关于多项式小分数部分的一个注解

设f(x)为任意一实系数多项式,N.G.Moshchevitin在他的文章[8]中给出了集合{α∈R∶ limn→∞ infnlog n‖af(n)‖＞0}的Hausdorff维数的下界.在本文中,我们延用文[8]的方法并结合齐次Moran集的维数理论给出这个集合Hausdorff维数的精确值.     

丢翻图方x2 + a2=2yn解法的计算研究

本文研究了一类丢番图方程的解.利用对Thue方程解的估计和方程解的连分式展开,获得了所求丢番图方程解的个数、解上界的估计和一般的求解算法.最后利用该算法给出了1≤a≤108的所有解.     

A New Proof of Diophantine Equation （^n2） = （^m4）

By using algebraic number theory and p-adic analysis method, we give a new and simple proof of Diophantine equation （^n2） = （^m4）     

一类弹性系统的精确L2-能控性

该文研究带有压电驱动器的Rayleigh梁系统的精确能控性.先用算子半群方法和提升结果[9]建立了Rayleigh梁方程解的正则性;再用Hilbert唯一性方法结合Diophantine逼近理论的某些结果得到了系统的精确L2-能控性.     

On some Diophantine fourier series

We continue our study on arithmetical Fourier series by considering two Fourier series which are related to Diophantine analysis. The first one was studied by Hardy and Littlewood in connection with the classification of numbers and the second one was studied by Hartman and Wintner by Lebesgue integration theory.     

Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in Rn akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the fundamental homogeneous theorems of R.C. Baker (1978) [2], Dodson, Dickinson (2000) [18] and Beresnevich, Bernik, Kleinbock, Margulis (2002) [8]. In the case of planar curves, the complete Hausdorff dimension theory is developed.     

Cohomology relative to a system of closed forms on the torus

To a system of closed one‐forms on the torus, we associate a differential complex and compute the induced cohomology groups provided that a related matrix satisfies a Diophantine condition.     

丢番图方程X~2-(a~2+1)Y~4=3-4a

设a≥2是正整数.本文证明了:当a=2时,方程X~2一(a~2+1)Y~4=3-4a仅有正整数解(X,Y)=(20,3);当a=3时,该方程仅有2组互素的正整数解(X,Y)=(1,1)和(79,5);当a≥4且4a+1非平方数时,该方程最多有4组互素的正整数解(X,Y);当a≥4且4a+1为平方数时,该方程最多有5组互素的正整数解(X,Y).