Expanding graphs and invariant means

All the known explicit constructions of expander families are essentially obtained by considering a sequence of finite index normal subgroupsN _i , and taking the Cayley graphs of /N _i w.r. to the projection of aglobal finite set of generators of . For many of these examples (e.g. =SL ₂, /N _i SL ₂( ) we present first constructions of new, different, sets of generators for the finite quotients, which make the Cayley graphs an expander family. An intrinsic connection between the expanding property and uniqueness of the Haar measure on an appropriate compact group, as an invariant mean, is established and used in the construction of such generators.Partially sponsored by the Edmund Landau Center for research in Mathematical Analysis, supported by the Minerva Foundation (Germany).     

Extractable energy from erbium-ytterbium co-doped pulsed fiber amplifiers and lasers

An analytic model is developed for evaluating the extractable energy from high energy pulsed erbium-ytterbium co-doped fiber amplifiers and lasers. The energy extraction capabilities under the limitation of spurious lasing, due to amplified spontaneous emission (ASE), are mapped for various numerical apertures, single and multi transverse mode evolution and operating wavelengths. The model provides an assessment for the maximum pulse energy that can be extracted from a given erbium-ytterbium co-doped fiber. In addition, the model can be used to determine the repetition rate and optimal length, under which the laser source will be optimally operated in order to achieve a required extracted energy, without spurious lasing. The results show a clear advantage in using 915 nm wavelength pump source over 975 nm, at high average power operation, due to augmented 1 μm ASE at 975 nm pump wavelength, as a result of the Yb³⁺ population inversion.     

Idiotypic network dysregulation

The pathogenesis of autoimmune disease is still an enigma. Whereas the diverse clinical manifestations of many autoimmune diseases cannot be explained by the existence of autoantibodies, idiotypic dysregulation may provide an alternative explanation. Experimental models, serum level changes of pathogenic idiotypes during exacerbation and remission, and the increased expression of pathogenic idiotypes following common infections all support this notion. In this article we review experimental models of autoimmune disease induction (systemic lupus erythematosus, antiphospholipidsyn drome, Goodpasture's syndrome, autoimmune thyroiditis, and vasculitis) by manipulation of the idiotypic network and discuss the utilization of idiotypes for the immunotherapy of autoimmune diseases and other conditions that involve the immune system (e.g., atherosclerosis).     

Properties of dynamic rupture and energy partition in a solid with a frictional interface

We study properties of dynamic ruptures and the partition of energy between radiation and dissipative mechanisms using two-dimensional in-plane calculations with the finite element method. The model consists of two identical isotropic elastic media separated by an interface governed by rate- and state-dependent friction. Rupture is initiated by gradually overstressing a localized nucleation zone. Different values of parameters controlling the velocity dependence of friction, the strength excess parameter and the length of the nucleation zone, lead to the following four rupture modes: supershear crack-like rupture, subshear crack-like rupture, subshear single pulse and supershear train of pulses. High initial shear stress and weak velocity dependence of friction favor crack-like ruptures, while the opposite conditions favor the pulse mode. The rupture mode can switch from a subshear single pulse to a supershear train of pulses when the width of the nucleation zone increases. The elastic strain energy released over the same propagation distance by the different rupture modes has the following order: supershear crack, subshear crack, supershear train of pulses and subshear single pulse. The same order applies also to the ratio of kinetic energy (radiation) to total change of elastic energy for the different rupture modes. Decreasing the dynamic coefficient of friction increases the fraction of stored energy that is converted to kinetic energy. General considerations and observations suggest that the subshear pulse and supershear crack are, respectively, the most and least common modes of earthquake ruptures.     

Ideal bicombings for hyperbolic groups and applications

For every hyperbolic group and more general hyperbolic graphs, we construct an equivariant ideal bicombing: this is a homological analogue of the geodesic flow on negatively curved manifolds. We then construct a cohomological invariant which implies that several Measure Equivalence and Orbit Equivalence rigidity results established in Monod and Shalom (Orbit equivalence rigidity and bounded cohomology, preprint, to appear) hold for all non-elementary hyperbolic groups and their non-elementary subgroups. We also derive superrigidity results for actions of general irreducible lattices on a large class of hyperbolic metric spaces.     

Comparative characteristics of coherent and incoherent microwave scattering in dense inhomogeneous layers

Results of experiments on measuring forward scattering of waves in the range 88–100 GHz propagating in dense inhomogeneous layers consisting of grainy polymer materials are presented. Experiments were carried out with coherent and incoherent radiation. A comparison of the results demonstrates that incoherent radiation averages the depolarization effects and is preferable in comparison with coherent radiation for diagnostics of dense inhomogeneous materials. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 11–14, September, 2006.     

Likonides A and B: new ansa farnesyl quinols from the marine sponge Hyatella sp

[structure: see text] Two novel ansa farnesyl quinols, designated likonides A and B, were isolated together with avarone from the Kenyan sponge Hyatella sp. The compounds are of a unique ansa structure. The structures and stereochemistry of the compounds were elucidated by interpretation of MS, two-dimensional NMR, and CD experiments.     

Volume rheology of a two-phase system

Colloid and Polymer Science - Die allgemeine volumetrische Spannungs-Dehnungs-Beziehung eines Zweiphasensystems ist hier in solcher Weise formuliert, da\ sie für elastische viskose (Kriechen)...     

On variational principles for the generalized principal eigenvalue of second order elliptic operators and some applications

Dedicated to Professor Shmuel Agmon     

Infrared multiphoton excitation: Energy distribution of reacting molecules from overtone excitation studies

A method is offered to estimate quantitatively the energy distribution of molecules reacting after being excited by multiphoton absorption of infrared radiation. The method is based on the comparison of the real time reaction kinetics obtained in the infrared multiphoton experiment with those observed upon excitation of a vibrational overtone. Results obtained for the dissociation of tetramethyldioxetane under low-pressure conditions are used as a demonstration.