Instead of Gronwall\'s inequality,the non-linear Bihari inequality is crutial in dealing with the non-Lipschitz equations.Moreover,we emphasize that the dominating functions in non-Lipschitz conditions always satisfy concavity and some non-integrability near zero.The concavity is for using Jensen\'s inequality.Because of the non-integrability near zero,we can apply the comparison theorem of ordinary differential equations together with Bihari\'s inequality to yield many results.

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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.

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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.

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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.

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Inequality proof of various ways, they were: use derivative testify inequality nature, Includes using functional monotonicity and extreme value, the function and the concave and convex inequality, proving is concave and convex function in the original definition of equivalent definitions and a lemma is proposed on the basis of relevant concave and convex function of several theorems about inequality, and briefly discusses how to use the definitions and theorems in proof of inequality.

不等式的證明方法多種多樣户外露出网站，它們分別是：用導(dǎo)數(shù)性質(zhì)證明不等式；包括利用函數(shù)單調(diào)性，極值與最值亚洲巨制av剧情在线，函數(shù)凹凸性證明不等式丰满的人妻一级毛片中文，其中在給出凹凸函數(shù)原始定義等價的解析定義和一個引理的基礎(chǔ)上提出有關(guān)凹凸函數(shù)關(guān)于不等式的幾個定理，并簡要闡述了利用定義和定理在證明不等式中的運用欧美激情性A片在线观看⑧。

In dual Brunn-Minkowski theory, we study the properties of the dual harmonic quer-massintegrals systematically and establish some inequalities for the dual harmonic quer-massintegrals, such as the Minkowski inequality, the Brunn-Minkowski inequality, the Blaschke-Santalo inequality and the Bieberbach inequality. We establish the dual Brunn-Minkowski inequality for dual affine quermassintegrals. Recently we learned that Gardner have independently proved it by a different method. The polar body of a convex body is an important object in the context of convex geometry. Hence, after we studied the intersection bodies, it is natural to consider the inequalities for their polar bodies.

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The stability region estimation of the singularly perturbed systems can be replaced by that of the adjoint systems, and an optimization method based on linear matrix inequality was provided to reduce the conservativeness in the estimation.

將原系統(tǒng)穩(wěn)定域估計問題轉(zhuǎn)化為低階伴隨系統(tǒng)穩(wěn)定域的估計問題，利用線性矩陣不等式(Linear matrix inequality亚洲中文字幕无码乱线， LMI)優(yōu)化方法估計伴隨系統(tǒng)的穩(wěn)定域以減少保守性超碰在线看。

However,To prove Inequality with elementary method,we often create complex computational process. The second ,we will take full advantage of the knowledge of calculus Inquiry Testimony of inequality,and concluded the higher mathematics to prove Inequality several main method and its application conditions.Constructors in the context of the use of the monotone function,Calculus value theorem,function and the most extreme value,integral, it can be a very effective solution to the inequality problem proof. At last,we summed up several convenient and simple way to prove Inequality.It will be play a great role in our problem Solving.

但是用初等方法證明往往會造成復(fù)雜的運算過程，本文接著充分利用微積分的知識探究不等式的證明方法黄色片你懂的，并指出微分學(xué)和積分學(xué)在不等式的證明的具體應(yīng)用美女裸体黄网站18禁止免费，那就是在構(gòu)造函數(shù)的背景下運用函數(shù)的單調(diào)性、微積分中值定理性小说在线视频、函數(shù)的極值和最值一级a看片免费视频、定積分，那么就可以十分有效地解決不等式中的證明問題麻豆精品视频在线免费观看，從而歸納出幾種方便而又簡捷的方法超碰在线黄色网，這樣對我們解題將會起到很大的作用。

For the characteristic of the ring permanent magnet torque motor used in direct drive numerical control round table suffering from the effect of load disturbances and parameters variations, a multi-objective mixed H2/H∞ static output feedback controller, which makes all poles of the closed-loop system be located within a prescribed linear matrix inequality region D to achieve pole placement, is designed based on LMI.

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Second, in the forth part, the writer used relationshipin quasi--variat iona1 inequal ity, pseudo-variational inequality and monotone variational inequality and used the solution of monotone GVIP to solute quasi?variational inequality,pseudo?variational inequality. Also some important conclusion were given.

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