Relaxation methods for solving linear inequality systems: converging results

The problem of finding a feasible solution to a linear inequality system arises in numerous contexts. In González-Gutiérrez and Todorov (Optim. Lett. doi:10.1007/s11590-010-0244-4, 2011), an algorithm, called extended relaxation method, for solving the feasibility problem has been proposed by the authors. Convergence of the algorithm has been proven. In this paper, we consider a class of extended relaxation methods depending on a parameter and prove their convergence. Numerical experiments have been provided, as well.     

Similarities and Differences between Crystal and Enzyme Environmental Effects on the Electron Density of Drug Molecules

The crystal interaction density is generally assumed to be a suitable measure of the polarization of a low-molecular weight ligand inside an enzyme, but this approximation has seldomly been tested and has never been quantified before. In this study, we compare the crystal interaction density and the interaction electrostatic potential for a model compound of loxistatin acid (E64c) with those inside cathepsin B, in solution, and in vacuum. We apply QM/MM calculations and experimental quantum crystallography to show that the crystal interaction density is indeed very similar to the enzyme interaction density. Less than 0.1 e are shifted between these two environments in total. However, this difference has non-negligible consequences for derived properties.     

On Linear Inequality Systems with Smooth Coefficients

A linear inequality system with infinitely many constraints is polynomial [analytical] if its index set is a compact interval of the real line and all its coefficients are polynomial [analytical] functions of the index on this interval. This paper provides sufficient conditions for a given closed convex set to be the solution set of a certain polynomial or at least analytical system.The authors are indebted to Dr. J. M. Almira for valuable comments and suggestions.     

Photoinduced dichroism and birefringence in films of Mordant Pure Yellow/poly(vinyl alcohol): simultaneous real-time investigations at two wavelengths

Photoinduced anisotropy in films of azo-dye Mordant Pure Yellow (MPY) dissolved in a polyvinyl alcohol matrix, is investigated. The photodichroism and photoinduced birefringence are measured in real time for two wavelengths, 488 nm (in the absorption band) and 633 nm (outside it), on excitation with an Ar⁺ laser beam. It is shown that strong dichroism is induced without changing the average optical density of the film, and the kinetic curves of the birefringence and the dichroism are substantially different. The conclusion is made that the photoprocesses of the dye molecules cause a reconstruction of the matrix.     

On Subspace Lattices I. Closedness Type Properties and Tensor Products

We study properties of subspace lattices related to the continuity of the map Lat and the notion of reflexivity. We characterize various “closedness” properties in different ways and give the hierarchy between them. We investigate several properties related to tensor products of subspace lattices and show that the tensor product of the projection lattices of two von Neumann algebras, one of which is injective, is reflexive.     

Non-linear extremal problems for analytic two-dimensional Riemann-Stieltjes integrals

We examine certain non-linear extremal problems for two-dimensional Riemann-Stieltjes integrals \(\varphi (z) \equiv \int {_D \int {g(z,\zeta )d\mu (\zeta ),} \zeta \in D \equiv [\zeta |\left| \zeta \right|} \leqslant 1]\) ,z∈Δ≡[z‖|z|<1] whereg(z, ζ) is a continuous function in (z, ζ)∈[Δ×D] and an analytic function forz∈Δ and μ(ζ) is a unit mass measure onD. In particular, if the mass is distributed on the segment [a, b], we obtain the well-known Ruscheweyh results for the one-dimensional Riemann-Stieltjes integrals \(\varphi (z) \equiv \int_a^b {g(z,t)d\mu (t),z \in \Delta } \) . In particular, ifg(z,σ)≡z/(1—zσ), we determine the maximal domain of univalence and the radii of starlikeness and convexity of order α, ?∞<α<1, of the corresponding functions ?(z). A particular study is made of the functions of classesS ₁(D) andS ₂(D) which is similar to the study of the functions of the corresponding classesS ₁(C) andS ₂(C) of Schwarz analytic functions. In addition to obtaining maximal domains of univalence, we also determine the unique extremal functions for each of the functional studied.