定理

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。

By using the theory of factor theorem and determinant in higher Alge-bra, the factorization method of Circulant Symmetric function is given.

本文利用高等代数的因式定理理论和行列式理论，给出了轮换对称函数的因式分解方法。

Based on the Logic of context,CL,defined in [1],circumscription and default theory are introduced into context reasoning, its related definitions and theoremsare also provided.

基于文［1］定义的context逻辑CL，本文分别引入限制理论和缺省理论到con－text推理中，给出有关的定义和定理。

In addition, the voltage-current characteristic of linear resistive components is the general solution of Clairaut equation, and the voltage-current characteristic of non- linear components is the singular solution of Clairaut equation.

论文摘要：本文讨论了任意伏安特性电阻元件满足的基本微分方程以及非线性电路的功率匹配问题的几个定理，指出任意伏安特性电阻元件均满足非线性一阶的clairaut方程，并且，线性电阻元件的伏安特性是clairaut 方程通解，而非线性电阻元件的伏安特性是clairaut 方程的奇解。

Applying partition of positive integers and Anzahl theorem of subgroups of classical groups, a class of authentication codes was obtained and all parameters of this scheme were computed. Simultaneously, supposing that the secret key was chosen according to the uniform probability distribution, security analysis of the scheme was given.

利用正整数的无序分拆及典型群子群的计数定理得到了一类认证码，计算出了全部参数，并给出了密钥等概率选取时的安全性分析。

In this paper, we prove that if Ф is parallel and A+G+μB=0 for some functions λ,μ, then Ф=0, which gives the classification of the hypersurfaces in S(superscript n+1) with parallel Mbius form and A+G+μB=0 from the classification theorem in paper of Li H.

本文证明了如果x的Mbius形式Ф平行，并且A+λG+μB=0，其中λ，μ分别是定义在M上的光滑函数，那么Φ=0，由此及李海中、王长平（2003年）文献中的分类定理给出了S(上标 n+1)中具有平行的Mbius形式及满足A＋λG+μB=0的超曲面的分类。

Firstly , using the conditional independence test built the Bayesian network structure , and desensitizes remote sensing data of study area . Secondly , applying Bayesian network theorem as classification principle classifies every single pixel to a pixel of maximum probability sort .

采用贝叶斯网络分类对具有典型干旱特征的库车县土壤盐渍化情况进行监测，首先应用条件独立性测试原理建立贝叶斯网络结构，把研究区遥感数据进行离散化，然后应用贝叶斯定理作为分类原则，将每个像元分为像元最大概率的类别。

Based on the methods and techniques of covering theory, the structure of module category of tame concealed algebra, one-point extension, vector space category, finite enlargement, degeneration theory, stable equivalence and combinatorial method, we will classify all of the three-point algebras with Gabriel quiver the system quiver Q according to representation type. We get the classification theorem: Let A=kQ/I be a three-point algebra given by the system quiver Q.

本文综合利用覆盖理论，tame concealed代数模范畴的结构，单点扩张，向量空间范畴，有限enlargement，退化理论，稳定等价以及组合的方法等多种方法和技巧，将所有由系统箭图Q给出的三点代数按表示型进行分类，得到如下分类定理：Q是系统箭图，I是kQ的一个admissible理想。

The profile distributions of silicate, phosphate and nitrate suggest that the organic material decomposition in area is mainly through nitrification during early diagenesis. Based on benthic fluxes of nutrients calculated using Fick's first law, benthic fluxes of silicate, phosphate and nitrate are -886.45~42.62 mol/(m^2d),-3.04~5.83 mol/(m^2d) and -189.43~21.05 mol-(m^2d), respectively, and perhaps silicate and nitrate are one of the major sources of nutrients for bottom water. Our results also reveal temporal and spatial variations of benthic fluxes for silicate, phosphate and nitrate, which may be related to sedimentation environment changes caused by global climatologic change.

在水－沉积物介面附近矽酸盐、磷酸盐和硝酸盐都存在著极陡的浓度梯度，Fick扩散定理的计算结果表明，研究区内矽酸盐、磷酸盐和硝酸盐的海底扩散通量分别为-886.45～42.62mol/、-3.04～5.83mol/和-189.43～21.05mol/，且矽酸盐和硝酸盐主要是从沉积物向底层水体扩散，是底层水体营养盐的来源之一；研究区内矽酸盐、磷酸盐和硝酸盐的海底扩散通量存在著一定的时间和空间变化，这可能与因全球气候变化而导致的沉积环境的改变有关。

The Fary-Milnor theorem states that the total curvature of a knotted simple closed curve in R^3 is greater than 4π.

Fary-Milnor 定理：一条空间中的简单封闭扭结其总曲率必大於4π。

For a big chunk of credit-card losses; the number of filings (and thus charge-off rates) would be rising again, whether

年美国个人破产法的一个改动使得破产登记急速下降，而后引起了信用卡大规模的亏损。

Eph. 4:23 And that you be renewed in the spirit of your mind

弗四23 而在你们心思的灵里得以更新