Visualisation of biopolymer mixtures using confocal scanning laser microscopy (CSLM) and covalent labelling techniques

Confocal scanning laser microscopy (CSLM) has been used to study the behaviour of mixtures of proteins, gelatine, whey proteins and β-lactoglobulin, and polysaccharides, dextran, gellan gum, carrageenan, gum Arabic, and starch. CSLM proved to be a suitable technique to visualise the microstructure of these (phase separated) mixtures in two and three-dimensional images. Contrast through fluorescence is obtained either by covalent labelling (polysaccharides and proteins) or non-covalent labelling (proteins and starch). Double and triple labelling allows the visualisation of individual components in a complex mixture of biopolymers.     

Chain enumeration and non-crossing partitions

A formula is established for the number of chains with designated ranks in the non-crossing partition lattice. As corollaries, certain results of Kreweras are obtained. Non-crossing partitions are then generalized in two ways, and similar problems are solved.     

On a fixed point theorem for partially ordered sets

An elementary combinatorial proof is presented of the following fixed point theorem: Let P be a finite partially ordered set with a cut-set X. If every subset of X has either a meet or a join, then P has the fixed point property. This theorem is strengthened to include a certain class of infinite partially ordered sets, as well.     

Difference Equations and Discriminants for Discrete Orthogonal Polynomials

We prove that any set of polynomials orthogonal with respect to a discrete measure supported on equidistant points contained in a half line satisfy a second order difference equation. We also give a discrete analogue of the discriminant and give a general formula for the discrete discriminant of a discrete orthogonal polynomial. As an application we give explicit evaluations of the discrete discriminants of the Meixner and the Hahn polynomials. A difference analogue of the Bethe Ansatz equations is also mentioned.Research partially supported by NSF grant DMS 99-70865     

Magneto-optical spectroscopy of Yb ions in huntite structure

We report the first measurements of magnetic circular dichroism (MCD) and magneto-optical activity (ratio of zero moments of MCD and absorption bands) of Yb³⁺ ion in the trigonal single crystals Yb_xTm_1−xAl₃(BO₃)₄ as a function of temperature in the range of 100-293 K. Magneto-optical activity follows the Curie-Weiss law with the Weiss constant θ=−55 K for Yb_0.1Tm_0.9Al₃(BO₃)₄ crystal. The value and origin of the magneto-optical activity is theoretically analyzed.     

Linear and quadratic magneto-optical effects observed in La0.7Sr0.3MnO3 thin films in transmitted light

Magnetic linear dichroism (MLD) is observed in polycrystalline La_0.7Sr_0.3MnO₃ films in transmitted light. The spectral and temperature dependences of the MLD are determined for the energy E of the light wave ranging from 1.5 to 3.5 eV. The experimental spectra are fitted by a sum of Lorentzian curves. The MLD spectrum exhibits more features in comparison to the spectra of magnetic circular dichroism (MCD), which we measured earlier using the same film samples. Various temperature behaviors of the intensities of the Lorentzian components centered at different E values have been revealed. This can be related to the effect of the surface states on the magneto-optical characteristics of the samples.