长短波相互作用方程组的无穷序列新解

本文对长短波相互作用方程组作行波变换后转化成第一种椭圆方程,利用第一种椭圆方程的解和Bcklund变换,构造了长短波相互作用方程组的无穷序列新解.这里包括了椭圆函数解、双曲函数解、指数函数解和有理函数解.     

Bézier曲面的广义细分

将矩形和三角形Bézier 曲面的基于直线的细分推广到基于曲线的细分.运用多项式曲线细分矩形和三角形Bézier曲面,并以参数变换和多项式开花为工具, 计算出细分后每个子曲面片的Bézier控制顶点.曲线细分使细分方式的选择更灵活, 细分后的子曲面片及其边界的形状更丰富多彩,而且该方法能推广到有理情况.     

广义Fitzhugh Nagumo方程的无穷序列新解

利用辅助方程的几种结论,构造了广义Fitzhugh-Nagumo方程的多种无穷序列新解.步骤一,利用函数变换与首次积分,给出了辅助方程的新解、Bcklund变换和解的非线性叠加公式.步骤二,通过函数变换,将广义Fitzhugh-Nagumo方程的求解问题转化为非线性常微分方程的求解问题.步骤三,利用符号计算系统Mathematica与辅助方程的几种结论,构造了广义Fitzhugh-Nagumo方程的多种无穷序列新解.     

对笔记本电脑、台式机的观察

陌生的友善Compaq公司在1996年10月减缓了对其它厂商施加的价格压力。传统低价位强式机、笔记本产品的领导者,如Acer公司和Packard Bell公司,得以有片刻喘息之机。Compaq为什么变换手段、“宽大为怀”了呢?也许计算机智能公司提供的数据能够说明问题,在过去的一年里,Packard Bell的市场份额已丢掉大     

基于Bell态纠缠交换的身份认证协议

提出了一种新的量子身份认证协议,该协议以Bell态为传输载体,利用Bell态纠缠交换和Bell基测量对通信用户进行身份认证。两个Bell态的传送过程中不需要做任何的幺正变换,只需要执行Bell基测量和按位异或运算就可以实现信息的传输。整个过程中,量子载体操作简单且容易实现。此外,也验证了此协议的正确性。     

运用多项式曲线在多项式曲面上裁剪Bézier曲面

在多项式曲面的定义域上,以两多项式曲线及两直线段围成的简单区域作为裁剪区域,运用参数变换将该区域变换到标准正方形区域,以多项式开花为工具,将裁剪区域对应的子曲面片表示成Bézier曲面形式。对于参数平面上的复杂裁剪区域,则分割为若干简单区域来进行。该裁剪算法能处理形状较为复杂的曲面裁剪,方法对任意多项式曲面适用,而且能推广到有理情况。     

满秩仿Hermite多项式矩阵的J一谱分解计算

基于仿等价变换实现了满秩仿Hermite多项式矩阵的J-谱分解计算.对于一个满秩的仿Hermite多项式矩阵,首先用仿等价变换将其变换为单模的满秩仿Hermite多项式矩阵,进一步再用仿等价变换将其变换为常数满秩矩阵,最后变换为J-矩阵.将这些变换矩阵积累起来,得到满秩仿Hermite多项式矩阵的J-谱分解.在作者发展的多项式矩阵运算程序库的基础上,给出了实现所提出的计算方法的算法.数例表明,该方法是有效的.     

满秩仿Hermite多项式矩阵的J-谱分解计算

基于仿等价变换实现了满秩仿Hermite多项式矩阵的J-谱分解计算.对于一个满秩的仿Hermite多项式矩阵,首先用仿等价变换将其变换为单模的满秩仿Hermite多项式矩阵,进一步再用仿等价变换将其变换为常数满秩矩阵,最后变换为J-矩阵.将这些变换矩阵积累起来,得到满秩仿Hermite多项式矩阵的J-谱分解.在作者发展的多项式矩阵运算程序库的基础上,给出了实现所提出的计算方法的算法.数例表明,该方法是有效的.     

相位调制信号的小波参数估计方法及其Cramer-Rao界

现代雷达广泛使用相位调制信号,相位参数的有效估计对辐射源的识别和分类具有重要意义。运用小波变换方法对多项式相位信号的相位系数进行了估计,给出了小波变换方法下的估计多项式相位调制信号相位系数的Cramer-Rao下限,并提出了一种新的相位系数估计算法。理论分析和仿真结果表明利用小波变换方法估计相位调制信号的相位系数参数估值更精确,可以得到更低的Cramer-Rao下限。     

可验证的(n,n)门限量子秘密共享方案

基于中国剩余定理和Bell态,构造了一种可验证的秘密共享方案。在分发阶段,分发者Alice通过量子信道将秘密份额分发给参与者。在恢复阶段,Alice产生一个2 bit的Bell态,参与者与Alice对该Bell态进行一系列酉变换以重构秘密信息。分析结果表明,该方案能抵抗截获-重发攻击、纠缠-测量攻击、参与者攻击和特洛伊木马攻击。     

Wick类型的随机广义Kdv方程的精确解

在Kondratiev分布空间(S)-1中通过埃尔米特变换和Painleve′分析导出了Wick-类型的随机广义Kdv方程的Backlund变换,并且把Wick-类型的随机广义Kdv方程变成广义系数Kdv-方程,再利用Backlund变换求出广义系数Kdv方程的精确解,最后通过埃尔米特逆变换求出随机广义Kdv方程在系数取不同白色噪音泛函条件下的精确解.     

