分担一个多项式的全纯函数的唯一性(英文)

本文主要研究了全纯函数分担一个非零多项式的唯一性问题,并且得到了:若f,g为2个非常数的超越整函数,n,k,l为3个正整数且满足5l>4n+5k+7.如果[L(f)](k)与[L(g)](k)IM分担次数小于或等于5的非零多项式P(z),则或者f(z)=λ1eλQ(z)+c,g(z)=λ2e-λQ(z)+c,或者f(z)与g(z)满足代数方程R(f,g)≡0,这里Q(z)=∫z0p(z)dz,λ1,λ2,λ及c为4个常数,且满足等式(λ1λ2)n(nλ)2=-1,并且R(ω1,ω2)=L(ω1)-L(ω2).此外,就[L(f)](k)与[L(g)](k)IM或CM分担不动点的情形也进行了详细的研究。     

两尺度矩阵与正交小波

设尺度函数φ(x)∈V0生成L2(R)的一个多分辨分析{Vj},W0+V0=V1,小波Ψ∈W0,两尺度关系是(x)=∑kpk(2x-k),Ψ(x)=∑kqk(2x-k),傅立叶变换式为^(ω)=P(z)^(ω2),^Ψ(ω)=Q(z)^(ω2),z=e-iω/2,两尺度矩阵为M(z)=P(z)P(-z)Q(z)Q(-z).{Ψ(x-k)k∈Z}为W0的标准正交基的充要条件是对几乎所有的z∈T两尺度矩阵M(z)为酉矩阵.     

分担一个多项式的全纯函数的唯一性

本文主要研究了全纯函数分担一个非零多项式的唯一性问题，并且得到了：若f,g为2个非常数的超越整函数，n,k,l为3个正整数且满足5l>4n+5k+7.如果［L(f)］(k)与［L(g)］(k)IM分担次数小于或等于5的非零多项式P(z)，则或者f(z)=λ1eλQ(z)+c,g(z)=λ2e－λQ(z)+c, 或者f(z)与g(z)满足代数方程R(f,g)≡0，这里Q(z)=∫z0p(z)dz,λ1,λ2,λ及c为4个常数, 且满足等式(λ1λ2)n(nλ)2=－1,并且R(ω1,ω2)=L(ω1)－L(ω2).此外，就［L(f)］(k)与［L(g)］(k)IM或CM分担不动点的情形也进行了详细的研究。
     

分担一个多项式的全纯函数的唯一性

本文主要研究了全纯函数分担一个非零多项式的唯一性问题,并且得到了:若f,g为2个非常数的超越整函数,n,k,l为3个正整数且满足5l＞4n+5k+7.如果[L(f)](k)与[L(g)](k)IM分担次数小于或等于5的非零多项式P(z),则或者f(z)=λ1eλQ(z)+c,g(z) =λ2e-λQ+(z),或者f(z)与g(z)满足代数方程R(f,g)≡0,这里Q(z)=fz0P(z)dz,λ1,λ2,λ及c为4个常数,且满足等式(λ1λ2)n(nλ)2 =-1,并且R(ω1,w2)=L(ω1)-L(w2).此外,就[L(f)](k)与[L(g)](k)IM或CM分担不动点的情形也进行了详细的研究.     

亚纯函数的级的估计

f(z)是一个亚纯函数,g(z)是f(z)的一个齐次微分多项式且f(z)与g(z)有相同的级。方程f(z)=0,f(z)=∞,g(z)=1的根分布在射线束;re~(iω)_1,re~(i(?))_1,…re~(iω)_(?)(r≥0,q≥1)上,并且δ(0,f)+δ(∞,f)+δ(1,g)>0。则f的级ρ必是有穷的,且 ρ≤β=sup{π/ω_2-ω_1,π/ω_3-ω_2,…,π/ω_(q+1)-ω_q} [ωq+1=2π+ω_1]     

