查询词典 inequalities

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,. Here, we will give an independent proof of the existence for inequality (2.1.3), and by the way, give an estimate on the width of the bi-enclosing annulus of closed convex curves in the plane.

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。

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。

By restricting the covariance structure, some theorems of the complete convergence and strong law of large numbers for PA random variables sequences are obtained by applying the properties and inequalities of PA random variables.

在这里通过对协方差结构的限制，应用关于PA随机变量序列的性质、不等式，建立了PA随机变量序列的完全收敛定理和强大数定律。

Chapter 4 proves the strong law of large numbers,Glivenko-Cantelli Lemma underΓ-weak dependence, and we can further investigate moment inequalities for associated r.v.s.in terms of this dependent coefficient.

第五章我们在Wasserstein距离意义下根据随机变量序列的有限维联合分布以及它的边际分布的乘积之间的渐近独立性提出了一种新的相依系数，并且给出了一些具体的例子。

The basic idea is: split the variables into smaller nonnegative quantities, then, collect the terms and see whether the coefficients all are nonnegative. The method has been used to prove symmetric polynomial inequalities for so many years that the origin is unavailable.

将各变量按一定方式分割成较小的非负量，将变量替换后的多项式合并同类项，然后看是否所有的系数都是非负的。

In this paper,some characterizations of solutions for a system of vector variational inequalities are derived under the a.

该文研究了一类向量变分不等式组，在PPM条件下，对其解进行了一些刻画此外，给出了该向量变分不等式组的一个间隙函数，并在强单调条件下，证明了它是弱尖极小的。

By using the projection method, we prove the existence and uniqueness of solutions for this new system of generalized variational inequalities.

在本文中，我们首先引入了一类新的关于松弛协强制映射的广义变分不等式组，通过用度量投影的方法，我们证明了这类广义变分不等式组解的存在性和唯一性。

Furthermore, it is shown that this condition is equivalent to the solvability problem of a system of linear matrix inequalities, and its solutions provide a parametrized represent...

在此基础上，通过建立并求解一个凸优化问题，给出了最优保性能控制律的设计方法。

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。

Linear system of inequalities is widely used in many fields; it is usually solved as a linear programming problem by simplex method and interior-point method.

线性不等式组应用广泛，一般可以看作线性规划问题用单纯形法或者内点法来求解。

Lugalbanda was a god and shepherd king of Uruk where he was worshipped for over a thousand years.

Lugalbanda 是神和被崇拜了一千年多 Uruk古埃及喜克索王朝国王。

I am coming just now,' and went on perfuming himself with Hunut, then he came and sat.

我来只是现在，'歼灭战perfuming自己与胡努特，那麼，他来到和SAT 。