Pell方程组x2-ay2=1和 z2-by2=1的解数

设a,b是不同的正整数,本文证明了当max(a,b)＞10126时,Pell方程组x2-ay2=1和z2-by2=1至多有2组正整数解(x,y,z).     

关于Goormaghtigh方程(x~3-1)/(x-1)=(y~n-1)/(y-1)

本文证明了：Ｇｏｏｒｍａｇｈｔｉｇｈ方程适合的例外解（ｘ，ｙ，ｎ），满足以及     

含两时滞捕食-被捕食系统的稳定性及分歧

本文研究一类含两相异时滞的捕食－被捕食系统的稳定性及分歧。首先，我们讨论两相异时滞对系统唯一正平衡点的稳定性的影响，通过对系数与时滞有关的特征方程的分析，建立了一种稳定性判别性。其次，将一个时滞看成分歧参数，而另一个看作固定参数，我们证明了该系统具有HOPF分歧特性。最后，我们讨论了分歧解的稳定性。     

数学实验课的教学模式研究

本文主要探讨工科数学教学中数学实验课的多个层次和开设数学实验课的几种方式 ,并且介绍我们的一些具体做法和面临的一些问题     

广义Lebesgue-Ramanujan-Nagell方程研究的新进展

广义Lebesgue-Ramanujan-Nagell方程是数论中一类重要的Diophantine方程.本文介绍了此类方程的近期结果和尚未解决的问题.     

广义 n-皇后问题

它们分别称为Γ_(?) 的第 i 行 ,第 j 列,第 p 条左对角线与第 q 条右对角线.形象地,第 p 条左对角线是从棋盘左下角数起的第 p 条从左上方到右下方的斜线;而第 q 条右对角线是从棋盘左上角数起的第 q 条与左对角线正交的斜线.对Γ_(?) 的任一子集 X,记     

Double folding model calculation applied to fusion reactions

The interaction potential between a spherical and a deformed nucleus is calculated within the double-folding model for deformed nuclei.We solve the double folding potential numerically by using the truncated multipole expansion method.The shape,separation and orientation dependence of the interaction potential,fusion cross section and barrier distribution of the system 16O+154Sm are investigated by considering the quadrupole and hexadecapole deformations of 154Sm.It is shown that the height and the position of the barrier depend strongly on the deformation and the orientation angles of the deformed nucleus.These are quite important quantities for heavy-ion fusion reactions,and hence produce great effects on the fusion cross section and barrier distribution.     

Theoretical study of the CH3 + NS and related reactions: mechanism of HCN formation

More than thirty equilibrium and transition structures on the [CH₃NS] potential energy surface have been located using the B3LYP/6-311 + + G(d,p) method. Thioformaldoxime (3) turns out to be the most stable isomer followed by thionitrone (2), a three-membered ring, thionitrosyl methane (1) and thiazyl methane. These isomers are connected to each other by 1,2H and 1,3H shifts and ring—chain rearrangement, but the associated energy barriers are rather high, making most of them stable with respect to unimolecular transformations. Starting from CH₃ + NS, a possible initial atmospheric reaction, HCN formation appears to be the most favoured process through a cascade involvement of 1, 2 and 3. The standard heats of formation, ΔH ⁰ _f,298 are calculated to be: 3, 149kJmol^?1; and 1, 218kJmol^?1; using the CCSD(T)/6-311+ +G(3df,2p) method, with an error of ±10kJ mol^?1.     

新型数据采集系统芯片ADμC812在物理实验中的应用

ADμC812是新一代数据采集系统芯片，它将A／D，D／A转换器与8051完全兼容的内核等器件集成在一块芯片上，利用ADμC812的ISP功能，可制造出具有远程升级能力的智能化仪器；利用ADμC812的DMA功能，能解决物理实验中某些需要进行高速数据采集的问题。     

测定树木中总氮和总磷的新方法

本文采用过硫酸盐氧化树样中的总氮为硝态氮、总磷为磷酸盐,用分光光度法测定总氮量和总磷量,测得结果表明,本法所得精密度和准确度是比较好的,本方法能批量处理样品;省时、省电、省试剂、环境污染少。本法适用于树木中总氮总磷的测量。