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??In this paper, we consider a perturbed compound Poisson risk model with dependence, where the dependence structure for the claim size and the inter-claim time is modeled by a generalized Farlie-Gumbel-Morgenstern copula. The integro equations, the Laplace transforms and the defective renewal equations for the Gerber-Shiu functions are obtained. For exponential claims, some explicit expressions are obtained, and some numerical examples for the ruin probabilities are also provided.     

Quantum states with continuous spectrum for a general time-dependent oscillator

We investigated quantum states with continuous spectrum for a general time-dependent oscillator using invariant operator and unitary transformation methods together. The form of the transformed invariant operator by a unitary operator is the same as the Hamiltonian of the simple harmonic oscillator:I’ = p²/2 +ω ² q ²/2. The fact thatω ² of the transformed invariant operator is constant enabled us to investigate the system separately for three cases, whereω ² > 0,ω ² < 0, andω ² = 0. The eigenstates of the system are discrete forω ² > 0. On the other hand, forω ² <− 0, the eigenstates are continuous. The time-dependent oscillators whose spectra of the wave function are continuous are not oscillatory. The wave function forω ² < 0 is expressed in terms of the parabolic cylinder function. We applied our theory to the driven harmonic oscillator with strongly pulsating mass.     

一类二阶变系数线性系统的解

给出一类二阶变系数线性系统的解的求法，并得到解的表达式．     

Exact Solution to the One-Dimensional Dirac Equation with Time Varying Mass

We directly use the quantum-invariant operator method to obtain the closed-form solution to the one-dimensional Dirac equation with a time-changing mass with a little manipulation. The solution got is also applicable forthe case with time-independence mass.     

Two-dimensional problem of natural convection in a rectangular domain with local heating and heat-conducting boundaries of finite thickness

Time-dependent natural convective heat transfer in a closed rectangular domain with heat-conducting boundaries of finite thickness is investigated numerically in the case of local heating on the inner side of the vertical wall. Convection-radiation heat transfer takes place on one of the outer boundaries of the solution domain. The inhomogeneous temperature distribution in the gas cavity is clearly manifested when the Grashof number Gr > 10⁶. Circulation flows can be distinguished in various zones of the solution domain on the basis of the numerical investigations carried out. These flows are due to the effect of the heat-release source, the propagation of perturbations induced by elements of the rigid wall, and the dynamics of conductive heat transfer in the solid material. The scales of the effect of the Grashof number on the hydrodynamic and thermal characteristics are indicated.     

Generalized Langevin equations with time-dependent temperature

A generalized Langevin equation describing the evolution of a particle in a heat bath with a time-dependent temperature is derived for a simple model. The temperature is controlled by introducing dissipative terms in the dynamical equations of the heat bath particles. The Langevin equation contains a term that is specifically associated with the variation of the temperature.     

Micro-Effects on Continuous-Injection Heat Conduction Calorimetry

A localized-constant model involving two capacities reliably describes two injection calorimeters: a mass-variation calorimeter and a constant-volume calorimeter (TAM 2277 by Thermometric). The model distinguishes the place and the types of dissipation, and its parameters depend on the rates and on the heat capacities of the liquids. In the case of the TAM 2277 calorimeter, the dependence between the detected heat of mixing and the injection rate is revealed. The proposed model permits the inclusion of perturbations on the baseline originating from the temperature variation of the thermostat. This revised version was published online in July 2006 with corrections to the Cover Date.     

Piecewise optimal linearization method for nonlinear stochastic differential equations

A method for estimating the dynamical statistical properties of the solutions of nonlinear Langevin-type stochastic differential equations is presented. The non-linear equation is linearized within a small interval of the independent variable and statistical properties are expressed analytically within the interval. The linearization procedure is optimal in the sense of the Chebyshev inequality. Long-term behavior of the solution process is obtained by appropriately matching the approximate solutions at the boundaries between intervals. The method is applied to a model nonlinear equation for which the exact time-dependent moments can be obtained by numerical methods. The calculations demonstrate that the method represents a significant improvement over the method of statistical linearization in time regimes far from equilibrium.Supported in part by the National Science Foundation under Grants CHE77-16307 and PHY76-04761.     

Nonautonomous Kato classes of measures and Feynman-Kac propagators

The behavior of the Feynman-Kac propagator corresponding to a time-dependent measure on is studied. We prove the boundedness of the propagator in various function spaces on , and obtain a uniqueness theorem for an exponentially bounded distributional solution to a nonautonomous heat equation.