F展开法在求解一类Klein-Gordon方程中的应用

提出了一种求数学物理问题中非线性发展方程周期波解的扩展F展开法,是近来提出的Jacobi椭圆函数展开法的概括.利用齐次平衡原则和扩展F展开法,求出了一类Klein-Gordon方程更丰富的用Jacobi椭圆函数表示的周期波解.     

浅论《和陶饮酒》在苏诗中的独特地位

在陶渊明的接受史上,苏轼处于非常重要的地位。苏轼先后共追和陶诗124首。在这124首和陶诗中《和陶饮酒》20首的写作背景及写作心态与其他和陶诗迥异,这也造成了它与其他和陶诗的内容及风格上的显著差异。因此,它在苏轼诗歌中具有独特的地位,即:它是苏轼岭南诗的前奏,是此前苏诗与此后苏诗的转折点。     

都市女性的自我言说——张爱玲、施叔青作品中女性的都市情结

上世纪40年代的上海女作家张爱玲,80年代的台湾女作家施叔青都曾以香港为背景,写出了她们的“香港传奇”和“香港故事”。她们用独特的女性视角揭示了都市女性苍凉的生存境遇,并对女性解放问题进行了深入探讨。从作家笔下的城市建构、都市女性生存境遇及都市女性的出路三方面来谈张爱玲、施叔青作品中女性与都市的情感纠葛。     

Nonlinear steady states of hyperelastic membrane tubes conveying a viscous non-Newtonian fluid

We study possible steady states of an infinitely long tube made of a hyperelastic membrane and conveying either an inviscid, or a viscous fluid with power-law rheology. The tube model is geometrically and physically nonlinear; the fluid model is limited to smooth changes in the tube’s radius. For the inviscid case, we analyse the tube’s stretch and flow velocity range at which standing solitary waves of both the swelling and the necking type exist. For the viscous case, we first analyse the tube’s upstream and downstream limit states that are balanced by infinitely growing upstream (and decreasing downstream) fluid pressure and axial stress caused by fluid viscosity. Then we investigate conditions that can connect these limit states by a single solution. We show that such a solution exists only for sufficiently small flow speeds and that it has a form of a kink wave; solitary waves do not exist. For the case of a semi-infinite tube (infinite either upstream or downstream), there exist both kink and solitary wave solutions. For finite-length tubes, there exist solutions of any kind, i.e. in the form of pieces of kink waves, solitary waves, and periodic waves.     

压电层合梁静动力学分析的高精度梁单元

给出了一个对复合材料压电层合梁进行数值分析的高精度压电层合梁单元。基于Shi三阶剪切变形板理论的位移场和Layer-wise理论的电势场,用力-电耦合的变分原理及Hamilton原理推导了压电层合梁单元列式。采用拟协调元方法推导了一个可显式给出单元刚度矩阵的两节点压电层合梁单元,并应用于压电层合梁的力-电耦合弯曲和自由振动分析。计算结果表明,该梁单元给出的梁挠度和固有频率与解析解吻合良好,并优于其它梁单元的计算结果,说明了本文所给压电层合梁单元的可靠性和准确性。研究结果可为力-电耦合作用下压电层合梁的力学分析提供一个简单、精确且高效的压电层合梁单元。     

非线性离散薛定谔方程的显式精确解

利用双曲函数方法,研究了具有广泛、深刻物理背景的非线性离散薛定谔方程,得到了它的显式精确解,包括钟型孤波解、冲击型孤波解、钟型-冲击型组合孤波解及一些新的孤波解结构。这种方法也适用于求解其他离散的非线性方程（组）。     

对杨兆鋆关于"双曲线焦点位置作图问题"的研究

京师同文馆的数学教育在清末数学教育史上占有一定的地位,客观评价京师同文馆的数学教育离不开对其学生的考察.为此,探讨了其培养出的学生杨兆鋆在双曲线焦点位置作图问题方面的工作,指出杨氏在此方面的工作是以清末中算家李善兰为代表的对圆锥曲线研究重要方向的继承和发展.杨氏此方面的工作从一定程度上反映了西方数学传入后对当时中国数学界的一些影响.     

Bright solitary waves on a torus: Existence,stability and dynamics for the nonlinear Schrödinger model

Motivated by recent developments in the realm of matter waves, we explore the potential of creating solitary waves on the surface of a torus. This is an intriguing perspective due to the role of curvature in the shape and dynamics of the coherent structures. We find different families of bright solitary waves for attractive nonlinearities including ones localized in both angular directions, as well as waves localized in one direction and homogeneous in the other. The waves localized in both angular directions have also been partitioned into two types: those whose magnitude decays to zero and those who do not. The stability properties of the waves are examined and one family is found to be spectrally stable in a suitable parametric regime while most are spectrally unstable, a feature that we comment on. Finally, the nature of the ensuing nonlinear dynamics is touched upon.     

试析沈石溪笔下狼形象的母爱

沈石溪,一个倍受欢迎的动物小说作家,塑造了一批栩栩如生的狼形象,他极力赞誉狼的重要本性之一——母爱,以狼母爱之伟大照出如今社会中人类某些人性的沉沦,是希望对人类有某些启示意义。     

Numerical study using ADM for the modified regularized long wave equation

The modified regularized long wave (MRLW) equation is solved numerically by Adomian decomposition method (ADM) with some initial conditions. The method leads to high accurate and efficient results. Three polynomial invariant conditions are evaluated to determine the conservation properties of the problem. The convergence of Adomian decomposition method applied to the MRLW equation is proved. Moreover, the interaction of solitons and the development of the Maxwellian initial condition into solitary waves are considered.