多复变数完全拟凸映射的分解定理

设Ω1(∪) Cn1,Ω2(∪)Cn2为凸的Reinhardt域,f(z,w)=(f1(z,w),f2(z,w))′为Ω1×Ω2上的正规化全纯映射.本文证明f为Ω1×Ω2上的正规化双全纯完全拟凸映射当且仅当f(z,w)=(Φ1(z),Φ2(W))′,其中ΦjΩj→Cnj是Ωj(j=1,2)上的正规化双全纯完全拟凸映射.     

Reinhardt域B_p上正规化双全纯完全准凸映射的齐次展式

本文主要研究C~n中有界凸Reinhardt域B_p上正规化双全纯完全准凸映射的齐次展开式问题,设f(z):B_p→C~n(p＞2)是一个正规化双全纯完全准凸映射,k是满足k＜p≤k+1的自然数,那么f_j(z)=z_j+α_(j2)z_j~2+…+α_(jk)z_j~k+O(|z|~(K+1)),其中f_j是f的第j个分量,j=1,2…．,n．     

一些圆域上的凸映射扩充

在本文中,我们考虑了一些圆域.并且我们给出了这些圆域上的正规化双全纯凸映射的扩充定理.特别地,我们发现某些圆域上的正规化双全纯凸映射有形式.f(z)-(f_1(z_1),…,f_n(z_n)),其中f_j:D→C是双全纯凸映射.     

A Remark on the Generalized Roper-Suffridge Extension Operator for Almost Stalike Mappings of Order α

Suppose f is an almost starlike function of orderαon the unit disk D.In this paper,we will prove thatΦ_(n,β_2,γ_2,…,β_n,γ_n)(f)(z)=(f(z_1),((f(z_1)/z_1))~β_2(f′(z_1))~(γ_2)z_2,…, ((f(z_1)/z_1))~(β_n)(f′(z_1))~(γ_n)z_n)′preserves almost starlikeness of orderαonΩ_(n,p_1,p_2,…,p_n)={z= (z_1,z_2,…,z_n)′∈C~n:(sum from j=1 to n)|z_j|~(p_j)<1},where 0相似文献   

C~n中单位多圆柱上一类B型α次准凸映射齐次展开式各项的精确估计

本文给出Cn中单位多圆柱上一类B型α次准凸映射f(z)齐次展开式各项的精确估计,其中f(z)=(f1(z),f2(z),...,fn(z))T是k折对称映射(或z=0是f(z)-z的k+1阶零点),且满足sup∥z∥=1,∥w∥=1∥Dmf(0)(zm-1,w)∥=sup∥z∥=1∥Dmf(0)(zm)∥,m=2,3,...所得到的估计包含已有文献的许多结论.     

简单分歧数值解的L_p估计

§1.问题的提出 考虑单参数二阶椭圆拟线性微分方程:λ∈R,Ω?R~N(N=1,2)是多角形凸域(要求?Ω是Lipschitz连续的)或光滑域.[a_(ij)]∈C~1满足正定条件.f(x,y)∈C~2f(x,0)≡0,f_y(x,θ)≥0,但f_y(x,0)?0,?x∈Ω.记||·||_(j,p,Ω),p≥1,j=0,1,2为通常的W~(j,p)(Ω)范.H_0~1?W_0~(1,2),(·,·)为H_0~j中通     

全纯映射子族上改进的Roper-Suffridge算子

设m∈N且m≥2,f是单位圆盘D上的正规化双全纯函数,P:Cn-1→C是m次齐次多项式.研究了单位球上改进的Roper-Suffridge算子F(z)=(f(z1)+f'(z1)P(z0),[f'(z1)]1/mz0)',其中z0=(z2,z3…,zn).当m=2时,该算子由Muir引入.当P≡0和m=2时,此算子就是著名的Roper-Suffridge算子.给出了∥P∥分别满足不同条件时,改进的算子分别保持α次的殆星和α次的星形映射性质.此结果推广了最近许多已有结果,而且方法更易于操作.特别地,当f(z1)=z1和m=n=2时,这就导出了多复变几何函数论中构造具体实例的经典形式F(z)=(z1+a22,z2)'.     

简单分歧数值解的L_p估计

§1.问题的提出 考虑单参数二阶椭圆拟线性微分方程:λ∈R,Ω?R~N(N=1,2)是多角形凸域(要求?Ω是Lipschitz连续的)或光滑域.[a_(ij)]∈C~1满足正定条件.f(x,y)∈C~2f(x,0)≡0,f_y(x,θ)≥0,但f_y(x,0)?0,?x∈Ω.记||·||_(j,p,Ω),p≥1,j=0,1,2为通常的W~(j,p)(Ω)范.H_0~1?W_0~(1,2),(·,·)为H_0~j中通     

A Remark on the Generalized Roper-Suffridge Extension Operator for Spirallike Mappings of Type β and Order α

Suppose f is a spirallike function of type β and order α on the unit disk D.let Ωn,p1,p2,…,pn={z=(z1,z2,…,zn)'∈Cn:nΣj=1|zj|pj<1},where 1≤p1≤2,pj≥1,j=2,…,n,are real numbers. In this paper,we will prove that Фn,β2,у2…βn,уn(f)(z)=(f(z1),(f(z1)z1)β2(f'(z1))у2z2,…,(f(z1)z1)βn(f'(z1))уnzn)' Preserves spirallikeness of type β and order α on Ωn,p1,p2,…pn.     

