二次不等式

This text studies the obstacle problems associated with nonhomogeneous elliptic equation, gives the definition of solutions of second order degenerate nonhomogeneous obstacle problems, and making use of the Poincaré inequality and others,acquire some properties of these solutions and their lead number,filling up the blank of an nonhomogeneous obstacle problem research.

本文研究了非齐次椭圆方程的障碍问题，给出了二阶非齐次障碍问题解的定义，利用Poincar啨不等式，获得非齐次障碍问题的解及其导数的一些性质，填补了对非齐次障碍问题研究的空白。

Based on the primal-dual logarithmic-barrier method, a new algorithm for convex quadratic programming with equality and non-equality constrains is discussed.

在此基础上提出了求解带有等式约束和不等式约束的凸二次规划的牛顿内点算法。

Based on the characteristics of the electrohydraulic servo system,the transient optimal control method using the p Q character of servo valve as constraint condition of inequality is presented.

文章分析了线性二次型最优控制不适用于电液伺服主动抗振系统的原因，并根据电液伺服抗振系统特点，提出了以伺服 p- Q特性各不等式约束条件的瞬时最优控制方法。

The other classfies the calculation of MBPS into the solution of inequation based on heuristic knowledge of MBPS of optimal directional coordination setting in complex multiloop network and comes into equivalence of 0-1 integral second layout problem. On the basis of the principle of Gene Optimal Evolution, a new approach to determine MBPS is first presented and decreases the computational complexity of MBPS problem.

其二，利用复杂环网方向保护最优整定配合中最小断点集的启发知识，将MBPS的计算归结为解不等式，进而等价为0—1整数二次规划问题，基于基因遗传优化计算原理，首次提出了MBPS问题的基因遗传算法，降低了问题的计算复杂性。

If the knowledge was closely related the many disciplines or many branches of a discipline,then this knowledge is certainly important,but the quadratic form,european space inner product,Jensen inequality are basic content of algebra,real letters,calculus in higher mathematics.

如果某一知识跟很多学科或者一个学科的很多分支有着密切联系，那么这个知识肯定是很重要的，而二次型、欧式空间内积、詹森不等式都是高等数学中代数、实函、微积分的基本内容。

In modeling heavy tails,we focus on multivariate t distributions and derive the moment generating function of the quadratic approximation.Then we use Fourier transform,Chebychev's Inequality and numerical technique inversion to approximate VaR value of portfolio,compared with Cornish-Fisher Expansions normal model and Delta-Normal model.

在推导出多个外汇期权的投资组合的二次近拟的矩母函数表达式基础上，本文使用傅里叶变换、切比雪夫不等式、数值转换计算求出投资组合的VaR的值，并和基于多元正态分布Cornish-Fisher模型以及基于Delta-正态模型计算所得的VaR值了进行比较。

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。

We estab-lish,under some mild assumptions,a locally quadratic convergence theoremfor Method I and prove a semi-local convergence theorem for Method II.Applications of the two methods to complementarity,variational inequalityand optimization problems are investigated as well.

在某些适当的假设下，我们证明了方法I的局部二次收敛性和方法II的半局部收敛性；还研究了两个方法在求解互补问题，变分不等式问题及约束优化问题中的应用。

In this paper, we show that when the data matrices are $2\times 2$ and $3\times 3$-dimensional, we can transfer the problem into an optimization problem with quadratic matrix inequality constraints, based on another equivalent robust optimization problem converted from the original one.

本文表明，当数据矩阵为2乘2阶，3乘3阶矩阵时，我们可以把上述问题转化成二次矩阵不等式约束的最优化问题。

Combining RFD with SDS,the program can automatically prove an extensive class of geometric inequalities involving radicals.

将RFD算法和差分代换方法相结合，给出了一大类具有相当难度的几何不等式的机器证明。此前该课题仅有的工作是杨路关于二次根式的结果。

But we don't care about Battlegrounds.

但我们并不在乎沙场中的显露。

Ah! don't mention it, the butcher's shop is a horror.

啊！不用提了。提到肉，真是糟透了。