Obtaining the dividends-penalty identities by interpretation

The dividends-penalty identity is a relation between three functions: the discounted penalty function without dividends, the discounted penalty function if a barrier dividend strategy is applied, and the expected discounted dividends until ruin. The classical model of risk theory is modified in that the deterministic premiums are replaced by a compound Poisson process with exponential jumps. In this model, the dividends-penalty identity is new and can be derived by interpretation. Then the dividends-penalty identity in the classical model is obtained as a limit.     

Observation of single Ca ions for trace isotope analysis

We developed an ion trap — laser cooling system for observing the laser induced fluorescence (LIF) of a single ion, in the view of utilizing it for the trace isotope analysis of Ca. We observed stepwise LIF signals, which correspond to the numbers of trapped ⁴⁰Ca⁺ ions (⁴⁰Ca/Ca = 96.9%). The detection efficiency was evaluated and the observation of single ions demonstrated the experimental feasibility of trace isotope analysis. Furthermore, as the next step towards trace isotope analysis, we report observation of the even calcium isotopes, ⁴⁴Ca (⁴⁴Ca/Ca = 2.09%) and ⁴⁸Ca (⁴⁸Ca/Ca = 0.187%), without the use of a selective loading method.     

Lie-trotter product formulas for nonlinear filtering

The nonlinear filtering problem for a diffusion process whose drift and diffusion coefficients depend parametrically on a finite-state jump process involves the solution of a vector system of linear, stochastic partial differential equations. A Lie-Trotter product formula is proven to hold for this system and a recursive implementation is discussed.     

具有跳扩散的美式期权二叉树计算格式的收敛速率

American put option with jump-diffusion can be modelled as a vari- ational inequality problem with an integral term.Under the stability condition (σ~2Δt)/(Δx~2)≤1,whereΔx=ln(S_n 1)/(S_n),the convergence rate O((Δx)~(2/3) (Δt)~(1/3))of the explicit finite scheme for this problem is obtained by using penalization technique. The binomial tree scheme of this model,which is equivalent to the explicit scheme, is convergent by the same rate.     

A jump inversion theorem for the enumeration jump

Abstract. We prove a jump inversion theorem for the enumeration jump and a minimal pair type theorem for the enumeration reducibilty. As an application some results of Selman, Case and Ash are obtained. Received: 15 May 1998     

The Use of Modulated Temperature Programs in Thermal Methods

Temperature modulation has long been used in various aspects of thermal methods. Historically, the principle areas of application have been the determination of kinetic parameters using variants of the temperature jump method and the measurement of heat capacity by AC calorimetry. More recently the introduction of temperature modulation in a variety of techniques has been used in combination with deconvolution algorithms to separate sample responses that are dependent on rate of change of temperature from those principally dependent on temperature. Finally, temperature modulation is important in the new field of micro-thermal analysis. This revised version was published online in July 2006 with corrections to the Cover Date.     

A numerical technique for laminar swirling flow at the interface between porous and homogenous fluid domains

There have been a few recent numerical implementations of the stress‐jump condition at the interface of conjugate flows, which couple the governing equations for flows in the porous and homogenous fluid domains. These previous demonstration cases were for two‐dimensional, planar flows with simple geometries, for example, flow over a porous layer or flow through a porous plug. The present study implements the interfacial stress‐jump condition for a non‐planar flow with three velocity components, which is more realistic in terms of practical flow applications. The steady, laminar, Newtonian flow in a stirred micro‐bioreactor with a porous scaffold inside was investigated. It is shown how to implement the interfacial jump condition on the radial, axial, and swirling velocity components. To avoid a full three‐dimensional simulation, the flow is assumed to be independent of the azimuthal direction, which makes it an axisymmetric flow with a swirling velocity. The present interface treatment is suitable for non‐flat surfaces, which is achieved by applying the finite volume method based on body‐fitted and multi‐block grids. The numerical simulations show that a vortex breakdown bubble, attached to the free surface, occurs above a certain Reynolds number. The presence of the porous scaffold delays the onset of vortex breakdown and confines it to a region above the scaffold. Copyright © 2008 John Wiley & Sons, Ltd.     

Deterministic impulse control in native forest ecosystems management

This paper illustrates an application of impulse control systems analysis to the management of renewable resources. We obtain an explicit definition for the impulse optimal strategy in the case of a nonlinear natural system which models certain types of forests. The result is in agreement with an econo-ecological conservative action on the forest. The examples developed in this paper associate new theories on impulse or jump control with natural forest management. In addition, we compare our results with the classical ones. We also show that a nonoptimal managing action on the forest is frequently the cause for significant medium-term losses.This work was supported by CONICET, Consejo Nacional de Investigaciones Científicas y Técnicas, and by the Universidad Nacional del Litoral, Argentina.     

Dynamics of a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise

With the development of information technology, rumors propagate faster and more widely than in the past. In this paper, a stochastic rumor propagation model incorporating media coverage and driven by Lévy noise is proposed. The global positivity of the solution process is proved, and further the basic reproductive number R₀ is obtained. When R₀ < 1, the dynamical process of system with Lévy jump tends to the rumor-free equilibrium point of the deterministic system, and the rumor tends to extinction; when R₀ > 1, the rumor will keep spreading and the system will oscillate randomly near the rumor equilibrium point of the deterministic system. The results show that the oscillation amplitude is related to the disturbance of the system. In addition, increasing media coverage can effectively reduce the final spread of rumors. Finally, the above results are verified by numerical simulation.     

Multi-centred hydrogen bonds between water and perchlorate anion

Results of classical molecular dynamics simulations are presented for the re-orientational dynamics of water hydrogen bonded to perchlorate anion. Different mechanisms of bond formation are presented. Due to its regular tetrahedron geometry the perchlorate anion can make classical as well as bifurcated and trifurcated hydrogen bonds. The angular variation of water in the first solvation shell of perchlorate suggests the transitional character of multi-centred hydrogen bonds. As a result water molecules can slide around the anion.