查询词典 cauchy inequality

Secondly, we consider stochastic LQ optimal control problem driven by Lévy processes and Brownian motion. By applying the -Lévy formula, Gronwall's inequality, Young's inequality and Cauchy-Schwarz inequality, we obtain the closeness property of the solution of multi-dimensional backward stochastic Riccati differential equations.

第二部分首先研究由布朗运动和Lévy过程共同驱动的随机LQ最优控制问题，接着利用-Lévy公式、Gronwall不等式、Young不等式及Cauchy-Schwarz不等式证明多维倒向随机Riccati微分方程适应解的闭性质，并利用此性质证明一维BSRDE解的存在唯一性。

Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwalls type, an energy inequality is got and a priori estimate is established.

接下来经过分部积分和Cauchy不等式，并利用Gronwall型引理得到一个能量不等式，对解的范数给出先验估计。

First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and accuracy of the-th approximate value is estimated by the n-tb approximate value.

首先利用Cauchy场不等式证明了一个基本不等式；其次采用Galerkin方法来构造适当的基函数，并利用Cauchy不等式给出了其特征值计算的误差佑计式；最后得到计算梁横向振动问题的特征值的近似值的算法，而且可以用第n次近似值来估计第n-1次的近似值的精确度。

Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwall's type, an energy inequality is got and a priori estimate is established.

接下来经过分部积分和Cauchy不等式，并利用Gronwall型引理得到一个能量不等式，对解的范数给出先验估计。

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。

In this paper,quadratic form theory,the European space inner product nature and Jensen inequality are three ways to prove cauchy inequality,and bthe relation between Cauchy inequality and higher mathematics was illustrated briefly.

本文运用二次型理论、欧式空间中内积性质和詹森不等式三种方法证明柯西不等式，并简要说明柯西不等式与高等数学之间的联系。

In this paper, by virtue of some relevant results of Fourier Analysis and Cauchy Inequality, we begin with working on the necessary and sufficient condition for the existence of the periodic solution to a kind of compound-type linear periodical system with constant coefficients and periodical force term f.

高存臣 ，唐瑞娜，阎庆旭本文首先利用Fourier分析的有关结论和Cauchy不等式，对一类具有滞后与超前偏差变元的n阶常系数混合型线性周期系统周期解存在唯一性的充要条件进行了讨论。

The asymptotic behavior of the weak solution is obtained when an enthalpy function is made in L(superscript 2 subscript +) and a differential inequality is proved after using Cauchy inequality, Poincare inequality and the definition of weak solution.

在L(上标2 下标+)空间上构造了一个熵函数，利用带ε的Cauchy不等式和poincare不等式及弱解的定义，推导出了此函数满足的一个微分方程不等式，通过求解微分方程，证明了弱解的渐近性问题。

Applying the De Caen"s inequality of sum of the squares of the degree and Cauchy"s inequality, we obtain a strict lower bound and a strict upper bound of the largest Laplace eigenvalues only in terms of vertex number of a unicycle graph. Applying the Laplace matrix theorem of trees, we obtain an upper bound of the second smallest Laplace eigenvalues of a unicycle. Extremal graph whose second smallest Laplace eigenvalues reach the obtained upper bound is determined. We also obtain an upper bound of the second largest Laplace eigenvalues in terms of vertex number of the largest connected branch of unicycle graph, and obtain a theoretical method to calculate the second largest Laplace eigenvalues of unicycle graph. We obtain an upper bound of any Laplace eigenvalues in terms of vertex number of a unicycle graph. We also obtain the distribution of Laplace eigenvalues in the inter [0,n] in terms of the matching number.

本文得到了以下几个方面的结果： 1、利用图度平方和的De Caen不等式和Cauchy不等式给出单圈图的最大Laplace特征值仅依赖于顶点数的严格的上下界；利用树的Laplace理论给出了单圈图次小Laplace特征值的一个上界，并刻画了达到该上界的极图；利用子图的连通分支的顶点个数给出了单圈图次大Laplace特征值的一个上界，并给出了单圈图次大Laplace特征值一个理论上的一个求法；利用单圈图的阶数给出了其一般Laplace特征值的一个上界；利用单圈图的匹配数给出其Laplace矩阵谱在区间[0，n]上的分布情况。

The Wielandt inequality is an improvement on the general Cauchy-Schwarz inequality, and its applications to statistics were studied. In a note, Wang and Ip (1999) gave the Wielandt inequality in matrix version in terms of the Lo|¨wner partial ordering.

Wielandt不等式是对著名的Cauchy-Schwarz不等式的一种改进，该不等式被广泛应用于统计理论中线型模型的研究方面，因此研究更一般形式的Wielandt不等式有重要的意义。

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