关于半离散单调核逆向的Hilbert型不等式

应用权系数的方法及参量化思想,建立了两个具有同样最佳常数因子的、半离散且单调核逆向的Hilbert型不等式,还考虑了其等价式     

对偶Brunn-Minkowski不等式的逆

20世纪80年代Milman曾指出:反向Brunn-Minkowski不等式是凸几何的一个深刻的结果.考虑了对偶情况,建立了一个反向的对偶Brunn-Minkowski不等式.进一步,均值积分差的反向对偶Brunn-Minkowski型不等式也被建立.     

Reverse Inequalities for Subelliptic Functions

Mathematical Notes - We study a wedge $$mathscr{K}(A)$$ of solutions of the inequality $$A(u) ge 0$$ , where $$A$$ is a linear elliptic operator of order $$2m$$ . For the elements of the wedge,...     

两个著名不等式的加强式及其反向不等式

从一对离散型双向不等式出发，推广到相应的积分型双向不等式，然后通过代换，获得积分型Holder不等式和积分型H．Minkowski不等式的加强式及其反向不等式，从而拓广其应用范围。     

Operator Inequalities Reverse to the Jensen Inequality

Mathematical Notes -     

常曲率平面上的逆Bonnesen型不等式

利用积分几何中估计包含测度的思想给出常曲率平面上一些新的逆Bonnesen型不等式.这些不等式在欧氏平面上为著名的Bottema不等式的改进形式与新的逆Bonnesen型不等式.     

关于Polya-Szegoe不等式

本文给出两个改进的不等式,使改进后的每一个新的不等式均含有Polay-Szeg（o）两个不等式改进在内.     

平面Bonnesen型不等式

将用积分几何方法给出平面等周不等式以及Bonnesen型不等式,平面区域D的面积、周长、最大内接园半径及最小外接园半径的一些几何不等式的简单证明.     

On Quasimonotone Variational Inequalities

In this paper, we study variational inequalities with multivalued mappings. By employing Fan's lemma, we establish the existence result for the dual formulation of variational inequalities with semistrictly quasimonotone mappings. We also show that similar results for quasimonotone variational inequalities do not hold.     

矩阵的几个不等式

利用谱分解定理和几个标量不等式,得到了矩阵加权几何均值和酉不变范数的几个不等式,它们是Kittaneh和Manasrah所得相关结果的改进.     

On Multidimensional Ostrowski-Type Inequalities

Ukrainian Mathematical Journal - Sharp Ostrowski-type inequalities are proved for multidimensional sets and functions of bounded variation.     

On Simultaneous Diagonal Inequalities

Let F₁, ..., F_t be diagonal forms of degree k with real coefficientsin s variables, and let be a positive real number. The solubilityof the system of inequalities |F₁(x)|<,...,|F_t(x)|< in integers x₁, ..., x_s has been considered by a number of authorsover the last quarter-century, starting with the work of Cook[9] and Pitman [13] on the case t = 2. More recently, Brüdernand Cook [8] have shown that the above system is soluble providedthat s is sufficiently large in terms of k and t and that theforms F₁, ..., F_t satisfy certain additional conditions. Whathas not yet been considered is the possibility of allowing theforms F₁, ..., F_t to have different degrees. However, with therecent work of Wooley [18,20] on the corresponding problem forequations, the study of such systems has become a feasible prospect.In this paper we take a first step in that direction by studyingthe analogue of the system considered in [18] and [20]. Let₁, ..., _s and µ₁, ..., µ_s be real numbers such thatfor each i either _i or µ_i is nonzero. We define the forms and consider the solubility of the system of inequalities in rational integers x₁, ..., x_s. Although the methods developedby Wooley [19] hold some promise for studying more general systems,we do not pursue this in the present paper. We devote most ofour effort to proving the following theorem.     

关于几个新不等式

本文利用Redheffer不等式,Jordan不等式和Jensen不等式给出了一些新的不等式作为应用推广了文[1]的一个结果。     

On Quasimonotone Variational Inequalities

The purpose of this paper is to prove the existence of solutions of the Stampacchia variational inequality for a quasimonotone multivalued operator without any assumption on the existence of inner points. Moreover, the operator is not supposed to be bounded valued. The result strengthens a variety of other results in the literature.     

On Vector Integral Inequalities

The first author introduced an integration theory of vector functions with respect to an operator-valued measure in complete bornological locally convex vector spaces. In this paper some important results behind this Dobrakov-type integration technique in non-metrizable spaces are given. Received: December 10, 2007., Accepted: May 6, 2008.     

华罗庚－王中烈型不等式

用控制不等式理论和动态规划方法推广了华罗庚-王中烈的不等式，并建立了类似的其他结果．     

目标流形为Heisenberg群能量极小映射的逆Poincaré不等式

研究目标流形为Heisenberg群能量极小映射的性质, 得到关于能量极小映射的逆Poincaré不等式.     

On Reverse Hypercontractivity

We study the notion of reverse hypercontractivity. We show that reverse hypercontractive inequalities are implied by standard hypercontractive inequalities as well as by the modified log-Sobolev inequality. Our proof is based on a new comparison lemma for Dirichlet forms and an extension of the Stroock–Varopoulos inequality. A consequence of our analysis is that all simple operators ${L = Id - \mathbb{E}}$ as well as their tensors satisfy uniform reverse hypercontractive inequalities. That is, for all q < p < 1 and every positive valued function f for ${t \geq \log \frac{1-q}{1-p}}$ we have ${\| e^{-tL}f\|_{q} \geq \| f\|_{p}}$ . This should be contrasted with the case of hypercontractive inequalities for simple operators where t is known to depend not only on p and q but also on the underlying space. The new reverse hypercontractive inequalities established here imply new mixing and isoperimetric results for short random walks in product spaces, for certain card-shufflings, for Glauber dynamics in high-temperatures spin systems as well as for queueing processes. The inequalities further imply a quantitative Arrow impossibility theorem for general product distributions and inverse polynomial bounds in the number of players for the non-interactive correlation distillation problem with m-sided dice.     

目标流形为Heisenberg群能量极小映射的逆Poincardé不等式

研究目标流形为Heisenberg群能量极小映射的性质,得到关于能量极小映射的逆Poincaré不等式.     

Reverse Functional Inequalities and Their Applications to Nonlinear Elliptic Boundary Value Problems

We establish some reverse inequalities. We give applications to nonlinear elliptic boundary value problems containing a parameter which have two branches of solutions u (0) and U (>0) of which the first is continuous at the origin and the second increases indefinitely as 0.