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数学进展
  1993年, 第22卷, 第5期 刊出日期:1993-10-25 上一期    下一期
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组合拓扑方法在组合学和图论中的应用
谢力同,刘桂真
数学进展. 1993, 22 (5): 385-390.  
摘要  
本文介绍组合拓扑方法在图论和组合学中的应用,探索一些新的离散问题和连续问题的联系,介绍目前有关这方面的新结果及发展动向。本文主要介绍同调理论在图论中的应用,与图有关的复形及性质,不动点定理在离散问题中的应用等。文中提出了一些新结果及可供研究的新问题。
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研究论文
偏微分方程的函数论方法及应用和计算(英文)
闻国椿
数学进展. 1993, 22 (5): 391-401.  
摘要  
本文主要介绍了偏微分方程一些边值问题的函数论方法。首先给出了边值问题的适定提法;其次研究了多复变函数、Clifford代数、某类抛物型方程、一些复合型方程组和双曲型方程组各种边值问题的可解性;进而使用一阶椭圆型方程组间断边值问题的结果,解决了渗流理论、空气动力学与弹性力学中提出的若干自由边界问题;最后还讨论了某些椭圆边值问题与拟共形映射的近似解法。从此文可以看出;函数论方法在处理偏微分方程时的一些优点。
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单叶调和映射
张玉林
数学进展. 1993, 22 (5): 402-410.  
摘要  
由于在极小曲面理论中的作用,对调和映射的研究已有较长时间。1984年以来,经典解析单叶映射的理论被推广至调和单叶映射,并获得许多结论。这些工作引起人们对它的浓厚兴趣。该文介绍这一课题某些重要成果的概貌,并指出一些尚未解决的问题。它共分六个部分:映射定理,单叶调和函数的数值估计;特殊映射;变分方法;境界性质和在极小曲面中的应用。
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关于Tchebycheff-Fourier级数的(H,λ)平均的逼近(英文)
盛淑云
数学进展. 1993, 22 (5): 411-421.  
摘要  
我们定义了(H,λ)求和法,它含有(N,p_n),(R_n~γ)和(V_(mn))求和法。讨论了函数f(x)∈C~r[-1,1](r∈N_0)以及f(x)∈W~rH~a(r∈N_0,0 Related Articles
复合算子和一类解析Toeplitz算子的约化子空间
孙善利
数学进展. 1993, 22 (5): 422-434.  
摘要  
本文利用复合算子完全刻画了符号为两个Blaschke因子乘积的解析Toeplitz算子的约化子空间。
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极值复特征的值域(英文)
黄心中
数学进展. 1993, 22 (5): 435-440.  
摘要  
本文考虑单位圆U={Z||Z|<1}到自身上的极值拟共形映照复特征的值域。在复特征值域的适当限制下,得到一个判别极值复特征的充要条件。作为特殊情形,改进了Qrtel和Smith的结果。
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关于面积平均p叶函数(Ⅱ)
董新汉
数学进展. 1993, 22 (5): 441-448.  
摘要  
假设f(z)=z~p是△={|z|<1}内面积平均p叶的(如果必要,△={|z|<1}\(-1,0])。本文的主要结论是:(1)如果设M(r)=max|f(z)|,则(1-r)~(2p/k)M(r)→a_k≤1(r→1),a_k=1的充要条件是f(z)=z~p(1-xz~k)~(-2p/k),|x|=1.1.进一步,如果1≤k<4p,我们有|a_n|n~(1-2p/k)→akΓ(2p/k)~(-1)(n→∞)。(2)如果k=p=1,则||a_n|-|a_(n+1)|| Related Articles
改进的R.Nevanlinna第二基本定理
钟华梁
数学进展. 1993, 22 (5): 449-453.  
摘要  
设f(z)是超越亚纯函数,a为任一非负整数,ε为任意正数,a_r~((i))(v=1,2…,q_i,i=01,…,n)均为有穷非零复数,满足i=0,1…,n,若f(0)≠0,∞,f~((i))(0)≠0,则对0 Related Articles
RESEARCH ANNOUNCEMENTS Limit of Bernstein- Bezier Curves for Periodic Control Nets
齐东旭,Robert Schaback
数学进展. 1993, 22 (5): 454-455.  
摘要  
Let n≥1 control points .b_0, b_1,…,b_(n-1)∈ R~d be given. These control points arerepeated by b_(j+kn): =b_j for 0≤j≤n - 1, and all k∈Zto form an infinite periodic sequence. The centrold of the points is denoted by
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On the Polynomials in Several Indeterminates Which can be Extended to Permutation Polynomial Vectors Over Z/p~lZ
张起帆
数学进展. 1993, 22 (5): 456-457.  
摘要  
Let m be a number, and f_1 (x_1 ,…,x_n ),…,f_k(x_1,…,x_n )∈ Z(x_1,…,x_n), k≤n. Iffor any(α_1,…α_k) ∈ Z~k, the congruenee systemhas just m~(n-k) solutions, then the system f_1,…,f_k is called an orthogonal system
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On Indirect Proof of Local Index Theorem for Signature Operator
虞言林
数学进展. 1993, 22 (5): 458-459.  
