Algebraic Manipulation of Polynomial Matrices: A Survey

A concise review is given of some recent methods for performingalgebraic operations on polynominal matrices. The problems addressedare division, inversion, and extraction of greatest common divisorof a pair of matrices. Based on a presentation at the International Symposium on theMathematical theory of Networks and Systems, Amsterdam, June1989.     

THE PHOTOREACTION OF A RHODAMINE 6G MONOLAYER ADSORBED ON QUARTZ STUDIED BY SURFACE SECOND HARMONIC GENERATION

Abstract— A monolayer of rhodamine 6G on quartz in air exhibited photochemistry upon laser irradiation in the first absorption band. The course of the reaction was followed in real time by the surface second harmonic generation method. It was observed that the photoproduct had an enhanced non-linear coefficient, relative to rhodamine 6G. Absorption spectra showed that this was not a result of a stronger resonance enhancement of the signal by the photoproduct. Consideration of the factors to which the surface second harmonic signal is sensitive suggested that the enhancement arose from an increased charge transfer character of the photoproduct's electronic transitions, and a reorientation of its transition dipole.     

Convergence of Projected Hessian Approximations in Quasi-Newton Methods for the Nonlinear Programming Problem

Two recently proposed algorithms for the problem of minimizationsubject to nonlinear equality constraints are examined. Bothmaintain quasi-Newton approximations to the projection of theHessian of the Lagrangian, onto the (linearized) manifold ofactive constraints at each iteration. We show that both algorithmscan be used with a more general quasi-Newton updating rule,and, using the analysis of Stoer (1984), that the sequence ofprojected Hessian approximations is convergent.     

Long-wavelength thermal convection in a weak shear flow

The problem of thermal convection in an imposed shear flow isexamined for a horizontal layer of fluid between poorly conductingboundaries. The horizontal scale H of the convective motionnear its onset is much greater than the depth h of the fluidlayer, with h/H being proportional to the one-fourth power ofa Biot number appearing in the condition applied to the temperatureat the horizontal boundaries. It is known that an asymptoticexpansion in powers of h/H yields a nonlinear long-wavelengthevolution equation for the depth-averaged temperature fieldthat is spatially isotropic in the absence of an imposed shearflow, but is strongly anisotropic for ‘strong’ shear.We derive in this paper a nonlocal long-wavelength equationthat bridges these two cases, and that contains each case inthe zero-shear and large-shear limits. Using this evolutionequation, we show how the shear flow stabilizes the longitudinalrolls to the zigzag instability, and how a preference for asquare planfonn on a periodic square lattice gives way to apreference for longitudinal rolls near onset. The longitudinalrolls may then become unstable as the Rayleigh number is increased.The analytical work is illustrated by some numerical simulationsof the full three-dimensional Boussinesq Navier-Stokes equations.The problem of pattern selection on a hexagonal lattice is alsodiscussed, and some new results are presented.     

THE EFFECT OF A CHALCOGENAPYRYLIUM DYE WITH AND WITHOUT PHOTOLYSIS ON MITOCHONDRIAL FUNCTION IN NORMAL AND TUMOR CELLS

A chalcogenapyrylium dye 8b, which is under investigation for the photodynamic therapy of malignant gliomas (brain tumors), was evaluated for inhibition of mitochondrial function both before and after exposure to laser light of 800 nm. Neoplastic and normal cells forced to use mitochondrial substrates were killed by the light-activation of intracellular 8b as well as exposure to classic mitochondrial inhibitors, rotenone and sodium azide. Correspondingly, cells in glucose-rich media showed little decrease in viability due to the photolysis of intracellular 8b or the presence of mitochondrial toxins. The toxicity of 8b without light activation was found to be the same regardless of the cell's energy source. Measurement of cellular ATP generated during treatment also showed the photolysis of intracellular 8b to be more inhibitory towards mitochondrial function than the unactivated parent compound. We conclude that the chalcogenapyrylium dyes localize to the mitochondrion and that photoactivation results in mitochondrial injury.