不等式

Retarded term; Impulsive term; Integral inequality; Nonlinear equation; Volterra inequality; Bihari inequality

时滞项；脉冲项；积分不等式；非连续函数； Volterra型不等式； Bihari型不等式

The first model is the optimization problems with s linear objective function subject to a system of fuzzy relation equations and a system of fuzzy relation inequalities, which are solved by using path method and 0-1 integer programming with branch and bound method.

第一种为约束为模糊关系方程和模糊关系不等式的具有线性目标函数的优化问题，采用路径法及0-1整数规划中的分枝定界法对其求解；第二种为约束为模糊关系方程和模糊关系不等式的格线性规划问题，采用直接法、路径法及0-1整数规划法对其求解；第三种为模糊关系不等式为模糊的，即约束中有一个可接受的容差，采用容差法及正负理想法对其求解；第四种是一种新的可能性模糊线性规划问题，采用模糊数大小比较法、"切片-粘贴"法及正负理想法，并设计了随机模拟的遗传算法对其求解；第五种为期望值模型，利用期望值将其转化为清晰约束系数的线性规划问题的方法。

First of all, Cauchy inequality is used to obtain a basic inequality. Secondly, the functions of basis are made by Galerkin method, and the error estimates of eignevalues are obtained by Cauchy inequality. At last, the computational method of the approximate value of the eigenvalues turns out immediately, and accuracy of the-th approximate value is estimated by the n-tb approximate value.

首先利用Cauchy场不等式证明了一个基本不等式；其次采用Galerkin方法来构造适当的基函数，并利用Cauchy不等式给出了其特征值计算的误差佑计式；最后得到计算梁横向振动问题的特征值的近似值的算法，而且可以用第n次近似值来估计第n-1次的近似值的精确度。

In this paper,quadratic form theory,the European space inner product nature and Jensen inequality are three ways to prove cauchy inequality,and bthe relation between Cauchy inequality and higher mathematics was illustrated briefly.

本文运用二次型理论、欧式空间中内积性质和詹森不等式三种方法证明柯西不等式，并简要说明柯西不等式与高等数学之间的联系。

The asymptotic behavior of the weak solution is obtained when an enthalpy function is made in L(superscript 2 subscript +) and a differential inequality is proved after using Cauchy inequality, Poincare inequality and the definition of weak solution.

在L(上标2 下标+)空间上构造了一个熵函数，利用带ε的Cauchy不等式和poincare不等式及弱解的定义，推导出了此函数满足的一个微分方程不等式，通过求解微分方程，证明了弱解的渐近性问题。

Markov's inequality and Chebyshev's inequality are very important in probabilistic theory.

Markov不等式和Chebyshev不等式是概率论中两个重要的不等式。

In order to study the popular curve shortening flow in the plane, Gage[3] has shown in 1983 the following inequality, if k is the signed curvature of a closed convex plane curve γ with length L and enclosing area A, then one gets Gage calls it an isoperimetric inequality in [3], but he does not show that the equality holds if and only if the curve γ is a circle, while as an isoperimetric-type inequality, one should prove this kind of result.

Gage称之为等周不等式，但他没有证明其中等号成立当且仅当，γ为圆周，而作为等周型的不等式是应该证明这种结果的，本文我们利用单位速率外法向量流，通过努力证明了这种结果，从而把Gage不等式加强成更加等周的形式。

Thirdly,quasi-normal inequalities of a-variation maximal operator and a-conditional variation maximal operator of scalar predictable tree martingales areidentified by the use of martingale transforms and by the construction of convex or concave function method;on this basis and with the help of previsiblity or regu-larity,Burkholder-Davis-Gundy\'s inequality of a-variation maximal operator and a-conditional variation maximal operator of scalar predictable tree martingales are iden-tified by the application of Hardy-Lorentz interpolation theory.At the same time,bythe use of G.

再次，应用鞅变换和构造凸或凹函数方法证明了标量值可料树鞅的α-方极大算子和α-条件方极大算子的拟范数不等式；然后，在这些拟范数不等式的基础上，应用Hardy-Lorentz空间插值方法证明了当树鞅是可控或正规树鞅时关于标量值可料树鞅α-方极大算子和α-条件方极大算子的Burkholder-Davis-Gundy's不等式成立。

Especially, we study the applications of Jensen inequality of convex function in proving inequalities.

在此基础上，利用凸函数的Jensen不等式，证明了一些应用初等数学知识难以证明的初等不等式，显示出凸函数在不等式证明中的重要性。

Is in the elementary grade, differential calculus and integral calculuses these three manifestations, look for it in the inside structure and prove the thought up of organic unify;Combine to these are not some application of in other respect equation.

本文主要介绍几个重要不等式如不等式等在初等、微分和积分这三个方面的表现形式，寻找其在内在结构和证明思想上的有机统一；并给出这些不等式在其他方面的一些应用。

Chrysanthemum of 10 thousand birthday is lax to edaphic requirement, with the arenaceous qualitative loam with fecund, good drainage had better.

万寿菊对土壤要求不严，以肥沃。排水良好的砂质壤土为好。

He unstepped the mast and furled the sail and tied it.

他拔下桅杆，把帆卷起，系住。