广义Gr(o)tzsch环函数的近似凹凸性

In this paper, the so-called approximate convexity and concavity properties of generalized Groetzsch ring function μa （r） by studying the monotonieity,convexity or concavity of certain composites of μa（r） are obtained.     

有限偏差映射的加权Grotzsch问题

考虑如下的极值问题: $$ \inf_{f\in \mathcal{F}}\iint_{Q_{1}}\varphi(K(z,f))\lambda(x)|\rmd z|^{2}, $$ 其中$\mathcal{F}$ 是从矩形$Q_1$ 到矩形$Q_2$ 并保持端点且具有有限线性偏差 $K(z,f)$的所有同胚映射$f$的集合, $\varphi$ 是正的严格凸的递增函数, 而$\lambda(x)$ 是正的加权函数. 作者在文``{\it Sci China Math}, 2016, 59(4):673--686''中证明了当 $\varphi''$ 无界时, 上述极值问题存在唯一的极值映射$f_{0}(z)=u(x)+\rmi y$. 本文考虑$\varphi''$ 有界的情形, 得到如下结果: 当$Ll$ 时, 极值映射可能不存在. 借助于 Martin 和 Jordens 的方法, 构造了一族最小序列使得其极限达到最小值.     

Hardy-Hilbert型积分不等式的一个推广及其应用

本文讨论带参数的Hardy-Hilbert型积分不等式.利用改进了的Hlder不等式对它进行了推广,作为其应用,给出了Hardy-Littlewood不等式的推广.     

On the Distribution of Integral Ideals and Hecke Gr¨ossencharacters

The author uses analytic methods to study the distribution of integral ideals and Hecke Grossencharacters in algebraic number fields. Nowak＇s results on the distribution of integral ideals, and Chandrasekharan and Good＇s results on the distribution of Hecke GrSssencharacters are improved.     

On the Distribution of Integral Ideals and Hecke Gr(o)ssencharacters

The author uses analytic methods to study the distribution of integral ideals and Hecke Gr(o)ssencharacters in algebraic number fields.Nowak's results on the distribution of integral ideals,and Chandrasekharan and Good's results on the distribution of Hecke Gr(o)ssencharacters are improved.     

拟共不变集和拟圆的特征

证明了ＮＥＤ集在拟共形映照下的像仍是ＮＥＤ集，建立了关于拟圆的一个充分必要条件。     

一个二阶方程的振动性质及其应用

本文研究了一个二阶微分方程的解及其振动性质,利用它获得了一般二阶自共轭方程的振动性判别准则,特别对其中一类二阶微分方程的振动性给出了定量的判别方法.推广了E.Hille的工作,使E.Hille的研究结论成为本文结果的极特殊的情形,同时对一类具有“积分小”系数或可化为具有“积分小”系数的二阶微分方程的振动性与非振动性给出了简便、精确的判别方法.     

SOME PROPERTIES OF CENTROSYMMETRIC MATRICES AND ITS APPLICATIONS

In this paper, some properties of centrosymmetric matrices, which often appear in the construction of orthonormal wavelet basis in wavelet analysis, are investigated. As an application, an algorithm which is tightly related to a so-called Lawton matrix is presented. In this algorithm, about only half of memory units are required and quarter of computational cost is needed by exploiting the property of the Lawton matrix and using a compression technique, it is compared to one for the original Lawton matrix.     

Grobner-Shirshov Basis for Degenerate Ringel-Hall Algebras of Type F4

In this paper, by using the Frobenius morphism and the multiplication formulas of the generic extension monoid algebra, the authors first give a presentation of the degenerate Ringel-Hall algebra, and then construct the Gr\"{o}bner-Shirshov basis for degenerate Ringel-Hall algebras of type $F_4.$     

G_2型量子群的Gelfand-Kirillov维数

用Gr(o|¨)bner-Shirshov基和PBW代数方法来计算G_2型量子群的Gelfand.Kirillov维数.得到的结论是G_2型量子群的Gelfand-Kirillov维数为14.     

