Abstract. In this article, we study the global solution of the elementary waves interaction problem for the nonlinear chromatography equations. We constructively obtain the solutions when the initial data are three piecewise constant states. The global structures and large time-asymptotic behaviors of the solutions are analyzed case by case. During the process of the interaction, it is easy to ...

The authors present a higher-order Godunov method for the solution of the twoand three-dimensional equations of ideal magnetohydrodynamics (MHD). This work is based both on a suitable operator-split approximation to the full multidimensional equations, and on a one-dimensional Riemann solver. TIlls Riemann solver is sufficiently robust to handle the nonstrictly hyperbolic nature of the MHD equa...

The Riemann problem is solved for 2 x 2 systems of hyperbolic conservation laws having quadratic flux functions. Equations with quadratic flux functions arise from neglecting higher order nonlinear terms in hyperbolic systems that fail to be strictly hyperbolic everywhere. Such equations divide into four classes, three of which are considered in this paper. The solution of the Riemann problem i...

In this paper, we consider a certain class of discrete pseudo-differential operators in a sharp convex cone and describe their invertibility conditions in L2-spaces. For this purpose we introduce a concept of periodic wave factorization for elliptic symbol and show its applicability for the studying. Key–Words: Discrete operator, Multidimensional periodic Riemann problem, Periodic wave factoriz...

We covered Riemann integrals in the first three weeks in MA502 this semester (Chapter 11 in [1]). This report explores a necessary and sufficient condition for determining Riemann integrability of f(x) solely from its properties. This condition is known as Lebesgue’s criterion and elucidating the proof of this condition is the aim of this report. This report revisits the concepts learnt in MA50...

A Riemann-Lie algebra is a Lie algebra G such that its dual G∗ carries a Riemannian metric compatible (in the sense introduced by the author in C. R. Acad. Sci. Paris, t. 333, Série I, (2001) 763–768) with the canonical linear Poisson structure of G∗ . The notion of Riemann-Lie algebra has its origins in the study, by the author, of Riemann-Poisson manifolds (see Differential Geometry and its A...

We determine, for all genus g ≥ 2 the Riemann surfaces of genus g with exactly 4g automorphisms. For g 6= 3, 6, 12, 15 or 30, this surfaces form a real Riemann surface Fg in the moduli space Mg: the Riemann sphere with three punctures. We obtain the automorphism groups and extended automorphism groups of the surfaces in the family. Furthermore we determine the topological types of the real form...

Techniques for using the Monte Carlo method to evaluate fuzzy Riemann integrals and improper fuzzy Riemann integrals are proposed in this paper. Owing to the α-level set of the (improper) fuzzy Riemann integral being the closed interval whose end points are the classical (improper) Riemann integrals, it is possible to invoke the Monte Carlo method to approximate the end points of the α-level cl...

We derive the wave equation obeyed by electromagnetic fields in curved spacetime. We find that there are Riemann and Ricci curvature coupling terms to the photon polarisation which result in a polarisation dependent deviation of the photon trajectories from null geodesics. Photons are found to have an effective mass in an external gravitational field and their velocity in an inertial frame is i...

We derive a lubrication model describing gravity-driven thin film flow of a suspension of heavy particles in viscous fluid. The main features of this continuum model are an effective mixture viscosity and a particle settling velocity, both depending on particle concentration. The resulting equations form a 2 × 2 system of conservation laws in the film thickness h(x, t) and in φh, where φ(x, t) ...