拟凸条件下变分问题解的正则性

本文研究变分问题(1)■(u:Ω)=∫_Ωf(x,u,Du)dx的极小函数的正则性,其中Ω■R~n是有界开域,u:Ω→R-~N,Du:Ω→R(nN),f: ×R~N×R(nN)→R。定义称函数f满足严格拟凸条件,是指存在常数v>0,使得对任意的(x_0,u_0,p_0)∈Ω×R~N×R(nN)和φ∈C~∞_0(Ω,R~N),都有■(2)其中|Ω|是Ω的Lebesgue测度。定理设u∈H~(1,2)(Ω,R~N)是泛函f的极小函数,即对任意的φ∈H_0~(1,2)(Ω,R~N),都有■而f(x,u,p)满足下列假设 (H1) f满足严格拟凸性,即(2)成立, (H2) f关于p的二阶导数存在,且存在常数L>0,使得■对任意的(x,u,p)∈Ω×R~N×R~(nN),都有■ (3)|f_(pp)(x,u,p)|≤L_0 (H3) 存在[0,∞]上的连续、有界、凹的函数∞(t),使得(4)■(5)■(6)■且ω(t)≤At~α,其中A,α是正常数。那么存在常数δ∈(0,1)和开集Ω_0Ω,使得|Ω-Ω_0|=0,Du∈C~6(Ω_0,R(nN))。     

On a class of self-similar processes with stationary increments in higher order Wiener chaoses

We study a class of self-similar processes with stationary increments belonging to higher order Wiener chaoses which are similar to Hermite processes. We obtain an almost sure wavelet-like expansion of these processes. This allows us to compute the pointwise and local Hölder regularity of sample paths and to analyse their behaviour at infinity. We also provide some results on the Hausdorff dimension of the range and graphs of multidimensional anisotropic self-similar processes with stationary increments defined by multiple Wiener–Itô integrals.     

A REPRESENTATION FORMULA RELATED TO SCHR(O)DINGER OPERATORS

Schr(o)dinger operator is a central subject in the mathematical study of quantum mechanics.Consider the Schrodinger operator H = -△ V on R, where △ = d2/dx2 and the potential function V is real valued. In Fourier analysis, it is well-known that a square integrable function admits an expansion with exponentials as eigenfunctions of -△. A natural conjecture is that an L2 function admits a similar expansion in terms of "eigenfunctions" of H, a perturbation of the Laplacian (see [7], Ch. Ⅺ and the notes), under certain condition on V.     

On a class of Riemann surfaces

It is considered the class of Riemann surfaces with dimT1 = 0, where T1 is a subclass of exact harmonic forms which is one of the factors in the orthogonal decomposition of the spaceΩH of harmonic forms of the surface, namely The surfaces in the class OHD and the class of planar surfaces satisfy dimT1 = 0. A.Pfluger posed the question whether there might exist other surfaces outside those two classes. Here it is shown that in the case of finite genus g, we should look for a surface S with dimT1 = 0 among the surfaces of the form Sg\K , where Sg is a closed surface of genus g and K a compact set of positive harmonic measure with perfect components and very irregular boundary.     

CONTENTS OF VOLUME 30

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Instructions for contributions

正Applied Mathematics-A Journal of Chinese Universities,Series B(Appl.Math.J.Chinese Univ.,Ser.B)is a comprehensive applied mathematics journal jointly sponsored by Zhejiang University,China Society for Industrial and Applied Mathematics,and Springer-Verlag.It is a quarterly journal with     

Journal of Mathematical Research with Applications Guide for Authors

正Journal overview:Journal of Mathematical Research with Applications(JMRA),formerly Journal of Mathematical Research and Exposition(JMRE)created in 1981,one of the transactions of China Society for Industrial and Applied Mathematics,is a home for original research papers of the highest quality in all areas of mathematics with applications.The target audience comprises:pure and applied mathematicians,graduate students in broad fields of sciences and technology,scientists and engineers interested in mathematics.     

Staircase transportation problems with superadditive rewards and cumulative capacities

A cumulative-capacitated transportation problem is studied. The supply nodes and demand nodes are each chains. Shipments from a supply node to a demand node are possible only if the pair lies in a sublattice, or equivalently, in a staircase disjoint union of rectangles, of the product of the two chains. There are (lattice) superadditive upper bounds on the cumulative flows in all leading subrectangles of each rectangle. It is shown that there is a greatest cumulative flow formed by the natural generalization of the South-West Corner Rule that respects cumulative-flow capacities; it has maximum reward when the rewards are (lattice) superadditive; it is integer if the supplies, demands and capacities are integer; and it can be calculated myopically in linear time. The result is specialized to earlier work of Hoeffding (1940), Fréchet (1951), Lorentz (1953), Hoffman (1963) and Barnes and Hoffman (1985). Applications are given to extreme constrained bivariate distributions, optimal distribution with limited one-way product substitution and, generalizing results of Derman and Klein (1958), optimal sales with age-dependent rewards and capacities.To our friend, Philip Wolfe, with admiration and affection, on the occasion of his 65th birthday.Research was supported respectively by the IBM T.J. Watson and IBM Almaden Research Centers and is a minor revision of the IBM Research Report [6].