弱拟凸集的一些性质及其应用

在文[1]中,我们提出了赋范线性空间中伪凸、弱拟凸等广义凸集的概念,并探究了其逼近性质.本文将给出[1]中所提出的广义凸集中最弱的一种集——弱拟凸集的最佳逼近特征、强唯一性及弱拟凸集的强分离定理.并把所获的结果应用到 L_p(T,m)空间中去,得到了 L_1(T,m)空间中最佳逼近的特征和唯一性及 L_p(T,m)(1相似文献   

ON THE SPECTRAL PROPERTIES OF M-MATRICES AND ITS APPLICATIONS

1.IntroductionAndPreliminariesThespectralpropertiesofM-matricesplayanimportantroleinnonnegativemainstheory,andhavebeenappliedtostudythenumericalsolutionoflinearsystems.Recentlylmanyarticleshavediscussedwiththistopics(see[l--5]).ThepurposeofthispaperistoestablishthespectralinequalitiesofsingularM-matrices.ByapplyingthesepropertiesweanswerpartiallyanopenproblemandsolveanopenproblemposedbySchneiderin[4,5],somerecelltresultI2'4'6]onsplittingsofanM-matrixarealsoimproved.Allnotationsanddefinitio…     

求首尾和r-循环矩阵的极小多项式的算法

研究了域上首尾和r-循环矩阵，利用多项式环的理想的Groebner基的算法给出了任意域上首尾和r-循环矩阵的极小多项式和公共极小多项式的一种算法.同时给出了这类矩阵逆矩阵的一种求法。     

SUPERAPPROXIMATION PROPERTIES OF THE INTERPOLATION OPERATOR OF PROJECTION TYPE AND APPLICATIONS

AbstractSome superapproximation and ultra-approximation properties in function, gradient and two-order derivative approximations are shown for the interpolation operator of projection type on two-dimensional domain. Then, we consider the Ritz projection and Ritz-Volterra projection on finite element spaces, and by means of the superapproximation elementary estimates and Green function methods, derive the superconvergence and ultraconvergence error estimates for both projections, which are also the finite element approximation solutions of the elliptic problems and the Sobolev equations, respectively.     

Sets of minimal Hausdorff dimension for quasiconformal maps

For any , there is a compact set of (Hausdorff) dimension whose dimension cannot be lowered by any quasiconformal map . We conjecture that no such set exists in the case . More generally, we identify a broad class of metric spaces whose Hausdorff dimension is minimal among quasisymmetric images.

     

单形中面的性质及其应用

本文首先给出单形中面的概念，得到了单形中面的一些性质，作为其应用，建立了涉及单形中面的两个不等式。     

求鳞状循环因子矩阵的极小多项式的算法

提出了任意域上鳞状循环因子矩阵 ,利用多项式环的理想的Go bner基的算法给出了任意域上鳞状循环因子矩阵的极小多项式和公共极小多项式的一种算法 .同时给出了这类矩阵逆矩阵的一种求法 .在有理数域或模素数剩余类域上 ,这一算法可由代数系统软件Co CoA4 .0实现 .数值例子说明了算法的有效性     

Ekeland变分原理的推广及其应用

本文给出一般形式的Ekeland变分原理,并讨论泛函强制性条件与一般形式的 (PS)’条件之间的关系.     

Estimation for the Dilatation of the Generalized Beurling-Ahlfors' Extension

51.IntroductionLethbeahomeomorphismontherealaxisR,andsatisfyh(lco)=loo.Wecallaquasisymmetricfunction.lfthereexistsa'constantMsuchthatM-1Sp(x,t)SM,x,teR,(l.2)then(1.2)iscalledtheM-condition-Byvirtueoftheclassicresultofpaper[lj,ifp(x,t)sat-isfiestheM-condition,thenthereexistsaK(M')-quasiconformaIextensiononthel1alfplaneH,whichisthewell-knownBeurling-Ahlfors'extension:ytz)=u(x,y) iv(x,y),whereAfterpaper[lj,manyworkshavebeendoneforestimatingK-Particularly,itshouldbere-markedheretl1atM.Leht…