We give the Lax representations for for the elliptic, hyperbolic and homogeneous second order Monge-Ampère equations. The connection between these equations and the equations of hydrodynamical type give us a scalar dispersionless Lax representation. A matrix dispersive Lax representation follows from the correspondence between sigma models, a two parameter equation for minimal surfaces and Mong...

We find a Lax pair for the geometrically exact discrete Hamiltonian equations for the discrete elastic rod. This is paper III in a series. III. Lax Pair for Discrete Dynamics of Discrete Elastic DNA Shi, McClain, and Hearst

In this paper, we focus on the intuitionistic propositional logic extended with a local operator [22] (also called nucleus [21]); such is commonly named lax after [9]. We prove that unification finitary in and supply algorithms for computing basis of unifiers recognizing admissibility inference rules, following analogous known results logic.

This paper is devoted to the construction of numerical fluxes for hyperbolic systems. We first present a GFORCE numerical flux, which is a weighted average of the Lax-Friedrichs and Lax-Wendroff fluxes. For the linear advection equation with constant coefficient, the new flux reduces identically to that of the Godunov first order upwind method. Then we incorporate GFORCE in the framework of the...

Timed automata, and machines alike, currently lack a general mathematical characterisation. In this paper we provide a uniform coalgebraic understanding of these devices. This framework encompasses known behavioural equivalences for timed automata and paves the way for the extension of these notions to new timed behaviours and for the instantiation of established results from the coalgebraic th...

Classical and recent numerical schemes for solving hyperbolic conservation laws were analyzed for computational efficiency and application to nonideal gas flows. The Roe-Pike approximate Riemann solver with entropy correction, the Harten second-order scheme and the extension of the Roe-Pike method to secondorder by the MUSCL strategy were compared for one-dimensional flows of an ideal gas. Thes...

ABSTRACT Genetic resistance is the most efficient tool in crop disease management. Peanut smut currently one of important peanut diseases, with its incidence increasing terms both damage level and area covered. The aim this study was to assess response different genotypes obtained by Facultad de Agronomía y Veterinaria Universidad Nacional Río Cuarto (Argentina) their yield. During 2016/17, 201...

In this letter, a definition of the higher dimensional Lax pair for a lower dimensional system which may be a chaotic system is given. A special concrete (2+1)-dimensional Lax pair for a general (1+1)-dimensional three order autonomous partial differential equation is studied. The result shows that any (1+1)-dimensional three order semi-linear autonomous system (no matter it is integrable or no...