On the Levi and Lebesgue properties

The paper is devoted to a question if the Levi property is preserved by direct sums and quotients. The three-space problem for the Levi and Lebesgue properties in topological Riesz spaces is also investigated.     

Numerical solution of the two-dimensional Poincaré equation

This paper deals with numerical approximation of the two-dimensional Poincaré equation that arises as a model for internal wave motion in enclosed containers. Inspired by the hyperbolicity of the equation we propose a discretisation particularly suited for this problem, which results in matrices whose size varies linearly with the number of grid points along the coordinate axes. Exact solutions are obtained, defined on a perturbed boundary. Furthermore, the problem is seen to be ill-posed and there is need for a regularisation scheme, which we base on a minimal-energy approach.     

On Rockafellar’s theorem using proximal point algorithm involving -maximal monotonicity framework

On the basis of the general framework of H-maximal monotonicity (also referred to as H-monotonicity in the literature), a generalization to Rockafellar’s theorem in the context of solving a general inclusion problem involving a set-valued maximal monotone operator using the proximal point algorithm in a Hilbert space setting is explored. As a matter of fact, this class of inclusion problems reduces to a class of variational inequalities as well as to a class of complementarity problems. This proximal point algorithm turns out to be of interest in the sense that it plays a significant role in certain computational methods of multipliers in nonlinear programming. The notion of H-maximal monotonicity generalizes the general theory of set-valued maximal monotone mappings to a new level. Furthermore, some results on general firm nonexpansiveness and resolvent mapping corresponding to H-monotonicity are also given.     

Existence and examples of quantum isometry groups for a class of compact metric spaces

We formulate a definition of isometric action of a compact quantum group (CQG) on a compact metric space, generalizing Banica's definition for finite metric spaces. For metric spaces (X,d)$(X,d)$ which can be isometrically embedded in some Euclidean space, we prove the existence of a universal object in the category of the compact quantum groups acting isometrically on (X,d)$(X,d)$. In fact, our existence theorem applies to a larger class, namely for any compact metric space (X,d)$(X,d)$ which admits a one-to-one continuous map f:X→Rⁿ$f:X\to {\mathbb{R}}^n$ for some n   such that _d0(f(x),f(y))=?(d(x,y))$d_0(f(x),f(y))=?(d(x,y))$ (where _d0$d_0$ is the Euclidean metric) for some homeomorphism ?   of R⁺${\mathbb{R}}^{+}$.     

On algebraic equations satisfied by correlators in Wess-Zumino-Witten models

Apart from the Knizhnik-Zamolodchikov differential equations, correlation functions in Wess-Zumino-Witten models of conformal field theory satisfy a certain system of algebraic equations. We show that hypergeometric solutions of KZ equations constructed in [3] do satisfy these algebraic equations.     

On extension theory inL 2-spaces

We present the first steps towards a general extension theory inL ²-spaces. By this theory it is possible to construct all perturbations of the Laplacian supported by a closed setN even if the classical capacity ofN equals zero.     

Multiple-injection affinity capillary electrophoresis to estimate binding constants of receptors to ligands

Multiple-injection affinity capillary electrophoresis (MIACE) is used to determine binding constants (K _b) between receptors and ligands using as model systems vancomycin and teicoplanin from Streptomyces orientalis and Actinoplanes teichomyceticus, respectively, and their binding to D-Ala-D-Ala peptides and carbonic anhydrase B (CAB. EC 4.2.1.1) and the binding of the latter to arylsulfonamides. A sample plug containing a non-interacting standard is first injected followed by multiple plugs of sample containing the receptor and then a final injection of sample containing a second standard. Between each injection of sample, a small plug of buffer is injected which contains an increasing concentration of ligand to effect separation between the multiple injections of sample. Electrophoresis is then carried out in an increasing concentration of ligand in the running buffer. Continued electrophoresis results in a shift in the migration time of the receptor in the sample plugs upon binding to their respective ligand. Analysis of the change in the relative migration time ratio (RMTR) or electrophoretic mobility (μ) of the resultant receptor–ligand complex relative to the non-interacting standards, as a function of the concentration of ligand yields a value for K _b. The MIACE technique is a modification in the ACE method that allows for the estimation of binding affinities between biological interactions on a timescale faster than that found for standard ACE. In addition sample volume requirements for the technique are reduced compared to traditional ACE assays. These findings demonstrate the advantage of using MIACE to estimate binding parameters between receptors and ligands.     

The Blow-up Rate of Solutions to Boundary Blow-up Problems for the Complex Monge–Ampère Operator

A regularity result for solutions to boundary blow-up problems for the complex Monge–Ampère operator in balls in is proved. For certain boundary blow-up problems on bounded, strongly pseudoconvex domains in with smooth boundary an estimate of the blow-up rate of solutions are given in terms of the distance to the boundary and the product of the eigenvalues of the Levi form.