等价

Firstly, we focus on the influence of the inclusion of equivalent relation on the information entropy, which is explained through 8 propositions. Secondly, we also investigate the relation between the Shafer's evidence theory and equivalent relation.

又章主要从两方面进行论证：①等价关系的粗细对信息熵的影响，这点通过8个命题来说明；②等价关系与证据理论之间的联系。

Robust estimation, RLS Estimation, M estimation, Independent observations, Correlated observations, Function model, Random model, Outliers analysis, Outliers Confirmation, Outliers Disposal, Infectant Distribution, Equivalent weights, Equivalent variance-covariance

稳健估计，稳健最小二乘估计， M 估计，独立观测，相关观测，函数模型，随机模型，粗差分析，粗差定位，粗差处理，污染分布，等价权，等价方差-协方差

This article compared the integrand of infinite integral and unbounded function integral by comparing the infinitesimal with the infinity, obtained the corresponding equivalence theorem of criterion of convergence of abnormal integral, and gave out the proof.

将无穷积分及无界函数积分的被积函数运用无穷小和无穷大比较的方法进行比较，得到了相应的反常积分敛散性极限审敛法的等价定理，并给予证明，从而可运用等价定理灵活的判断反常积分的敛散性。

In allusion to Funar Conjecture :"If a random triangle lies in a closed unit square,then its inscribed circle s radius,r≤(5-1)/4",an equivalent minimum problem about a function of 2-variables is studied;the stagnation point and its value,value on the boundary of the function of 2-variables are studied,the equivalent problem is proved correct,so the Funar Conjecture is proved correct.

针对Funar猜想："设任意三角形位于闭单位正方形内，则该三角形的内切圆半径，r≤(5-1)/4"，研究了与其等价的某二元函数的最小值问题；利用对此二元函数驻点及其取值、边界取值讨论，证明了等价问题成立，进而此Funar猜想得证。

Experimental results show that the method is effective,the clustering results described by rules set are interpretable and rational.

知识的这种粒度结构通过等价关系的等价类表示。聚类就是将一组分布未知的数据对象按照

Secondly, the invertible assignment problem are studied. At last, we explored the conditions on the invertible completion of part matrix Mx and obtained the characterizations of the relovent operator of invertible completion.

利用构造分块初等矩阵、算子广义逆、极分解、谱分解为工具，深入地研究了算子对的逆补Mxy、算子逆配置的一系列等价刻画及一般性结论、缺项算子矩阵存在逆补Mx的等价刻画，并获得了逆补的预解集的性质刻画。

Adopting generalized Jordan block and algebra equivalence transform method, all of the transfer functions at different load points can be transformed to state-space description with time variable. The steady robustness of three different mode of control systems were researched by mathematic analysis. It shows that: for the high order inertia controlled object with the characteristic of nonlinear and time-variable that described by the set of transfer functions, the Luenberger function observer established according to its any algebra equivalence state-space description, if some conditions can be met, there would be a matrix of T with n′n satisfied the Sylvester matrix equation TA- FT=GC.

采用广义约当块及代数等价变换方法，可将分段的传递函数描述转换为变参数的状态空间描述，对3种典型控制系统的稳定鲁棒性所进行的理论研究表明，对同一组传递函数描述的具有非线性和时变特性的高阶惯性受控对象，依据其任一代数等价的状态空间描述所构建的Luenberger函数观测器，在满足一定的条件时，存在n′n解阵T满足Sylvester矩阵方程TA- FT=GC。

The forth algorithm is the same as the third one with an addition of finite termination criteria. Although the latter two algorithms have only linear rate of convergence, they are especially suitable for large-scale and sparse problems, with features of simple formula, small storage, sparsity preservation and easy implementation.

前者借助NCP函数把互补问题转化为等价的非光滑方程组，再用带参数的光滑方程组近似这些非光滑方程组，最后用牛顿型方法求解所得到的光滑方程组，希望通过光滑参数趋于零得到原来互补问题的解；后者基于等价不动点格式，构造了一个光滑迭代算法和一个具有有限终止性质的算法，虽然这种迭代算法仅有线性收敛速度，但由于其格式简单、存储量小、保稀疏性、非常易于计算机实现等特点，故较适用于求解大规模稀疏问题。

Observable transformation between different formal description models. Using the ETS-based testing theory, formal transformation methods from LOTOS and Estelle to ETS are proposed respectively.

不同形式描述模型之间的可观察等价性转换根据基于扩展标号变迁系统的协议一致性测试理论，分别提出了LOTOS和Estelle到ETS的形式转换方法，证明了它们的可观察等价性，并举例说明。

Secondly,it is proved that monotonicity is equivalent to the law of proof by contradiction,and a simpler equivalent condition to monotonicity is given.

首先，讨论了择优逻辑的若干基本性质，并给出了单调性的一个充要条件；其次，证明了单调性与反证律等价，并给出了单调性的一个更为简洁的充要条件；最后，讨论了解释集合是归纳集时的单调性，证明了单调性与择优蕴涵的退化等价。

Cynanchum Lingtai apricot production in the average weight 65 grams, the brightly-colored fruit, juicy rich, sweet-sour taste, sweet from the nucleolus, when the late Qing Dynasty famous Shaanxi, Gansu provinces, the Qing imperial court Tongzhi tribute for years.

灵台生产的牛心杏平均单果重65克，果实色泽鲜艳，汁多味浓，甜酸适口，离核仁甜，清末时就驰名陕、甘两省，清同治年间曾为朝廷贡品。

Chenopodium album,Solanum nigrum, and Amaranthus retroflexus were very susceptible to the herbicides. Polygonum persicaria and Abutilon theophrasti were relatively less susceptible to the herbicides, and Lycopersicon esculentum was not susceptible to it. The relationship between reduction rates of weed biomass and PPM values of weed leaves 2,4, and 6 days after treatment was established.

供试的6种杂草对该混剂的敏感性存在显著差异：红心藜Chenopodium album、龙葵Solanum nigrum和反枝苋Amaranthus retroflexus对该混剂最敏感，ED90值分别为47.65、71.67和29.17g/hm2；春蓼Polygonum persicaria和苘麻Abutilon theophrasti敏感，ED90值分别为96.91、114.20g/hm2；而番茄不敏感。