How should one define a (weak) crystal?

We compare two proposals for the study of positional long-range order: one in terms of the spectrum of the translation operator, the other in terms of the Fourier spectrum. We point out that only the first one allows for the consideration of molecular, as opposed to atomic, (weakly) periodic structures. We illustrate this point on the Thue-Morse system.     

All-fibre optical system for exciting and detecting the vibration of silicon microresonator sensors

An all-fibre optical system for optical interrogation and detection of the vibrations of a silicon microresonator is reported. Metal-coated silicon microresonators are excited by intensity modulated laser light delivered through an optical fibre, while the vibration of the resonators is detected by an optical fibre interferometer. Measurements have shown that an average optical power of 10 μW is sufficient to maintain the flexural vibration of the resonator. When the resonator is used as a pressure sensor, its resonant frequency changes from 62 kHz to 130 kHz as the pressure varies from -0°6 bar to 1 bar (gauge). A silicon resonator with 700 nm aluminium coating functions as a temperature sensor, showing a frequency shift from 262 kHz to 251 kHz when the temperature changes from 25 °C to 80 °C.     

Hamiltonian circle actions on symplectic manifolds and the signature

Let M be a symplectic manifold with a Hamiltonian circle action with isolated fixed points. We prove that σ (M) = b₀(M) − b₂(M) + b₄(M) − b₆(M) + … where σ (M) is the signature of M and b_i(M) is the ith Betti number of M.     

Isomorphism of the Baumslag-Solitar groups

Necessary and sufficient conditions for the isomorphism of two groups, each defined by a single relation of the type a^–1b^ma=bⁿ, are obtained.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 12, pp. 1684–1686, December, 1991.     

Energy transfer between the flavin chromophores of electron-transferring flavoprotein fromMegasphaera elsdenii as inferred from time-resolved red-edge and blue-edge fluorescence spectroscopy

Both a mode-locked argon-ion laser and synchrotron radiation were used as excitation sources to obtain time-resolved polarized fluorescence of the two FAD cofactors in electron transferring flavoprotein fromMegasphaera elsdenii. Red-edge excited and blue-edge detected fluorescence anisotropy decay curves did not contain a fast relaxation process which was observed upon mainband excitation and detection. This relaxation was assigned to homo-energy transfer between the two FAD cofactors. Failure of energy transfer as observed with edge spectroscopy on this protein excludes restricted reorientational motion of the flavins as a possible mechanism of depolarization. From the global analysis of the fluorescence anisotropy decay surface obtained at multiple excitation and detection wavelengths, the distance between and the relative orientation of the flavins could be estimated. The methodology described has general applicability in other multichromophoric biopolymers and has the potential to acquire accurate geometrical parameters in these systems.     

OXIDATION OF ASCORBIC ACID AS AN INDICATOR OF PHOTOOXIDATIVE STRESS IN THE EYE

When whole retinal pigmented epithelium (RPE) cells isolated from bovine eyes are incubated with 14C-labeled ascorbic acid and exposed to a visible laser, the ascorbic acid is oxidized to dehydro-L-ascorbic acid (DHA). The amount of ascorbic acid which is oxidized is proportional to the radiant exposure of the sample (i.e. the total amount of radiation per unit area delivered over the exposure time). Blue light is more effective than red light in driving the reaction. The amount of label appearing in the DHA fraction is increased if unlabeled DHA is present in the reaction mixture, indicating that some redox cycling of ascorbate is occurring in the RPE cells. The ascorbic acid oxidizing activity does not depend on intact cells, is not inactivated by heating the cells to 80 degrees C, and appears to reside mainly in the subcellular fraction which contains melanin pigment granules. The ascorbic acid oxidation may be caused by free radicals formed when melanin is illuminated with light. This reaction appears to be a useful method for quantifying the production of free radicals during photooxidative stress.     

A cavity with reduced mode conversion for gyrotrons

Mode conversion at discontinuities of an ordinary gyrotron cavity is examined. It is shown how the production of unwanted spurious modes can be reduced substantially by introducing smooth transition regions between the individual parts of the cavity. The cavity of the 140 GHz KfK gyrotron operating in the TE_10,4 mode is used as an example. Cavity and adjacent tapered output waveguide are optimized as a single unit.