单位圆盘上全纯映照模的精细Schwarz引理

记DC为单位圆盘,B~p={z∈C~n:n∑i=1|z_i|~p1},1p+∞.该文证明了若f∈H_m(D,B~p),则|▽||f||(z)≤m|z|~(m-1)/1-|z|~(2m)(1-||f(z)||~2),z∈D.同时,当p为偶数时,该文也讨论了相应的极值问题,所得结论推广了一些相关结果.     

单位圆盘上全纯映照模的精细Schwarz引理北大核心CSCD

记DC为单位圆盘,B^p={z∈C^n:n∑i=1|z_i|~p<1},1相似文献   

Use Cesro Means To Describe Two Classes of Functions

Let H(D)be the collection of functions which are analytic in the unitdisc D.we call B_0={f∈H(D),(?)(1-|z|~2)|f’(z)|=0}litlle Bloch space.Letf∈H(D),0相似文献   

关于corona(日冕)问题

设Δ={|z|<1},H~∞(Δ)表示Δ上一切有界解析函数全体所组成的函数族.它是一个Banach代数,因若f和g∈H~∞ (Δ),则fg∈H~∞(Δ),且||fg||_∞≤||f||_∞·||g||_∞.设对单位圆内任何一点z,令M_z={f∈H~∞(Δ):f(z)=0},则M_z是H~∞ (Δ)的一个极大理想.设 表示 H~∞(Δ)的极大理想空间,则它在弱拓扑下成为一个紧致的Hausdorff空间.若对z,|z|<1,则点赋值     

单叶函数的几条判别法

对于单位圆盘内的解析函数f（z），本文根据给出了判别函数f（z）为单叶函数的几条判别法则，其中D0f（z）=f(z),D1f(z)=Df(z)=zf1(z),Dnf（z）=D(Dn-1f(z)),n∈N.     

Q_p空间中K-泛函与光滑模等价性

<正>1引言令g(·,w)为复平面单位圆盘D(|z|1)上极点在W的Green函数g(z,w)=-log|φ_w(z)|,z,w∈D,其中φ_w为从D到其上的M(o|¨)bius变换φ_w(z)=(w-z)/(1-wz).记H(D)为D上全纯函数全体,dm(z)为Lebesgue测度.称函数f属于Q_p空间(0≤P∞)是指f(z)∈H(D)且满足||f||_(Q_p)~2:=supw∈D∫_D|f'(z)|~2g~p(z,w)dm(z)+∞.易知~([1]),||·||_(Q_p)为半模.若取模为|f(0)|+||f||_(Q_p),则Q_p空间为Banach空间,且有     

从混合模空间到Zygmund-型空间的一些积型算子

设D={z∈C:|z|1}是复平面上的单位圆盘,H(D)表示D上的所有解析函数的集合,ψ_1,ψ_2∈H(D),n是一个非负整数,φ是D到D的一个解析自映射,μ是一个权函数.研究从混合模空间到Zygmund-型空间的积型算子T_(ψ_1,ψ_2,φ)~n的有界性和紧性特征,其中T_(ψ_1,ψ_2,φ)~nf(z)=ψ_1(z)f~((n))(φ(z))+ψ_2(z)f~((n+1))(φ(z)),f∈H(D).     

关于多元多项式凸逼近

§1.引言 在多项式保形逼近理论中面临以下两个基本问题: 问题1.对于k≥2,R~k中是否存在k维紧凸集E及C(E)上的保凸正线性算子列L_n:C(E)→P_n满足:?凸函数f∈C(E),||L_nf-f||_E→0(n→∞)? 问题2.对于k≥2以及R~k中的任意k维紧凸集E和任意凸函数f∈C(E),是否存在一列多项式p_n∈P_n,使每一个p_n在E上为凸函数,并且||p_n-f||_E→0(n→∞)?     

ON AN INVERSE THEOREM OF APPROXIMATION

The author gives some disagreement to the following result,which is published in [1].Let {L_n(f(}be mass-concerntative,φ_n→0+(n→∞),0<α≤2 andC~(-1)≤(φn+1)/(φn)≤C(n=1,2,…)for some constrant C>0.Then for any f∈C[-2a,2a],||L_n(f)-f||σ[-a,a]=O(φ_n~α)implies f∈Lip*α,whereLip*a={f∈C[-2a,2a]|w_2(f,δ)[-2a,2a]=O(δ~α)}.Then some similar results on C_(2π)are given,and further some results on C[-2a,2a]areestablished by adding some proper conditions.     

涉及重级零点的亚纯函数的拟正规定则

设F为区域D内的只有重级零点的亚纯函数族,H(z)为区域D内的非常数亚纯函数,且存在v∈N,使得对于任意的a∈C,n(D,1/H(z)-a)≤v.如果对于任意的f∈F,f′(z)≠H′(z),那么F在区域D内v阶拟正规.     

