用物理方法解方程

如果求解方程tanx=x或Ntanx=tan(Nx)(N为大于等于2的自然数)定有不少的同学无从下手.然而,在物理课上我却无意中发现一种特殊的解法.     

Equation of State of Dense Liquid Nitrogen in the Region of the Dissociative Phase Transition

We have measured the equation of state for liquid nitrogen compressed dynamically to a pressure of 10-60 GPa by employing a two-stage light-gas gun.The data show a continuous phase transition above the shock pressure of 33GPa,as indicated previously by shock wave experiments.A theoretical model has been derived to examine the experimental data by inducing a molecular dissociative fraction.According to theoretical and experimental date the phase transition was thought to be a molecular dissociative phase transition.     

Duffing方程的唯三周期解问题

考虑Duffing方程x+g(x,t)=h(t),在g(x,t)满足简单的凸凹性条件。以及g＇(x,t)跨越第一共振点时,本文指出,当强迫振动项h(t)充分小时,所讨论的Duffing方程的2π周期解恰有三个.     

非保守力学系统Nielsen方程的形式不变性

研究非保守力学系统Nielsen方程的形式不变性.给出非保守力学系统Nielsen方程的形式不变性的定义和判据,研究形式不变性和Noether对称性的关系,并举例说明结果的应用 关键词： 非保守力学系统 Nielsen方程 形式不变性 Noether对称性     

概率收缩与PN空间的方程

本文引入概率赋范空间(简称PN空间)中概率收缩的概念,借助这个概念,证明了几个PN空间非线性算子方程解的存在唯一性定理,所得结果推广了Altman相应的结果.     

一类型集值积分方程解的存在性

本文设(X,)是Banach空间,L(X)是X的非空有界闭子集族,H是导出的Hausdorff度量.此外,∧是一指标集.作为准备,我们有以下Chen和Shin的结果对集值映象情形的推广: 引理设T_λ:X→L(X)(λ∈∧),使得这里函数φ满足(φ):φ:[0,∞)→[0,∞)不减,φ(t)0),且(?)α≥0,存在β>1及收敛序列{t_k}:t_0=0,t_1≥α,t_(k 1)=t_(k φ)(β(t_k-t_(k-1))(k=1,2,…),则存在     

Positive and Nontrivial Solutions for the Urysohn Integral Equation

We establish new criteria for the existence of either positive or nonzero solutions of the Urysohn integral equation. We also discuss the existence of an interval of positive eigenvalues and sufficient conditions for the existence of at least a positive eigenvalue with a nonzero or positive eigenfunction for the Urysohn integral operator. Among others, we employ techniques based on fixed point index theory for compact maps, which are new for this type of equation.     

氢氟烃/烷烃二元混合物的气液相平衡

整理了已公开发表的氢氟烃(HFC)/烷烃(HC)二元混合物气液相平衡实验数据,对实验数据进行了热力学一致性检验。采用PR方程加van der Waals混合规则描述该类混合物的气液相平衡性质,优化得到了11种混合物的二元交互作用系数,经比较表明采用优化结果能够高精度再现气液相平衡实验数据,比k_(ij)取0的计算结果有很大改善.     

A TVD Type Wavelet-Galerkin Method for Hamilton-Jacobi Equations

In this paper,we use Daubechies scaling functions as test functions for the Galerkin method,and discuss Wavelet-Galerkin solutions for the Hamilton-Jacobi equations.It can be proved that the schemesare TVD schemes.Numerical tests indicate that the schemes are suitable for the Hamilton-Jacobi equations.Furthermore,they have high-order accuracy in smooth regions and good resolution of singularities.     

脉冲中立型时滞抛物方程的振动性

本文研究了一类脉冲中立型时滞抛物方程解的振动性及强振动性,获得了此类脉冲中立型时滞抛物方程解振动和强振动的代数判据.