关于S\''{a}rk\"{o}zy和S\''{o}s问题的一个注记

令$k,\ell \geq 2$是正整数.令$A$是无限非负整数的集合.对$n\in \mathbb{N}$, 令$r_{1,k,\ldots,k^{\ell-1}}(A, n)$表示方程$n=a_0+ka_1+\cdots +k^{\ell-1}a_{\ell-1}$, $a_0, \ldots, a_{\ell-1}\in A$解的个数. 在本文中, 我们证明了对所有$n\geq 0$, $r_{1,k,\ldots,k^{\ell-1}}(A, n)=1$当且仅当$A$是$k^\ell$进制展开中数位小于$k$的所有非负整数的集合. 这个结果部分回答了S\''{a}rk\"{o}zy and S\''{o}s关于多维线性型表示的一个问题.     

关于指数丢番图方程a~x+(3a~2-1)~y=(4a~2-1)~z的正整数解(英文)

本文通过计算Jacobi符号,运用代数数的对数线性型的下界估计,证明了:当整数a>1时,指数丢番图方程a~x+(3a~2-1)~y=(4a~2-1)~z仅有正整数解(x,y,z)=(2,1,1).     

一类指数丢番图方程的解

设m为正整数,且a=8m~3+3m,b=3m~2+1,c=4m~2+1.本文同时使用两个代数数的对数线性型下界估计,两个有理数方幂之差的P-adic赋值的下界估计的一些结果,以及二次域的类数与本原素因子的深刻结论,证明了,当m为任意正整数时,指数丢番图方程a~x+b~y=c~z仅有正整数解(x,y,z)=(2,1,3).     

Design and Synthesis of Macrocyclic Polyoxazoles

Two macrocyclic polyoxazoles with different sizes and numbers of side chains were designed and synthesized from the linear-type precursors obtained by the iterative application of oxazole formation reaction via effective trimerization or dimerization respectively under highly diluted conditions in one pot.     

Continuity properties for commutators of multilinear type operators on product of certain Hardy spaces

Similar to the property of a linear Calderdn-Zygmund operator, a linear fractional type operator Is associated with a BMO function b fails to satisfy the continuity from the Hardy space Hp into Lp for p ≤ 1. Thus, an alternative result was given by Y. Ding, S. Lu and P. Zhang, they proved that [b,Iα] is continuous from an atomic Hardy space Hp b into Lp, where Hp b is a subspace of the Hardy space Hp for n/（n ＋ 1） 〈 p ≤ 1. In this paper, we study the commutators of multilinear fractional type operators on product of certain Hardy spaces. The endpoint （Hp1 b1 ×... × HP2, Lp） boundedness for multilinear fractional type operators is obtained. We also give the boundedness for the commutators of multilinear Calderdn-Zygmund operators and multilinear fractional type operators on product of certain Hardy spaces when b ∈ （Lipβ）m（Rn）.     

A new trimeric furanocoumarin from Heracleum rapula

A new trimeric linear-type furanocoumarin,rapultririn A(1),was isolated from the underground part ofHeracleum rapula.The structure of this new compound was elucidated by NMR,MS spectroscopic methods.     

刻度问题与刻度分布模型

刻度问题与刻度分布模型杨克昌（湖南岳阳大学４１４０００）１问题的提出我们首先提出一个新颖有趣也有一定深度的“刻度问题”．有一长５０厘米的直尺，因使用日久，尺上所有刻度都已磨灭，限在尺上刻划１０条刻度，使得可用该尺度量１至５０之间任意整数厘米长度．问这...     

关于Mahler和Gelfond的线性型转换定理

本文证明了Mahler和Gelfond的两个线性型转换定理本质上是等价的,亦即除去某些非本质性的常数因子改变外,两个定理是互相蕴含的.     

关于丢番图方程$x^y+y^x=z^z$

利用$p$-adic对数线性型估计, 证明了方程x^y+y^x=z^z满足x,y,z均大于1的整数解(x,y,z)必然两两互素且有z<2.8*10^9.