Abstract. In this paper we introduce a definition of the local conservation property for numerical methods solving time dependent conservation laws, which generalizes the classical local conservation definition. The motivation of our definition is the Lax-Wendroff theorem, and thus we prove it for locally conservative numerical schemes per our definition in one and two space dimensions. Several...

The Lax-Richtmyer theorem is extended to work in the framework of Stetter's theory of discretizations. The new result applies to both initial and boundary value problems discretized by finite elements, finite differences, etc. Several examples are given, together with a comparison with other available equivalence theorems. The proof relies on a generalized Banach-Steinhaus theorem.

BACKGROUND Ideal bowel preparation regimen for a suitable colonoscopy should be safe, and well tolerated, and should rapidly clear gastrointestinal tract. Soluble polyethylene glycol (PEG) is the most common cleansing drug and Senna or C-Lax (Cassia angustifolia Vahl) is an alternative herbal one. This study was designed to compare the efficacy of PEG and C-lax in bowel preparation. METHODS In ...

Lax logical relations are a categorical generalisation of logical relations; though they preserve product types, they need not preserve exponential types. But, like logical relations, they are preserved by the meanings of all lambda-calculus terms. We show that lax logical relations coincide with the correspondences of Schoett, the algebraic relations of Mitchell and the pre-logical relations o...

We investigate a novel intuitionistic modal logic, called Propositional Lax Logic, with promising applications to the formal veri cation of computer hardware. The logic has emerged from an attempt to express correctness `up to' behavioural constraints | a central notion in hardware veri cation | as a logical modality. The resulting logic is unorthodox in several respects. As a modal logic it is...

In this letter, we consider the second Hamiltonian structure of the constrained modified KP hierarchy. After mapping the Lax operator to a pure differential operator the second structure becomes the sum of the second and the third Gelfand-Dickey brackets defined by this differential operator. We simplify this Hamiltonian structure by factorizing the Lax operator into linear terms.

We consider integrable boundary conditions for both discrete and continuum classical integrable models. Local integrals of motion generated by the corresponding “transfer” matrices give rise to time evolution equations for the initial Lax operator. We systematically identify the modified Lax pairs for both discrete and continuum boundary integrable models, depending on the classical r-matrix an...

By exploiting the description of topological spaces by either neighborhood systems or filter convergence, we obtain a neighborhood-like presentation of categories of lax algebras. The simplicity of this presentation pinpoints the importance of the Kleisli extension, which is introduced as a particular lax extension of the associated monad functor.

Recently, more and more data are published and exchanged by XML on the Internet. However, different XML data sources might contain the same data but have different structures. Therefore, it requires an efficient method to integrate such XML data sources so that more complete and useful information can be conveniently accessed and acquired by users. The tree edit distance is regarded as an effec...

In recent years the Federal Aviation Administration (FAA) has made reduction of runway incursions a priority for surface operations throughout the national airspace system. In a series of experiments conducted in April 2001, NASA studied alternatives designed to improve the efficient movement of surface traffic and reduce runway incursions at Los Angeles International Airport (LAX). The experim...