查询词典 integral inequality

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 Taylor formula holds the very important status in the differential calculus, especially in solves in some concrete problems to have the extremely important application, for instance the proof inequality, the judgment improper integral collects the divergence, asks the function the limit, asks the function the higher order derivative, determines certain complex progressions to collect the divergence, solves certain differential equation, as well as approximate calculation in and so on application, therefore this article will do the thorough research to these seven aspects.

摘 要：泰勒公式在微分学中占有非常重要地地位，尤其在处理1些具体的茄题中有10分重要的应用，比如证明不等式，判断广义积分的敛散性，求函数的极限，求函数的高阶导数，判定某些复杂级数的敛散性，求解某些微分方程，以及近似计算等中的应用，因此本文将对这七个方面做深入的研究。关键词：泰勒公式；不等式；广义积分；极限；高阶导数；复杂级数；微分方程

To avoid this, a robustness index is proposed as a replacement for the gain margin. Optimal controller design is the achievable by minimizing a designated error integral criterion for a load disturbance subject to inequality constraints on phase margin and the new robustness index.

因此，本文提出一强韧性指标来取代传统的增益边距，最佳强健控制器即可在相位边距和此指标的不等式限制下，透过将负载扰动产生之特定误差积分最小化来取得。

By means of the Hausdorff-Young inequality of convolution integral, the convergence of the updating rule is analyzed in the sense of Lebesgue-p norm. Invention of the nonlinearity and the interaction on convergence are discussed.

通过卷积的 Hausdorff-Young 不等式，本文分析了学习控制律在 Lebesgue-P 范数意义下的收敛性，讨论了系统的非线性性和关联性对控制律收敛性的影响。

Singular perturbation of three-point boundary value problem for third order nonlinear equation is studied by using of Volterra type integral operator and differential inequality techniques.

讨论了三阶非线性微分方程三点边值问题的奇摄动。

If any part of the cyclic process is irreversible,the inequality applied and the cyclic integral is negative.

a若回圈的任一部份包括不可逆自发的步骤，则回圈的积分为负，且不等式即成立。

In Chapter Ⅲ, by considering functions H k that may not have nonpositive partial derivative on s and employing integral averaging technique and Hardy inequality, the oscillation for a class of high order nonlinear differential equations and high order nonlinear damped differential equations is discussed, new oscillation criteria are established.

第二章利用广义Riccati技巧、积分平均技巧以及微分不等式理论，讨论了一类二阶非线性常微分方程的振动性，得到了若干新的振动准则，并讨论了该方程具有强迫项时解的渐近性态。

Main results:(1) For the stochastic Volterra type integral equation with singular kernels,it is the first time to be investigated under non-Lipschitz conditions. The existence-uniqueness and Hlder\'s continuity are established.Here,an extended Minkowski\'s inequality plays a key role.

主要结论：(1)关于具有奇异核的随机Volterra型积分方程，我们首次在非Lipschitz条件下进行研究，得到解的存在唯一性和Hlder连续性(此处证明的一个关键步骤应用了推广的Minkowski不等式)。

Direct and inverse theorems of approximation by this kind of operators are discussed, and the Jackson—type integral estimation of approximation and Steckin — Marchaud inequality of weak type of uniform approximation for these operators are obtained.

讨论了一元Bernstein型算子的逼近正逆定理，建立了该算子逼近的Jackson型积分估计式和一致逼近的弱Steckin-Marchaud型不等式。

Using the new comparative method, the variation of constants formula, M-matrix theory, integral differential inequality, new theoretical results on global exponential stability of neural networks with bounded time-varying delays and Lipschitz continuous activation functions have been obtained.

利用新的比较方法的思想，改进了一维线性和非线性纯时滞微分系统的3/2稳定性定理，推广了Yorke条件到具两个时滞项的情形，将Yorke等人的3/2稳定性定理推广到具两个时滞项的线性和非线性纯时滞微分系统，进一步还推广到N维纯时滞微分系统，为纯时滞神经网络的研究打下理论基础。

This one mode pays close attention to network credence foundation of the businessman very much.

这一模式非常关注商人的网络信用基础。

Cell morphology of bacterial ghost of Pasteurella multocida was observed by scanning electron microscopy and inactivation ratio was estimated by CFU analysi.

扫描电镜观察多杀性巴氏杆菌细菌幽灵和菌落形成单位评价遗传灭活率。