查询词典 absolutely convex hull

Moreover, based on the symmetric Rouche's theorem, a necessary and sufficient condition for the Hurwitz stability of the convex combinations of polynomials is proposed. This condition is simple and can be easily applied to the Hurwitz stability analysis of the convex combinations of polynomials.

而且基于对称Rouche定理给出了多项式凸组合Hurwitz稳定的一个充要条件，该充要条件直观简明，用于分析多项式凸组合的Hurwitz稳定性十分方便。

After some experimental results obtained in machining samples with complex ruled surface, concave spherical surface, convex surface and samples with both concave and convex surface are analyzed, the value of these samples in practical prodúction is discussed.

通过对一些典型的复杂直纹曲面样件以及凹球面、凸球面和凸凹复合球面样件加工实验分析，探讨了这些样件在实际生产中的应用价值。

Under generalized cone-subconvexlikeness for vector valued mappings in locally-convex Hausdorff topological vector spaces, by using separation theorem for convex sets, optimality necessary conditions are derived.

在局部凸Hausdorff拓扑线性空间中，在近似锥－次类凸假设下，利用凸集分离定理得到了最优性必要条件。

And based on this result, we also prove the connectedness of G-properly efficient solution set when the vector objected function is both like-convex and quasi-convex.

在此基础上，还得到向量目标函数既似凸又拟凸的多目标最优化问题G-恰当有效解集是连通的结论。

Based on refrence,the relationship between convexity and strict convexity of fuzzy mapping is discussed and the result that convex fuzzy mapping is the sufficient condition for strictly convex fuzzy mapping is obtained.

在已有文献的基础上，讨论了模糊映射的凸性和严格凸性之间的关系，得到了凸模糊映射为严格凸模糊映射的充分条件。

We established abstract functional spaces, proved that the plastic deformation power rate functional is strict convex and the friction power rate functional and the tensional stress power rate functional are convex. So, strict convexity of the total power rate functional 〓 can be obtained. Further, By nonlinear analysis theory, we proved the existence and uniqueness of minimal point of functional 〓.

本文首先建立了抽象的泛函空间，证明了塑性变形功率泛函是严格凸泛函，摩擦功率泛函和外力功率泛函是凸泛函，从而得到总能耗率泛函的严格凸性，进一步地，利用非线性分析的理论，得到总能耗率泛函有唯一的极小值点。

Moreover, we get the sufficient and necessary condition of in Orlicz spaces.Chapter 3 Extreme points and strongly extreme points in Orlicz spaces equipped with the generalized Orlicz norm: In this paper, the conceptions of the generalized Orlicz norm and the generalized Luxemburg norm are introduced, and the criteria of extreme points and strongly extreme points of Orlicz function spaces equipped with the generalized Orlicz norm are obtained. Moreover, criteria of space strictly convex and mid-point locally uniform convex are given.

第三章 赋广义Orlicz范数的Orlicz函数空间的端点和强端点：本章在Orlicz空间推广了Orlicz范数和Luxemburg范数，引入了广义Orlicz范数和广义Luxemburg范数的定义，并给出了赋广义Orlicz范数的Orlicz函数空间的端点和强端点的判据，进而得到了赋广义Orlicz范数的Orlicz函数空间严格凸和中点局部一致凸的充要条件。

In the first part, we will first deal with the strong Bonnesen-style inequality (2.1.3) for closed convex curves in the plane (the numbers of formulae and references are those of them in the context below). Bonnesen had first proved the weaker inequality (2.1.2) in [12] and several years later, he outlined in his monograph [13] various Bonnesen-style inequalities including (2.1.3), he considered, however,(2.1.3) as a direct consequence of Kritikos\' theorem for convex bodies in higher dimensional Euclidean spaces,.

具体地讲，在第一部分中，首先讨论平面上闭凸曲线的强Bonnesen型不等式(2.1.3)(公式的编号和参考文献的编号引自后面的正文)，Bonnesen在文[12]中先证明了较弱的不等式(2.1.2)，几年以后，在他的著作[13]中，讨论了多种Bonnesen型不等式，其中包括不等式(2.1.3)，不过，他把(2.1.3)作为高维欧氏空间中凸体的Kritikos定理的直接推论，我们这里对不等式(2.1.3)给出独立的存在性证明，并且还对平面闭凸曲线的bi-enclosing环的宽度给出了一个估计。

Optimization; parametric quadratic convex programming; set-valued map; directional derivative; linear stability; solution-set map; parametric linear programming; error bound; subdifferential map; lower locally directionally Lipschitzian; upper locally di-rectionally Lipschitzian; locally directionally Lipschitzian; convex function; quasidiferential; kernelled quasidiferential; quasi-kernel; star-kernel; star-diferential; Penot diferential; subderivative; superderivative; epiderivative; set-valued optimization; set-valued analysis; subdifferential; optimization condition;ε-dual; scalization; generalized subconvexlike-cone;ε-Lagrange multiplier

基础科学，数学，运筹学最优化；集值映射；方向导数；线性稳定；最优解集映射；参数线性规划；参数凸二次规划；误差界；次微分映射；下局部方向Lipschitzian；上局部方向Lipschitzian；局部方向Lipschitzian；凸函数；拟微分；核拟微分；拟核；星核；星微分； Penot-微分；上导数；下导数； Epi-导数；集值优化；集值分析；集值映射的次微分；最优性条件；广义锥次类凸；ε-对偶；数乘；ε-Lagrange乘子

A necessary and sufficient condition for the existence of guaranteed cost control is derived. Furthermore, it is shown that this condition is equivalent to the solvability of a system of linear matrix inequalities, and its solution provides a parameterized representation of guaranteed cost controllers. Based on that, the design of the optimal guaranteed cost controller is formulated as a convex optimization problem, which can be solved by the existing convex optimization techniques.

通过采用线性矩阵不等式的方法，导出了存在保性能控制律的一个充要条件，进而，证明了该条件等价於一组线性矩阵不等式的可解性问题，并用这组线性矩阵不等式的可行解给出了保性能控制律的一个参数化表示。

The shaping method of noncircular part and the tool holder's radial motion characters in noncircular turning process are discussed in detail in the thesis.

论文详细研究了非圆零件的成型方法和加工过程中刀架的径向运动规律。

I have not really liked him,I do not like his this kind of disposition.

我没有真的喜欢他，我不喜欢他的这种性格。