On Weakly Formulated Sylvester Equations and Applications

We use a “weakly formulated” Sylvester equation

Structural characterization of the trans-equatorial isomer of (aqua)(ethylenediamine-N,N,N′-tripropionato)chromium(III) trihydrate,[Cr(edtrp)(H2O)] · 3H2O

The structure of trans-equatorial [Cr(edtrp)(H₂O)] · 3H₂O (edtrp^3– is the anion of ethylenediamine-N,N,N-tripropionic acid) was determined by single crystal X-ray diffraction. The chromium(III) ion is surrounded octahedrally by the two nitrogen and three oxygen atoms of the quinquedentate edtrp^3–, forming a five-membered diamine ring and the three six-membered -propionato chelate rings. The remaining coordination position is occupied by the H₂O ligand. The crystal structure conformation is compared to the result of recent molecular mechanics analysis. The ring strain of R and G chelate rings was found to be in agreement with the previously proposed mechanisms for the C—N bond cleavage and recombination.     

A posteriori estimates for eigenvalue/vector approximations

We combine abstract eigenvalue/eigenvector estimates (from our earlier work) with a saturation assumption for finite element solution of associated stationary problem to obtain a posteriori estimates of the accuracy of finite element Rayleigh–Ritz approximations. Attention will be payed to the interplay between the accuracy estimate for the finite element method and a strategy for generating an adapted mesh. The obtained results use a preconditioned residuum of Neymeyr and extend his study of eigenvalue approximations with eigenvector estimates. We also prove that this eigenvalue estimator is equivalent to the global error. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On relative perturbation theory for eigenvalues and eigenvectors of block operator matrices

We are concerned with singularly perturbed spectral problems which appear in engineering sciences. Typically under the influence of a singular perturbation the model can be approximated by a simpler, perturbation independent model. Such reduced model is usually better amenable to analytic or numeric analysis. However, the question of the quality of approximation has to be answered. Frequently, correctors which yield an improved solution–capturing important phenomena which the reduced model does not “see”–to the original problems are required. We tackle both question for self-adjoint eigenvalue/eigenvector problems posed in a general Hilbert space. Our technique is constructive and is based on methods (relative perturbation theory) of modern Numerical Linear Algebra. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Fractionation of styrene-methyl methacrylate copolymer

Styrene-methyl methacrylate copolymer was fractionated by the column elution and coacervate extraction techniques. Different solvent-nonsolvent combinations were used; both batchwise and continuous column elution fractionations were carried out. Successful resolution of fractions according to molecular weight was achieved. The effect of the solvent-precipitant pair on the fractionation efficiency, as tested by gel permeation chromatography, is discussed. The results of continuous column elution depend significantly on the elution rate.     

Analysis of novel passive cooling strategies for free-standing silicon photovoltaic panels

Journal of Thermal Analysis and Calorimetry - Silicon-based photovoltaic (PV) panels are sensitive to operating temperatures, especially during exposure to high solar irradiation levels. The...     

Relative Convergence Estimates for the Spectral Asymptotic in the Large Coupling Limit

We prove optimal convergence estimates for eigenvalues and eigenvectors of a class of singular/stiff perturbed problems. Our profs are constructive in nature and use (elementary) techniques which are of current interest in computational Linear Algebra to obtain estimates even for eigenvalues which are in gaps of the essential spectrum. Further, we also identify a class of “regular” stiff perturbations with (provably) good asymptotic properties. The Arch Model from the theory of elasticity is presented as a prototype for this class of perturbations. We also show that we are able to study model problems which do not satisfy this regularity assumption by presenting a study of a Schroedinger operator with singular obstacle potential.