Numerical Solutions of the Hattendorff Differential Equation for Multi-state Markov Insurance Models

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

Numerical Solutions of the Hattendorff Differential Equation for Multi-state Markov Insurance Models

We provide methodology and numerical results for the Hattendorff differential equa- tion for the continuous time evolution of the variance of L(j)t , the loss at time t random variable for a multi-state process, given that the state at time t is j.

ON SUFFICIENT CONDITIONS OF EXPONENTIAL STABILITY FOR SYSTEMS OF LINEAR AUTONOMOUS DIFFERENTIAL EQUATIONS WITH AFTEREFFECT

We consider systems of linear autonomous functional differential equa-tion with aftereffect and propose an approach to obtain effective sufficient conditions of exponential stability for these systems. In the approach we use the positiveness of the fundamental matrix of an auxiliary system (a comparison system) with concentrated and distributed delays.

Natural convection in an enclosure with fins in the presence of non-uniform temperature pro-file at vertical wall

The development of energy instrumentation, electronic industry and energy in general is inextrica-bly linked with the intensification of heat and mass transfer occurring in the base units and aggre-gates of energy systems. One of the approaches to solving this problem is to create an extended heat transfer surface by introducing a rib structure or porous inserts. This work is devoted to math-ematical modeling of natural convection in an enclosure in the presence of a rib structure and non-uniform temperature profile on one of the vertical walls. The governing partial differential equa-tions written using dimensionless non-primitive variables “stream function – vorticity – tempera-ture” based on the Boussinesq approximation, in combination with initial and boundary conditions, have been worked out on the basis of the finite difference method. The developed computational model was varified using the mesh independence test and benchmark problems solved by other au-thors. Numerical investigations of unsteady natural convection of viscous fluid in a cavity with a variable temperature on the left wall under an influence of a rib structure have been carried out for the following values of governing parameters: Pr = 0.71, 103 < Ra < 106, and the number of ribs varied from one to three. Distributions of streamlines and isotherms, as well as the dependences of the average Nusselt number and average cavity temperature, were obtained for a steady mode. As a result of the analysis, it has been found that the addition of solid ribs allows to enhance the heat transfer for low Rayleigh numbers, while for Ra  105 one can find an attenuation of convective heat transfer. A growth of the fins heat conductivity characterizes the heat transfer enhancement.

Solution of Lord-Shulmans and dual-phase-lag theories problem on a photothermal rotational semiconductor medium with voids and initial stress

This paper discusses a photo-thermal rotational semiconductor medium with ini?tial stress, and voids by considering two thermoelastic theories: Lord-Shulman and Dual-Phase-Lag models. The equations of motion, temperature, voids, and photothermal have been investigated under two generalized thermoelastic theory. The technique of normal mode has been applied to solve the differential equa?tions system with appropriate boundary conditions. Quantities of physical interest such as displacement, stress components, concentration, temperature, and carrier density are calculated and displayed graphically to demonstrate the effect of the external parameters. The obtained results, by using the two theories, show that the dual-phase-lag theory gives an origin results comparing with obtained results by Lord-Shulman theory. By neglecting the initial stress and voids, and considering the only dual-phase-lag theory, then the results obtained in this paper are deduced to the results of Abbas et al. [1].

Solution of Lord-Shulmans and dual-phase-lag theories problem on a photothermal rotational semiconductor medium with voids and initial stress

This paper discusses a photo-thermal rotational semiconductor medium with ini?tial stress, and voids by considering two thermoelastic theories: Lord-Shulman and Dual-Phase-Lag models. The equations of motion, temperature, voids, and photothermal have been investigated under two generalized thermoelastic theory. The technique of normal mode has been applied to solve the differential equa?tions system with appropriate boundary conditions. Quantities of physical interest such as displacement, stress components, concentration, temperature, and carrier density are calculated and displayed graphically to demonstrate the effect of the external parameters. The obtained results, by using the two theories, show that the dual-phase-lag theory gives an origin results comparing with obtained results by Lord-Shulman theory. By neglecting the initial stress and voids, and considering the only dual-phase-lag theory, then the results obtained in this paper are deduced to the results of Abbas et al. [1].

Hybrid Monte Carlo techniques with a minimal interface

Hybrid Monte Carlo Techniques for the solution of elliptical and parabolic partial differential equa tions have been developed. This paper primarily con cerns the implementation of these techniques with a small, general-purpose digital conputer, a modest analog computer, and a minimal interface.