不等式

Finally this paper showed the application of double chord-power integral inequality from the geometry probability.

最后本文从几何概率上进一步说明了双弦幂积分不等式的应用。

The linear function applicable scope is broad, when the reservoir turnover water volume and the time, the student leaves the staircase mouth population and the time and the time and the motion communication speech spends the comparison and so on the relational question has the important application;The study linear function, may deepen in the life the linear question understanding and the understanding, is helpful in solves some simple function problem; The linear function some problem solving method has the universality in mathematics, the linear function related theory may use for to solve some other mathematics problem, For instance the dual linear equation group, a Yuan inequality, a Yuan quadratic equation most value question and some complex mathematics question, the light is studies the linear function the theory is insufficient, the key is can utilize actual the linear function goes is our final goal.

一次函数的适用范围广，在蓄水池的进出水量与时间、学生出楼梯口人数与时间与时间和移动通讯的话费比较等的关系问题时均有重要的应用；学习一次函数，可以加深生活中线性问题的认识与理解，有助于解决一些简单的函数问题；一次函数的一些解题方法在数学中具有普遍性，一次函数的有关理论可以用来解决一些其它的数学问题，比如二元一次方程组、一元一次不等式、一元二次方程的最值问题及一些复杂的数学问题，光是学习一次函数的理论是不够的，关键是能把一次函数运用到实际中去才是我们最终的目的。

Secondly,the author puts emphasis on "the simple linear programming"----the teaching design's whole blueprint in high school, the strategy on how to deal with the relation between dual inequality and linear programming; how to establish the linear programming model; the strategy on how to find the optimal solution; the several situations of the optimal solution's positions.

其次重点研究了"高中简单的线性规划"教学设计的总体构想；处理线性规划与二元一次不等式关系的策略；如何建立线性规划模型；线性规划问题中最优解的找法策略，最优解的位置的几种情况。

To strengthen the inequality symbol with the training, 2. to expanse the applications of trigonometric functions to polar coordinates and Parameter equation, 3. to adjust Permutation and combinationwith Probability and Statistics, 4.to strengthen applications of Higher Geometry in the Elementary Geometry.

对此问题本文试着从中学数学教学的角度，在以下几个方面进行探讨：1 加强带符号的不等式的训练，2 扩充三角函数在参数方程和极坐标中的应用，3 排列组合与概率统计的调整，4 高等几何在初等几何中的应用。

You can say that the proof uses nothing beyond elementary matrix theory, repeated use of the triangle inequality, and the pigeonhole principle.

你可以简要地说其实证明就是初等矩阵理论，三角不等式和鸽笼原理的运用。

Ii The problems of optimal control of piecewise linear affine descriptor systems are studied by using some elementary matrix transformations and line matrix inequalities.

二、运用初等矩阵变换和线性矩阵不等式，初步研究了分段线性仿射广义系统的二次最优控制问题，得到了系统二次最优控制的上界、下界，估计成立的条件。

It s difficult to discuss the existence of nontrivial solution for an elliptic equation involving critical exponent.

利用集中紧引理和Hardy不等式克服这个困难，运用山路引理证明了一类非线性椭圆方程非平凡解的存在性

Keywords: meshless method;adaptive algorithm;elliptic equation; variational inequality.

中文关键词：无网格方法；自适应算法；椭圆型方程；变分不等式

In chapter 4, we state and prove Campanato type Theorem, Morrey type Theorem and some embedding Theorems for the maps.

在第四章，我们证明Campanato型和Morrey型不等式和一些嵌入定理。

Technical analysis; AR-ARCH model; covariance inequality; Strong law of large numbers; Glivenko-Cantelli Lemma ; empirical distribution function; central limit theorem; dependence coefficients

基础科学，数学，概率论、数理统计技术分析； AR-ARCH模型；协方差不等式；强大数定律； Glivenko-Cantelli引理；经验分布函数；中心极限定理；相依系数

Breath, muscle contraction of the buttocks; arch body, as far as possible to hold his head, right leg straight towards the ceiling (peg-leg knee in order to avoid muscle tension).

呼气，收缩臀部肌肉；拱起身体，尽量抬起头来，右腿伸直朝向天花板（膝微屈，以避免肌肉紧张）。

The cost of moving grain food products was unchanged from May, but year over year are up 8%.

粮食产品的运输费用与5月份相比没有变化，但却比去年同期高8％。