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.

因此，為了簡化這些不等式的證明過程，通過閱讀大量的相關(guān)資料，本文從數(shù)學(xué)的基本概念入手A级黄色网站免费看，運(yùn)用了1種巧妙的方法——概率方法，即根據(jù)不等式的主要特征处女开破视频，結(jié)合概率論的1些基本概念和公式老师挤奶水A片无码网站，通過建立1個適當(dāng)?shù)母怕誓Ｐ停x以1些隨機(jī)事件或隨機(jī)變量的具體含義国产欠欠自拍激情一集黄片，再利用概率論的理論加以證明，討論了柯西不等式中国黄色网站大全免费看，級數(shù)不等式欧美级黄片，詹森不等式和幾個1般不等式的證明。

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.

本文開始給出了凸函數(shù)的定義及等價定義999精品无码一级A片，并證明了它們之間的等價關(guān)系天堂中文在线www天堂在线；接著提出了凸函數(shù)的判定定理，對一個函數(shù)是否是凸函數(shù)提供判斷依據(jù)三上悠亚精品区在线看AV网站；然后對凸函數(shù)的運(yùn)算性質(zhì)影音先锋av在线网址、基本性質(zhì)、微分性質(zhì)极品萝在线永久视频欧美、積分性質(zhì)四個方面的性質(zhì)進(jìn)行了總結(jié)一本一道aV无码中文字幕黑人，并給予了證明；最后證明了凸函數(shù)的幾個著名不等式詹森不等式精品一级片手机在线免费观看、赫爾德不等式国产亚洲日韩在线人成aaaa、柯西不等式，給出了這幾個不等式的一些應(yīng)用實例，并舉例說明凸函數(shù)的基本性質(zhì)和積分性質(zhì)在不等式證明過程中的重要作用久久国产亚洲欧美久久。

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.

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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.

在對偶Brunn-Minkowski理論中超碰在线综合网，我們引入了對偶調(diào)和均質(zhì)積分概念免费观看欧美日韩亚网红在线，系統(tǒng)的研究了它的性質(zhì)，并建立對偶調(diào)和均質(zhì)積分的Brunn-Minkowski不等式99国产精品久久久久，Blaschke-Santalo型不等式和Bieberbach不等式玖玖色综合加勒比在线视频免费精品；接著我們建立了對偶仿射均質(zhì)積分的對偶Brunn-Minkowski不等式，最近我們得知這個不等式被Gardner用另外的方式證明五十路漂亮无码；凸體的極體是凸幾何中一個重要概(來源：2525ABf8C論文網(wǎng)www.abclunwen.com)念欧美大片在线视观看喷水，既然相交體和投影體有對偶關(guān)系，因此在研究完投影體的極體之后自然要研究相交體的極體被cao的美女。

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.

二操操综合。第四部分利用了擬變分不等式2021色综合,另类日韩、偽變分不等式及強(qiáng)變分不等式之間的關(guān)系，利用已知的單調(diào)廣義變分不等式的解的情況來研究擬變分不等式人人妻人人操97、偽變分不等式及強(qiáng)變分不等式的解的情況人人上人人搞人人插，并得出一些重要的理論。

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)動不變密度公式有著本質(zhì)的不同欧美xxxxx又大又粗，本文從二維平面和三維空間兩個角度久久精品国产日本VA，利用弦冪積分不等式，Schwarz不等式18禁毛片免费无遮挡无风险，Holder不等式等不等式分別得到了一系列雙弦冪積分不等式国产精品18久久久久久不卡。

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，利用關(guān)于兩個〓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)〓取極端值時遇到的困難欧美人人爱；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.

八十年代為變分不等式問題的很重要的發(fā)展階段超级碰人人操，出現(xiàn)了一系列的變分不等式ccc欧美在线视频观看，如向量變分不等式、一般變分不等式日韩一级AV黄色片、擬變分不等式日日射日日干、類變分不等式及廣義變分不等式。

inequality with absolute value：含絕對值的不等式

奇數(shù)集 the set of all odd numbers | 含絕對值的不等式 inequality with absolute value | 一元二次不等式 one-variable quadratic inequality

Cauchy inequality Cauchy：不等式{卽schwary}不等式

懸鏈曲面;懸索曲面 catenoid | Cauchy inequality Cauchy不等式{卽schwary}不等式 | Cauchy distribution Cauchy分布

inequality constraint：不等式約束

"不等式","inequality" | "不等式約束","inequality constraint" | "不等式運(yùn)算子","inequality operator"

Inequality：不等式

第九章 不等式與不等式組 9.1 不等式 用小于號或大于號表示大小關(guān)系的式子,叫做不等式(inequality). 使不等式成立的未知數(shù)的值叫做不等式的解. 能使不等式成立的 x 的取值范圍,叫做不等式的解的集合,簡稱解集 (solution set).

quasi variational inequality：擬變分不等式

向量變分不等式:vector variational inequality | 擬變分不等式:quasi-variational inequality | 廣義變分不等式:general variational inequality

Generalized Variational Inequality：廣義的變分不等式

廣義變分不等式問題:and phrases:generalized variational inequality | 廣義的變分不等式:Generalized Variational Inequality | 廣義變分不等式組:generalized variational inequality

Generalized Variational Inequality：廣義變分不等式組

廣義的變分不等式:Generalized Variational Inequality | 廣義變分不等式組:generalized variational inequality | 對稱變分不等式:symmetric variational inequality prob-lems

Generalized Variational Inequality：廣義變分不等式

變分不等式問題:Variational Inequality Problem | 廣義變分不等式:Generalized Variational Inequality | 似變分不等式:Variational-like inequality

vector variational inequality：向量變分不等式

變分不等式:variational inequality | 向量變分不等式:vector variational inequality | 擬變分不等式:quasi-variational inequality

general variational inequality：廣義變分不等式

擬變分不等式:quasi-variational inequality | 廣義變分不等式:general variational inequality | 變分不等式問題:variational inequality problems