查询词典 cauchy inequality

Hilbet-type inequality is important in analysis and its applications. In recent years, by improving the way of weight coefficient, some research on the extensions and applications of this type of inequalities are developed. In this paper, we give a Hilbert infinite series inequality with the best constant factor whose kernel is a negative quadratic form by applying the method of weight coefficients. And an equivalent form is considered.

Hilbert型不等式在分析中有重要作用，近年来，由于改进权系数的方法，发展了这类不等式，并进一步推广应用和研究，应用权系数方法给出的一个带有最佳常数的核为负二次型齐次的Hibert型无穷级数不等式，同时考虑了它的等价形式。

Hobbes has become the focus of this thesis, mainly because of his extreme individualism. But If even in such extreme Hobbesian social contract theory claims that inequality still exist between men and women, then what is the source of inequality?

霍布斯之所以为本文论述代表，主要著眼於霍布斯极端的个人主义；若是即便在霍布斯此等极端的社约论主张之中，男女之间尚存在著对照鲜明的不平等，那麼不平等的来源究竟为何？

Based on a delay-dependent bounded real lemma, the condition under which a decentralized robust H(subscript ∞) output feedback controller exists is derived and it is available to be attributed to a solution to the problem of nonlinear matrix inequality which can be expressed in terms of a homotopy function properly selected. Then, with the homotopic iteration method and the Schur complement lemma introduced, the solution can be converted into an iterative solution to the linear matrix inequality.

基于一个时滞依赖有界实引理，将系统鲁棒分散H动态输出反馈控制器的解归结为一个非线性矩阵不等式的求解问题；选取适当的同伦函数来表示该非线性矩阵不等式，采用同伦迭代算法及Schur补引理，将求解非线性矩阵不等式转化为线性矩阵不等式的迭代求解问题。

We obtained a kind of sufficient condition for 2-harmonic submanifolds becoming minimal submanifolds in hyperbolic space and an integral inequality like Simons integral inequality.

得到了双曲空间中2-调和子流形成为极小子流形的一个充分条件，以及一个Simons型积分不等式。

This paper presents some approximate algorithms for minimax nonlinear programs with inequality constraint s by using maximum entropy method and algorithms relevant to nonlinear programming with inequality constraint s,and convergence theorems concerning these algorithms are given.

结合极大熵方法与不等式约束非线性规划的有关算法，提出了求解不等式约束极小极大非线性规划的一种近似法，并讨论了算法的有关收敛

By redefining multiplier associated with inequality constraint as a positive definite function of the originally-defined multiplier, it is no longer necessary to convert inequality constraints into equality constraints by slack variables in order to reuse the method dedicated to equality constraints for constructing Lagrange neural networks.

若重新定义与不等式约束相关的乘子为正定函数，则在构造Lagrange神经网络时，可直接使用处理等式约束的方法处理不等式约束，不需再用松驰变量将不等式约束转换为等式约束，减小了网络实现的复杂程度。

As the condition of super-elasticity happening,a velocity constraint inequality is built.If the mass's velocity dissatisfies the inequality,the authors need to restrict and modulate the velocity,avoiding the super-elasticity.

该方法建立了一个速度约束不等式，作为超弹性现象是否发生的判断依据；并对不满足约束条件的质点速度进行约束调整，进而避免了超弹性现象的发生。

Using differential calculus knowledge to testify inequality, Calculus of higher mathematics is the core and calculus method of higher mathematics is typical of the whole mathematical method, the method is introduced for calculus ideas to solve the problem of finding an inequation, to make way for obtaining inequalities can be simple, the application of differential mid-value theorem and Taylor formula illustrate some of the inequality proof method.

运用微分学知识证明不等式；微积分是高等数学的核心，微积分思想方法是高等数学乃至整个数学的典型方法，微积分思想方法的引入为解决不等式证明的难题找到了突破，用来解不等式可使解题思路变得简单，文章应用微分中值定理及泰勒公式举例说明了部分不等式的证明方法。

In two inequalities concerning the circumradius and inradius of an n dimensional simplex in the n dimensional Euclidean space E n were obtained, Thus, the n dimensional Euler inequality and the inequality in , were improved.

给出了n维欧氏空间En中的两个关于单形外接球半径和内径的几何不等式，同时进一步改进了文［1］和［2］中的n维欧拉不等式。

The classical Poincaré s inequality plays a very important role in stability theory as well as in some other areas. It is widely used in academic research. For instance, the Poincarés integral inequality plays a pivotal role in the Arnolds non-linear stability theory.

在很多问题的研究中，经典的Poincaré不等式是一个非常重要的工具，用这个经典不等式作为研究问题的工具非常普遍，如Poincaré积分不等式在Arnold的非线性稳定性理论中起着关键性的作用。

Hearing loss has always been a problem in those over 65 years old.

听力损失一直是一个问题，在这些65岁以上。

Man's best friend isn't feeling the love as the economy sours.

金融海啸中，人类最好的朋友感到&爱意不再&。