In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associat...In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.展开更多
We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyze a v...We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyze a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest is seen as being embedded in a frame process which is a critical Galton Watson process. In this context, we address problems such as extinction, fixation, size of the population at fixation and survival probability to a bottleneck effect of the environment.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10671156the Natural Science Foundation of Shaanxi Province of China under Grant No.SJ08A05
文摘In terms of our new exact definition of partial Lagrangian and approximate Euler-Lagrange-type equation, we investigate the nonlinear wave equation with damping via approximate Noether-type symmetry operators associated with partial Lagrangians and construct its approximate conservation laws in general form.
文摘We first recall some basic facts from the theory of discrete-time Markov chains arising from two types neutral and non-neutral evolution models of population genetics with constant size. We then define and analyze a version of such models whose fluctuating total population size is conserved on average only. In our model, the population of interest is seen as being embedded in a frame process which is a critical Galton Watson process. In this context, we address problems such as extinction, fixation, size of the population at fixation and survival probability to a bottleneck effect of the environment.
