查询词典 inequalities

Providing also a self-contained presentation of classical isoperimetric inequalities for eigenvalues and 30 open problems, this book will be useful for pure and applied mathematicians, particularly those interested in partial differential equations, the calculus of variations, differential geometry, or spectral theory.

为eigenvalues和30个开放式问题也提供古典isoperimetric 不平等的拘谨的赠送，这本书将是对纯并且被使用数学家有用的，特别是对偏微分方程，变分法，不同几何学或者光谱的理论感兴趣的那些。

Let a =∈〓. Then corresponding to 62 equivalence classes in χ for ～, we have 144polynomial elements in one variable in canonical basis, each of them also cor-responds to a region which consists of six independent inequalities.

定理。设a=∈〓。那么与χ关于～的62个等价类对应，在典范基中有144个单变量多项式元素，每个单变量多项式元素也对应一个由六个独立不等式构成的区域。

Our first main result is (see §9.1) 9.1. Theorem. Let a =∈〓.χ={i =｜〓=〓}, where 〓 is the unique longestelement in Weyl group of complex semi-simple Lie algebra for type 〓. Thencorresponding to 62 equivalence classes in χ for certain equivalent relation ～,we have 62 monomial elements in canonical basis, each of them correspondsto a region which consists of six independent inequalities.

我们的第一个主要结果是群的唯一最长元素，那么与χ的关于某种等价关系～的62个等价类对应，在典范基中有62个单项式元素，每个单项式元素对应一个由六个独立不等式构成的区域。

In this paper,taking Cauchy inequality for example,we discussed some problems on inequalities teaching in middle schools.

以经典的柯西不等式为例，从不等式的证明、推广以及它们的一些应用，对在中学数学教学中的一些问题进行讨论

Therefore,in order to simplify the proving process of these inequalities.Though reading a lot of relevant resource,we begin with the basic concept of math,and use an ingenious way――probabilistic method, which means that according to the main features of inequality theory,combining the basic concepts and formulas of probability,through creating one suitable probability model,giving some concrete meanings of random events or random variables,proving through probability theory,we discuss the Cauchy inequality,Class inequality,Jensen inequality,and several common inequality's proofs.

因此，为了简化这些不等式的证明过程，通过阅读大量的相关资料，本文从数学的基本概念入手，运用了1种巧妙的方法——概率方法，即根据不等式的主要特征，结合概率论的1些基本概念和公式，通过建立1个适当的概率模型，赋以1些随机事件或随机变量的具体含义，再利用概率论的理论加以证明，讨论了柯西不等式，级数不等式，詹森不等式和几个1般不等式的证明。

However the young country still had problems and as the 19th centaury drew to a close the widening social inequalities lead to rising discontent.

波旁王朝为了重建统治，采用激进举措迫使当地精英阶层进行合作，其残酷手段反而促进了南美洲统一战线的最终形成。

I. d. Bernoulli random variables. First, we can get the upper bound with order from Chebyshev inequality. Second, a better upper bound was gotten with the new inequalities, which can fasten the convergence rate.

并对服从两点分布的独立随机变量X1，X2，…，X进行研究，首先利用Chebyshev不等式得到随机变量偏离方差ES的上界，但它只有阶的收敛速度，然后利用新的不等式得到一个新的上界，它有更快的收敛速度，这在探讨收敛速度时有着重要的理论意义。

By transforming the nonlinear saturation constraint into the special linear constraint, the problem of solving the feedback controller with saturated actuator is converted to the design of controller with linear constraint. The stochastic stability is ensured by using the intersection of ellipsoid invariant set of different modes existing in the attraction domain of the closed loop system. In this case, solving controllers can be equivalent to a solvability problem of linear matrix inequalities.

通过将非线性饱和约束转化为特殊的线性约束，使具有饱和执行器的控制器求解问题转化为线性约束控制器的求解问题，利用位于闭环系统吸引域内的不同模态下椭圆不变集的交集来保证系统的随机稳定性，此时控制器的求解可等效为线性矩阵不等式的可解性问题。

A sufficient condition for quadratic stability of fuzzy closed loop system is given in terms of linear matrix inequalities.

但是对于实际中广泛存在的非线性离散系统的保成本控制问题还没有得到充分的研究。

Moreover, we pointed out some errors in the litterature concerning the closure property of two families of ageing notions and gave a new proof; established probability inequalities for some common used discrete ageing notions, and obtained some comparison results of inspection paradox.

另外，我们指出文献中关于两类寿命分布类卷积封闭性证明的错误，并纠正其错误；建立了常见的离散型寿命分布类对应的概率不等式；给出了检查悖论中的一些随机比较结果。

I'm strongly against the death penalty — it's an eye for an eye.

我不赞成死刑——这是以牙还牙的报复行为。

And to get you the support you need, we're enlisting all elements of our national power: our diplomacy and development, our economic might and our moral suasion, so that you and the rest of our military do not bear the burden of our security alone.

并给你们所须的支援，我们正徵召国家所有各种的力量：我们的外交及发展，我们的经济力量与道德劝说，所以你们与其他军人不须要孤独地负起国家安全的责任。