ON THE FEIGENBAUM''''S FUNCTIONAL EQUATION_f~P (λx )=λf (x)

ＯＮ ＴＨＥ ＦＥＩＧＥＮＢＡＵＭ＇Ｓ ＦＵＮＣＴＩＯＮＡＬ ＥＱＵＡＴＩＯＮ_ｆ~Ｐ（λｘ）＝λｆ（ｘ）￥ＬＩＡＯＧＯＮＧＦＵＡｂｓｔｒａｃｔ：ＴｈｅａｕｔｈｏｒｃｏｎｓｉｄｅｒｓｔｈｅＦｅｉｇｅｎｂａｕｍ＇ｓｆｕｎｃｔｉｏｎａｌｅｑｕａｔｉｏｎｆＰ...     

关于迭代方程G（f（x），f~（n_1）（x），…，f~（n_k）（x））＝F

关于迭代方程Ｇ（ｆ（ｘ），ｆ￣（ｎ＿１）（ｘ），…，ｆ￣（ｎ＿ｋ）（ｘ））＝Ｆ（ｘ）的连续解司建国（滨州师范专科学校数学系，山东２５６６０４）关键词迭代方程，连续解，存在性；唯一性，稳定性．分类号ＡＭＳ（１９９１）３９Ｂ１２／ＣＣＬＯ１７５．１４本文...     

THE POSITIVE SEMIDEFINITE SOLUTION OF THE MATRIX EQUATION （A^TXA, B^TXB） = （C,D）

In this paper, we consider the positive semidefinite solution of the matrixequation (A^TXA, B^TXB) = (C,D). A necessary and sufficient condition for the existence of such solution is derived using the generalized singular value decomposition.The general forms of positive semidefinite solution are given.     

THE NAGUMO EQUATION ON SELF－SIMILAR FRACTAL SETS

The Nagumo equationut ut=△u+bu(u-a)(1-u),t＞0 is investigated with initial data and zero Neumann boundary conditions on post-critically finite (p.c.f.) self-similar fractals that have regular harmonic structures and satisfy the separation condition. Such a nonlinear diffusion equation has no travelling wave solutions because of the“pathological” property of the fractal. However, it is shown that a global Hoelder continuous solution in spatial variables exists on the fractal considered. The Sobolev-type inequality plays a crucial role, which holds on such a class of p.c.f self-similar fractals. The heat kernel has an eigenfunction expansion and is well-defined due to a Weyl‘s formula. The large time asymptotic behavior of the solution is discussed, and the solution tends exponentially to the equilibrium state of the Nagumo equation as time tends to infinity if b is small.     

迭代方程nΣi=1λiF^i=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： ｎΣｉ＝１λｉＦ＾ｉ（ｚ）＝Ｆ（ｚ）， （＊） 用优函数方法研究方程（＊）的局部解析解的存在性问题。     

关于函数y=f（x）与y=│f（x）│

本对函数ｙ＝ｆ（ｘ）与ｙ＝│ｆ（ｘ）│的部分性质进行了比较和分析,指出了它们性质上的区别与联系。     

SOLVING COLORED YANG-BAXTER EQUATION BY WU＇S METHOD

In this article, we discuss nonsymmetric solutions of the colored Yang-Baxter equation dependent on spectral as well as colored parameters and give all seven-vertex solutions by Wu＇s method. It is also proved that the solutions are composed of six groups of basic solutions up to five solution transformations. Moreover, al l solutions can be classified into two categories called Baxter type and free-fermion type.     

ON A FUNCTIONAL EQUATION

In this article, the author derives a functional equation η（s）=[（π/4）^s-1/2√2/π Г（1-s）sin（πs/2）]η（1-s） （1） of the analytic function η（s） which is defined by η（s）=1^-s-3^-s-5^-s＋7^-s＋… （2） for complex variable s with Re s 〉 1, and is defined by analytic continuation for other values of s. The author proves （1） by Ramanujan identity （see [1], [3]）. Her method provides a new derivation of the functional equation of Riemann zeta function by using Poisson summation formula.     

