p-adic Measures of Algebraic Independence for the Values of Ramanujan Functions and Klein Modular Functions

In this paper, we give the p-adic measures of algebraic independence for the values of Ramanujan functions and Klein modular functions at algebraic points.     

满足Mahler型代数函数方程的函数值的p-adic超越度量

这篇文章给出了满足Mahler型代数函数方程的函数值的p-adic超越度量．     

A Mini Max Theorem for the Functionals with Hemicontinuous Gateaux Derivative and the Solution of the Boundary Value Problem for the Nonlinear Wave Equation

In this paper, a mini max theorem was showed mega which the paper proves a new existent and unique result on solution of the boundary value problem for the nonlinear wave equation by using the mini max theorem.     

Construction of Green＇s Functions for the Two-Dimensional Static Klein-Gordon Equation

In contrast to the cognate Laplace equation, for which a vast number of Green＇s functions is available, the field is not that developed for the static Klein-Gordon equation. The latter represents, nonetheless, a natural area for application of some of the methods that are proven productive for the Laplace equation. The perspective looks especially attractive for the methods of images and eigenfunction expansion. This study is based on our experience recently gained on the construction of Green＇s functions for elliptic partial differential equations. An extensive list of boundary-value problems formulated for the static Klein-Gordon equation is considered. Computerfriendly representations of their Green＇s functions are obtained, most of which have never been published before.     

C~∞-solutions for the Second Type of Generalized Feigenbaum's Functional Equations

This work focuses on the second type of generalized Feigenbaum's equation(f(x)) = f(f((x))),f(0) = 1, 0 ≤ f(x) ≤ 1, x ∈ [0, 1],where (x) is C∞-increasing function on [0, 1] and satisfies that (0) = 0, 0 (x) 1(x ∈ [0, 1]).Using constructive method, we discuss the existence of C∞-single-valley solutions whose derivatives are not equal to 0 on origin of the above equation.     

Turán Quadrature Formulas and Christoffel Type Functions for the Chebyshev Polynomials of the Second Kind

An explicit representation for the Cotes numbers of Turán quadrature formulas based on the zeros of the Chebyshev polynomials of the second kind and its asymptotic behavior are given. The asymptotic formula for the corresponding Christoffel type functions is also provided. This revised version was published online in June 2006 with corrections to the Cover Date.     

Measure-Preservation and the Existence of a Root of <Emphasis Type="Italic">p</Emphasis>-Adic 1-Lipschitz Functions in Mahler’s Expansion

In this paper, we provide necessary and sufficient conditions for 1-Lipschitz functions that are uniformly differentiable mod p on ?_p to be measure-preserving, in Mahler’s expansion, and show that these conditions can be modified to guarantee the existence of a root of p-adic Lipschitz functions.     

Bäcklund transformation and conservation laws for the variable-coefficient <Emphasis Type="Italic">N</Emphasis>-coupled nonlinear Schrödinger equations with symbolic computation

Considering the integrable properties for the coupled equations, the variable-coefficient Ncoupled nonlinear Schrödinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Bäcklund transformation for such a coupled system denoting in the Γ functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.     

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript> and <Emphasis Type="Italic">L</Emphasis><Superscript>∞</Superscript> norm estimates of the cost of the controllability for heat equations

This paper is concerned with the bound of the cost of approximate controllability and null controllability of heat equations, i.e., the minimal Lp norm and L∞ norm of a control needed to control the system approximately or a control needed to steer the state of the system to zero. The methods we use combine observability inequalities, energy estimates for heat equations and the dual theory.     

Mahler型函数值的代数无关度量

In this paper,we give the algebraic independence measures for the values of Mahler type functions in complex number field and p-adic number field,respectively.     

Mahler型函数值代数无关性的p-adic度量

本文给出Mahler型函数值代数无关性的p-adic度量.     

Mahler型函数值的代数无关度量

利用初等的结式方法研究满足多项式形式的函数方程组的Mahler型函数的零点估计,给出了满足非线性函数方程组的Mahler型函数在代数点值的代效无关度量．     

Mahler函数值的代数无关性

给出M ah ler型函数值超越次数的下界.     

Algebraic Independence of Certain Generalized Mahler Type Numbers

In this paper the generalized Mahler type number Mh（g;A,T） is defined, and in the case of multiplicatively dependent parameters gi, hi（1 ≤ i ≤ s） the algebraic independence of the numbers Mhi （gi; A, T）（1 ≤ i ≤ s） is proved, where A and T are certain infinite sequences of non-negative integers and of positive integers, respectively. Furthermore, the algebraic independence result on values of a certain function connected with the generalized Mahler type number and its derivatives at algebraic numbers is also given.     

Integer transfinite diameter and polynomials with small Mahler measure

In this work, we show how suitable generalizations of the integer transfinite diameter of some compact sets in give very good bounds for coefficients of polynomials with small Mahler measure. By this way, we give the list of all monic irreducible primitive polynomials of of degree at most with Mahler measure less than and of degree and with Mahler measure less than .

     

Mahler型函数值的代数无关度量

利用初等的结式方法研究满足多项式形式的函数方程组的Mahler型函数的零点估计,给出了满足非线性函数方程组的Mahler型函数在代数点值的代数无关度量.