一个拟从属函数的系数极值

设函数 f(z)、d(z)、ω(z) 在 |z|<1 内解析,且 |d(z)|≤1,|ω(z)|<1,ω(0)=0.函数 d(z) 是有界的,ω(z) 适合 Schwarz 引理条件.记 g(z)=d(z)f(ω(z)),称g(z) 拟从属于 f(z),记为 g相似文献   

多自由度振动系统的同相振动性

采用反射函数法研究了多自由度振动系统x′=p(t)x, 当p(t)=diag(A(t),B(t))时,给出其等价系统y′=A(t)y, z′=B(t)z同相振动的充分必要条件,其中A(t)=(aij(t))2×2, B(t)=(bij(t))2×2, y=(y1,y2)T, z=(z1,z2)T, p(t+2ω)=p(t), ω>0, t∈R, x∈R4, p(t)为连续可微的矩阵函数.     

几种收敛速率较高的迭代求解程序

为求解方程f(x)=0,我们提出了下列二种迭代程序:x_n~(1)=ω(x_(n-1)~((m-1)),x_(n-1)~(m),x_(n-1)~(m)),x_n~(2)=ω(x_(n-1)~((m-1)),x_(n-1)~(m),x_m~(1)),x_n~(3)=ω(x_(n-1)~((m-1)),x_(n-1)~(m),x_n~(2),x_n~(m)=ω(x_(n-1)~((m-1)),x_(n-1)~(m),x_n~((m-1))),(?)n∈N_0和z_(n 1)=ω(x_n,y_n,x_n),y_(n 1)=ω(x_n,z_(n 1),z_(n 1)),x_(n 1)=ω(x_n,z_(n 1),y_(n 1)),其中ω(x,y,z)=z-f(z)/f(x,y),f(x,y)=f(x)-f(y)/(x-y),它们的收敛阶分别为m (m~2 4)~(1/2)/2和2 3~(1/2)。本文分别建立了程序(I_m)和程序(Ⅱ)的收敛性定理,并就两个定理作了六点注记。文中还给出了一个数值例子     

涉及微分多项式的亚纯函数的正规族

设F是区域D内的一族亚纯函数,k,m,q是正整数,P(ω)=ωq+aq-1(z)ωq-1+…+a1(z)ω是一多项式,H(f,f′,…,f(k))是满足γH*0的微分多项式,a(z),b(z),c(z)是区域D内的解析函数,且a(z)≠b(z),c(z)≠0.若对于任意的f∈F,f的零点的重数至少是k+1,且有(1)P(f(k)(z))+H(f,f′,…,f(k))=a(z)时,f(z)=0;(2)P(f(k)(z))+H(f,f′,…,f(k))=b(z)时,f(z)=c(z),则F在D内正规.     

勒襄特多项式的推广

1.我们知道勒襄特多项式的拉伯拉斯第一积分为 P_n(z)=1/πz+(z~2-1)~(1/2)cosφ}dφ,(1.1) 这里(z~2-1)~(1/2)可取其中任意一支。因此有 P_n(z)=1/2π〔{z+(z~2-1)~(1/2)cosφ}~n+{z-(z~2-1)~(1/2)cosφ}~n〕dφ.(1.2) 于是定义 P_n(z,ω)=1/2π〔{z+(z~2-1)~(1/2)cosφ}~n+{z-(z~2-1)~(1/2)cosφ}~n〕dφ,0≤ω≤π;(1.3)     

Markedness and its Interpretation in Language Use

Language markedness is a common phenomenon in languages, and is reflected from hearing, vision and sense, i.e. the variation in the three aspects such as phonology, morphology and semantics. This paper focuses on the interpretation of markedness in language use following the three perspectives, i.e. pragmatic interpretation, psychological interpretation and cognitive interpretation, with an aim to define the function of markedness.     

Features of Women's language

Language is a means of verbal communication. People use language to communicate with each other. In the society, no two speakers are exactly alike in the way of speaking. Some differences are due to age, gender, statue and personality. Above all, gender is one of the obvious reasons. The writer of this paper tries to describe the features of women＇s language from these perspectives： pronunciation, intonation, diction, subjects, grammar and discourse. From the discussion of the features of women＇s language, more attention should be paid to language use in social context. What＇s more, the linguistic phenomena in a speaking community can be understood more thoroughly.     