摘要  
In proving the local index theorem of the signature operator, people used aGilkey theorem, which was described on page 284 in [1], and thought it as the keypoint for the proof. Now we point out that things could be otherwise. Let us begin with some notions. Let R be a set of letters R_(i_1, ...i_3, ), where s= 4,5,6,..., and 1≤i_1,…,i≤2n, and let g be a set of letters g_(ij) with 1≤i,j≤2n,and let 1/(detg) be a letter. A polynomial in R,g, 1/(detg) means a polynomial in finite
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Primitive Roots and Linearized Polynomials
韩文报
数学进展. 1993, 22 (5): 460-462.  
摘要  
Let f(x) = sum from t=0 to n α_ix~i∈GF(p)[x],we associate it with a ploynomial f~*(x)=sum from i=0 to n α_ix~(p~i),f(x) and f~*(x)are called p-associates of each other. f~*(x) is called a p-ploynomial,customary to speak of linearized polynomial. Let f(x)=x~m- 1/g(x), m = m_1~r, q = p~m, g(x)∈GF(p)[x],r be the order of g(x). Cohen and the author observed that if m_1≥2, there alwaysexsists a primitive roots ζ∈GF(q) suck that f~*(ζ) = f~*(c), here f~*(c)≠0. In fact
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Arnold Conjecture for Product of Monotone Manifolds
卢广存
数学进展. 1993, 22 (5): 463-465.  
摘要  
Let (M,ω) be a 2n-dimensional compact symplectic manifold. Then every smoothr-periodic Hamiltonian function H:S~r×M→R gives rise to a Hamiltonian vectorfiele X_H:S~r×M→TM via i_(X_H)ω = dH, where S~r= R/rZ,r>0. We consider the timedependent Hamiltonian differential equation
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Weinstein Conjecture and Holomorphic Spheres
卢广存
数学进展. 1993, 22 (5): 466-468.  
摘要  
The Weinstein conjecture is one of the central problems in the symplectic geo-metry. Let (M,ω) be a symplectic manifold. Given a compact smooth bypersurfaceS(M,ω) we denote by (S) the collection of all periodic Hamiltonian trajectoriesou S. In [6] A. Weinstein proposed the following conjecture. Conjecture If S is a compact bypersurface of contact type with H~1(S;R) =
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Decay of Solutions to 2-Dimensional Navier Stokes Equations
张领海
数学进展. 1993, 22 (5): 469-472.  
摘要  
In this paper we want to establish sharp rates of both L~2 and L~∞ decay of glo-bal solutions to the initial value problems for 2-dimensional incompressible Navier-Stokes equations, with, initial data U_0(x)∈L_1∩L~2. U_t + U·U -△U + p = 0,·U = 0,U(x,0) = U_0(x), (1)where U = U(x,t) = (U_1(x,t),U_2(x,t)) is a real vector valued function, △is 2-di-mensional Laplace operator, is gradient operator. We will present a simple method for establishing the decay results.
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Stability of Solitary Waves for the Nonlinear Derivative Schrodinger Equation
郭柏灵,吴雅萍
数学进展. 1993, 22 (5): 473-475.  
摘要  
1 IntroductionConsider tke following nonlinear quintic derlvative Schrodinger equation u_t=iu_(xx)+ig(|u|~2)u+[(S_0+S_2|u|~2)u]_x,x∈R (1)with g(|u|~2)=c_3|u|~2+c_5|u|~4 (2)and s_0,s_2,c3,c_5 real constants Problem(1)-(2)appears in various physical applications,such as plasma physics,nonlinear optics,and nonrelativistic quantum physics. For the case s_0=s_w=0,equ.(1)becomes the classical nonlinear Schrodinger e-quation,which has been studied by many authors,especially for the stability ofsolitary waves.In this case(1)can be written in the following abstract Hamil-
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Second Equivalence Theorem of Multivariate Polynomial System and Eigenproblem
冯果忱,吴文达,黄铠
数学进展. 1993, 22 (5): 476-477.  
摘要  
In[1,2] we have constructed the Joint eigenproblem equivalent to multivariatepolynomial system and presented an algorithm to solve latter.In this paper we willstudy another equivalence theorem for the same problem.The computation of thecorresponding eigenvalues is numerically stable. Consider multivarite polynomial system
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ABSTRACTS OF DOCTORIAL DISSERTATIONS
数学进展. 1993, 22 (5): 478-480.  
摘要  
Spectral Analysis for a Kind ofPseudodifferential Operators andResonances for One-dimensional Di-fferential Operators,Fan Qihong(樊启洪),Peking University,Supervisor:M.T.Cheng(程民德)and X.P.Wang(王雪平),Approved:1991,7. The works in this dissertation in-clude the spectral analysis for a kindof nonsemibounded pseudodifferentialoperators and the resonance problemsfor one-dimensional differential oper-ators.They are motivated by Titch-marsh’s work on spectrum for one-
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