一个三角形几何不等式的推广

首先从第3届国际数学奥林匹克IMO竞赛命题中一个三角形几何不等式出发,将问题推广到对更一般的三角几何不等式及多边形几何不等式的研究.然后利用凸函数的Jensen不等式,得到更一般的三角形几何不等式及圆外切多边形几何不等式,推广了原命题.     

关于三个未解决的不等式问题

通过求二阶导数或列举反例的方法可解决《常用不等式（第四版）》末尾提出的问题3、问题13和问题62,另外,利用Lyapunov不等式及Moran不等式可给出其问题190中一个不等式的下界.     

A Note on Some Inequalities of $GG$-$E$-Convexity

In this paper, we define GG-E-convexity and GG-E-concavity. We also establish some inequalities in relation to GG-E-convex function using various integral inequalities with enough examples of various categories, which verifies our results.     

The Berezin and Garding Inequalities

Let ? be a convex function on ?, let ?(σ) be a pseudodifferential operator with symbol σ, let Λ_σ be the set of its eigenvalues, and let m(λ) be the multiplicity of an eigenvalue λ ∈ Λ_σ. Under certain natural assumptions about properties of pseudodifferential operators, we prove that \(\sum {_{\lambda \in \Lambda _\sigma } m(\lambda )} \varphi (\lambda ) \leqslant \operatorname{Tr} L(\varphi (\sigma )) + R\), where R is an error term of the same order as the remainder term in the Garding inequality.     

三角形Toeplize矩阵的三角本原指数

讨论了三角形 Toeplize矩阵与一元多项式的关系以及非负三角形 Toeplize矩阵的三角本原指数 ,证明了 n阶非负上三角 Toeplize矩阵的三角本原指数集 Sn={1 ,2 ,… ,k-1 ,k,k1,k2 ,… ,ks,n-1 },其中 k是满足 k >4n -3 -12 和 n -1k +1 =n -1k 的最小整数 .     

A Class of Schur Convex Functions and Several Geometric Inequalities

Schur convexity, Schur geometrical convexity and Schur harmonic convex-ity of a class of symmetric functions are investigated. As consequences some known inequalities are generalized. In addition, a cl...     

Free Triangle Orders

We define a new class of ordered sets, called free triangle orders. These are ordered sets represented by a left-to-right ordering on geometric objects contained in a horizontal strip in the plane. The objects are called 'free triangles', and have one vertex on each of the two boundaries of the strip and one vertex in its interior. These ordered sets generalize the classes of trapezoid and triangle orders studied by Bogart, Möhring, and Ryan, represented by trapezoids and triangles respectively, contained within a strip in the plane, and are a special case of the orders of tube dimension 2 introduced by Habib and co-workers, which are represented by any set of convex bodies contained within a strip in the plane. Our main result is that the class of free triangle orders strictly contains the class of trapezoid orders.     

一类加强不等式的推广

本文给出了 n个正数 x1 ,x2 ,… ,xn 的如下不等式 :∏nk=1( xαk+x-αk )≥ ( Aαn( x) +A-αn ( x) ) n ,每个 xk≤ xα,∏nk=1( xαk+x-αk )≤ ( Aαn( x) +A-αn ( x) ) n ,每个 xk≥ e.其中 α>0 ,xα=[4α2 +1 +2 α]12α ,常数 e=2 .71 81 82 81 8… ,An( x) =1n∑nk=1xk.     

基于三角基的网格形状变形

研究了在散乱数据的三角剖分后对所形成的空间三角形网格进行变形的具体操作算法.首先给出描述三角形网格各顶点空间位置的内在结构矩阵,然后插值于相应的结构矩阵,实现三角形网格之间的形状变形.该文的另一个特点是引入三角基函数作为混合函数,得到了更优的结果.     

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.     

凸函数的几个Hadamard型不等式

对于凸函数建立了几个新的 Hadamard型不等式 ,比如f ∑nk=1qkak∫A+yA- yg(x) dx ∫A+yA- yf (x) g(x) dx ∑nk=1qkf (ak) ∫A+yA- yg(x) dx和f (pa +qb) p∫ξaf (x) g(x) dx∫ξag(x) dx+q∫bξf (x) g(x) dx∫bξg(x) dx pf (a) +qf (b)等 ,推广了前人所做的工作 .     

关于凸函数的一般平均不等式

本文提出并证明了凸函数的最一般的平均不等式 ,是凸函数的幂平均、双参数平均不等式的进一步推广     

关于凸函数的新不等式

考虑由Fejér不等式的右边部分生成的差值.通过建立积分恒等式,在导函数满足M-Lipschitz条件和导函数有界这两种情况下,给出这个差值的界的估计.     

华罗庚--王中烈型不等式的矩阵形式及推广

本文对华罗庚~- 王中烈型不等式进行了研究.利用矩阵方法给出了一些已有的华罗庚~- 王中烈型不等式的简单证明和推广,并得到了一些新的华罗庚~- 王中烈型不等式.     

凸函数的Hadamard不等式的若干推广

本文获得两个定理 ,它们均是不等式f a +b2 1b -a∫baf (x) dx f (a) +f (b)2(其中 f是 [a,b]上的连续凸函数 )的推广 .     

Fibonacci三角形

利用 Pell方程和递推序列的方法证明了在 k=1 ,2 ,3 ,4,5时 ,以 Fibonacci数 Fn,Fn,Fn- k为边的Fibonacci三角形不存在 .     

Covering the Hecke Triangle Surfaces

In the mid-1980s an equivalence was established between the simple closed geodesics on the Riemann surfaces obtained as quotients of the upper half plane H by any of the following subgroups of the modular group (1) : , (3), and ³. An axis of a hyperbolic element of (1) projects to a simple closed geodesic on one of these surfaces if and only if it does so on the other two.This equivalence was used to obtain a variety of Diophantine and geometric results. In subsequent related investigations, the role of (1) was assumed by the Hecke triangle group G_q for q 3. (For q = 3, we have (1) = G₃.) These works employed the analog of ³, denoted _q.In the context of the G_q, the present paper gives the analog of , which we denote _q. As in the case q = 3, we have [_q:_q] = 2. A rather full discussion of geometry of _q\ H is given. In particular, we demonstrate that the equivalence of simple closed geodesics on _q\ H and _q\ H does not hold for q 7.As of this writing, we have not been able to obtain an appropriate analog of (3).     

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.     

Inequalities for the Gamma function and estimates for the volume of sections of

Let and let be a -dimensional subspace of . We prove that , for and whenever . We also consider and other related cases. We obtain sharp inequalities involving Gamma function in order to get these results.

     

The Generalization on Inequalities of Hermite-Hadamard's Integration

Some new inequalities of Hermite-Hadamard's integration are established.As for as inequalities about the righthand side of the classical Hermite-Hadamard's integral inequality refined by S Qaisar in [3],a new upper bound is given.Under special conditions,the bound is smaller than that in [3].