Mode Localization Induced by a Nonlinear Control Loop

We present the analysis of a nonlinear controlsystem that is used to excite and maintain a specified amplitude ofoscillation in the Jet Propulsion Laboratory vibratory gyroscope.This experimental application shows that nonlinear localizationthrough active means can be implemented in a practical system when itis desirable to confine the response to a favorable mode. Theclosed-loop system response predicted by the model shows very closeagreement with the experimental results for a significant range ofcontroller parameters. We also experimentally demonstrate that theactively localized motion is eliminated through bifurcation, similarto what was observed in previous passive localization studies appliedto extended flexible oscillators.     

Homological approximations for profinite and pro-p limit groups

Abstract

We study homological approximations of the profinite completion of a limit group (see Thm. A) and obtain the analogous of Bridson and Howie’s Theorem for the profinite completion of a non-abelian limit group (see Thm. B).     

A Mössbauer study of ultrathin Fe(110)/Ag(111) heterostructures grown by molecular beam epitaxy

We have grown good quality single crystal heterostructures of Fe(110) / Ag(111) with a high degree of epitaxy not previously achieved for films this thin. The iron-free mica substrates are transparent to gamma rays and aid in the epitaxial growth process. These films were characterized by reflection high-energy electron diffraction (RHEED), residual gas analysis (RGA), and transmission Mössbauer spectroscopy. The film with the thickest Fe component (8 monolayers) showed a hyperfine field comparable to bulk while the films with the thinnest Fe components (1.3 and 2.0 monolayers) showed an enhanced hyperfine field at 4.2 K. All the films were magnetically ordered at all the temperatures measured. Most importantly, and in contrast to other work, the direction of magnetization was in-plane for all of the films.     

Mean sample spacings, sample size and variability in an auction-theoretic framework

In terms of a standard model for English auctions and sealed-bid auctions, we study the impact of an increase in bidding competition and in variance of the distribution of valuations on the winner's expected rent using tools from order statistics and stochastic ordering.     

Mercury determination by CV-AAS in wastewater and sewage sludge from a stabilization pond system

The mercury concentrations in wastewater and sewage sludge of a stabilization pond system have been evaluated. The system is built by three parallel facultative ponds followed by two systems of three maturation ponds in series. The samples of wastewater and sludge were digested using nitric acid and placed into a Parr-type bomb for 4 h at 110 degrees C. Mercury was measured by Cold Vapour Atomic Absorption Spectrometry (CV-AAS) at 253.7 nm with sodium tetrahydroborate as reductant. The methodologies were checked with an USEPA quality control sample, a standard reference material from NIST and with another method of mineralization (cold mineralization) showing good results. Concentrations of mercury in wastewater between 1.47 +/- 0.75 microgl(-1) have been found at the entrance of the system and 0.74 +/- 0.0 microgl(-1) at the exit, while in sludge the results were between 0.29 +/- 0.12 microgkg(-1) in the facultative pond and 0.04 +/- 0.02 microgkg(-1) in the second maturation pond (exit).     

Random fixed points of set-valued operators

Some random fixed point theorems for set-valued operators are obtained. The measurability of certain marginal maps is also studied. The underlying measurable space is not assumed to be a Suslin family.

     

New flexible synthesis of pyrazoles with different,functionalized substituents at C3 and C5

Syntheses of pyrazoles featuring a functionalized side chain attached to carbon 3 and varying alkyl and aryl substituents attached to carbon 5 are presented. Installation of R = methyl, isopropyl, tert-butyl, adamantyl, or phenyl groups at C5 is reported here, starting by coupling protected alkynols with acid chlorides RCOCl, forming alkynyl ketones, which are reacted with hydrazine to form the pyrazole nucleus. Alcohol deprotection and conversion to a chloride gave 5-substituted 3-(chloromethyl)- or 3-(2-chloroethyl)pyrazoles. This sequence can be done within 2 d on a 30 g scale in excellent overall yield. Through nucleophilic substitution reactions, the chlorides are useful precursors to other polyfunctional pyrazoles. In the work here, derivatives with side chains LCH(2)- and LCH(2)CH(2)- at C3 (L = thioether or phosphine) were made as ligands. The significance of the ligands made here is that by placing a ligating side chain on a ring carbon (C3), rather than on a ring nitrogen, the ring nitrogen not bound to the metal and its attached proton will be available for hydrogen bonding, depending on the steric environment created by R at C5.