大边数图的禁止路色数

研究了具有禁止路的条件色数，若把这一色数记作X(G,^7Pj)，得出了大边数图G的X（G，^7Pj）值在不同情形下为[n/(j-1)]或[(n-1)/(j-1]。     

一族Liouville可积系及其Hamilton结构

指出了获得可积系的方法一般是在零曲率框架Ut-V(n)x+[U,V(n)]=0中进行,所选取的V的形式为V=∑m≥0Vmλ-m,Vm=ambmcm-am.构造了一个等谱问题,特别是对于该等谱问题,选取的V中既含有谱位势,又含有a,b,c的关于x的导数项,得到了一个新的Lax对.利用屠格式获得了一族新的Liouville可积系,具有Hamil ton结构.     

多步Runge-Kutta方法线性辛的必要条件(英)

给出多步Runge-Kutta方法关于线性Hamilton系统是线性辛的一些必要条件。     

一类三波作用模型的不变代数曲面、Hamilton结构及无穷远动力学行为

首先利用代数几何中的消除理论给出一类三波作用模型存在不变代数曲面的充分条件; 其次, 构造出该系统无穷多个Hamilton-Poisson结构, 即该系统是双Hamilton的; 最后, 利用R³中的Poincaré紧致化技巧完整刻画该系统在无穷远处的动力学行为.     

一个模型量子系统的辛差分格式

根据非自治哈密顿系统的辛差分格式，构造了适用于一个哈密顿显含时间的模型量子系统的辛差分格式。并应用这一格式计算了不同能量本征态的几率分布和总能量的时间演变。     

A FURTHER GENERALIZATION OF JUNG''''S THEOREM

Let G be a graph of order n. We define the distance between two vertices u andv in G, denoted by d(u, v), as the minimum value of the lengths of all u-v paths. We writeσ_k(G)=min{∑_i=1~k d(v_i)|{v_1, v_2,…, v_k} is an independent set in G} and NC2(G)=min {|N(u)∪N(v)| | d(u, v)=2}. We denote by ω(G) the number of components of agraph G. A graph G is called 1-tough if ω(G\S)≤|S| for every subset S of V(G) withω(G\S)>l. By c(G) we denote the length of the longest cycle in G; in particular, G iscalled a Hamiltonian graph if c(G)=n. H.A. Jung proved that every 1-tough graphwith order n≥11 and σ2≥n-4 is Hamiltonian. We generalize it further as follows: ifG is a 1-tough graph and σ3(G)≥n, then c(G)≥min {n,2NC2(G)+4}. Thus, theconjecture of D. Bauer, G. Fan and H.J. Veldman in [2] is completely solved.     

A NEW HIERARCHY OF LAX AND LIOUVILLE INTEGRABLE EVOLUTION EQUATIONS ASSOCIATED WITH AN ISOSPECTRAL PROBLEM IN THE LOOP ALGEBRA A2

In this paper, an isospectral problem with five potentials is investigated in loop algebra A2 such that a new hierarchy of evolution equations with five arbitrary functions is obtained. And then by fixing the five arbitrary functions to be certain flmctions and using the trace identity, the generalized Hamiltonian structure of the hierarchy of evolution equations is given, it is shown that this hierarchy of equations is Liouville integrable. Finally some special cases of the isospectral problem are also given.     

Lagrange相交数的下界估计

本文给出了Ｔ￣（２ｎ），ＣＰ￣ｍ与ＣＰ￣ｍ的乘积中一类Ｌａｇｒａｎｇｅ子流形相交数的下界估计。     

四阶杆振动方程的sinh(x)辛格式

本文首先考虑建立四阶杆振动方程的哈密顿方程组,然后利用Hyperbolic函数sinh(x)构造具有周期边界条件的具任意阶精度的辛格式,并讨论其稳定性,最后的数值结果表明,辛格式具有良好的长时间数值行为.     

一类次二次Hamilton系统的次调和解的存在性

运用临界点理论中的极小极大方法,得到一类次二次Hamilton系统的次调和解的存在性定理。