积分不等式

Convex body; star body; Brunn-Minkowski inequality; dual harmonic quermassintegrals; dual affine quermassintegrals; dual mixed bodies; affine surface area; isotropic measure

基础科学，数学，几何、拓扑凸体；星体； Brunn-Minkowski不等式；对偶调和均质积分；对偶仿射均质积分；对偶混合体；仿射表面积；迷向测度

In chapter 3, we study the Bihari type inequality of integral equation with retarded term, we consider the inequality of integral equation as follows:In this section we will get some new result about the inequality (3.1.1) on t_0,∞.

我们考虑了下面的积分方程不等式这节我们将得到不等式(3.1.1)在t_0，∞上的一些新结论，同时将给出一个反例，修正了文

Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwalls type, an energy inequality is got and a priori estimate is established.

接下来经过分部积分和Cauchy不等式，并利用Gronwall型引理得到一个能量不等式，对解的范数给出先验估计。

Secondly, through integrating by parts and using Cauchy inequality, thanks to a lemma of Gronwall's type, an energy inequality is got and a priori estimate is established.

接下来经过分部积分和Cauchy不等式，并利用Gronwall型引理得到一个能量不等式，对解的范数给出先验估计。

Based on the higher mathematics method proved inequalities are summarized, and the proposed using the function extreme value and the monotonicity and concave and convex function sex, and mean value theorem, Taylor formula, integral these common higher mathematics method, combining with concrete examples of each kind of method to solve the problems for type, and the key problem of the specific steps, and points out that the inequality proof of higher mathematics method used properly, improve the difficult easy to ability to solve problems.

本文对不等式证明中的高等数学方法作了归纳总结，提出了利用函数的单调性，极值与最值，函数凹凸性，中值定理，泰勒公式，积分这些常用的高等数学方法，并结合具体实例阐述了每一种方法的适用类型、解决问题的关键和证明问题的具体步骤，指出在不等式证明中恰当地运用高等数学方法可以化难为易，提高解题能力。

The main results are as follows: the relations between local fractional integrated semigroups and the corresponding Cauchy problem, global fractional integrated semigroups and regularized semigroups are given; introduction of the notion of regularized resolvent families, and the generation theorem and analyticity criterions for regularized resolvent families are obtained; the spectral inclusions between fractional resolvent family and its generator, and the approximation for fractional resolvent families in the cases of generators approximation and fractional orders approximation; elliptic operators with variable coefficients generating fractional resolvent family on L^2 by using numerical range techniques; and the L^p theory for elliptic operators with real coefficients highest order are obtained by Sobolev''s inequalities and the a priori estimates for elliptic operators; and a kind of coercive differential operators generates fractional regularized resolvent family by applying the Fourier multiplier method, functional calculus and some basic properties of Mittag-Leffler functions.

主要结论是：给出了局部分数次积分半群和相应的Cauchy问题的关系以及分数次积分半群和正则半群的关系；引入了正则预解族的概念，并给出了其生成定理和解析生成法则；给出了分数次预解族与其生成元的谱包含关系，并研究了在生成元逼近和分数阶逼近两种情况下相应的预解族的逼近问题；利用数值域方法证明了具变系数的椭圆算子在L^2上生成分数次预解族；利用Sobolev不等式和椭圆算子的先验估计证明了具变系数的椭圆算子在其最高项系数为实数时在L^p上生成分数次预解族；运用Fourier乘子理论、泛函演算和Mittag-Leffler函数证明了一类强制微分算子可以生成分数次正则预解族，并给出了该预解族的范数估计。

Using integral nature, Using integral theorem for inequality proof to find.

利用积分性质；主要利用积分定理来为不等式的证明找到捷径。

This paper considers weighted estimate s of polynomial operator spectra by using the methods of integral,Rayleigh theorem and Schwartz inequality and establishes the inequality of upper bound of the(n+1) spectrum by depending on the former n spectra and the estimated coefficient is independent of the measure of the domain.

考虑多项式算子谱的带权估计，利用分部积分、Rayleigh定理、Schwartz不等式等方法，建立了用前n个谱来估计第n+1个谱的上界的不等式，且其估计系数与区域度量无关。

This thesis works for theoretical study on isoperimetric problem and related inequalities by using theory of geometry analysis, way of integral transformations and analysis inequalities.

本学位论文利用几何分析中的凸体理论，积分变换方法和解析不等式理论，研究了凸体和星体的等周问题和相关的不等式问题。

Study on proof of sum of products equality and its application

给出了积分上限函数在证明等式和不等式、计算累次积分、证明微分中值定理和积分中值定理中的应用。

Do you know, i need you to come back

你知道吗，我需要你回来

Yang yinshu、Wang xiangsheng、Li decang,The first discovery of haemaphysalis conicinna.

1〕 杨银书，王祥生，李德昌。安徽省首次发现嗜群血蜱。