THE DISTRIBUTION OF LATTICE POINTS IN ELLIPTIC ANNULI

We study the distribution of the number of lattice points lyingin thin elliptical annuli. It has been conjectured by Bleherand Lebowitz that if the width of the annuli tends to zero andtheir area tends to infinity, then the distribution of thisnumber, normalized to have zero mean and unit variance, is Gaussian.This has been proved by Hughes and Rudnick for circular annuliwhose width shrinks to zero sufficiently slowly. We prove thisconjecture for ellipses whose aspect ratio is transcendentaland strongly Diophantine, also assuming the width shrinks slowlyto zero.     

ASYMPTOTIC EXPANSION OF DIRAC-TYPE DISTRIBUTION ASSOCIATED WITH A CLASS OF HYPERSURFACES WITH DEGENERATED CRITICAL POINTS

1IntroductionTheformeran.thorgivesin[4]ageneralizationofHadamardgstheoryoffundamentalsolutionstothecaseofberthorderlinearholomorphicPDEandproveditsidentitywiththedistributionalfundamentalsolution.TheessenceofHadamard'sprocedure[6]istofindfundamentalsolutionintheformofwherek(x)=0istheequationofthecharacteristicconoidwithx=0asthevertex,andk(x)isholomorphicnearx=0.Whentheequationisnon-degenerated,k(x)hasalsoanondegeneratedHessianatx=0.ReplacehAin(1)byhi,(1)givesadistributionwithAasaparameter.…     

凸域与矩形网格交点的分布问题

本文研究了凸域与矩形网格交点的分布问题.通过研究凸域的运动测度,得到了概率分布结果.     

CONFORMAL MEASURES ASSOCIATED TO ENDS OF HYPERBOLIC n-MANIFOLDS

Let be a non-elementary Kleinian group acting on the closedn-dimensional unit ball and assume that its Poincaréseries converges at the exponent . Let M be the -quotient ofthe open unit ball. We consider certain families = {E₁, ...,E_p} of open subsets of M such that is compact. The sets E_i are the ends of M and is a completecollection of ends for M. We associate to each end E an -conformalmeasure such that the measures corresponding to different endsare mutually singular if non-trivial. Additionally, each -conformalmeasure for on the limit set () of can be written as a sumof such conformal measures associated to ends E . In dimension3, our results overlap with some results of Bishop and Jones(The law of the iterated logarithm for Kleinian groups, Cont.Math. 211 (1997), 17–50.).     

A CLASS OF HARMONIC STARLIKE FUNCTIONS WITH RESPECT TO SYMMETRIC POINTS ASSOCIATED WITH WRIGHT GENERALIZED HYPERGEOMETRIC FUNCTION

Making use of Wright operator we introduce a new class of complex-valued harmonic functions with respect to symmetric points which are orientation preserving, univalent and starlike. We obtain coefficient conditions, extreme points, distortion bounds, and convex combination.     

THE ASSOCIATED FAMILIES OF SEMI-HOMOGENEOUS COMPLETE HYPERBOLIC AFFINE SPHERES

Hildebrand classified all semi-homogeneous cones in R~3 and computed their corresponding complete hyperbolic affine spheres.We compute isothermal parametrizations for Hildebrand's new examples.After giving their affine metrics and affine cubic forms,we construct the whole associated family for each of Hildebrand's examples.The generic member of these affine spheres is given by Weierstrass P,ζ and σ functions.In general any regular convex cone in R~3 has a natural associated S~1-family of such cones,which deserves further studies.     

等距节点三角插值的Lebesgue常数的渐近展开

设 f(x)是以2π为周期的一个周期函数,我们知道对于[0,2π]上的2n 1个节点 θ_k=k(2π/(2n 1)),k=0,1,2,…,2n,(1)存在唯一的n次三角多项式L_n(f,θ),满足L_n(f,θ_k)=f(θ_k),k=0,1,2,…,2n。这里     

OSCILLATION OF NONLINEAR HYPERBOLIC DIFFERENTIAL EQUATION WITH IMPULSES

In this paper, oscillatory properties of solutions for nonlinear impulsive hyperbolic differential equation are investigated and some new sufficient conditions are established.     

