Efraim Shmerling

Asymptotic behavior of roots of random polynomial equations

We derive several new results on the asymptotic behavior of the roots of random polynomial equations, including conditions under which the distributions of the zeros of certain random polynomials tend to the uniform distribution on the circumference of a circle centered at the origin. We also derive a probabilistic analog of the Cauchy-Hadamand theorem that enables us to obtain the radius of convergence of a random power series.

Stability of stochastic jump-parameter semi-Markov linear systems of differential equations

The asymptotic stability of stochastic Itô-type jump-parameter semi-Markov systems of linear differential equations is examined. A system of integral matrix equations is derived which has the property that the existence of a positive definite solution of the system implies the asymptotic stability of the stochastic semi-Markov system. Finally, an illustrative example is presented.

Stability and Optimal Control for Semi-Markov Jump Parameter Linear Systems

We consider continuous-time and discrete-time jump parameter linear control systems with semi-Markov coefficients and solution jumps that coincide with jumps of a semi-Markov random process. First, we derive stability conditions for semi-Markov systems of differential equations. We then determine necessary optimality conditions for the solutions of continuous-time and discrete-time control systems.

Algorithms for generating random variables with a rational probability-generating function

Two algorithms for generating random variables with a rational probability-generating function are presented. One of them implements the recently developed general range reduction method, and the other is an extension of the alias method designed for generating discrete finite-valued random variables to the case where the generated random variable is infinite-valued. An example of a random variable which was efficiently generated by random number generators implementing the presented algorithms is given. Possible ways of improving the complexity of the presented algorithms are discussed.

A Fuel Efficiency Evaluation of Gas-Turbine-Engine-Based Hybrid Vehicles

The purpose of the contribution is evaluating the fuel efficiency of gas turbine (GT) engine-based hybrid vehicles, which can be manufactured utilizing modern technologies. An analytical equation for calculating fuel consumption is derived taking into account specific properties of hybrid vehicles. European Union Directives and regulations of the United Nations Economic Commission for Europe are adopted to evaluate the fuel efficiency. The equation is first verified by calculating the mileage of several commercial hybrid passenger vehicles and then applied to GT-based hybrid vehicles. It is revealed that even though GT engine possesses relatively poor efficiency, reduced turbine-generator weight results in a lower overall weight of the vehicle, leading to fuel consumption decrease. The estimated fuel efficiency of GT engine-based vehicles is shown to be on a par with the efficiency of widely employed diesel and gasoline engine-based vehicles.

A Sufficient Stability Condition for Linear Stochastic Markovian Systems

Asymptotic stability of the zero solution for stochastic jump parameter systems of differential equations given by dX(t)=A(ξ(t))X(t)dt+H(ξ(t))X(t)dw(t), where ξ(t) is a finite‐valued Markov process and w(t) is a standard Wiener process, is considered. It is proved that the existence of a unique positive solution of the system of coupled Lyapunov matrix equations derived in the paper is a sufficient asymptotic stability condition.

Algorithm and software for defining the distribution of eigenvalues of random symmetric matrices via simulation

A simulation algorithm for defining the distribution of eigenvalues of a random symmetric matrix with arbitrary continuous joint probability density function of its entries is presented. The algorithm requires only a uniform random number generator. As a numerical example, the probability that eigenvalues of a certain random symmetric matrix satisfy a given condition is calculated using software implementing the algorithm.