A new ansatz is presented for a Lax pair describing systems of particles on the line interacting via (possibly nonsymmetric) pairwise forces. Particular cases of this yield the known Lax pairs for the Calogero-Moser and Toda systems, as well as their relativistic generalisations. The ansatz leads to a system of functional equations. Several new functional equations are described and the general...

The Davey-Stewartson I equation is a typical integrable equation in 2+1 dimensions. Its Lax system being essentially in 1+1 dimensional form has been found through nonlinearization from 2+1 dimensions to 1+1 dimensions. In the present paper, this essentially 1+1 dimensional Lax system is further nonlinearized into 1+0 dimensional Hamiltonian systems by taking the Bargmann constraints. It is sho...

We construct a Lax pair for the E (1) 6 q-Painlevé system from first principles by employing the general theory of semi-classical orthogonal polynomial systems characterised by divided-difference operators on discrete, quadratic lattices [arXiv:1204.2328]. Our study treats one special case of such lattices – the q-linear lattice – through a natural generalisation of the big q-Jacobi weight. As ...

In this work, the authors study Bonnet Problems using Cartan moving frames and associated structure equations. The Cartan structural forms are written in terms of the first and second fundamental forms, and the Lax system is consequently reinterpreted; orthonormal moving frames are obtained solutions to this Bonnet-Lax system, via numerical integration. Certain classifications of families of su...

The activation of T cells and the initiation of an immune response is tightly controlled through the crosstalk of both positive and negative regulators. Two adaptors that function as negative regulators of T cell activation are adaptor in lymphocytes of unknown function X (ALX) and linker for activation of X cell (LAX). Previously, we showed that T cells from mice deficient in ALX and LAX displ...

A new system of coupled higher-order nonlinear Schrödinger equations is proposed which passes the Painlevé test for integrability well. A Lax pair and a multi-field generalization are obtained for the new system.

The gauge-invariant description of zero-curvature representations of evolution equations is applied to the problem of how to distinguish the fake Lax pairs from the true Lax pairs. The main difference between the true Lax pairs and the fake ones is found in the structure of their cyclic bases. In this note, we use the gauge-invariant description of zero-curvature representations of evolution eq...

Lax Logic is an intuitionistic modal logic which has so far been investigated at the propositional level. It has shown itself to have applications in the formal veriication of hardware|a logical modality is used to capture and express the correctness of speciicationsùp to' behavioural constraints. A translation from Quantiied Lax Logic to a quantiied classical modal logic is presented which ena...

BACKGROUND Recently, radiofrequency (RF) devices have been introduced and commercialized for nonablative procedures in dermatology and plastic surgery for the treatment of age-related rhytides and lax skin. OBJECTIVE The objective was to assess the efficacy and safety of a novel RF device (Accent, Alma Lasers, Ltd, Caesarea, Israel) for the treatment of rhytides and lax skin. METHODS AND MA...