Oracle Inequalities for Efromovich–Pinsker Blockwise Estimates

Oracle inequality is a relatively new statistical tool for the analysis of nonparametric adaptive estimates. Oracle is a good pseudo-estimate that is based on both data and an underlying estimated curve. An oracle inequality shows how well an adaptive estimator mimics the oracle for a particular underlying curve. The most advanced oracle inequalities have been recently obtained by Cavalier and Tsybakov (2001) for Stein type blockwise estimates used in filtering a signal from a stationary white Gaussian process. The authors also conjecture that a similar result can be obtained for Efromovich–Pinsker (EP) type blockwise estimators where their approach, based on Stein's formula for risk calculation, does not work. This article proves the conjecture and extends it upon more general models which include not stationary and dependent processes. Other possible extensions, a discussion of practical implications and a numerical study are also presented.     

Efficient synthesis of an aldehyde‐capped polythiophene containing fluorinated electron‐withdrawing groups

To incorporate an acceptor type polythiophene segment onto a supramolecular block copolymer for potential light harvesting applications, effective synthetic routes for the end‐functionalized and acceptor‐substituted polythiophenes are critical. The Ullmann coupling reaction can be utilized to obtain electron‐deficient polythiophenes and to attach terminal thiophene units that carry functional groups. In this article, the reactions involving a 2,5‐dibromothiophene monomer containing an electron‐withdrawing fluorinated ester and 5‐bromo‐2‐thiophenecarboxaldehyde (the end‐capper) were studied in detail. It was found that the Ullmann coupling reaction of the dibromide is very fast (completed in a few minutes) and the terminal bromine group does not survive long under the reaction condition. These findings lead to the development of an effective procedure for aldehyde end‐capping of electron‐deficient polythiophenes. Polymers with molecular weights around 4000 Da are routinely obtained. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 45: 41–47, 2007     

Fourier transform IR product study of the reaction of CFO radicals with O2 at 298 K

Experimental results are presented of a Fourier transform IR product study at 298 K of the reaction system CFO+O₂ at oxygen pressures between 3 and 250 mbar. Pulsed photolysis of oxalyl fluoride (CFO)₂ or formyl fluoride (CHFO) at 193 nm was used to produce CFO. As stable products we detected bis-fluoroformyl peroxide, carbonyl fluoride and carbon dioxide. The yields of the peroxide and of CF₂O were measured as a function of [O₂]/[precursor] and are discussed qualitatively.     

Photooxidation of aqueous trichloroethylene using a buoyant photocatalyst with reaction progress monitored via micro-headspace GC/MS

Although photooxidation has previously been shown to be successful in removing organic contaminants from water, methods combining the rapid photooxidation of the desired contaminant with easy catalyst manipulation and removal are few and far between. In the absence of an easy means of catalyst removal, the photooxidation process becomes more costly and time consuming, and photocatalysis cannot be employed as an in situ method for the remediation of aqueous organic contaminants. In this study, the photocatalyst was added to an aqueous trichloroethylene (TCE) solution in the form of TiO₂-coated buoyant microspheres. The solution, placed in a flow-cell photoreactor along with the buoyant catalyst, was irradiated with a UV-filtered Xenon light source. Limited sample sizes necessitated the development of a low-cost headspace GC/MS analysis method, utilizing a standard direct-injection autosampler. This analytical technique aptly monitored reaction progress and indicated that aqueous TCE concentration decreases by nearly 90% in the first hour of irradiation. Subsequent solvent extraction GC/MS analysis indicated that the TCE is initially sorbed by the photocatalyst spheres, but as irradiation continued, TCE is removed from the catalyst spheres surfaces. During the course of irradiation, the expected TCE mineralization product hydrochloric acid appeared, as indicated by a decrease in pH and ion chromatography analysis. The microsphere-born catalyst was easily removed from the treated solution by filtration. Thus, it is possible that a method for effective, low-cost in situ photooxidation of aqueous organic contaminants will be realized in the near future.     

Mössbauer Studies and Magnetic Properties of Y3−x Ce x Fe5O12

It is shown that in-situ ^166mHo (I = 7) in a spherical single crystal of HoF₃ can be used as sensitive internal thermometer to thermally detect NMR (NMR-TDNO) from the 100% abundant stable ¹⁶⁵Ho (I = 7/2) nuclei. In addition, new ^166mHo NMRON results are reported. Both the ^166mHo NMRON and ¹⁶⁵Ho NMR-TDNO spectra show three distinct quadrupolar split sub-resonances, in zero applied field. The data is used to make estimates of the Ho magnetic moments and quadrupole parameters for the ^166mHo and ^166mHo sites.     

Analytical formulas for the velocity field induced by an infinitely thin vortex ring

Three different analytical solutions are presented for a potential vortex ring using three different streamfunctions. Verification studies confirm that all three approaches are valid. It is found that the solution obtained using the Biot–Savart law is the most efficient method due to its simplicity. It is shown that all analytical results are accurate to within machine accuracy and sample calculations are included. Copyright © 2004 John Wiley & Sons, Ltd.