The generalized non-linear Schrödinger model on the interval

The generalized (1+1)-D$(1+1)\text{-}\mathrm{D}$ non-linear Schrödinger (NLS) theory with particular integrable boundary conditions is considered. More precisely, two distinct types of boundary conditions, known as soliton preserving (SP) and soliton non-preserving (SNP), are implemented into the classical glN$g{l}_N$ NLS model. Based on this choice of boundaries the relevant conserved quantities are computed and the corresponding equations of motion are derived. A suitable quantum lattice version of the boundary generalized NLS model is also investigated. The first non-trivial local integral of motion is explicitly computed, and the spectrum and Bethe ansatz equations are derived for the soliton non-preserving boundary conditions.     

Universal ratios in the 2D tricritical ising model

We consider the universality class of the two-dimensional tricritical Ising model. The scaling form of the free energy leads to the definition of universal ratios of critical amplitudes which may have experimental relevance. We compute these universal ratios by a combined use of results coming from perturbed conformal field theory, integrable quantum field theory, and numerical methods.     

One-pot synthesis of polyfunctionalized cyclic urea derivatives

[reaction: see text] Unexpectedly, imidazolidin-2-ones are easily obtained from beta-keto esters upon treatment with tert-butyl nosyloxycarbamate and calcium oxide under mild conditions. The structure of the product was established by X-ray crystallography.     

Partially isometric immersions and free maps

In this paper we investigate the existence of “partially” isometric immersions. These are maps \({f:M\rightarrow \mathbb{R}^q}\) which, for a given Riemannian manifold M, are isometries on some sub-bundle \({\mathcal{H}\subset TM}\). The concept of free maps, which is essential in the Nash–Gromov theory of isometric immersions, is replaced here by that of \({\mathcal{H}}\) –free maps, i.e. maps whose restriction to \({\mathcal{H}}\) is free. We prove, under suitable conditions on the dimension q of the Euclidean space, that \({\mathcal{H}}\) –free maps are generic and we provide, for the smallest possible value of q, explicit expressions for \({\mathcal{H}}\) –free maps in the following three settings: 1–dimensional distributions in \({\mathbb{R}^2}\), Lagrangian distributions of completely integrable systems, Hamiltonian distributions of a particular kind of Poisson Bracket.     

Rapid colorimetric determination of reduced and oxidized glutathione using an end point coupled enzymatic assay

A simple and rapid colorimetric coupled enzymatic assay for the determination of glutathione is described. The proposed method is based on the specific reaction catalyzed by γ-glutamyltransferase, which transfers the γ-glutamyl moiety from glutahione to an acceptor, with the formation of the γ-glutamyl derivative of the acceptor and cysteinylglycine. The latter dipeptide is a substrate of leucyl aminopeptidase, which hydrolyzes cysteinylglycine to glycine and cysteine that can be easily measured spectrophotometrically. The proposed method was used to measure the content of glutathione in acid extracts of bovine lens, to follow the NADPH-dependent reduction of glutathione disulfide (GSSG) to reduced glutathione (GSH) catalyzed by the enzyme glutathione reductase and to determine the glutathione content in human astrocytoma ADF cells subjected to oxidative stress. The results obtained showed that the method can be suitably used for the determination of GSH and GSSG in different biological samples and to monitor tissue or cell redox status under different conditions. It is also applicable for following reactions involving GSH and/or GSSG.

The Elliptic Scattering Theory of the 1/2-XYZ and Higher Order Deformed Virasoro Algebras

Bound state excitations of the spin 1/2-XYZ model are considered inside the Bethe Ansatz framework by exploiting the equivalent Non-Linear Integral Equations. Of course, these bound states go to the sine-Gordon breathers in the suitable limit and therefore the scattering factors between them are explicitly computed by inspecting the corresponding Non-Linear Integral Equations. As a consequence, abstracting from the physical model the Zamolodchikov-Faddeev algebra of two n-th elliptic breathers defines a tower of n-order Deformed Virasoro Algebras, reproducing the n = 1 case the usual well-known algebra of Shiraishi-Kubo-Awata-Odake [1]. Communicated by Vincent Rivasseau To our friend Daniel, ad memoriam Submitted: February 2, 2006; Accepted: March 10, 2006     

Reverse shuttling in a fullerene-stoppered rotaxane

The preparation and characterization of a solvent-switchable rotaxane that shuttles in the opposite direction to that expected are reported. The reverse shuttling is confirmed by NMR spectroscopy and can be monitored by cyclic voltammetry. The electrochemically generated anions on the fullerene moiety are stabilized by the closer proximity of the macrocycle.