高次曲线拟合定积分计算公式的导出及程序实现

导出比S impson公式精度更高的三次、四次曲线近似的高次曲线拟合定积分公式,并给出实现该算法的C语言源程序.     

耦合非线性Klein-Gordon方程组的周期解

利用修正的Jacobi椭圆函数展开方法,获得了一类耦合非线性Klein-Gordon方程新的周期解.在极限条件下,这些解退化成孤波解.借助于Mathematica软件,此方法能部分地在计算机上实现.这种方法也可以用来求解其它的非线性方程.     

一类五阶非线性发展方程新的周期解

通过构造辅助方程，把一类五阶非线性发展方程的求解问题转化为非线性代数方程组的求解问题，由此求得了该类五阶非线性方程的新的周期解．在极限情形，也得到了孤波解和三角函数解．     

一类非齐次边值的非线性椭圆方程的可解性

对于一类非齐次边值的非线性椭圆方程,应用变分方法研究了参数λ,μ∈R以及实数p,q在1到2N/(N-2)范围内此类方程的可解性,得到了一些新的结果.     

A Secure MAKAP for Wireless Communication

A mutual authentication and key establishment protocol proposed by Aydos et al, for wireless communication based on elliptic curve cryptography can provide authentication between the user and server and they agreement a session key in the end of it. Unfortunately, Mangipudi pointed out Aydos＇ scheme was incurred the man-in-middle attack denial-of-service attack and impersonation based on man-in-middle attack. Then he proposed an improved scheme m overcome the above weakness. However, there is an attack which can forge the message required in the protocol and impersonation a valid user to the server.     

平面上一类一阶拟线性椭圆型方程组的非线性边值问题

本文基于连续性方法和利用已建立的一个积分算子,研究了Douglis意义超复函数论的非线性Riemann边值问题的可解性,解可用逐次逼近法构造出来。     

Fast multiplication on certain elliptic curves

The multiplication of points on elliptic curves is the most important operation in the implementation of elliptic curve cryptosystems. Based on Frobenius map, a fast multiplication on the curves defined by y" + xy = x + x~ + 1 over finite fields of characteristic 2 is given, and its optimality in the sense of using minimal numbers of additions of points is proved.     

一个3×3矩阵谱问题及其 Darboux 变换

构造了一个基于3×3 矩阵谱问题的 Lax 对, 求出了该 Lax 对所对应的梯队. 该梯队不仅包含了 KdV 和 mKdV 方程, 还包含了高阶 NLS 方程. 此外, 根据谱问题的规范变换, 导出了此谱问题的 Darboux 变换, 并得出了其精确解.     

二阶非线性椭圆型复方程的间断边值问题

讨论了二阶非线性椭圆型方程在多连通区域上的间断边值问题。提出此边值问题的一种新的适定提法，并给出这种变态边值问题的先验估计式，然后使用上述解的估计与Schauder不动点原理，证明这种变态边值问题解的存在性，进而导出原边值问题的可解条件。     

Ways to produce and measure atto- and femtosecond soft X-ray pulses

The ways to produce and measure atto-and femtosecond soft X-ray pulses are reported. The laser phase relation of high-order harmonic generation(HHG) shows two different radiation energy distribu-tions in time(or laser phase) domain. These energy-phase relations are helpful for realizing the dy-namic processes of HHG. Two presented parameterized formulas can be used to calculate the durations of the energy distributions with a bandwidth of the pulse. These formulas are useful in calculating and simulating pulses transports and interactions with mediums. The time structures of atto-and femto-second soft X-ray pulses can be directly measured with photoelectron spectrum transfer equations and the related laser phase determination methods without any previous pulse shape and the instantane-ous frequency assumptions. These equations and methods can be used to evaluate and improve the technical parameters of the ultra-short X-ray sources. They have wide measurement ranges and high time resolutions,which may enable ultra-fast measurements to reach metrological precisions,and lead to a new tide of scientific researches in physics,chemistry,biochemistry,etc. The application of atto-and femtosecond X-rays as well as the theoretical and technical problems in measurements are briefly discussed.