Hadamard's inequality and Trapezoid Rules for the Riemann-Stieltjes integral

We obtain Midpoint and Trapezoid Rules for the Riemann-Stieltjes integral which engender a natural generalization of Hadamard's integral inequality. Error terms are then obtained for this Riemann-Stieltjes Trapezoid Rule and other related quadrature rules.     

分数次积分下关于s-凸函数的新Hermite-Hadamard型不等式

建立了一个关于Riemann-Liouville分数次积分的恒等式,利用此恒等式,得到了一些函数为可微且s-凸映射的关于分数次积分的新Hermite-Hadamard型积分不等式,并且对于可微的s-凹函数也得到一些新的结果.文中的新结果推广了部分已有研究的结论.最后给出了一个应用实例.     

两类Hadamard型不等式的推广

通过引入两个函数,讨论了它们的凸性和单调性,由此得到下凸函数的Hadamard不等式的改进,推广了有关文献的结果.又根据GA-下凸函数与下凸函数的关系,得到GA-凸函数的Hadamard不等式的改进与推广.     

Some Improvements on Hermite-Hadamard's Inequalities for $s$-Convex Functions

Using an integral identity for a once differentiable mapping, this paper establishes Hadamard's integral inequalities for $s$-convex and $s$-concave mappings. In particular, our results improve and extend some known ones in the literature. Finally, these inequalities are applied to special means.     

Some inequalities of Hermite-Hadamard type for s-convex functions

In this paper several inequalities of the left-hand side of Hermite-Hadamard’s inequality are obtained for s-convex functions.     

关于HADAMARD不等式的注记

本文主要研究一类Ｆ－矩阵的性质，这类矩阵包含对称半正定矩阵，完全非负矩阵，τ矩阵和Ｍ－矩阵为其子类。我们不仅对Ｆ－矩阵改进了Ｈｄａｍａｒｄ不等式，而且证明对此类矩阵Ｈａｄａｍａｒｄ不等式成立等式的充要条件是它的每条对角线，除主对角线外，都含有零元。     

The BEM analysis on bending fracture problem of thin plate

In this paper, based on Betti's reciprocal theorem, a set of boundary integral equations of thin plate with a crack is introduced. These boundary integral equations can be used to solve the bending fracture problem of thin plate. In the analysis process a higher-order singular integral equation will be induced. Using the concept of the Hadamard's principal value the higher-order singular integral can be solved conveniently. By this method we have found the analytical solution of a thin plate with a straight crack under pure bending load and indicated how to use the BEM to analyze the bending and fracture problem for thin plate with a straight crack. At the end of the paper some numerical examples are given. Numerical results show the accuracy and efficiency of the algorithms.     

一个加强的Hardy-Hilbert型不等式

引入独立参数,应用权系数的方法及Hadamard不等式,建立了一个加强的具有最佳常数因子的Hardy-Hilbert型不等式及其等价形式.     

一个新的与Hadamard不等式相关的映射

对于一个最近发表的凸函数的Hadamard不等式的推广形式的不等式,本文引进了—个与这个不等式相关的的映射,从而给出了该不等式连续的加细.同时提及了它的某些应用.     

Integrability for the Jacobian of orientation preserving forms

This paper considers the integrability for the Jacobian of orientation-preserving forms in anisotropic Sobolev classes. The main result is a sufficient condition ensuring integrability of the Jacobian, which can be regarded as a refinement of the result of Iwaniec and Sbordone.