the proper domain block and range block,this paper get an algorithum which can get higher decoding PSNR and speed than the basic fractal algorithum.3 Give a new method to calculate the scale factor . The calculation of basic algorithum is complex and enormous . The factor of scale is an important variable of the basic algorithm. Now there are two methods to calculate the factor of scale .A new method was given to calculate the factor of scale. The calculation load and complexity are reduced by the new method. Compared with the basic algorithm , the method can reduce coding time.4 The basic fractal algorithum is based on the Collage theorem and contraction mapping theorem . A mathematic model based on basic fractal algorithum is given .

本文的主要工作及创新点主要包括以下几点：1一般情况下，一种图像压缩的方法对不同特点的图像，压缩效果会有所不同，本文利用分形压缩编码对不同特点的图像进行编码，分析了分形编码对不同图像的编码适用性，利用去掉8种变换的分形编码算法与简单的均匀量化编码方案相结合，得到了一种可以调节压缩比与解码质量的分形编码方案，该提高编码速度6倍以上。2分形编码的特点之一是分形解码的分辨率无关性，即对于一组分形编码可以将其解码到任意分辨率下，本文利用分形编码的这一特点，结合不同的量化编码方案，选择合适的定义域块与值域块及适当的编解码分辨率，得到了一种提高解码质量，编码速度提高12倍以上的加速算法。3比例因子是基本分形算法中的一个重要变量，目前有两种计算比例因子的方法，文中给出了一种新的求比例因子的方法，该方法简化了求比例因子的计算，从整体上减小了基本分形算法的计算量，简化了算法4分形压缩的数学基础是不动点定理与拼贴定理，本文根据基本的自动分形编码方法，建立数学模型对其进行推导，得到了用普通数学的极限理论解释分形编码的数学表达式，从而对由基本分形编码得到的解码图像中的像素点的值给出了确定的表达式。

Meanwhile, we also provide methods for computing the weighted polar decomposition, and study error bounds for the approximate generalized positive semidefinite polar factor and perturbation bounds for weighted polar decomposition in various norms.

针对这个新的矩阵分解，我们证明了其唯一性定理，给出了其唯一性条件，讨论了其极因子的最佳逼近性质；同时，我们还探讨了矩阵加权极分解的计算问题，研究了由迭代算法引起的极因子的误差界，极因子在各种范数下的各种形式的扰动界等。

The use of the Chinese remainder theorem transforms the operation of producing the multiplicative inverses into two corresponding operations with shorter numbers and a faster combination step so that, compared with methods not using the Chinese remainder theorem, an acceleration by factor 4 can be achieved.

采用中国余数定理，形成将倍数逆数的运算转换为两个具有较短数字和一个较快结合的运算的步骤，使得相较于没有中国余数定理的方法可获得因子4的加速。

Firstly properties of the HJ SDF are revealed, and some useful conclusions are obtained. Then by the HJ SDF's properties and the two fund separation theorem, the mean-variance spanning is investigated and the spanning condition is gotten. It is proved by the mathematical method that the spanning condition gotten from HJ SDF is equivalent to the spanning condition gotten from the other methods.

首先研究了HJ随机折现因子的性质，得到了一些有意义的结论；然后结合HJ随机折现因子的性质和两基金分离定理，对均值－方差张成进行了研究，得到了相应的张成条件；最后，从数学上证明，基于HJ随机折现因子得到的张成条件与基于其它方法得到的张成条件是等价的。

In chapter 1, similarity and perturbations of nest subalgebras of factor von Neumann algebras are studied. A similarity theorem is given (see Theorem 1. 2. 3), and it is shown that similar nests in a factor von Neumann algebra are close.

第一章研究因子von Neumann代数中套的相似性和套子代数的摄动，获到一个相似定理（定理1.2.3），其几何意义是：因子von Neumann代数中相似的套聚拢在一起并可向外扩展。

In addition, by utilizing Jacobi two square numbers theorem and Lagrange four square numbers theorem and some theta function identities, we also prove the known results of number theory: two triangular number theorem, four triangular number theorem, and the number of representations of a positive integer by various quadratic forms in terms of divisor functions

包括Jacobi二平方数定理，Lagrange四平方数定理等，然后利用这些结果结合几个theta函数恒等式，我们获得了把任意一个正整数表示成两个三角数或四个三角数的和以及其他的二次形式的方法数，这些方法数都是用因子函数来表示的。

The labia have now been sutured together almost completely.The drains and the Foley catheter come out at the top.

此刻阴唇已经几乎完全的缝在一起了，排除多余淤血体液的管子和Foley导管从顶端冒出来。

To get the business done, I suggest we split the difference in price.

为了做成这笔生意，我建议我们在价格上大家各让一半。