New Exact Solutions to the Combined KdV and mKdV Equation

The modified mapping method is developed to obtain new exact solutions to the combined KdV and mKdV equation. The method is applicable to a large variety of nonlinear evolution equations, as long as odd- and even-order derivative terms do not coexist in the equation under consideration.     

渐近周期Lotka-Volterra互惠系统的持久性

讨论了一类系数是渐近周期的连续函数的两种群Lotak-Volterra互惠系统的全局渐近性。     

Nonturnpike Optimal Solutions and Their Approximations in Infinite Horizon

Recently, the authors have proposed a new necessary and sufficient condition for turnpike optimality in calculus of variations with singular Euler equation. The method is based on a characterization of the value function and generalizes the well known method based on the Green theorem. Furthermore, it allows the optimality of a competition between several turnpikes to be characterized. For a class of such problems not enjoying the turnpike property, we give an explicit formula for the value function and show how to characterize the optimal solution as the limiting solution of a family of perturbed problems satisfying the turnpike property. The considered problems are scalar with infinite horizon.     

短正合列的弱可裂

把短正合列的可裂推广到短正合列的弱可裂，并对弱可裂进行了等价刻画，最后还运用左弱可列证明了平坦模的一个充要条件。     

New solitons and kink solutions for the Gardner equation

The Gardner equation, also called combined KdV–mKdV equation, is studied. New hyperbolic ansatze are proposed to derive solitons solutions. The tanh method is used as well to obtain kink solutions.     

The concentration effect on the ‘hydrophobic’ and ‘hydrophilic’ behaviour around DMSO in dilute aqueous DMSO solutions. A computer simulation study

We have carried out a molecular dynamics study of dimethyl sulfoxide (DMSO) in water at 298 K at two different densities by simulating two different concentrations: 0.055 and 0.19 mole fraction. We have found an enhancement in the structure of water, an effect that becomes more pronounced as the concentration of DMSO increases. At both concentrations there is a well-defined hydration structure around the oxygen atom of DMSO, which is able to establish strong hydrogen bonds with surrounding water molecules. An increase in the concentration of DMSO depletes the solution of bulk water molecules, reducing the number of hydrogen bonds that water can have in the immediate vicinity of DMSO but increasing the strength of the hydrogen bonds made between the oxygen atom of DMSO and water. There is clear evidence of ‘hydrophobic’ hydration around the methyl groups of DMSO, which is enhanced as the concentration of DMSO increases.     

Global and exploding solutions in a model of self-gravitating systems

We study asymptotic properties of solutions to an extension to arbitrary dimensions of the astrophysical model proposed by Chavanis et al. to explain phenomena of gravitational collapse in clouds of self-gravitating particles. In particular, we show that in the two-dimensional case the solutions can be continued to global ones, while in three space dimensions large data of negative energy blow up in a finite time. Relations between isothermal, Streater's energy-transport and the present models are also studied.     

环上半线性椭圆型方程正解的存在性和唯一性

本文讨论了半线性椭圆方程△u+f(u)=0在三种边界条件下正解的存在性和唯一性,给出了正解存在和唯一的一些条件.     

Two classes of piecewise-linear difference equations with eventual periodicity three

In this paper, we will study two classes of difference equations which are piecewise-linear and of similar forms. We will show that all nontrivial solutions of one equation are eventually periodic with prime period three. We will show this result for one case of the second equation.