A CHARACTERIZATION OF THE SOLUTIONS OF p－ORDER FEIGENBAUM＇S FUNCTIONAL EQUATION WITH TOPOLOGICAL ENTROPY 0

ＡＣＨＡＲＡＣＴＥＲＩＺＡＴＩＯＮＯＦＴＨＥＳＯＬＵＴＩＯＮＳＯＦｐ－ＯＲＤＥＲＦＥＩＧＥＮＢＡＵＭ＇ＳＦＵＮＣＴＩＯＮＡＬＥＱＵＡＴＩＯＮＷＩＴＨＴＯＰＯＬＯＧＩＣＡＬＥＮＴＲＯＰＹ０（廖公夫）￥ＬｉａｏＧｏｎｇｆｕ（Ｄｅｐｔ．ｏｆＭａｔｈ．，Ｊｉ...     

泛函微分方程的Lipschitz稳定性

本文给出了泛函微分方程一致Lipschitz稳定的Liapunov－Razumikhin型判据和实例．     

DISCUSSION ON THE CONTINUOUS SOLUTIONS OF A FUNCTIONAL EQUATION

1 IntroductionIn an issue of the American Mathematical Monthly [1] the following problemwas raised:"Determine all homeomorphisms f from [0,1] onto [0,1] that are solutionsof the functional equationf(Zx -- f(x)) = x for all x E [0,IJ.',Ratti and Lin [2] generalized the problem in two different directions. In thispapert we consider the following functional equationf(cr(x) df(x)) = F(x), (1.1)where c < 0,d > 0, c d = 1. We shall give the sufficient conditions ofthe existence, uniqueness a…     

具有时滞的n维Lienard型方程的调和解

本文讨论具有周期扰动的ｎ维时滞Ｌｉｅｎａｒｄ型方程ｐ（ｔ）的调和解．给出了存在调和解的若干充分条件,推广了ＧｅＷｅｉｇａｏ（１９９１）文中的相关结果．     

ON THE EQUIVALENCE OF THE ABEL EQUATION

This article uses the reflecting function of Mironenko to study some complicated differential equations which are equivalent to the Abel equation. The results are applied to discuss the behavior of solutions of these complicated differential equations.     

ON THE MINIMAL NONNEGATIVE SOLUTION OF ONSYMMETRIC ALGEBRAIC RICCATI EQUATION

We study perturbation bound and structured condition number about the minimalnonnegative solution of nonsymmetric algebraic Riccati equation,obtaining a sharp per-turbation bound and an accurate condition number.By using the matrix sign functionmethod we present a new method for finding the minimal nonnegative solution of this al-gebraic Riccati equation.Based on this new method,we show how to compute the desiredM-matrix solution of the quadratic matrix equation X~2-EX-F=0 by connecting itwith the nonsymmetric algebraic Riccati equation,where E is a diagonal matrix and F isan M-matrix.     

Euclid域中Diophantus方程的整数解

本文研究了两个典型Diophantus方程的整数解的问题.利用二次域中的重要理论和二次代数整数环中算术基本定理,获得了两个典型Diophantus方程在Euclid域中的所有整数解,推广了文献[6]的结果.     

关于广义Ramanujan-Nagell方程的一点注记

本文研究了广义Ramanujan-Nagell方程的正整数解,利用初等方法,得到了它的所有偶数解,从而部分地解决了该方程的求解问题.     

QUENCHING ON BOUNDARY TO THE NEWTON FILTRATION EQUATION(Ⅰ)

This paper discusses the global existence and quenching of the solution tothe Newton filtration equation with the nonlinear boundary condition. The authors alsodiscuss the profile of the quenching solution in the quenching time and obtain the quenchingrate of the quenching solution.