预解集

We also introduce and study a new system generalized nonlinear variational inclusions for fuzzy mappings in Hilbert space.

我们利用极大单调映象的预解算子技巧，建立了这类模糊映象的变分包含组与非线性集值映象的不动点问题之间的等价关系，再利用Nadler的不动点定理给出了这类变分包含组的解的存在性定理。

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。

By using the polar decomposition, spectral decomposition, the spectral theory of operators, the intersection of the spectra of operator completions are obtained.

5深刻研究缺项算子矩阵Mx存在逆补的一般性条件，并获得了补矩阵Mx的所有预解集交集的特性。

Using the resolvent operator technique, we construct a new algorithm for approximating the solution of this class of variational inclusions, and discuss ...

利用新的预解式算子技巧得出一系列广义集值拟变分包含问题的逼近解。

The notion of - resolvent operator of set-valued mappings is introduced.

利用η-预解算子在有限维空间中探讨了集值混合拟类变分不等式问题和广义集值变分包含问题存在唯一解的条件；利用分析的方法在实Hilbert空间中讨论了集值混合拟类变分不等式问题解集的非空性。

The problem is researched that under what conditions the - resolvent operator of - subdifferential mapping of a proper functional is aLipschitz continuous single-valued mapping on whole space.

利用冲一预解算子分析了有限维欧氏空间中的广义参数集值变分包含问题唯一解的灵敏性；利用预解算子分析了有限维欧氏空间中的一般参数集值变分包含问题解集的灵敏性。

The research is carried on from four aspects. One is, based on answering the above open problem on a finite dimensional Euclidean space by means of partially ordered theory, to research the existence of solutions, global error bounds of proximal solutions and sensitivity of parametric unique solutions and present a class of variable-parameter three-step iterative algorithms for generalized set-valued variational inclusion problems by using - resolvent operator of set-valued mapping.Two is to consider the convexity, closedness and boundedness of the solution set of general set-valued variational inclusion problems and the sensitivity of the parametric solution set by means of graphical convergence theory. Three is to discuss directly the existence of solutions by using analytical methods for set-valued mixed quasi-variational-like inequalities and suggest a class of direct variable-parameter three-stepiterative algorithms for solving generalized set-valued variational inclusions.

研究分有三个方面：一是借助于偏序理论在有限维欧氏空间中解决了上述公开问题，在此基础上利用集值映射的η-预解算子，研究了广义集值变分包含问题解的存在性、逼近解的全局误差界、参数唯一解的灵敏性，并提出了一类变参数三步迭代算法；二是借助于图收敛理论研究了一般集值变分包含问题解集的凸性、闭性和有界性以及参数解集的灵敏性；三是用分析的方法直接讨论了集值混合拟类变分不等式问题解的存在性并提出了一类求解广义集值变分包含问题的直接变参数三步迭代算法。

An iterative algorithm for a class of set- value d mixed variational inequalities is presented by means of resolvent operators of set- value d mappings, and the convergence of the iterative algorithm is discussed.

摘要利用集值映射的预解算子，提出了求解一类集值混合变分不等式问题的迭代算法，并讨论了该算法的收敛性，推广了已有文献的结果。

Thesame rank Lipschitz continuous development of single-valued mappings is proven by means of partially ordered theory on finite dimensional Euclidean spaces.

借助于冲一预解算子研究了有限维欧氏空间中的集值混合类变分不等式问题和广义集值变分包含问题的全局误差界。

After the formalization of the RMA problems, methods for normalizing the original stochastic decision matrix are proposed. For discrete RMA problems, the concepts of C-type solution and S-type solution are defined, and the inclusion relations between different sets of solution in the same type and between different sets of solution in different types are concluded. For continuous RMA problems, the decision analysis based on Dα-dominance relation is illustrated.

在对风险型多属性决策问题进行形式化描述之后，按照离散和连续两种情况，分别给出了风险型多属性决策属性数据的预处理方法；对离散风险型多属性决策问题，定义了C-类解和S-类解，并给出了各类解集之间的包含关系；对连续风险型多属性决策问题，给出了基于Dα优势关系的分析方法。

As she looked at Warrington's manly face, and dark, melancholy eyes, she had settled in her mind that he must have been the victim of an unhappy attachment.

每逢看到沃林顿那刚毅的脸，那乌黑、忧郁的眼睛，她便会相信，他一定作过不幸的爱情的受害者。

Maybe they'll disappear into a pothole.

也许他们将在壶穴里消失