Factorization method and general second order linear difference equation

This paper addresses an investigation on a factorization method for difference equations. It is proved that some classes of second order linear difference operators, acting in Hilbert spaces, can be factorized using a pair of mutually adjoint first order difference operators. These classes encompass equations of hypergeometic type describing classical orthogonal polynomials of a discrete variable

Integrable Systems Related to Deformed so(5)\mathfrak{so}(5)

We investigate a family of integrable Hamiltonian systems on Lie-Poisson spaces $\mathcal{L}_+(5)$ dual to Lie algebras $\mathfrak{so}_{\lambda, \alpha}(5)$ being two-parameter deformations of $\mathfrak{so}(5)$. We integrate corresponding Hamiltonian equations on $\mathcal{L}_+(5)$ and $T^*\mathbb{R}^5$ by quadratures as well as discuss their possible physical interpretation

Integrable Hamiltonian systems related to the Hilbert--Schmidt ideal

By application of the coinduction method as well as Magri method to the ideal of real Hilbert-Schmidt operators we construct the hierarchies of integrable Hamiltonian systems on the Banach Lie-Poisson spaces which consist of these type of operators. We also discuss their algebraic and analytic properties as well as solve them in dimensions N=2,3,4.Comment: 36 page

Molecular anatomy of interendothelial junctions in human blood-brain barrier microvessels.

Immunogold cytochemical procedure was used to study the localization at the ultrastructural level of interendothelial junction-associated protein molecules in the human brain blood microvessels, representing the anatomic site of the blood-brain barrier (BBB). Ultrathin sections of Lowicryl K4M-embedded biopsy specimens of human cerebral cortex obtained during surgical procedures were exposed to specific antibodies, followed by colloidal gold-labeled secondary antibodies. All tight junction-specific integral membrane (transmembrane) proteins--occludin, junctional adhesion molecule (JAM-1), and claudin-5--as well as peripheral zonula occludens protein (ZO-1) were highly expressed. Immunoreactivity of the adherens junction-specific transmembrane protein VE-cadherin was of almost similar intensity. Immunolabeling of the adherens junction-associated peripheral proteins--alpha-catenin, beta-catenin, and p120 catenin--although positive, was evidently less intense. The expression of gamma-catenin (plakoglobin) was considered questionable because solitary immunosignals (gold particles) appeared in only a few microvascular profiles. Double labeling of some sections made possible to observe strict colocalization of the junctional molecules, such as occludin and ZO-1 or JAM-1 and VE-cadherin, in the interendothelial junctions. We found that in human brain microvessels, the interendothelial junctional complexes contain molecular components specific for both tight and adherens junctions. It is assumed that the data obtained can help us find the immunodetectable junctional molecules that can serve as sensitive markers of normal or abnormal function of the BBB