The present work is concerned with unsteady free convection flow of an incompressible electrically conducting micropolar fluid, bounded by an infinite vertical plane surface of constant temperature. A uniform magnetic field acts perpendicularly to the plane. The state space technique is adopted for the one-dimensional problems including heat sources with one relaxation time. The resulting formulation is applied to a problem for the whole space with a plane distribution of heat sources. The reflection method together with the solution obtained for the whole space is applied to a semispace problem with a plane distribution of heat sources located inside the fluid. The inversion of the Laplace transforms is carried out using a numerical approach. Numerical results for the temperature, the velocity, and the angular velocity distributions are given and illustrated graphically for the problems considered.

Discrete-time forward interest rate curve models are studied, where the curves are driven by a random field. Under the assumption of no-arbitrage, the maximum likelihood estimator of the volatility parameter is given and its asymptotic behaviour is studied. First, the so-called martingale models are examined, but we will also deal with the general case, where we include the market price of risk in the discount factor.

This paper gives very significant and up-to-date analytical and numerical results to the three-dimensional heat radiation problem governed by a boundary integral equation. There are two types of enclosure geometries to be considered: convex and nonconvex geometries. The properties of the integral operator of the radiosity equation have been thoroughly investigated and presented. The application of the Banach fixed point theorem proves the existence and the uniqueness of the solution of the radiosity equation. For a nonconvex enclosure geometries, the visibility function must be taken into account. For the numerical treatment of the radiosity equation, we use the boundary element method based on the Galerkin discretization scheme. As a numerical example, we implement the conjugate gradient algorithm with preconditioning to compute the outgoing flux for a three-dimensional nonconvex geometry. This has turned out to be the most efficient method to solve this type of problems.

The aim of the present analysis is to apply the Adomian decomposition method for the solution of a fractional differential equation as an alternative method of Laplace transform.

We investigate the relationships between the infinitely many characteristic zeros (or modes) of linear systems subject to point delays and their delay-free counterparts based on algebraic results and theory of analytic functions. The cases when the delay tends to zero or to infinity are emphasized in the study. It is found that when the delay is arbitrarily small, infinitely many of those zeros are located in the stable region with arbitrarily large modulus, while their contribution to the system dynamics becomes irrelevant. The remaining finite characteristic zeros converge to those of the delay-free nominal system. When the delay tends to infinity, infinitely many zeros are close to the origin. Furthermore, there exist two auxiliary delay-free systems which describe the relevant dynamics in both cases for zero and infinite delays. The maintenance of the delay-free system stability in the presence of sufficiently small delayed dynamics is also discussed in light of $H_{\infty }$-theory. The main mathematical arguments used to derive the results are based on the theory of analytic functions.