Wronskian Form Solutions for a Variable Coefficient Kadomtsev–Petviashvili Equation

Starting from a simple transformation, and with the aid of symbolic computation, we establish the relation- ship between the solution of a generalized variable coefficient Kadomtsev-Petviashvili （vKP） equation and the solution of a system of linear partial differential equations. According to this relation, we obtain Wronskian form solutions of the vKP equation, and further present N-soliton-like solutions for some degenerated forms of the vKP equation. Moreover, we also discuss the influences of arbitrary constants on the soliton and N-soliton solutions of the KPII equation.     

网络形式背景下的知识流动方法研究

将形式背景与复杂网络分析结合,研究如何从网络节点之间的有向关系出发分析节点内涵属性之间的有向流动趋势。首先,定义知识流动算子和知识流动矩阵,研究有向对象之间的知识流动。其次,定义知识流动网络形式背景和知识流团,进一步研究网络中知识流团的网络特征值,用来描述网络中知识流团的平均影响力和影响力差异。另外,结合引文网络与标准加权直接引用(NWDC)方法构建知识流动矩阵和属性链接值,依次提出知识出入度矩阵构建算法、知识流动矩阵构建算法。针对链接值预测问题提出改进链路预测方法、链接值预测方法,并与6种ML算法结合应用于Web of Science核心期刊库下载的数据集中,结果表明这两种预测方法效果优于链路预测且链接值预测方法效果最好。最后,根据链接值预测方法预测冷热门知识,并由冷热门知识流团的网络特征值对该结果进行验证。     

An algorithm and its application for obtaining some kind of infinite-dimensional Hamiltonian canonical formulation

Using factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical evolution equation, infinite-dimensional Hamiltonian canonical system, factorization of differential operator, commutator,evolution equation, infinite-dimensional Hamiltonian canonical system, factorization of differential operator, commutatorProject supported by the National Natural Science Foundation of China (Grant No~10562002) and the Natural Science Foundation of Nei Mongol, China (Grant No~200508010103).2007-05-09{\partial}/{\partial x}Corresponding author．E-mail：alatanca@imu．edu.cn/qk/85823A/200711/25754042.html0200, 03405/9/2007 12:00:00 AMUsing factorization viewpoint of differential operator, this paper discusses how to transform a nonlinear evolution equation to infinite-dimensional Hamiltonian linear canonical formulation. It proves a sufficient condition of canonical factorization of operator, and provides a kind of mechanical algebraic method to achieve canonical $`{\partial}/{\partial x}'$-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.http://cpb.iphy.ac.cn/CN/10.1088/1009-1963/16/11/002https://cpb.iphy.ac.cn/CN/article/downloadArticleFile.do?attachType=PDF&id=1088382007-11-20'-type expression, correspondingly. Then three examples are given, which show the application of the obtained algorithm. Thus a novel idea for inverse problem can be derived feasibly.