Schroedinger operators with the q-ladder symmetry algebras

A class of the one-dimensional Schroedinger operators L with the symmetry algebra LB(+/-) = q(+/-2)B(+/-)L, (B(+),B(-)) = P(sub N)(L), is described. Here B(+/-) are the 'q-ladder' operators and P(sub N)(L) is a polynomial of the order N. Peculiarities of the coherent states of this algebra are briefly discussed

Solution of the Thirring Model with Imaginary Mass and Massless Scattering

The Thirring model with imaginary mass (or the sine-Gordon model with imaginary coupling) is deeply related to all the flows between minimal conformal theories. We solve this model explicitely using the Bethe ansatz. We find that there are Left and Right moving massless excitations with non trivial LR scattering. We compute the S matrix and recover the result conjectured by Fendley et al.Comment: 14 pages, 2 figures, uses harvmac macros. Preprint USC-94-00

Polysaccharides in Ocular Drug Delivery

Polysaccharides, such as cellulose, hyaluronic acid, alginic acid, and chitosan, as well as polysaccharide derivatives, have been successfully used to augment drug delivery in the treatment of ocular pathologies. The properties of polysaccharides can be extensively modified to optimize ocular drug formulations and to obtain biocompatible and biodegradable drugs with improved bioavailability and tailored pharmacological effects. This review discusses the available polysaccharide choices for overcoming the difficulties associated with ocular drug delivery, and it explores the reasons for the dependence between the physicochemical properties of polysaccharide-based drug carriers and their efficiency in different formulations and applications. Polysaccharides will continue to be of great interest to researchers endeavoring to develop ophthalmic drugs with improved effectiveness and safety.Peer reviewe

Effect of Double Substitution in Cationic Chitosan Derivatives on DNA Transfection Efficiency

Recently, much effort has been expended on the development of non-viral gene delivery systems based on polyplexes of nucleic acids with various cationic polymers. Natural polysaccharide derivatives are promising carriers due to their low toxicity. In this work, chitosan was chemically modified by a reaction with 4-formyl-n,n,n-trimethylanilinium iodide and pyridoxal hydrochloride and subsequent reduction of the imine bond with NaBH4. This reaction yielded three novel derivatives, n-[4-(n',n',n'-trimethylammonium)benzyl]chitosan chloride (TMAB-CS), n-[(3-hydroxy-5-(hydroxymethyl)-2-methyl-4-pyridine)methyl]chitosan chloride (Pyr-CS), and n-[4-(n',n',n''-trimethylammonium)benzyl]-n-[(3-hydroxy-5-(hydroxymethyl)-2-methyl-4-pyridine)methyl]chitosan chloride (PyrTMAB-CS). Their structures and degrees of substitution were established by H-1 NMR spectroscopy as DS1 = 0.22 for TMAB-CS, DS2 = 0.28 for Pyr-CS, and DS1 = 0.21, DS2 = 0.22 for PyrTMAB-CS. Dynamic light scattering measurements revealed that the new polymers formed stable polyplexes with plasmid DNA encoding the green fluorescent protein (pEGFP-N3) and that the particles had the smallest size (110-165 nm) when the polymer:DNA mass ratio was higher than 5:1. Transfection experiments carried out in the HEK293 cell line using the polymer:DNA polyplexes demonstrated that Pyr-CS was a rather poor transfection agent at polymer:DNA mass ratios less than 10:1, but it was still more effective than the TMAB-CS and PyrTMAB-CS derivatives that contained a quaternary ammonium group. By contrast, TMAB-CS and PyrTMAB-CS were substantially more effective than Pyr-CS at higher polymer:DNA mass ratios and showed a maximum efficiency at 200:1 (50%-70% transfected cells). Overall, the results show the possibility of combining substituent effects in a single carrier, thereby increasing its efficacy.Peer reviewe

Self-Similar Potentials and the q-Oscillator Algebra at Roots of Unity

Properties of the simplest class of self-similar potentials are analyzed. Wave functions of the corresponding Schr\"odinger equation provide bases of representations of the $q$-deformed Heisenberg-Weyl algebra. When the parameter $q$ is a root of unity the functional form of the potentials can be found explicitly. The general $q^3=1$ and the particular $q^4=1$ potentials are given by the equianharmonic and (pseudo)lemniscatic Weierstrass functions respectively.Comment: 15 pp, Latex, to appear in Lett.Math.Phy

Exact non-equilibrium current from the partition function for impurity transport problems

We study the partition functions of quantum impurity problems in the domain of complex applied bias for its relation to the non-equilibrium current suggested by Fendley, Lesage and Saleur (cond-mat/9510055). The problem is reformulated as a certain generalization of the linear response theory that accomodates an additional complex variable. It is shown that the mentioned relation holds in a rather generic case in the linear response limit, or under certain condition out of equilibrium. This condition is trivially satisfied by the quadratic Hamiltonians and is rather restrictive for the interacting models. An example is given when the condition is violated.Comment: 10 pages, RevTex. Final extended versio