到三定点相对距离的和等于定数的点的轨迹

本文研究了相对测度空间中的距离问题. 利用质点几何的理论方法获得如下结果:对任意给定的实数, 满足条件dT (P,A) + dT (P,B) + dT (P,C) =τ的点P的轨迹是凸十二边形或九边形(其中T:=ABC 是由给定的不同三点A, B, C构成的三角形), 所得结果丰富了相对距离研究领域的内容.     

关于平面四次Bézier曲线的拐点与奇点

在计算几何中,已给出了三次Bezier曲线的保凸性的充要条件,并进行了几何解释。本文则是导出形式简洁的拐点和奇点方程并对四次Bezier曲线的拐点和奇点的分布进行讨论。按Bezier曲线的拐点个数进行分类,还得到了四次Bezier曲线有奇点的充分必要条件,并给出几个数值实例,实例说明,不但非凸的单纯特征多角形可以有凸的Bezier曲线段,而且非单纯特征多角形也可以有凸的Bezier曲线段。四次Bezier曲线的奇点和拐点是可以共存的。     

C^n中子空间之间极端主角的一些应用

本文给出了Ｃ＾ｎ中子空间之间最大和最小主角在矩阵逼近，投影算子的扰动分析，群逆以及Ｏｒａｘｉｎ逆的扰动估计，条件数理论，Ｂｏｔｔ－Ｄｕｆｆｉｎ系统扰动分析中一些应用。     

具有双曲不变集系统的极限跟踪性

本文证明了Riemann流形上的微分同胚f在其双曲不变集附近具有相对于C1小扰动一致的极限跟踪性.还证明了如果f是C1-结构稳定的,则f具有极限跟踪性.     

具有双曲不变集系统的极限跟踪性

本文证明了Riemann流形上的微分同胚f在其双曲不变集附近具有相对于C1小扰动一致的极限 跟踪性.还证明了如果f是C1-结构稳定的,则,具有极限跟踪性.     

OSCILLATION OF IMPULSIVE HYPERBOLIC PARTIAL DIFFERENTIAL EQUATION WITH DELAY

In this paper, oscillation properties of the solutions of impulsive hyperbolic equation with delay are investigated via the method of differential inequalities. Sufficient conditions for oscillations of the solutions are established.     

不变子空间上特征值的扰动

1引言设矩阵A∈C~(n×n),B∈C~(m×m),Q∈C~(n×m)为列满秩矩阵,令R=AQ-QB．当R的范数很小的时候,我们分析矩阵B的特征值对A的特征值的逼近性．当A,B都是Hermite阵时,上述问题已经被Kahan解决．近年来,对可对角化矩阵的情形,取得了一些新的成果．[4][5][6]中给出了几个范数不等式,并应用于矩阵特征值     

ISOLATED POINTS OF THE APPROXIMATE POINT SPECTRUM OF CERTAIN LATTICE HOMOMORPHISMS ON Co (X)

Abstract

Suppose X is a locally compact Hausdorff space and C (X) the apace of all continuous complex valued functions on X which vanish at infinity. Let T be a (complex) linear lattice homomorphism on C_o (X) whose adjoint is also a lattice homomorphism. It is sham that every non-zero isolated point of the approximate point spectrum of T lies in the point spectrum of T. An example is given to show that the exclusion of zero is necessary, even when X is compact. The same techniques are then used to show that if also the spectrum of T is finite then T can be written, in a natural manner, as a direct sum of two such lattice homomorphisms; one being an n'th root of an invertible multiplication operator and the other quasi-nilpotent.     

MULTISCALE HOMOGENIZATION OF NONLINEAR HYPERBOLIC EQUATIONS WITH SEVERAL TIME SCALES

We study the multiscale homogenization of a nonlinear hyperbolic equation in a periodic setting.We obtain an accurate homogenization result.We also show that as the nonlinear term depends on the microscopic time variable,the global homogenized problem thus obtained is a system consisting of two hyperbolic equations.It is also shown that in spite of the presence of several time scales,the global homogenized problem is not a reiterated one.