Hamiltonian cycles in n-factor-critical graphs

A graph G is said to be n-factor-critical if G−S has a 1-factor for any SV(G) with |S|=n. In this paper, we prove that if G is a 2-connected n-factor-critical graph of order p with , then G is hamiltonian with some exceptions. To extend this theorem, we define a (k,n)-factor-critical graph to be a graph G such that G−S has a k-factor for any SV(G) with |S|=n. We conjecture that if G is a 2-connected (k,n)-factor-critical graph of order p with , then G is hamiltonian with some exceptions. In this paper, we characterize all such graphs that satisfy the assumption, but are not 1-tough. Using this, we verify the conjecture for k2.     

一类函数项级数的求和

以微分方程为工具 ,推出一类一致收敛且具有分析性质的函数项级数的求和公式 ,进而推广了五种基本幂级数 [1 ] 的和函数公式 .     

中心多项式与环的交换性

本文证明了环的一个交换性定理,它是文献[6-8]中相应结论的推广,     

与双原子相互作用的双模关联场的相位性质

根据Pegg和Barnett相位理论研究了与双原子相互作用的双模SU（1,1）相干场的相位特性,证明了光场每个模的相位及两个模的相位差均保持随机分布,给出了光场两个模的相位和方差的表达式,揭示了在适当的初始条件下,系统呈现原子的相干捕获现象。     

四波混频过程中差频与和频的竞争研究

Tunable intense Vacuum Ultraviolet (VUV) laser was generated by two-photon resonant four wave difference frequency mixing (ω-=2ωUV-ωT) in Xenon. In the experiment some resonance attenuations of the VUV were observed at certain difference frequencies. These attenuations occur when the sum frequencies ω+=2ωUV+ωT coincide with excited ns (n=10,11) and nd (n=8~13) states. The third order linear susceptibility χ(3)（2ωUV+ωT;ωUV,ωUV+ωT） is reasonably increased by the double resonance enhancement, so the conversion efficiency of sum frequency mixing can be very high and the power of the pump laser is decreased and thus the difference frequency output is attenuated.     

Gauss小波变换像空间的描述

在连续小波变换像空间是再生核Hilbert空间的基础上,针对经常用于边界检测并且使用效果非常好的Gauss小波,给出了其小波变换像空间的再生核具体表达式.并且当固定尺度因子和固定平移因子时,利用再生核空间理论,对Gauss小波变换像空间做了具体描述,分别给出了Gauss小波变换像空间中的等距恒等式和反演公式,这为进一步研究一般的小波变换像空间提供了理论基础.     

关于一个典型函数Fourier级数的Gibbs现象

In this paper,we point out that the Fourier series of a classical function∑∞k=1 sin kx/k has the Gibbs phenomenon in the neighborhood of zero.Furthermore,we estimate the upper bound of its partial sum and get:supn≥1‖n∑k=1sin kx/k‖∫x0sin x/xdx=1.85194,which is better than that in[1].