Commutativity of source generation procedure and Bäcklund transformation: A BKP equation

The source generation procedure is applied to a BKP-type equation and a modified BKP-type (m-BKP) equation, respectively. As a result, a BKP equation with self-consistent sources (ESCS) and a m-BKP ESCS are derived. It is also proved that the bilinear m-BKP ESCS constitutes a bilinear Bäcklund transformation for the BKP ESCS. This means that the commutativity between the source generation procedure and Bäcklund transformation is valid for the BKP equation.     

Auto-Bäcklund transformation and exact solutions of the generalized variable-coefficient Kadomtsev-Petviashvili equation

Based on the idea of the homogeneous balance (HB) method, an auto-Bäcklund transformation (BT) to the generalized variable-coefficient Kadomtsev-Petviashvili (GvcKP) equation is obtained with symbolic computation. By the use of the auto-BT and the ε-expansion method, we can obtain a soliton-like solution including N-solitary wave of the GvcKP equation. Especially, we get a soliton-like solution including two-solitary wave as an illustrative example in detail. Since the cylindrical KP (cKP) equation, the generalized cKP (GcKP) equation and the spherical KP (SKP) equation are all special cases of the GvcKP equation, we can also obtain the corresponding results of these equations respectively.     

Transformations and multi-solitonic solutions for a generalized variable-coefficient Kadomtsev–Petviashvili equation

Kadomtsev–Petviashvili equations with variable coefficients can be used to characterize many nonlinear phenomena in fluid dynamics and plasma physics more realistically than the equations with constant coefficients. Hereby, a generalized variable-coefficient Kadomtsev–Petviashvili equation with nonlinearity, dispersion and perturbed terms is investigated. Transformations, of which the consistency conditions are exactly the Painlevé integrability conditions, to the Korteweg–de Vries equation, cylindrical Korteweg–de Vries equation, Kadomtsev–Petviashvili equation and cylindrical Kadomtsev–Petviashvili equation are presented by formal dependent variable transformation assumptions. Using the Hirota bilinear method, from the variable-coefficient bilinear equation, the multi-solitonic solution, auto-Bäcklund transformation and Lax pair for the variable-coefficient Kadomtsev–Petviashvili equation are obtained. Moreover, the influence of inhomogeneity coefficients on solitonic structures and interaction properties is discussed for physical interest and possible applications.     

Integrability,soliton solutions and modulation instability analysis of a (2+1)-dimensional nonlinear Heisenberg ferromagnetic spin chain equation

We consider the Heisenberg ferromagnetic spin chain equation, which is governed by the (2+1)-dimensional nonlinear Schrödinger-type equation. Based on the Ablowitz–Kaup–Newell–Segur frame, we study the integrability of the equation by deriving its Lax pair and infinite conservation laws. By introducing a potential transformation, we obtain its Hirota bilinear form and soliton solutions. Based on the resulting lax pair, we construct Darboux transformation and multi-soliton solutions of the equation. Furthermore, we also find the other type of soliton solutions for the equation by considering its Bäcklund transformation. Finally, we discuss the linear stability analysis by considering its stability condition for the stationary solution of the equation, which can be used to analyze modulation instability. The technique presented in this work is analytical, which can be used to enrich the dynamical of the Heisenberg ferromagnetic spin chain equation.     

涉及景深的雾天图像增强的偏微分方程模型

提出了一种新的雾天交通图像增强算法,对大气物理散射模型两边同时取梯度,得到原始图像与无雾图像梯度场之间的关系,将无雾图像的恢复转化成梯度能量泛函求极值问题,由变分得到图像增强的偏微分方程模型。通过暗原色先验,得到块透射率和点透射率,用快速小波变换分解的方法将块透射率的低频和点透射率的高频融合计算得到透射率,最后用有限差分法求解欧拉方程获得无雾图像。仿真实验结果表明该算法能够有效提高图像的质量。     

Plus–minus algorithm — A method for derivation of the Bäcklund transformations

A new way of deriving Bäcklund transformations for nonlinear partial differential evolution equations is presented and applied to the following equations: Korteweg–de Vries, Gardner, Burgers, generalized KdV and the fifth order equations of the KdV hierarchies. The presented method is based on the assumption of the existence of particular forms of the Bäcklund transformations. This assumption is supported by the strong or semi-strong necessary condition concepts [Sokalski, K., Wietecha, T., Lisowski, Z., 2001. Acta Phys. Polon. B32, 17; Sokalski, K., Wietecha, T., Lisowski, Z., 2002. Int. J. Theor. Phys. Group Theory Nonlinear Opt., NOVA, 9, 331; Sokalski, K., Wietecha, T., Lisowski, Z., 2001. Acta Phys. Polon. B32, 2771; Sokalski, K., Wietecha, T., Sokalska, D. 2005. J. Nonlinear Math. Phys. 12, 31]. Its general form has been put within the framework of an algorithm and implemented in MAPLE.     

自洽场方法中广义本征值方程求解及其C++程序设计

本文研究自洽场方法中广义本征值方程求解的算法,并设计相应的C 程序来实现该算法。首先对重叠矩阵进行分解,并将广义本征值方程化为标准的本征值方程,再利用Householder变换将上一步变换所得的矩阵化为对称三对角矩阵,进而用QL方法求解这个三对角矩阵的本征值和本征矢量,从而得到自洽场方法中广义本征值方程的本征值和本征矢量。     

变流速输液管的周期和混沌振动

研究了参数激励和外激励联合作用下输流管道的非线性振动问题．只考虑管道变形的几何非线性因素,利用Hamilton原理得到单侧受简谐均布载荷作用下输液管的非线性动力学方程,对系统运动偏微分方程综合运用多尺度法和Galerkin离散方法,得到了主参数共振-1／2亚谐共振和1：2内共振情况下的平均方程．数值模拟结果表明参数激励和外激励联合作用下的悬臂输液管呈现周期运动、多倍周期运动和混沌运动的变化规律．