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.

本文開(kāi)始給出了凸函數(shù)的定義及等價(jià)定義，并證明了它們之間的等價(jià)關(guān)系女人被爽到呻吟的网站；接著提出了凸函數(shù)的判定定理欧美三级手机在线看，對(duì)一個(gè)函數(shù)是否是凸函數(shù)提供判斷依據(jù)；然后對(duì)凸函數(shù)的運(yùn)算性質(zhì)日本强伦姧人妻一区二区、基本性質(zhì)、微分性質(zhì)亚洲激情国产一区精品、積分性質(zhì)四個(gè)方面的性質(zhì)進(jìn)行了總結(jié)国产精品久久久，并給予了證明；最后證明了凸函數(shù)的幾個(gè)著名不等式詹森不等式人人干人人操在线、赫爾德不等式色哟一区二区在线看、柯西不等式和閔可夫斯基不等式以及這幾個(gè)不等式的應(yīng)用，并舉例說(shuō)明凸函數(shù)的基本性質(zhì)和積分性質(zhì)在不等式證明過(guò)程中的重要作用。

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欧美日韩性爱网络，它們分別是：用導(dǎo)數(shù)性質(zhì)證明不等式亚洲978eee；包括利用函數(shù)單調(diào)性，極值與最值99视屏在线，函數(shù)凹凸性證明不等式欧美最新视频，其中在給出凹凸函數(shù)原始定義等價(jià)的解析定義和一個(gè)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(gè)定理，并簡(jiǎn)要闡述了利用定義和定理在證明不等式中的運(yùn)用国产精华Av在线导航网站。

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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In order to reasonably depict four basic problems with friction, one Coulomb friction new form in first Kirchhoff stress is proposed to deal with finite deformation problems, other Coulomb friction form in incremental mode to elastoplastic flow theory; Hilbert function spaces concerning elastoplastical problems with friction are established, so it makes all operations and calculations in the treatise standardized within the scope of reasonably topologic structure; In view of functional extremum, the equivalence between generalized variational inequalities principles in elastoplasticity with friction and corresponding basic problems are testified by inducing Lagrangian multipliers, so it provides a rationally theoretical basis for numerical methods in elastoplasticity with friction; From the viewpoint of variational inequality, the theory of generalized variational inequalities in elasticity and elastoplasticity with frictional constraint is studied, and the uniqueness and existence of the solution of FEM is proofed under the proposed conditions of stress compatibility, and them FEM approximation and a discrete solution are discussed; Based on the principles of generalized variational inequalities in elastoplasticity with friction, direct generalized variational inequalities methods is pretended, which is a natural generalization and development of direct variational methods; Using generalized variational inequalities methods, some examples in metal forming including plane deformation, upset and extrusion are analyzed and the results prove that all the theories and methods in the paper are right, feasible, accurate and advanced.

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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.

二能看的黄色网站网址。第四部分利用了擬變分不等式、偽變分不等式及強(qiáng)變分不等式之間的關(guān)系欧美黑人大尺度又粗又长最新章节，利用已知的單調(diào)廣義變分不等式的解的情況來(lái)研究擬變分不等式国产女主播精品在线播放、偽變分不等式及強(qiáng)變分不等式的解的情況，并得出一些重要的理論可以看偷拍视频的网站。

Since there is natural different of the kinematic density formula for pairs of intersecting lines in two-dimensional surface and three-dimensional space, the inequalities for double chord-power integrals have studied from two side of two-dimensional surface and three-dimensional space using chord-power intergral inequality. Schwarz inequality. Holder inequality and so on.

由于二維平面和三維空間上的相交直線偶的運(yùn)動(dòng)不變密度公式有著本質(zhì)的不同国产免费小视频，本文從二維平面和三維空間兩個(gè)角度，利用弦冪積分不等式黄色免网站，Schwarz不等式成人网站香草视频在线观看免费，Holder不等式等不等式分別得到了一系列雙弦冪積分不等式。

IiBy the double 〓-inequalities obtained in our thesis,we solve the problemthat classical 〓 inequalities be invalid when the value of the indices of 〓 functionsbe extreme and unify some classical martingale inequalities,for example:we unifyImkeller's inequality and Doob's inequality to the same double 〓-inequality.

第二不卡视频在线一区二区，利用關(guān)于兩個(gè)〓函數(shù)的不等式解決了鞅的經(jīng)典〓不等式在〓函數(shù)數(shù)量指標(biāo)〓取極端值時(shí)遇到的困難欧美多人群p在线观看；統(tǒng)一了某些經(jīng)典鞅不等式（如將Imkeller不等式與Doob不等式統(tǒng)一為同一種雙〓不等式）。

In the eight ieth, variational inequa1 ity hasits important development phase and there were suchvari ati ona1 inequa1 it ies as vector vari at ionalinequal ity, general variati ona1 inequal ity quasi-variationa1 inequal ity, 1 ike--variat iona1 inequal ity andgenera1 ized vari at iona1 inequa1 ity.

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