We consider scalar conservation laws with convex flux and random initial data. The Hopf–Lax formula induces a deterministic evolution of the law of the initial data. In a recent article, we derived a kinetic theory and Lax equations to describe the evolution of the law under the assumption that the initial datum is a spectrally negative Markov process. Here we show that: (i) the Lax equations a...

This paper continues the convergence analysis in [M. Giles and S. Ulbrich, SIAM J. Numer. Anal., 48 (2010), pp. 882–904] of discrete approximations to the linearized and adjoint equations arising from an unsteady one-dimensional hyperbolic equation with a convex flux function. We consider a simple modified Lax–Friedrichs discretization on a uniform grid, and a key point is that the numerical sm...

Recent work in Philadelphia describes a shift in the phonology of the /ae/ system. Some native Philadelphian college students are abandoning the local Philadelphian split system in favor of the more geographically-widespread Nasal system (Labov et al. 2013; Prichard and Tamminga 2012). This shift involves changing the conditioning factors that determine which tokens are tense /aeh/ and which ar...

We present a new, nonautonomous Lax pair for a lattice nonautomous modified Korteweg–deVries equation and show that it can be consistently extended multidimensionally, a property commonly referred to as being consistent around a cube. This nonautonomous equation is reduced to a series of q-discrete Painlevé equations, and Lax pairs for the reduced equations are found. A 2× 2 Lax pair is given f...

A propositional logic program P may be identified with a PfPf -coalgebra on the set of atomic propositions in the program. The corresponding C(PfPf )-coalgebra, where C(PfPf ) is the cofree comonad on PfPf , describes derivations by resolution. Using lax semantics, that correspondence may be extended to a class of first-order logic programs without existential variables. The resulting extension...

2.1 Examples of conservative schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.1 The Godunov Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2 The Lax-Friedrichs Scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 The local Lax-Friedrichs Scheme . . . . . . . ....

Baxters's Q-operators for the simplest q-deformed model. Abstract In the present paper we describe the procedure of the Q-operators construction for the q-deformed model, described by the Lax operator, which is important to formulate the Bethe ansatz for the Sin-Gordon model. This Lax operator can also be considered as some massless limit of the Lax operator of SG model. We constructed two R op...

The aerial architecture of plants is determined primarily by the pattern of shoot branching. Although shoot apical meristem initiation during embryogenesis has been extensively studied by molecular genetic approaches using Arabidopsis, little is known about the genetic mechanisms controlling axillary meristem initiation, mainly because of the insufficient number of mutants that specifically alt...

Compared the additive benefits of laxative, behavior, and biofeedback treatments for encopresis, while attempting to identify treatment mechanisms and predictors of treatment outcome. 44 encopretic children, ages 6-15 years, were randomly assigned to either laxative therapy (LAX), LAX plus enhanced toilet training (ETT), or LAX + ETT + anal sphincter biofeedback (BF). Daily symptom diaries were...

For a small category B and a double category D, let LaxN (B,D) denote the category whose objects are vertical normal lax functors B //D and morphisms are horizontal lax transformations. It is well known that LaxN (B,Cat) ≃ Cat/B, where Cat is the double category of small categories, functors, and profunctors. In [19], we generalized this equivalence to certain double categories, in the case whe...