An unbounded energy growth of particles bouncing off two-dimensional (2D) smoothly oscillating polygons is observed. Notably, such billiards have zero Lyapunov exponents in the static case. For a special 2D polygon geometry--a rectangle with a vertically oscillating horizontal bar--we show that this energy growth is not only unbounded but also exponential in time. For the energy averaged over a...

the aim of this study was to analyze the effect of sex, season and year of birth on growth rate of biometric measurements and body weight gain of thoroughbred foals during first six months of life. 103 thoroughbred foals (53 colts and 50 fillies) from golejewko stud born between 2006 and 2008, were used in this study. thoroughbred foals born in winter months were characterized by significantly ...

We characterize the compensation demanded by investors in equilibrium for incremental exposure to growth-rate risk. Given an underlying Markov diffusion that governs the state variables in the economy, the economic model implies a stochastic discount factor process S and a reference stochastic growth process G for the macroeconomy. Both are modeled conveniently as multiplicative functionals of ...

The concept of growth rates in group theory has proven to be a potent tool for studying groups. For example, in 1981, Mikhail Gromov proved the set of finitely-generated virtually nilpotent groups are precisely the groups of polynomial growth. In this paper, we give an introduction to growth rate in group theory and provide many tools and examples to illustrate some of the methods used. We also...