查询词典 inequality sign

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，为了简化这些不等式的证明过程，通过阅读大量的相关资料，本文从数学的基本概念入手，运用了1种巧妙的方法——概率方法，即根据不等式的主要特征，结合概率论的1些基本概念和公式，通过建立1个适当的概率模型，赋以1些随机事件或随机变量的具体含义，再利用概率论的理论加以证明，讨论了柯西不等式，级数不等式，詹森不等式和几个1般不等式的证明。

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 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。

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.

不等式的证明方法多种多样，它们分别是：用导数性质证明不等式；包括利用函数单调性，极值与最值，函数凹凸性证明不等式，其中在给出凹凸函数原始定义等价的解析定义和一个引理的基础上提出有关凹凸函数关于不等式的几个定理，并简要阐述了利用定义和定理在证明不等式中的运用。

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.

在对偶Brunn-Minkowski理论中，我们引入了对偶调和均质积分概念，系统的研究了它的性质，并建立对偶调和均质积分的Brunn-Minkowski不等式，Blaschke-Santalo型不等式和Bieberbach不等式；接着我们建立了对偶仿射均质积分的对偶Brunn-Minkowski不等式，最近我们得知这个不等式被Gardner用另外的方式证明；凸体的极体是凸几何中一个重要概(来源：2525ABf8C论文网www.abclunwen.com)念，既然相交体和投影体有对偶关系，因此在研究完投影体的极体之后自然要研究相交体的极体。

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.

但是用初等方法证明往往会造成复杂的运算过程，本文接着充分利用微积分的知识探究不等式的证明方法，并指出微分学和积分学在不等式的证明的具体应用，那就是在构造函数的背景下运用函数的单调性、微积分中值定理、函数的极值和最值、定积分，那么就可以十分有效地解决不等式中的证明问题，从而归纳出几种方便而又简捷的方法，这样对我们解题将会起到很大的作用。

This article expounds on the essentials of all n avigation de sign ing, and, based on the theory of modern library comprehensive de sign ing, illustrates the sign ificance and detailed de sign ing methods of outdoor navigational system, indoor sign de sign ing and de sign ing of bookshelf sign s.

文章阐述了图书馆各种导向设计的基本要素，并以现代图书馆综合设计观点举例说明户外导向系统、内部标志及架位标识设计的重要意义和具体设计方法要点。

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.

3作为Gronwall不等式的推广，Bihari不等式在处理具有非Lipschitz系数的方程时不可或缺；同时应当注意，非Lipschitz条件中所涉及的控制函数总是满足凹性和某种零点处的不可积性：凹性是为了利用Jensen不等式；零点处的不可积性使得Bihari不等式与常微分方程中的比较定理结合在一起从而完成很多结论的证明。

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。

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。第四部分利用了拟变分不等式、伪变分不等式及强变分不等式之间的关系，利用已知的单调广义变分不等式的解的情况来研究拟变分不等式、伪变分不等式及强变分不等式的解的情况，并得出一些重要的理论。

In the long run, the cumulative effect of inequality on investment is negative.（2） Inequality has moderate effect on education, and the cumulative effect is positive.（3） The effect of inequality on investment overweighs its effect on education, so inequality has a strong indirect effect on growth instantaneously. The effect turns positive and then weakly negative.

研究发现：（1）收入差距在即期对投资有非常强的负面影响，之后影响变为正，再逐渐下降至微弱的负，从长期来看，收入差距对投资的累积影响始终为负；（2）收入差距对教育的影响较弱，其累积影响始终为正；（3）由于投资对于经济增长的作用超过了教育，因此收入差距对于经济增长的间接影响主要来自于投资的渠道。

Although translator has turned from being a crystal ball by which the original culture can unrestrainedly penetrate to another crystal ball by which the target culture can freely traverse, the translator's personal embodiment, in the process of cognitive act, are still absent in translation studies. Translators are still subjects without body or simply disembodied subjects.

译者虽然由原语文化可以自由穿透的玻璃球变成了译语文化可以自由穿越的玻璃球，但译者认知过程中的个体体验在翻译研究中依然缺席，译者依然仅仅是一个没有躯体体验的主体。

Chillingly, he claimed our technology is 'not nearly as sophisticated' as theirs and "had they been hostile", he warned 'we would be been gone by now'.

令人毛骨悚然的，他声称我们的技术是'并不那么复杂，像他们一样，和"如果他们敌意"，他警告说，'我们将现在已经过去了。