6,206 research outputs found
On Necessary and Sufficient Conditions for Preserving Convergence Rates to Equilibrium in Deterministically and Stochastically Perturbed Differential Equations with Regularly Varying Nonlinearity
This paper develops necessary and sufficient conditions for the preservation
of asymptotic convergence rates of deterministically and stochastically
perturbed ordinary differential equations with regularly varying nonlinearity
close to their equilibrium. Sharp conditions are also established which
preserve the asymptotic behaviour of the derivative of the underlying
unperturbed equation. Finally, necessary and sufficient conditions are
established which enable finite difference approximations to the derivative in
the stochastic equation to preserve the asymptotic behaviour of the derivative
of the unperturbed equation, even though the solution of the stochastic
equation is nowhere differentiable, almost surely
Regenerative fuel cells for space applications
After several years of development of the regenerative fuel cell (RFC) as the electrochemical storage system to be carried by the future space station, the official stance has now been adopted that nickel hydrogen batteries would be a better system choice. RFCs are compared with nickel hydrogen and other battery systems for space platform applications
Long Memory in a Linear Stochastic Volterra Differential Equation
In this paper we consider a linear stochastic Volterra equation which has a
stationary solution. We show that when the kernel of the fundamental solution
is regularly varying at infinity with a log-convex tail integral, then the
autocovariance function of the stationary solution is also regularly varying at
infinity and its exact pointwise rate of decay can be determined. Moreover, it
can be shown that this stationary process has either long memory in the sense
that the autocovariance function is not integrable over the reals or is
subexponential. Under certain conditions upon the kernel, even arbitrarily slow
decay rates of the autocovariance function can be achieved. Analogous results
are obtained for the corresponding discrete equation
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