集合性的

Being completely new methods , Rough Classifiers , Neutral Classifiers , and analysis of Extension Information have provided non-classical set analytic methods , and have filled the gap of traditional mathematic analytic methods .

特别提出了粗糙分类方法、软分类方法、发散性方法和蕴含性方法等崭新的数据挖掘方法，为建立动态的分析型信息系统提供了基于非经典集合的分析方法，弥补了经典数学分析方法的不足。

The convexity monotonicity and correlation theory of functions are studied.

用集合的近似凸性研究函数的拟凸性。

As an application of the above proof, we obtain at once that there is an open and dense set in the set of Ω-stable systems such that every system in the set satisfies Axiom A and the no-cycle condition (Axiom A and the strong transversality condition, respectively).

作为上述方法的一个运用，马上可以得出在Ω稳定系统的集合中有一开稠集满足公理 A 和无环性条件(对应的，公理 A 和强横截性条件)。

Based on the method of multi-objective fuzzy optimization and the overhead traveling crane design, a mathematical model of fuzzy optimization for main box beam section is established. A fuzzy goal anthology is constructed. The fuzziness of multi-objective function and constraints is defined. The transformation of the fuzzy constraints set to normal constraints set in real number domain is realized by applying optimal level cut set method. The optimal solution and optimal constraint value of sub-objective function in the feasible field are found using the genetic algorithms.

应用多目标模糊优化方法，以工程设计中桥式起重机箱形主梁设计为实例，建立了桥式起重机箱形主梁多目标模糊优化设计的数学模型，构造了模糊目标集，确定了多目标函数的模糊性和约束的模糊性，并应用最优水平截集法实现了模糊约束到实数论域上的集合转换，从而用遗传算法寻求到子目标函数在可行域空间的最优解和约束最优值。

We prove the strong compactness and N-compactness of fuzzy sets areequivalent in 〓 fuzzy topological space.

再次，证明了模糊集合的强紧性和良紧性在〓模糊拓扑空间中是等价的。

This thesis focuses on studying the matrix equa-tion problem systematically, and proposed an abstract algorithm of solving the matrixequation with constraints, and established a strict convergence theory. Using this algo-rithm, we can solve the sets of matrix equation satisfying some constraint conditions,such as symmetric, antisymmetric, centrosymmetric, centroskew symmetric, re?exive,antire?exive, bisymmetric, symmetric and antipersymmetric, symmetric orthogonalsymmetric, symmetric orthogonal antisymmetric, Hermite generalized Hamilton ma-trix;So we can solve the problem with this algorithm, if the set of constrain matrixcan make a subspace in matrix space, and this algorithm also can solve the optimalapproximation and least squares problem. So this abstract algorithm has universal andimportant practical value.

本篇硕士论文系统地研究了此类问题，并找到了求解约束矩阵问题的抽象算法，并建立严格的收敛性理论，利用这一算法可求解约束条件为对称矩阵、反对称矩阵、中心对称矩阵、中心反对称矩阵、自反矩阵、反自反矩阵，对称正交对称矩阵、对称正交反对称矩阵、双中心矩阵、Hermite广义Hamilton矩阵等；可以说只要约束矩阵集合在矩阵空间中构成子空间，都可以考虑用此算法求解，而且这一算法还能把矩阵方程解及其最佳逼近，最小二乘解及其最佳逼近统一处理，因此本文算法有普适性和重要的实用价值。

Renal sexual segment, the hypertrophied region of the distal convoluted tubule and/or the forehead of the collecting duct of kidneys in the reptiles of Diapsida Lepidosauria, especially in male individual of Squamata, is a secondary structure of the male.

肾性节是一种雄性副性结构，主要存在于爬行动物双孔亚纲 Diapsida 鳞龙下纲 Lepidosauria ，尤其是有鳞目的雄性，由肾脏的集合管前端或肾单位的远曲小管末端膨大特化而成。

Methhods:1:The chemical components of Chinese herbal medicines extracted with petroleum ether,chloroform, ethyl acetate,ethenol and water respectively were analyzed and compared.2.The specimens were analyzed with ultraviolet-visible absorption spectrophotometry.

(1)按中药多分子体系的脂溶性差异，分为石油醚、氯仿、乙酸乙脂、乙醇和水的溶出性成分集合，然后进行&对药&与非&对药&的对比分析；(2)用紫外-可见光光度计测定吸收光谱曲线。

Based on English definition of the six properties which a relation R defined on a set A and utilizing the logical characteristic of implications, two aspects of ordered-pair and the matrix MR are considered, and the properties of the R is analyzed one by one. A few useful conclusions are summarized as determining the properey of the R. The following collections are also analyzed between reflexive and irreflexive, symmetric and antisymmetric, symmetric and asymmetric and among irreflexive, antisymmetric and asymmetric.

根据定义在一个集合A上的关系R的六个性质的英文定义，利用蕴含式的逻辑特点，从有序对和关系R的矩阵M两个角度对每个性质逐一进行分析，得出在判定关系R的性质时可用的结论，并且分析了自反性与非自反性之间、对称性与反对称性之间、对称性与非对称性之间、非自反性和反对称性以及非对称性之间的联系。

Gloeosporioides is an aggregative species and has differentiation within species, the pathogen probably is a microspecies under C. gloeosporioides and exhibited some specialized and selective qualities in pathogenicity. According to its symptom, the disease was named as angular leaf spot.

由于胶胞炭疽菌是1个集合种，存在分化现象，该病原菌可能是分化出的1个小种，并在致病性方面表现出一定的专化性或选择性，根据该病害的症状命名为板栗角斑病。

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。