We extend our previous analysis of streamline diffusion finite element methods for hyperbolic systems of conservation laws to include a shockcapturing term adding artificial viscosity depending on the local absolute value of the residual of the finite element solution and the mesh size. With this term present, we prove a maximum norm bound for finite element solutions of Burgers' equation and t...

A method of wave mode determination, which was announced in Balikhin and Gedalin, is applied to AMPTE UKS and AMPTE IRM magnetic field measurements downstream of supercritical quasiperpendicular shock. The method is based on the fact that the relation between phase difference of the waves measured by two satellites, Doppler shift equation, the direction of the wave propagation are enough to obt...

In this paper, we describe a parallel solution scheme of inverse dynamics, and its application to flexible manipulators where elastic deformation and vibration normally occur in constituting link members. The scheme is developed by using the Finite Element Method (FEM), which evaluates the analyzed model in absolute Cartesian coordinates, with the equation of motion expressed in dimension of fo...

We present a family of exact solutions of the one-dimensional nonlinear Schro dinger equation which describes the dynamics of a bright soliton in Bose-Einstein condensates with the time-dependent interatomic interaction in an expulsive parabolic potential. Our results show that, under a safe range of parameters, the bright soliton can be compressed into very high local matter densities by incre...

In this note, the notion of absolute continuity of functions of two variables is discussed. We recall that the set of functions of two variables absolutely continuous in the sense of Carathéodory coincides with the class of functions admitting a certain integral representation. We show that absolutely continuous functions in the sense of Carathéodory can be equivalently characterized in terms o...

We present a cosmological model containing a cosmological constant Λ and a component with an inhomogeneous equation of state. We study the form of the inhomogeneous equation of state for which the model exhibits the relaxation of the cosmological constant, i.e. it asymptotically tends to the de Sitter regime characterized by a small positive effective cosmological constant. The effect of the re...

The mechanism for the relaxation of the cosmological constant is studied and elaborated. In the model used for the analysis of the relaxation mechanism the universe contains two components: a cosmological constant of an arbitrary size and sign and a component with an inhomogeneous equation of state. Owing to the dynamics of the second component the universe asymptotically tends to a de Sitter p...