同心圆的性质

如果几个圆的圆心是同一点,那么这几个圆就叫做同心圆,借助于圆幂定理可以得到同心圆的如下几个美妙的性质:     

问题

问题176 切点算几个公共点？二重根算几个根？     

三元调和函数的几个性质

在几个引理的基础上,利用曲面积分的性质证明了三元调和函数的几个性质.     

线性Hamilton系数的几个辛格式

本文利用二次Pad啨逼近的几个结果构造了线性Ｈａｍｉｌｔｏｎ系数的几个辛格式     

二阶非线性椭圆型微分方程解的振动比较定理

建立几个微分不等式,讨论了一类二阶非线性椭圆型微分方程解的振动性,得到几个新的振动比较定理．     

Banach空间值鞅上的拟局部算子

本文研究了拟局部算子在几个Banach空间值鞅空间上的有界性.给出了几个有界性定理,证明了鞅空间的简单原子分解.得到几个极大算子和p均方算子的一系列鞅不等式以及鞅空间的包含关系.     

浅析常数K值法在中值等式证明中的应用

本文引入k值法,找到合适的辅助函数,证明中值等式,并建立了几个新的结论及几个应用.     

一类矩阵的对角化

利用关于矩阵秩的几个引理，以及方阵A的多项式f（A）=0时，A可对角化的几个命题，进一步讨论一类矩阵可对角化的两个充分条件．     

对几个数学问题的思考

有几个常见的数学问题流传很广,长期以来,有些老师以及某些数学参考资料对这些问题的分析与解答有的有误,有的分析片面,对学生造成很不好的影响.笔者认为,现在有必要对这几个问题予以澄清,以正视听.下面谈谈笔者对这几个问题的思考.     

方程在数列中的应用

在学习数学归纳法时,我发现以下几个公式:这几个公式也就是通项公式为的数列的前n项和公式.仔细观察这几个数列,不难发现它们有一个     

On several new Hilbert-type inequalities involving means operators

In this paper, we establish several new Hilbert-type inequalities with a homogeneous kernel, involving arithmetic, geometric, and harmonic mean operators in both integral and discrete case. Such inequalities are derived by virtue of some recent results regarding general Hilbert-type inequalities and some well-known classical inequalities. We also prove that the constant factors appearing in established inequalities are the best possible. As an application, we consider some particular settings and compare our results with previously known from the literature.     

Operator-norm inequalities and interpolated trace inequalities

In this article, we investigate some operator-norm inequalities related to some conjectures posed by Hayajneh and Kittaneh that are related to questions of Bourin regarding a special type of inequalities referred to as subadditivity inequalities. While some inequalities are meant to answer these conjectures, other inequalities present reverse-type inequalities for these conjectures. Then, we present some new trace inequalities related to Heinz means inequality and use these inequalities to prove some variants of the aforementioned conjectures.     

On some dynamic inequalities of Steffensen type on time scales

In the present article, we investigate some new inequalities of Steffensen type on an arbitrary time scale using the diamond‐α dynamic integrals, which are defined as a linear combination of the delta and nabla integrals. The obtained inequalities extend some known dynamic inequalities on time scales and unify and extend some continuous inequalities and their discrete analogues.     

离散型Carlson's不等式的一些推广及改进

In this paper, we consider Carlson type inequalities and discuss their possible improvement. First, we obtain two different types of generalizations of discrete Carlson's inequality by using the Hlder inequality and the method of real analysis, then we combine the obtained results with a summation formula of infinite series and some Mathieu type inequalities to establish some improvements of discrete Carlson's inequality and some Carlson type inequalities which are equivalent to the Mathieu type inequalities. Finally, we prove an integral inequality that enables us to deduce an improvement of the Nagy-Hardy-Carlson inequality.     

Merit functions for general mixed quasi-variational inequalities

In this paper, we present some merit functions for general mixed quasi-variational inequalities, and we obtain the equivalent optimization problems to general mixed quasi-variational inequalities. Since the general mixed quasi-variational inequalities include general variational inequalities, quasi-variational inequalities and nonlinear (implicit) complementarity problems as special cases, our results continue to hold for these problems. In this respect, results obtained in this paper represent an extension of previously known results.     

Sequential pairing of mixed integer inequalities

We investigate a scheme, called pairing, for generating new valid inequalities for mixed integer programs by taking pairwise combinations of existing valid inequalities. The pairing scheme essentially produces a split cut corresponding to a specific disjunction, and can also be derived through the mixed integer rounding procedure. The scheme is in general sequence-dependent and therefore leads to an exponential number of inequalities. For some important cases, we identify combination sequences that lead to a manageable set of non-dominated inequalities. We illustrate the framework for some deterministic and stochastic integer programs and we present computational results showing the efficiency of adding the new generated inequalities as cuts.     

Some inequalities involving π and an application to Hilbert''s inequality

Some inequalities involving π are proved. As an application, we give some strengthened Hilbert's inequalities.     

关于正定矩阵的两个不等式

通过Hermite矩阵的谱分解及一个改进的Young不等式,得到了关于正定矩阵的两个不等式,所得结果是对一些经典的矩阵不等式的进一步推广.最后,作为应用,给出了著名的Holder不等式和Minkowsi不等式的一种反向形式.     

A Unified Treatment of Half-Discrete Hilbert-Type Inequalities with a Homogeneous Kernel

In this paper we provide a unified treatment of half-discrete Hilbert-type inequalities with a general homogeneous kernel. The main results are proved for the case of non-conjugate exponents. A special emphasis is given to determining conditions under which these inequalities include the best possible constants. As an application, we consider some operator expressions closely connected to established inequalities. Finally, we also provide improvements of derived half-discrete inequalities by virtue of the Hermite-Hadamard inequality.     

Functional inequalities for the Wright functions

In this paper, our aim is to show some mean value inequalities for the Wright function, such as Turán-type inequalities, Lazarevi?-type inequalities, Wilker-type inequalities and Redheffer-type inequalities. Moreover, we prove monotonicity of ratios for sections of series of Wright functions, the result is also closely connected with Turán-type inequalities. In the end of the paper, we present some other inequalities for the Wright function.