Multiplication Modules and a Theorem of P. F. Smith

P. F. Smith [7, Theorem 8] gave sufficient conditions on a finite set of modules for their sum and intersection to be multiplication modules. We give sufficient conditions on an arbitrary set of multiplication modules for the intersection to be a multiplication module. We generalize Smith"s theorem, and we prove conditions on sums and intersections of sets of modules sufficient for them to be multiplication modules. This revised version was published online in June 2006 with corrections to the Cover Date.     

Economy of effort in different speaking conditions. I. A preliminary study of intersubject differences and modeling issues

This study explores the hypothesis that clear speech is produced with greater "articulatory effort" than normal speech. Kinematic and acoustic data were gathered from seven subjects as they pronounced multiple repetitions of utterances in different speaking conditions, including normal, fast, clear, and slow. Data were analyzed within a framework based on a dynamical model of single-axis frictionless movements, in which peak movement speed is used as a relative measure of articulatory effort (Nelson, 1983). There were differences in peak movement speed, distance and duration among the conditions and among the speakers. Three speakers produced the "clear" condition utterances with movements that had larger distances and durations than those for "normal" utterances. Analyses of the data within a peak speed, distance, duration "performance space" indicated increased effort (reflected in greater peak speed) in the clear condition for the three speakers, in support of the hypothesis. The remaining four speakers used other combinations of parameters to produce the clear condition. The validity of the simple dynamical model for analyzing these complex movements was considered by examining several additional parameters. Some movement characteristics differed from those required for the model-based analysis, presumably because the articulators are complicated structurally and interact with one another mechanically. More refined tests of control strategies for different speaking styles will depend on future analyses of more complicated movements with more realistic models.     

The Formation of Porous Membranes by Filtration of Aerosol Nanoparticles

Flame-generated aerosol particles of Al₂O₃ were deposited by gas filtration on two types of porous and ceramic tubes of -Al₂O₃ with mean pore diameters of 450 and 2700nm, respectively. The particles were aggregates with average mobility diameters in the range of 30–100nm and primary particle diameters of 4–8nm. The particles are characterized by differential mobility analysis, transmission electron microscopy, and by their specific surface area. The deposited membranes are characterized by gas permeability measurements, scanning electron microscopy, and by their pore size distribution from nitrogen capillary condensation. The particles form a distinct, homogeneous membrane layer with a porosity of 90% on top of the substrate surface and only penetrate slightly into the substrate structure. The mean pore sizes of the deposited membranes determined by nitrogen condensation agree approximately with those determined by gas permeation and the specific surface area. The mean pore diameter varies in the range of 30–70nm. The gas permeability of the deposited membranes is related to the specific surface area but influenced by the high porosity. The mean pore size and the permeability of the membranes are almost independent of the substrate structure.The development of a membrane with uniform properties is preceded by a short initial period in which the deposited particles, with an equivalent membrane thickness of roughly 2m, have a significantly lower permeability than the ultimately developed uniform membrane layer. This effect is particularly significant for the aerosol particles with the lowest mean size, probably due to particles deposited in the pore mouths of the substrate.The particles and the deposited membranes are X-ray amorphous but retain their specific surface area on heating to even high temperatures. When the membranes are heated to 1473K for 10h, X-ray diffraction shows a mixture of - and -alumina, accompanied by a partial disintegration of the membrane and a considerable loss of surface area.     

Interacting dark energy with inhomogeneous equation of state

We have investigated the model of dark energy interacting with dark matter by choosing inhomogeneous equations of state for the dark energy and a nonlinear interaction term for the underlying interaction. The equations of state have dependencies either on the energy densities, the redshift, the Hubble parameter or the bulk viscosity. We have considered these possibilities and have derived the effective equations of state for the dark energy in each case.     

Generation of strong, homochiral bases by electrochemical reduction of phenazine derivatives

Electrochemical reduction of enantiomerically pure amino- and alkoxy-phenazine derivatives forms strongly basic radical anions which give asymmetric induction in the conversion of 3,4-epoxytetrahydrothiophene-1,1-dioxide into the allylic ester with facile regeneration of the phenazine.     

A simple and efficient large-scale synthesis of 3-hydroxyphthalans via oxa-Pictet-Spengler reaction catalyzed by nanosilica sulfuric acid

Nanosilica sulfuric acid is found to be a new, powerful and reusable heterogeneous catalyst for the rapid synthesis of 3-hydroxyphthalans via condensation of aromatic aldehydes and 3-hydroxybenzyl alcohols under conventional heating and microwave irradiation. Scale-up preparation of these heterocycles is also carried out.