具有一般扩散矩阵的非线性反应扩散方程组的群分类。III。三角扩散矩阵

Nonchaotic evolution of triangular configuration due to gravitational radiation reaction in the three-body problem

Continuing work initiated in an earlier publication [H. Asada, Phys. Rev. D {\bf 80}, 064021 (2009)], the gravitational radiation reaction to Lagrange's equilateral triangular solution of the three-body problem is investigated in an analytic method. The previous work is based on the energy balance argument, which is sufficient for a two-body system because the number of degrees of freedom (the semimajor axis and the eccentricity in quasi-Keplerian cases, for instance) equals that of the constants of motion such as the total energy and the orbital angular momentum. In a system with three (or mo…

非线性反应扩散对流方程的新条件对称性和精确解。III

New conditional symmetries and exact solutions of nonlinear reaction-diffusion-convection equations. III

对具有任意幂次非线性项的反应扩散对流方程的$Q$ -条件对称性进行了完整的描述。结果表明，在第一和第二部分的这项工作（见arXiv：math-ph/0612078和arXiv：0706.0814）中获得的结果不能扩展到新的功率非线性扩散和对流系数中产生的。

反铁磁Potts模型III的传递矩阵和配分函数零点。三角格色多项式

Transfer Matrices and Partition-Function Zeros for Antiferromagnetic Potts Models III. Triangular-Lattice Chromatic Polynomial

本文研究了m个\times n个三角网格条的色多项式P_G（q），其宽度m <= 12_P，9_F（分别具有周期性或自由横向边界条件）和任意长度n（具有自由纵向边界条件）。色多项式给出了q态Potts反铁磁体的配分函数的零温度极限。我们计算的转移矩阵的Fortuin-Kasteleyn表示，并获得相应的累积集的色零点在复q平面上的极限n \to \infty。我们重新计算的极限曲线巴克斯特在热力学极限m，n \to \infty，并找到新的有趣的功能与可能的物理后果。最后，我们分析了孤立极限点及其与Beraha数的关系。

一维粒子，一维场，一维相互作用。基于有限秩扰动方法的简单精确可解模型。III。作为辐射反应的线性摩擦

1D Particle, 1D Field, 1D Interaction. Simple Exactly Solvable Models based on Finite Rank Perturbations Methods. III. Linear Friction as Radiation Reaction

这篇论文是我的系列讲座的电子应用，主题是：“解微分方程和构建物理现象模型的形式方法”。主要面向：研究生及相关读者。内容：讨论线性摩擦的简单模型，这些模型的机理是基于辐射反应。我们将处理的相互作用是基于这样的方程组：d^2 q（t）/dt^2 =-Ω^2 q（t）+ f_{compl}（t，q，Q），d^2 u（t，x）/dt^2=c^{2}d^2 u（t，x）/dx^2 - 4 <$c δ（x-x_0）F_{src}（t，q，Q）+f_1（t，x），Q（t）= <l（t）.| u> >.数学中心：达朗贝尔-基尔霍夫公式。物理要点：辐射反应、制动辐射和摩擦现象。

Riccati-Ermakov systems and explicit solutions for variable coefficient reaction-diffusion equations

We present several families of nonlinear reaction diffusion equations with variable coefficients including Fisher-KPP and Burgers type equations. Special exact solutions such as traveling wave, rational, triangular wave and N-wave type solutions are shown. By means of similarity transformations the variable coefficients are conditioned to satisfy Riccati or Ermakov systems of equations. When the Riccati system is used, conditions are established so that finite-time singularities might occur. The solutions presented contain multi-parameters providing a control on the dynamics of the solutions. …