On the positivity of high-degree Schur classes of an ample vector bundle

Let X be a smooth projective variety of dimension n,and let E be an ample vector bundle over X.We show that any Schur class of E,lying in the cohomology group of bidegree(n-1,n-1),has a representative which is strictly positive in the sense of smooth forms.This conforms the prediction of Griffiths conjecture on the positive polynomials of Chern classes/forms of an ample vector bundle on the form level,and thus strengthens the celebrated positivity results of Fulton and Lazarsfeld(1983)for certain degrees.     

On a variant of Giuga numbers

In this paper, we characterize the odd positive integers n satisfying the congruence∑n -1 j=1 j n-1/2 ≡ 0 (mod n). We show that the set of such positive integers has an asymptotic density which turns out to be slightly larger than 3/8.     

GLOBAL ATTRACTIVITY IN A CLASS OF HIGHER-ORDER NONLINEAR DIFFERENCE EQUATION

In this paper the global attractivity of the nonlinear difference equation xn 1 = a bxn / A xn-k, n =0, 1, …，is investigated, where a, b, A ∈ (0, ∞), k is an positive integer and the initial conditions x- k, …，x- 1 and x0 are arbitrary positive numbers. It is shown that the unique positive equilibrium of the equation is global attractive. As a corollary, the result gives a positive confirmation on the conjecture presented by Kocic and Ladas [1,p154].     

非线性分数微分方程边值问题正解的存在性(英文)

In this paper,we study a Dirichlet-type boundary value problem（BVP） of nonlinear fractional differential equation with an order α∈(3,4],where the fractional derivative D^α_o⁺is the standard Riemann-Liouville fractional derivative.By constructing the Green function and investigating its properties,we obtain some criteria for the existence of one positive solution and two positive solutions for the above BVP.The Krasnosel’skii fixedpoint theorem in cones is used here.We also give an example to illustrate the applicability of our results.     

Some Simple Estimates for the Singular Values of Matrices

Abstract We first provide a simple estimate for ||A~(-1)||_∞ and ||A~(-1)||_1 of a strictly diagonally dominant matrixA. On the Basis of the result, we obtain an estimate for the smallest singular value of A. Secondly, by scalingwith a positive diagonal matrix D, we obtain some simple estimates for the smallest singular value of an H-matrix, which is not necessarily positive definite. Finally, we give some examples to show the effectiveness ofthe new bounds.     

本刊英文版Vol.28(2012),No.4论文摘要(英文)

<正>On a Variant of Giuga Numbers Jose Maria GRAU Florian LUCA Antonio M.OLLER-MARCEN In this paper,we characterize the odd positive integers n satisfying the congruence∑_(j=1)~(n-1) j~((n-1)/2) = 0(rood n).We show that the set of such positive integers has an asymptotic density which turns out to be slightly larger than 3/8.     

ON ALMOST SURE CONVERGENCE OF WEIGHTED SUMS OF RANDOM ELEMENT SEQUENCES

We mainly study the almost sure limiting behavior of weighted sums of the form ∑ni=aiXi/bn , where {Xn, n ≥ 1} is an arbitrary Banach space valued random element sequence or Banach space valued martingale difference sequence and {an, n ≥ 1} and {bn,n ≥ 1} are two sequences of positive constants. Some new strong laws of large numbers for such weighted sums are proved under mild conditions.     

OSCILLATORY BEHAVIOR OF SOLUTIONS OF CERTAIN THIRD ORDER MIXED NEUTRAL DIFFERENCE EQUATIONS

The objective of this paper is to study the oscillatory and asymptotic properties of the mixed type third order neutral difference equation of the form △(an△2(xn+bnxn-τ1+cnxn+τ2))+qnxβn+1-σ1+pnxβn+1+σ2=0,where{an},{bn},{cn},{qn}and{pn} are positive real sequences,β is a ratio of odd positive integers,τ1,τ2,σ1 and σ2 are positive integers.We establish some sufficient conditions which ensure that all solutions are either oscillatory or converges to zero.Some examples are presented to illustrate the main results.     

无穷区间上一阶奇异微分方程正解的存在性和不可比较性

By constructing a special cone and applying the fixed point theorem of cone compression and expansion, this paper investigates the existence of positive solutions for a class of first order singular boundary value problem （BVP, for short） on unbounded domains. Moreover, an incomparable result about two positive solutions for the BVP is also obtained and an example is given to illustrate the application of the main results.     

