Dependencies in multi-life statusses.

The usual assumption of independence of the remaining life times involved in joint-life and last survivor statuses is omitted. Given the marginal distributions of the remaining life-times, lower and upper bounds are derived for the single premiums of multi-life insurances and annuities.

Elliptical instability of a rapidly rotating, strongly stratified fluid

The elliptical instability of a rotating stratified fluid is examined in the regime of small Rossby number and order-one Burger number corresponding to rapid rotation and strong stratification. The Floquet problem describing the linear growth of disturbances to an unbounded, uniform-vorticity elliptical flow is solved using exponential asymptotics. The results demonstrate that the flow is unstable for arbitrarily strong rotation and stratification; in particular, both cyclonic and anticyclonic flows are unstable. The instability is weak, however, with growth rates that are exponentially small in the Rossby number. The analytic expression obtained for the growth rate elucidates its dependence on the Burger number and on the eccentricity of the elliptical flow. It explains in particular the weakness of the instability of cyclonic flows, with growth rates that are only a small fraction of those obtained for the corresponding anticyclonic flows. The asymptotic results are confirmed by numerical solutions of Floquet problem.Comment: 17 page

A straightforward analytical calculation of the distribution of an annuity certain with stochastic interest rate.

Starting from the moment generating function of the annuity certain with stochastic interest rate written by means of a time discretization of the Wiener process as an n-fold integral, a straightforward evaluation of the corresponding distribution function is obtained letting n tend to infinity. The advantage of the present method consists in the direct calculation technique of the n-fold integral, instead of using moment calculation or differential equations, and in the possible applicability of the present method to varying annuities which could be applied to IBNR results, as well as to pension fund calculations, etc.Distribution; Annuities; Processes; Evaluation;

Effects of Spatially Nonuniform Gain on Lasing Modes in Weakly Scattering Random Systems

A study on the effects of optical gain nonuniformly distributed in one-dimensional random systems is presented. It is demonstrated numerically that even without gain saturation and mode competition, the spatial nonuniformity of gain can cause dramatic and complicated changes to lasing modes. Lasing modes are decomposed in terms of the quasi modes of the passive system to monitor the changes. As the gain distribution changes gradually from uniform to nonuniform, the amount of mode mixing increases. Furthermore, we investigate new lasing modes created by nonuniform gain distributions. We find that new lasing modes may disappear together with existing lasing modes, thereby causing fluctuations in the local density of lasing states.Comment: 26 pages, 10 figures (quality reduced for arXiv

Acute and life-threatening remifentanil overdose resulting from the misuse of a syringe pump.

In the perioperative setting, syringe pumps are frequently used. They guarantee constant plasma levels of hypnotics, opioids, cardiovascular medication, insulin or other drugs. We present a case in which an inadvertent rapid intravenous injection of 2 mg remifentanil occurred due to the misuse of a syringe pum