in this paper, we propose the chebyshev wavelet approximation for the numerical solution of a class of integro-differential equation which describes the charged particle motion for certain configurations of oscillating magnetic fields. we show that the chebyshev approximation transform an integral equation to an explicit system of linear algebraic equations. illustrative examples are included t...

The paper proposes a mechanical model of SFD-sliding bearing flexible rotor system, employing RungeKutta method to tackle nonlinear differential equation, thus acquiring the dynamic response and the unbalanced response curve. Results obtained show the route of flexible rotor system from stable periodic motion to chaos state is: periodic motion—quasi-periodic motion—chaos —period doubling bifurc...

We present metrics for measuring state similarity in Markov decision processes (MDPs) with infinitely many states, including MDPs with continuous state spaces. Such metrics provide a stable quantitative analogue of the notion of bisimulation for MDPs, and are suitable for use in MDP approximation. We show that the optimal value function associated with a discounted infinite horizon planning tas...

In the present work, the motion of metallic and plastic particles of 5 mm diameter falling in a quiescent fluid is investigated experimentally. The goal of this investigation is to examine the effect of history force acting on a particle in a range of Reynolds numbers between 1000 and 5000. The instantaneous position of the particle was recorded using a high - speed camera (500 to 1000 frames p...

In this paper, we study an insurer’s optimal time-consistent strategies under themean–variance criterion with state dependent risk aversion. It is assumed that the surplus process is approximated by a diffusion process. The insurer can purchase proportional reinsurance and invest in a financial market which consists of one risk-free asset andmultiple risky assets whose price processes follow ge...

We consider the problem of determining the optimal investment level that a firm should maintain in the presence of random price and/or demand fluctuations. We model market uncertainty by means of a geometric Brownian motion, and we consider general running payoff functions. Our model allows for capacity expansion as well as for capacity reduction, with each of these actions being associated wit...

In this paper we consider the optimal control problem for a insurance company. Our objective is to maximize the expectation of discounted dividends and its terminal value which represents the company liquidation value upon the time of bankruptcy. The surplus of the insurance company is governed by the Brownian motion with a constant drift and a diffusion term. The company can manage its risk ex...

In this paper we obtain  exact solutions of the generalized Kuramoto-Sivashinsky equation, which describes manyphysical processes in motion of turbulence and other unstable process systems.    The methods used  to determine the exact solutions of the underlying equation are the Lie group analysis  and the simplest equation method. The solutions obtained are  then plotted.