SEPARATION PROPERTY OF POSITIVE RADIAL SOLUTIONS FOR A GENERAL SEMILINEAR ELLIPTIC EQUATION

The asymptotic behavior at infinity and an estimate of positive radial solutions of the equation △u + sum from i=1 to k cirli upi = 0, x ∈ Rn,(0.1)are obtained and the structure of separation property of positive radial solutions of Eq. (0.1) with different initial data α is discussed.     

Bergman kernel on generalized exceptional hua domain

We have computed the Bergman kernel functions explicitly for two types of generalized exceptional Hua domains, and also studied the asymptotic behavior of the Bergman kernel function of exceptional Hua domain near boundary points, based on Appell's multivariable hypergeometric function.     

New classes of domains with explicit Bergman kernel

We introduce two classes of egg type domains, built on general bounded sym-metric domains, for which we obtain the Bergman kernel in explicit formulas. As an aux-iliary tool, we compute the integral of complex powers of the generic norm on a boundedsymmetric domains using the well-known integral of Selberg. This generalizes matrix in-tegrals of Hua and leads to a special polynomial with integer or half-integer coefficientsattached to each irreducible bounded symmetric domain.     

第四类华罗庚域的Bergman核函数

本文给出了第四类华罗庚域H EIV上的Bergman核函数,全纯自同构群以 及semi—Reinhardt域上的完备标准正交函数系.     

有界域的Bergman核函数显式表示的最新进展

对多维复数空间的有界域，如何求出它的Bergman核函数的显表达式，是多复变研究中的一个重要方向。本文综述了迄今为止的所有重要结果以及方法上的进展，特别对新近引进的华罗域，综述了它们的Bergman核函数的显表达式及其计算方法上的创新。     

Bergman-Hartogs型域的全纯自同构群

我们考虑一类以有界对称域D为底的Bergman-Hartogs型域Ω={(wm(1),...,w(r),z)∈C1×···×Cmr×D:∥w(1)∥2p1+···+∥w(r)∥2prKD(z,z)-q},其中KD(z,z)是D上的Bergman核函数,r 1且为正整数,参数p1,...,pr1和q0为实数.我们给出它的全纯自同构群,并且证明当r=1时此自同构群为最大全纯自同构群;当r1时,若Ω的全纯自同构变换F将(0,z)∈{0}×D映到(0,z*)∈{0}×D,则F在我们给出的全纯自同构群中.     

华罗庚域研究的综述

华罗庚域的创建,统一了多复变中的对称典型域和蛋型域的研究,给多复变函数论提供了一个新的研究领域．对华罗庚域的研究,至今已经取得了一系列重要成果．本文简单介绍了华罗庚域创建的历史并着重介绍了华罗庚域上的Bergman核函数和Einstein-Khler度量的显表达式的计算,以及4个经典度量(Bergman度量,Carathéodory度量,Einstein-Kahler度量, Kobayashi度量)之间的等价关系,包括这些度量与Kobayashi度量的比较定理,阐述了Bergman度量等价于Einstein-Khler度量的这一丘成桐猜想在华罗庚域的特例Cartan-Hartogs域上也成立．着重指出了获得这些结果的新的思想和方法并提出了一些尚未解决的问题,以期更多的学者对华罗庚域感到兴趣并进行更深入的研究．     

第三类华罗庚域的Bergman核函数

本文主要是计算第三类华罗庚域的Bergman核函数的显式表达式.由于华罗庚域既不是齐性域又不是Reinhardt域,故以往求Bergman核函数的方法都行不通.本文用新的方法进行计算.关键之处有两点:一是给出第三类华罗庚域的全纯自同构群,群中每一元素将形为(W,Z0)的内点映为点(W*,0);二是引进了semi—Reinhardt的概念并求出了其完备标准正交函数系.     

Hua operator on vector bundle: Application to AdS/CFT correspondence of Dirac fields

Hua’s theory of harmonic functions on classical domains is generalized to the theory on holomorphic vector bundles over classical domains and further on vector bundles over the real classical domains and quaternion classical domains. In case of the simplest quaternion classical domain there is a relation between Hua operator and Dirac operator, by which an AdS/CFT correspondence of Dirac fields is established.