Tracing Possible Structural Asymmetry of Silica Gel Used for Precoating Thin-Layer Chromatography Plates

JPC – Journal of Planar Chromatography – Modern TLC - We have previously described unexpected two-dimensionality in the thin-layer chromatographic separation of pairs of enantiomers of...     

Loss in a rectangular optical waveguide induced by the crossover of a second waveguide

We calculate the loss induced in a single-mode rectangular optical waveguide by the presence of a second waveguide, perpendicular to the first, which crosses over the first waveguide at a variable distance d. Our calculation is applied to the analysis of several doped silica waveguides of practical importance for optical circuit design.     

The Computational Complexity of the Chow Form

We present a bounded probability algorithm for the computation of the Chowforms of the equidimensional components of an algebraic variety. In particular, this gives an alternative procedure for the effective equidimensional decomposition of the variety, since each equidimensional component is characterized by its Chow form. The expected complexity of the algorithm is polynomial in the size and the geometric degree of the input equation system defining the variety. Hence it improves (or meets in some special cases) the complexity of all previous algorithms for computing Chow forms. In addition to this, we clarify the probability and uniformity aspects, which constitutes a further contribution of the paper. The algorithm is based on elimination theory techniques, in line with the geometric resolution algorithm due to M. Giusti, J. Heintz, L. M. Pardo, and their collaborators. In fact, ours can be considered as an extension of their algorithm for zero-dimensional systems to the case of positive-dimensional varieties. The key element for dealing with positive-dimensional varieties is a new Poisson-type product formula. This formula allows us to compute the Chow form of an equidimensional variety from a suitable zero-dimensional fiber. As an application, we obtain an algorithm to compute a subclass of sparse resultants, whose complexity is polynomial in the dimension and the volume of the input set of exponents. As another application, we derive an algorithm for the computation of the (unique) solution of a generic overdetermined polynomial equation system.     

Bounds for non‐periodic mixtures of infinitely many materials

We prove bounds on the homogenized coefficients for general non‐periodic mixtures of an arbitrary number of isotropic materials, in the heat conduction framework. The component materials and their proportions are given through the Young measure associated to the sequence of coefficient functions. Upper and lower bounds inequalities are deduced in terms of algebraic relations between this Young measure and the eigenvalues of the H‐limit matrix. The proofs employ arguments of compensated compactness and fine properties of Young measures. When restricted to the periodic case, we recover known bounds. Copyright © 2005 John Wiley & Sons, Ltd.     

Existence for a degenerate diffusion problem with a nonlinear operator

We study a degenerate nonlinear variational inequality which can be reduced to a multivalued inclusion by an appropriate change of the unknown function. We establish existence, uniqueness and regularity results. An application arising in the theory of water diffusion in porous media is discussed as an example.      

Thermal behaviour of polyacrylamidoxime-copper chelates

The purpose of this work was to investigate the effect of several factors (anion type in the copper salt, pH and concentration of the salt solution) on the structure and thermo-oxidative degradation of the polyacrylamidoxime-copper chelates, by using elemental analysis, IR spectroscopy and dynamic thermogravimetry. The chelates containing copper ions as sulphate exhibit a better initial thermal stability than the polyacrylamidoxime fibre presumably due to the crosslinking generated by the intermolecular complexation of the ions; the removal of the sulphate anions takes place concomitantly with the second step of polymeric chain decomposition. The initial thermal decomposition of the chelates formed by copper ions as nitrate begins at lower temperatures as compared to the polyacrylamidoxime fibre, probably by the nitrate anion release, which partly overlaps the initial decomposition of the copper ion-crosslinked polymeric chains. Copper ions as either sulphate or nitrate catalyse the reactions involved in the main step of polyacrylamidoxime fibre decomposition; the higher the copper amount, the stronger the catalytic effect.     

Group algebras of Kleinian type and groups of units

The algebras of Kleinian type are finite-dimensional semisimple rational algebras A such that the group of units of an order in A is commensurable with a direct product of Kleinian groups. We classify the Schur algebras of Kleinian type and the group algebras of Kleinian type. As an application, we characterize the group rings RG, with R an order in a number field and G a finite group, such that the group of units of RG is virtually a direct product of free-by-free groups.     

Intra- and intermolecular fluorescence quenching in 7-(pyridyl)indoles

Three isomeric 7-(pyridyl)indoles reveal very different, solvent-dependent photophysical properties. Due to rapid excited state depopulation involving intramolecular hydrogen bonding, 7-(2′-pyridyl)indole is practically nonfluorescent at room temperature. In nonpolar and polar aprotic solvents, 7-(3′-pyridyl)indole and 7-(4′-pyridyl)indole fluorescence strongly, but the emission is quenched in alcohols. Syn and anti rotameric forms of 7-(3′-pyridyl)indole are detected, each quenched to a different degree. This differential quenching is interpreted as evidence of enhanced S₁ → S₀ internal conversion being more efficient in cyclic solvates, with alcohol molecules forming a bridge between the proton donor and acceptor groups of an excited chromophore.