查询词典 cauchy inequality

Firstly, the eigenvalue problem of a class of second order elliptic equation with critical potential and indefinite weights is considered. Then, using critical point theory, Trudinger-Moser inequality and the properties of the first eigenvalue, we prove the existence of a nontrivial solution for a class of nonlinear elliptic with critical potentialand indefinite weights in R~2. Secondly, we prove the existence of nontrivial solutions for a class of subcritical and critical elliptic systems with indefinite part in R~2 byusing a generalized linking theorem, Trudinger-Moser inequality and concentration-compactness principle.5. The existence of at least three weak solutions for discrete boundary value problem is established by using a three critical point theorem introduced by Ricceri.

首先，讨论了R~2中一类带不定权且含临界位势的二阶椭圆型方程的特征值问题，并借此特征值问题的第一特征值性质，利用山路引理及Trudinger-Moser不等式，证明了R~2中一类带不定权且含临界位势的非线性椭圆型方程非平凡解的存在性；其次，利用广义环绕定理，Trudinger-Moser不等式及集中列紧原理，得到了R~2上一类具有强不定部分的半线性椭圆型方程组在非线性项分别为次临界增长和临界增长情形下非平凡解的存在性。

Here, we will try our best to use the unit-speed outward normal flow to prove this result, and therefore to strengthen Gage's inequality as a more "" isoperimetric-type"" inequality. It will be the main task of the first part of the present thesis.

这是本文第一部分的主要任务，在这里我们还利用Minkowski支撑函数将Gage不等式叙述成一个积分不等式，这可以视为Gage不等式的分析形式。

We analyze the reason of the persistency of social stratification and the effect of inequality of educational quality on income inequality.

本文在人力资本理论和社会分层理论的基础上，建立个体从最大化个人效用出发，考虑地域间房屋租金和子女教育质量的差异，选择居住地的OGM模型。

Thus, pretax income inequality will be artificially high and the reduction in inequality also exaggerated.

因此，付税之前收入不平等将人为地是上流和对也被夸大的不平等的减少。

The solvability of quadratic matrix inequalities of singular H∞ control problems with infinite zeros is studied in this paper. It is proved that the quadratic matrix inequality can be solved directly via the generalized eigenvalue problems. The previous method of solving the quadratic matrix inequality involving complicated decompositions and transformations of the systems is avoided.

摘要研究具有无穷远零点的奇异H∞控制问题的二次矩阵不等式的可解性，证明了通过求解广义特征值问题，可以直接求得二次矩阵不等式的解，从而简化了原需通过复杂的系统分解和变换来求解二次矩阵不等式的方法。

Be based on these conditions, construction gives strict linear matrix inequality , filling property proved the Schur that uses matrix next to be below the condition of linear matrix inequality, system of earning closed circuit is asymptotic stability, specific condition feedback gave out to control a law in the meantime.

基于这些条件，构造出严格的线性矩阵不等式，然后利用矩阵的Schur补性质论证了在线性矩阵不等式的条件下，所得闭环系统是渐近稳定的，同时给出了具体的状态反馈控制律。

The effect of inequality on investment overweighs its effect on education, so inequality has a strong indirect effect on growth instantaneously. The effect turns positive and then weakly negative.

3收入差距对于投资的影响超过了对于教育的影响，因此收入差距对于经济增长的间接影响在即期也是非常强的负，之后变为正，再逐渐下降至微弱的负影响。

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 the Utev S.and Peligrad M.inequality of-mixing random variable sequence,we obtain the Hájeck-Rènyi inequality and three series theorem and Chung′s strong law of large numbers for-mixing random variable sequence,which extend and improve the corresponding results of Gan shixin and Wu Qunying,these resuls are consistent with that for independent random variable sequence.

不等式，得到了-混合随机变量序列的Hájeck-Rènyi不等式、三级数定理和Chung型强大数律，改进了甘师信与吴群英等人的结论，达到了与独立时一致的结果。

But it is not an easy task to directly extend the linear triangle geometric inequality to the n-simplex, thus there are many geometric inequalities worthing exploring and researching when we extend the linear geometric inequality to the tetrahedron and the n-simplex.

而三角形中的某些线性几何不等式直接推广到维单形并不是一件容易的事，因而在推广到四面体中乃至维单形时还有许多几何不等式值得探讨和研究。

I'd had it for 20 years when I found out that I was not alone with the symptoms and that thousands of people in the UK had Narcolepsy.

我想在这20年时，我发现我不是唯一的症状，以及有数以千计的人在英国有发作性睡病。

With these projects in full swing, the XPCC saw its education, science and technology, culture and other undertakings follow suit.

随着兵团国民经济体系的确立，兵团的教育、科技、文化等各项事业也得到长足发展。活跃的，全力进行中