两类带有确定潜伏期的SEIS传染病模型的分析

通过研究两类带有确定潜伏期的SEIS传染病模型,发现对种群的常数输入和指数输入会使疾病的传播过程产生本质的差异．对于带有常数输入的情形,找到了地方病平衡点存在及局部渐近稳定的阈值,证明了地方病平衡点存在时一定局部渐近稳定,并且疾病一致持续存在．对于带有指数输入的情形,发现地方病平衡点当潜伏期充分小时是局部渐近稳定的,当潜伏期充分大时是不稳定的．     

Backward bifurcation of an epidemic model with standard incidence rate and treatment rate

An epidemic model with standard incidence rate and treatment rate of infectious individuals is proposed to understand the effect of the capacity for treatment of infectives on the disease spread. It is assumed that treatment rate is proportional to the numbers of infectives below the capacity and is a constant when the number of infectives is greater than the capacity. It is proved that the existence and stability of equilibria for the model is not only related to the basic reproduction number but also the capacity for treatment of infectives. It is found that a backward bifurcation occurs if the capacity is small. It is also found that there exist bistable endemic equilibria if the capacity is low.     

A transverse spinning double pendulum

A transverse spinning double pendulum is introduced. This pendulum is of interest as a simple mechanical system with two degrees of freedom with rotation which is autonomous. In addition to having physical origins, the pendulum is constructable for experimental observation. Our main interest in introducing and analyzing this system is that it is the simplest physical system with the codimension two singularity – in the linearization about the trivial solution – associated with coalescence of four zero eigenvalues. It is the dynamics of the nonlinear system in the neighbourhood of this singularity that is of interest. We study this problem using normal form theory. An algorithm for the Cushman–Sanders normal form is constructed and analyzed. A representative model for the truncated normal form is presented. This truncated normal form has seven parameters; it is not integrable in general and it is predicted that the dynamics associated with this model will be quite complex.     

The Fraenkel‐Carnap question for Dedekind algebras

It is shown that the second‐order theory of a Dedekind algebra is categorical if it is finitely axiomatizable. This provides a partial answer to an old and neglected question of Fraenkel and Carnap: whether every finitely axiomatizable semantically complete second‐order theory is categorical. It follows that the second‐order theory of a Dedekind algebra is finitely axiomatizable iff the algebra is finitely characterizable. It is also shown that the second‐order theory of a Dedekind algebra is quasi‐finitely axiomatizable iff the algebra is quasi‐finitely characterizable.     

Traveling waves in a nonlocal dispersal population model with age-structure

This paper is concerned with the traveling waves in a single species population model which is derived by considering the nonlocal dispersal and age-structure. If the birth function is monotone, then the existence of traveling wavefront is reduced to the existence of a pair of super and subsolutions without the requirement of smoothness. It is proved that the traveling wavefront is strictly increasing and unique up to a translation. The asymptotic behavior of traveling wavefronts is also obtained. If the birth function is not monotone, the existence of traveling wave solution is affirmed by introducing two auxiliary nonlocal dispersal equations with quasi-monotonicity.     

AR（p）模型中的缺失数据估计

运用EM算法,对含有缺失数据的AR（p）模型进行参数估计,通过最大似然准则就非左端缺失的情况进行插补.最后,用蒙特卡洛方法给出实验分析,表明如下结果：（i）误差与AR模型的阶数正相关,与缺失比例正相关;（ii）当AR模型的特征根模长相对较小时,误差与数据长度负相关,且误差被控制在了标准差的30％以内;（iii）当模长中等时,误差基本控制在1个标准差左右;（iv）当模长较大时,误差与数据长度正相关,而且误差也相对较大.     

Perturbations from a source in a two-layer atmosphere bounded by the horizontal terrestrial surface

The problem of internal waves excited by a point source in a two-layer atmosphere is investigated in a linear formulation. The lower layer is bounded by a horizontal surface and, the upper layer is unbounded. It is assumed that the vertical displacements and velocities of the particles vary continuously at the layer boundaries, and that the Brunt Väisälä frequency is constant in each layer but experiences discontinuities at the common boundary of the layers; the source is situated in the lower layer. The asymptotic behaviour of the perturbations in the lower layer at long times is investigated. The solution is found using integral transforms and is expressed in terms of double integrals of many-valued analytic functions. A transformation is proposed which enables the solution to be expressed as the sum of single integrals. The behaviour of these integrals at long times is found by the stationary-phase method. It is shown that a critical cone exists across which the asymptotic behaviour of the system undergoes a change.     

Banach空间有界线性算子强连续双半群

本文在Ｂａｎａｃｈ空间上研究单参数有界线性算子族－强连续双半群。     

Global behavior of an SEIRS epidemic model with time delays

This is a study of dynamic behavior of an SEIRS epidemic model with time delays. It is shown that disease-free equilibrium is globally stable if the reproduction number is not greater than one. When the reproduction number is greater than 1, it is proved that the disease is uniformly persistent in the population, and explicit formulae are obtained by which the eventual lower bound of the fraction of infectious individuals can be computed. Local stability of endemic equilibrium is also discussed.     

An approximate solution for linear boundary-value problems with slowly varying coefficients

In this paper, an approximate closed-form solution for linear boundary-value problems with slowly varying coefficient matrices is obtained. The derivation of the approximate solution is based on the freezing technique, which is commonly used in analyzing the stability of slowly varying initial-value problems as well as solving them. The error between the approximate and the exact solutions is given, and an upper bound on the norm of the error is obtained. This upper bound is proportional to the rate of change of the coefficient matrix of the boundary-value problem. The proposed approximate solution is obtained for a two-point boundary-value problem and is compared to its solution obtained numerically. Good agreement is observed between the approximate and the numerical solutions, when the rate of change of the coefficient matrix is small.