Relaxation and convexity of functionals with pointwise nonlocality

It is shown that the relaxation of the integral functional involving argument deviations

in weak topology of a Lebesgue space (where and are standard measure spaces, the latter with nonatomic measure), coincides with its convexification whenever the matrix of measurable functions : satisfies the special condition, called unifiability, which can be regarded as collective nonergodicity or commensurability property, and is automatically satisfied only if . If, however, either 1$"> or 1$">, then it is shown that as opposed to the classical case without argument deviations, for nonunifiable function matrix one can always construct an integrand so that the functional itself is already weakly lower semicontinuous but not convex.

     

Noise in miniature microphones

The internal noise spectrum in miniature electret microphones of the type used in the manufacture of hearing aids is measured. An analogous circuit model of the microphone is empirically fit to the measured data and used to determine the important sources of noise within the microphone. The dominant noise source is found to depend on the frequency. Below 40 Hz and above 9 kHz, the dominant source is electrical noise from the amplifier circuit needed to buffer the electrical signal from the microphone diaphragm. Between approximately 40 Hz and 1 kHz, the dominant source is thermal noise originating in the acoustic flow resistance of the small hole pierced in the diaphragm to equalize barometric pressure. Between approximately 1 kHz and 9 kHz, the noise originates in the acoustic flow resistances of sound entering the microphone and propagating to the diaphragm. To further reduce the microphone internal noise in the audio band requires attacking these sources. A prototype microphone having reduced acoustical noise is measured and discussed.     

Use of 9-methylfluorene as an indicator in the titration of common group IA and group IIA organometallic reagents

9-Methylfluorene was tested as an indicator in the titration of commonly used organometallic reagents. This indicator is readily prepared in three steps from fluorenone. In THF solution the deprotonated indicator is red and exhibits a sharp endpoint. The highly basic reagents sec-butyllithium and tert-butyllithium can be titrated in ether solution, where the color of the deprotonated indicator is yellow.     

Invariant Manifolds and the Long-Time Asymptotics of the Navier-Stokes and Vorticity Equations on R2

We construct finite-dimensional invariant manifolds in the phase space of the Navier-Stokes equation on R ² and show that these manifolds control the long-time behavior of the solutions. This gives geometric insight into the existing results on the asymptotics of such solutions and also allows us to extend those results in a number of ways.     

Dendron rodcoils: synthesis of novel organic hybrid structures

Convergent and divergent syntheses of novel organic hybrid structures termed dendron rodcoils (DRC) containing dendritic, rodlike, and coillike segments are described. The aryl ester dendron masked with 32 trifluoromethyl groups is prepared via a convergent approach using 5-(tert-butyldimethylsiloxy)isophthalic acid as the monomer unit. The activation of the focal point of the dendron allows for successful coupling between the dendron and the diblock rodcoil molecules synthesized separately. In another example, the dendritic block is grown via divergent strategy from the terminus of rodcoil using 3,5-bis(tert-butyldimethylsiloxy)benzoic acid as an AB(2) monomer. A combination of catalyzed esterification reactions and silyl deprotection chemistry proved to be a very efficient method for construction of these nanosized structures with unusual molecular architecture. Both synthetic strategies allowed for the preparation of DRCs with nearly monodisperse dendritic blocks as demonstrated by NMR, MALDI-TOF, and GPC measurements.     

Correlation between formation conditions and breakdown voltage of anodic oxide films on aluminum

Two series of samples were investigated: a) aluminum films with a sublayer of tantalum; b) industrial aluminum alloys AMg-2m; D16; AMc; AD-1n. The optimum composition of re-anodizing electrolyte was chosen on the basis of a solution of citric acid and ethylene glycol. The results of investigations of the sparking voltage at re-anodizing for various aluminum alloys and thicknesses of primary porous oxide are presented. The analytical dependence of breakdown voltage value on forming voltage value for alloy AD-1n was obtained. The original design of re-anodizing cell allowing increase of the sparking voltage was developed.