亏数

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。

Firstly, we prove the existence and the uniqueness of the hyperfocal subalgebra when the coefficient field is split for a defect pointed group; then, considering the structural pattern of source algebras over arbitrary fields, by means of G-acted groups, we reduce the existence and the uniqueness of the hyperfocal subalgebra over an arbitrary field to the case that the coefficient field is split for a defect pointed group and the inertia group stablizes a hyperfocal subalgebra.

首先我们证明了如果系数域对亏点群是分裂的，则源代数的超聚焦子代数存在且共轭唯一；然后通过考虑任意域上源代数的结构模式，以G-作用群为手段，将超聚焦子代数的存在性和唯一性归结为系数域对亏点群是分裂的情况下惯性群稳定的超聚焦子代数的存在性和唯一性。

Firstly, we apply block AOR method to find the least square solution of minimal norm to the rank deficient linear systems where A is a complex m*n matrix with rank k.

首先，我们把求解线性方程组的块加速超松弛迭代法应用于求解亏秩线性方程组的最小范数最小二乘解，其中线性方程组的系数矩阵A是秩为k的m*n复矩阵。

Singular linear systems; Iterative methods;AOR method; JOR method; Rank deficient least squares problems;Semiconvergence; Optimum parameters; P-cyclic matrix; Consistently ordered matrix; Preconditioning; Matrix pencil; Eigenvalue bounds; Support number

奇异线性方程组；迭代法；AOR 方法；JOR方法；亏秩最小二乘问题；半收敛性；最优参数；P-循环矩阵；相容次序矩阵；预处理；矩阵对；特征界；支撑数

Using the judgment matrix of detectable and locatable of gross errors in surveying error and reliability theory, it is proved firstly that the number of zero column vectors in LZD\'s judgment matrix equals to the rank defects of LZD\'s coefficient matrix. And then, LZD\'s matching equation having the detectability and locatability of gross errors is verified by a series of tests. These conclusions powerfully support the following researches on algorithms of detecting DEM deformations in theory.

运用误差与可靠性理论中的粗差可发现和可定位判断矩阵，证明了LZD算法判断矩阵中零列向量的个数等于LZD算法系数阵列秩亏数，试验验证了LZD算法匹配方程具备粗差发现和定位能力，为DEM差异探测算法提供了理论支持。

Using the independence number and the girth, the upper bound of the Betti deficiency is obtained. A better lower bound on the maximum genus of a graph is obtained and a previous result is improved.

利用图的独立数和围长，得到了一个Betti亏数的上界，进而得到了最大亏格的一个比较好的下界，改进了黄元秋先前的一个结果。

In chapter two, we first consider the linear system WAWx=b, where A is an m*n rank-deficient matrix. Then we consider the weighted Frobenius norm on data, and get the formula of W-weighted Drazin inverse solution of the linear system.

第二章的前半部分介绍了线性系统 WAWx=b 的加 W 权的 Drazin 逆解在范数带参数的 Frobenius 范数意义下的条件数，这里矩阵 A 为一个 m*n 的秩亏阵。

However, as the name（read－only memory）implies, CD disks cannot be written onorchanged in any way.

然而，正如其名字所指出的那样，CD盘不能写，也不能用任何方式改变其内容。

Galvanizes steel pallet is mainly export which suits standard packing of European Union, the North America. galvanizes steel pallet is suitable to heavy rack. Pallet surface can design plate type, corrugated and the gap form, satisfies the different requirements.

镀锌钢托盘多用于出口，替代木托盘，免薰蒸，符合欧盟、北美各国对出口货物包装材料的法令要求；喷涂钢托盘适用于重载上货架之用，托盘表面根据需要制作成平板状、波纹状及间隔形式，满足不同的使用要求。