詹森

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。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational, basic, differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式，给出了这几个不等式的一些应用实例，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

At the beginning of this thesis, the author gives the definition and the equivalent definition of convex function, and then proves the equivalent relationship between them. Secondly the author proposes the decision theorem of convex function which provides a judgment basis of whether a function is a convex function. Thirdly the author summarizes and proves the convex function's operational ,basic , differential and integral property. Finally the author proves several famous convex function inequalities, such as Jensen inequality, Holder inequality, Cauchy inequality and Minkowski inequality. The author also provides the application of these inequalities and illustrates the importance of convex function's basic inequality and integral property in the proving process.

本文开始给出了凸函数的定义及等价定义，并证明了它们之间的等价关系；接着提出了凸函数的判定定理，对一个函数是否是凸函数提供判断依据；然后对凸函数的运算性质、基本性质、微分性质、积分性质四个方面的性质进行了总结，并给予了证明；最后证明了凸函数的几个著名不等式詹森不等式、赫尔德不等式、柯西不等式和闵可夫斯基不等式以及这几个不等式的应用，并举例说明凸函数的基本性质和积分性质在不等式证明过程中的重要作用。

But Jason and Meggie had made up their mind to chaperone their children.

但是詹森和麦姬已经下定决心要陪护他们的孩子。

Properties of measurable functions; approximation by simple functions and by continuous functions; convergence in measure; Egoroff's theorem; Lusin's theorem; Jensen's inequality.

可测函数。可测函数的性质；简单和连续函数逼近；测度收敛；叶果洛夫定理；鲁津定理；詹森不等式

Electricity generated by major dams like the Jensen Dam, TVA Project, Grand Coulee Dam and Hoover Dam still produce some of the lowest-priced $ clean electricity in America.

发电主要水坝如詹森坝的TVA项目，大古力坝和胡佛水坝仍然生产了，价格最低的，清洁电力在美国。

Electricity generated by major dams like the Jensen Dam, TVA Project, Grand Coulee Dam and Hoover Dam still produce some of the lowest-priced ($0.08/kWh), clean electricity in America.

发电主要水坝如詹森坝的TVA项目，大古力坝和胡佛水坝仍然生产了，价格最低的（$ 0.08/kWh ），清洁电力在美国。

Maggie and Jason::It's OK, we know a lot of people try to leave cutesy little messages on their machines, but not us.

马吉和詹森∶还好，我们知道有很多人设法将一些不好的东西留在他们的答录机里，但是我们不会。

Jason also said that he would make more money and they had daycare and he even had a male secretary.

詹森还说那样他会赚更多的钱，而且他们那里有日托中心，他甚至还会有一个男秘书。

So Jason and Mike met together when they all took a walk out on the deck.

因此，当他们都在甲板上散步时，詹森和迈克遇到了一起。

Neither the killing of Mr Zarqawi nor any breakthrough on the political front will stop the insurgency and the fratricidal murders in their tracks.

在对危险的南部地区访问时，他斥责什叶派民兵领导人对中央集权的挑衅行为。

In fact,I've got him on the satellite mobile right now.

实际上 我们已接通卫星可视电话了