低渗透非均质砂岩油藏启动压力梯度研究

理论推导与室内实验相结合,建立了低渗透非均质砂岩油藏启动压力梯度确定方法。首先借助油藏流场与电场相似的原理,推导了非均质砂岩油藏启动压力梯度计算公式。其次基于稳定流实验方法,建立了非均质砂岩油藏启动压力梯度测试方法。结果表明:低渗透非均质砂岩油藏的启动压力梯度确定遵循两个等效原则。平面非均质油藏的启动压力梯度等于各级渗透率段的启动压力梯度关于长度的加权平均;纵向非均质油藏的启动压力梯度等于各渗透率层的启动压力梯度关于渗透率与渗流面积乘积的加权平均。研究成果可用于有效指导低渗透非均质砂岩油藏的合理井距确定,促进该类油藏的高效开发。     

On Tragic Consciousness In The Works By Ernest Hemingway

As an American modern novelist who were famous in the literary world, Hemingway was not a person who always followed the trend but a sharp observer. At the same time, he was a tragedy maestro, he paid great attention on existence, fate and end-result. The dramatis personae's tragedy of his works was an extreme limit by all means tragedy on the meaning of fearless challenge that failed. The beauty of tragedy was not produced on the destruction of life, but now this kind of value was in the impact activity. They performed for the reader about the tragedy on challenging for the limit and the death.     

Achieving Unusual States of Matter Under High Pressure

正The periodicity of the elements and the non-reactivity of the inner-shell electrons are two related principles of chemistry,rooted in the atomic shell structure.Within compounds,Group I elements,for example,invariably assume the+1 oxidation state,and their chemical properties differ completely from those of the p-block elements.These general rules govern our understanding of chemical structures and reactions.Using first principles calcula-     

Exchange-Correlation and Electronic Excitation Energies from Pairing Matrix Fluctuations

We have developed an adiabatic connection to formulate the ground-state exchange-correlation energy in terms of pairing matrix linear fluctuations.This formulation of the exchange-correlation energy opens a new channel for density functional approximations based on the many-body perturbation theory.We illustrate the potential of such approaches with an approximation based on the particle-particle Random Phase Approximation(pp-RPA).This re-     

Density Functional Theory for the Response of Periodic Systems to Electric Fields Based on the Vector Potential Approach

正The electronic and nuclear(structural/vibrational)response of 1D-3D nanoscale systems to electric fields gives rise to a host of optical,mechanical,spectral,etc.properties that are of high theoretical and applied interest.Due to the computational difficulty of treating such large systems it is convenient to model them as infinite and periodic(at least,in first approximation).The fundamental theoretical/computational problem in doing so is that     

On the Thermodynamic Limit for Responses to Static Electromagnetic Fields

For molecular systems,the quantum-mechanical treatment of their responses to static electromagnetic fields usually employs a scalar-potential treatment of the electric field and a vector-potential treatment of the magnetic field.Although the potential for each field separately is associated with the choice of an(unphysical)origin,the precise choice of the origin for the electrostatic field has little consequences for the results.This is different for the     

An affordable accurate evaluation of the binding conformations predicted by molecular docking studies in bio-system

Franck-Condon factors bridge the gap between theoretical modeling and experimental observations for molecular electronic spectroscopy and electron transfer.Under the displaced harmonic oscillator approximation,multidimensional Franck-Condon factors are decomposed into a product of many one-dimensional(1D)Franck-Condon(FC)factors,and each 1D-FC factor is associated with one Huang-Rhys factor that determines the leading contribution of     

Call for Papers

<正>"The Journal of Shanghai Normal University:Mathematics"is published by Shanghai Normal University as regular issues of The Journal of Shanghai Normal University each year from 2014 in English.The editors-in-chief of the issues are professors Yuhao Cong and Maoan Han.The Journal of Shanghai Normal University was started in 1958 with