Normalized binomial mid-coefficients and power means

Let

     

On binomial Thue-Mahler equations

We give a rather sharp upper bound for the degree of a binomial Thue--Mahler equation in terms of the coefficients and the primes involved. Further, we establish explicit lower bounds for the greatest prime factor of a binomial binary form at integral points. Our estimates considerably generalize and improve the earlier results obtained in this direction.     

The relationship between the nonexistence of generalized bent functions and diophantine equations

Two new results on the nonexistence of generalized bent functions are presented by using properties of the decomposition law of primes in cyclotomic fields and properties of solutions of some Diophantine equations, and examples satisfying our results are given.     

孪生素数椭圆曲线在p=3时的整数点(英文)

本文研究了孪生素数椭圆曲线的整数点问题.运用初等数论方法,获得了一组孪生椭圆曲线的所有整数点.     

2+1 维变系数广义KP方程的椭圆周期解

运用Jacobi椭圆函数展开法求得了2 1维变系数广义KadoratsevPetviashvili方程的椭圆周期解及孤立波解．     

椭圆曲线y~2=x~3+27x-62的整数点

根据四次Diophantine方程的已知结果,运用初等数论方法证明了:椭圆曲线y~2=x~3+27x-62仅有整数点(x,y)=(2,0)和(28844402,±154914585540).     

Elliptic curves retaining their rank in finite extensions and Hilbert's Tenth Problem for rings of algebraic numbers

Using Poonen's version of the ``weak vertical method' we produce new examples of ``large' and ``small' rings of algebraic numbers (including rings of integers) where and/or the ring of integers of a subfield are existentially definable and/or where the ring version of Mazur's conjecture on the topology of rational points does not hold.

     

Proportionally modular diophantine inequalities

We study the sets of nonnegative solutions of Diophantine inequalities of the form with a,b and c positive integers. These sets are numerical semigroups, which we study and characterize.     

一类带奇异系数椭圆方程解的存在性

本文运用变分方法及Hardy不等式讨论了一类带奇异系数的临界椭圆方程，证明了在一定条件下方程解的存在性。     

Elliptic planar vector fields with degeneracies

This paper deals with the normalization of elliptic vector fields in the plane that degenerate along a simple and closed curve. The associated homogeneous equation is studied and an application to a degenerate Beltrami equation is given.

     

椭圆曲线上的基的选择与实现

在研究了椭圆曲线y2≡x3+ax+b(modp)上的点的一些性质后,提出了基的计算、验证、选择等算法,同时研究了基的选择、点积效率、安全性三者之间的关系.最后实现了以椭圆曲线基的选择.     

Solving constrained Pell equations

Consider the system of Diophantine equations , , where is a given integer polynomial. Historically, such systems have been analyzed by using Baker's method to produce an upper bound on the integer solutions. We present a general elementary approach, based on an idea of Cohn and the theory of the Pell equation, that solves many such systems. We apply the approach to the cases and , which arise when looking for integer points on an elliptic curve with a rational 2-torsion point.

     

Neumann Problem of Quasilinear Elliptic Equations with Limit Nonlinearity in Boundary Condition

This paper is concerned with the existence of solutions to the equation D_j(a^{ij}(x,u)D_i,u)-\frac{1}{2}D_sa^{ij}(x,u)D_iuD_ju + λ u = 0 on a bounded domain under the Neumann boundary condition a{ij}(x,u)D_iuϒ_j = lul^{\frac{2}{n-2}}u.     

退化椭圆型方程的一个边值问题

本文主要讨论在ｘ 轴上退化的二阶椭圆型偏微分方程的混合边值问题．     

Degenerate Nonlinear Boundary Value Problems for Fully Nonlinear Elliptic Equations of Second Order

In this paper, we will consider the degenerate nonlinear boundary value problems for nonlinear elliptic equations. We extend Lieberman & Trudinger's results from nondegenerate oblique derivative boundary values to degenerate boundary values.     

Vectors of given diophantine type

For a function ?(y) = o(y ^?1/s ), y → ∞, we prove the existence of vectors ?∈? ^s admitting, for any ε > 0, infinitely many simultaneous ?(1 + ε-approximations, but not admitting any simultaneous ?-approximations.