fn(z)+fm(z+c)=eAz+B的有限级亚纯解

该文研究了复平面上的差分方程fn(z)+fm(z+c)=eAz+B(c≠0)的有限级亚纯解,其中n,m为整数,A,B,c∈C为复数.     

A(α)-Acceptability of Rational Approximations to Function exp(z)

In this paper, two necessary and sufficient conditions, and a sufficient condition of A(α)-acceptability for (n, m) rationa approximation to function exp(z) are given, where a ∈ (0, x/2). A necesary and sufficient condition of A-acceptability for (n, m) rational approximation to exp(z) of order p is obtained, where n≤m≤p.     

关于亚纯函数φ(z)f~n(z)f~((k))(z)的值分布

设n和k为任意的正整数,f(z)是复平面上超越亚纯函数,φ(z)为f(z)的不恒为零的小函数,讨论了亚纯函数φ(z)fn(z)f(k)(z)值分布,并提出一个新的定理,进行了较为详细的证明.     

Estimates on μ(z)-homeomorphisms of the unit disk

In the theory ofK-quasiconformal mappings, Mori's theorem shows thatK-quasiconformal mappings on the unit disk satisfy the Hölder condition, where the coefficient 16 is best possible. In this paper, we prove that self-μ(z)-homeomorphisms on the unit disk have an analogical result to Mori's theorem when the integral mean dilatations are controlled by log function. An unimprovable inequality is obtained.     

Einige Eigenschaften der Lösungen vonw′=a(z)+b(z) w+c(z) w 2

Ohne ZusammenfassungHerrn A.Ostrowski zum sechzigsten Geburtstage gewidmet     

探索以(Fn-k,Fn,Fn)为边长的Fibonacci三角形

Fibonacci三角形是边长为Fibonacci数、面积为整数的三角形.存在以(F<,n-k>,F<,n>.F<,n>)为边长的Fibonacci三角形的情形可以被划分为三类(k时,不存在边长为(F<,n-k>,F<,n>.F<,n>)的Fibonacci三角形.     

Zeros of the partial sums of cos (z) and sin (z). I

We extend results of Szeg (1924) and Kappert (1996) on the location of the zeros of the normalized partial sums of cos(z) and sin(z), and their rates of convergence to the associated Szeg curves.     

微分方程f″ e~(az)f′ Q(z)f=F(z)的复振荡

该文研究了线性微分方程f″ eazf′ Q( z) f=F( z)的复振荡问题,其中Q( z)、F( z) ( 0 )是整函数,且σ( Q) =1 ,σ( F) < ∞,Q( z) =h( z) ebz,h( z)是多项式,b≠- 1是复常数,那么上述线性微分方程的所有解f( z)满足λ( f) =λ( f) =σ( f) =∞,　λ2 ( f) =λ2 ( f) =σ2 ( f) =1 .至多除去两个例外复数a及一个可能的有穷级例外解f0 ( z) .     

Some inequalities for polynomials satisfying p(z)≡znp(1/z)

Let be a polynomial degreen and let . Then according to Bernstein’s inequality ‖p’‖≤n‖p‖. It is a well known open problem to obtain inequality analogous to Bernstein’s inequality for the class II_n of polynomials satisfying p(z)≡zⁿp(1/z). Here we obtain an inequality analogous to Bernstein’s inequality for a subclass of II_n. Our results include several of the known results as special cases.     

关于f(f~(k)~n-a(z)的零点

本文讨论了杨重骏和杨乐等提出的一个猜想：设ｆ是一超越整函数，ｎ，ｋ是两个正整数，则当ｎ２时，ｆ（ｆ（ｋ）ｎ取任何非零有限值无穷多次，并证明了这个猜测，而且证明了，当ｆ是亚纯函数时的情形也成立，即有，设ｆ是超越亚纯函数，ｎ，ｋ是两个正整数，则当ｎ２时，ｆ（ｆ（ｋ）ｎ－ａ（ｚ）有无穷多个零点，其中ａ（ｚ）是ｆ的一个小函数     

SOME INEQUALITIES FOR POLYNOMIALS SATISFYING p(z)=z~n p(1/z)

Let p(z)=be a polynomial degree n and let Then accord-ing to Bernstein's inequality ||p'||相似文献   

Quadratic differentials (A(z − a)(z − b)/(z − c)2) dz2 and algebraic Cauchy transform

We discuss the representability almost everywhere (a.e.) in C of an irreducible algebraic function as the Cauchy transform of a signed measure supported on a finite number of compact semi-analytic curves and a finite number of isolated points. This brings us to the study of trajectories of the particular family of quadratic differentials A(z ? a)(z ? b)×(z ? c)^?2 dz². More precisely, we give a necessary and sufficient condition on the complex numbers a and b for these quadratic differentials to have finite critical trajectories. We also discuss all possible configurations of critical graphs.     

Transformations z(t) = L(t)y(ϕ(t)) of ordinary differential equations

The paper describes the general form of an ordinary differential equation of an order n + 1 (n ≥ 1) which allows a nontrivial global transformation consisting of the change of the independent variable and of a nonvanishing factor. A result given by J. Aczél is generalized. A functional equation of the form $f\left( {s,w_{00} \upsilon _0 ,...,\sum\limits_{j = 0}^n {w_{nj\upsilon _j } } } \right) = \sum\limits_{j = 0}^n {w_{n + 1j\upsilon j} + w_{n + 1n + 1} f\left( {x,\upsilon ,\upsilon _1 ,...,\upsilon _n } \right),}$ where $w_{n + 10} = h\left( {s,x,x_1 ,u,u_1 ,...,u_n } \right),w_{n + 11} = g\left( {s,x,x_1 ,...,x_n ,u,u_1 ,...,u_n } \right){\text{ and }}w_{ij} = a_{ij} \left( {x_i ,...,x_{i - j + 1} ,u,u_1 ,...,u_{i - j} } \right)$ for the given functions a _ij is solved on $\mathbb{R},u \ne {\text{0}}$ .     

The Value Regions of the Systems {f(z 1), f′(z 1)} and {f(z 1), f(z 2)} in the Class of Typically Real Functions

In the class T consisting of regular and typically real functions in the disk |x| < 1, the value regions of the system {f(z ₁), f(z ₁)} and {f(z ₁), f(z ₂)} are found for fixed z ₁ and z ₂. As an application, the value regions of f(z ₁) and f(z ₂) are found for f T with fixed value f(z ₁). Bibliography: 11 titles.     

迭代方程λ_if~i(z)=F(z)局部解析解的存在性

本文在复域中讨论一般多项式函数迭代方程用优函数方法研究方程（＊）的局部解析解的存在性问题．