On Bayes procedures

Summary A result of Doob regarding consistency of Bayes estimators is extended to a large class of Bayes decision procedures in which the loss functions are not necessarily convex. Rather weak conditions are given under which the Bayes procedures are consistent. One set involves restrictions on the a priori distribution and follows an example in which the choice of a priori distribution determines whether the Bayes estimators are consistent. Another example shows that the maximum likelihood estimators may be consistent when the Bayes estimators are not. However, the conditions given are of an essentially weaker nature than those established for consistency of maximum likelihood estimators.This paper was prepared with the partial support of the Office of Ordnance Research, U. S. Army, under Contract DA-04-200-ORD-171. While the paper was in press, its author Dr. Lorraine Schwartz suddenly died. Sit ei terra levis! (L. LC., J. N.)I am deeply indebted to Professor L. LeCam, under whose guidance I obtained the results established in my thesis and given in this paper.     

Probabilistic expectation and rationality in classical probability theory

Throughout the 18th century, the notion of probabilistic expectation was a matter of controversy among mathematicians. Despite its seminal role in the earliest formulations of mathematical probability, such as that of Huygens, expectation did not remain a fixed concept but underwent several striking shifts in definition. This paper argues that the conception of expectation was altered by mathematicians in a deliberate effort to capture the salient aspects of rational decision making. As the notion of rationality successively took on legal, economic, and then psychological overtones, the definition of probabilistic expectation followed suit.     

Localized grafting through chemical lift-off

In this work we present two techniques that provide localized functionalization of the surface of materials. Both lead to localized grafted thin organic films (10-200 nm). The localization is brought by a chemical lift-off process, which relies on patterned weakly bonded films as sacrificial layers, combined with electrochemical (SEEP) or chemical (GraftFast©) processes which provides the final robust pattern on the surface. Both grafting processes, which were recently described, take advantage of the redox activation of diazonium salts associated with vinylic monomers in aqueous solution, and lead to similar grafted polymer films. Thanks to the high difference in adhesion between the grafted polymer and the patterned sacrificial layer (either an ink or weakly bound self-assembled monolayers), the latter may be easily removed, which unveils uncovered areas of the substrate.     

Effect of soluble polymer binder on particle distribution in a drying particulate coating

Soluble polymer is frequently added to inorganic particle suspensions to provide mechanical strength and adhesiveness to particulate coatings. To engineer coating microstructure, it is essential to understand how drying conditions and dispersion composition influence particle and polymer distribution in a drying coating. Here, a 1D model revealing the transient concentration profiles of particles and soluble polymer in a drying suspension is proposed. Sedimentation, evaporation and diffusion govern particle movement with the presence of soluble polymer influencing the evaporation rate and solution viscosity. Results are summarized in drying regime maps that predict particle accumulation at the free surface or near the substrate as conditions vary. Calculations and experiments based on a model system of poly(vinyl alcohol) (PVA), silica particles and water reveal that the addition of PVA slows the sedimentation and diffusion of the particles during drying such that accumulation of particles at the free surface is more likely.     

Conformational Analysis of Fluorinated Pyrrolidines Using 19F–1H Scalar Couplings and Heteronuclear NOEs

A series of 3‐fluoropyrrolidines have been studied to investigate the influence of the stereoelectronic fluorine gauche effect on ring conformations in the solid state by single‐crystal X‐ray analysis and in solution phase by NMR spectroscopy. As part of these studies 1D ¹⁹F–¹H heteronuclear NOE (HOESY) experiments have been optimised for applications to small molecules and are described in detail. These have been employed to estimate ¹⁹F–¹H internuclear distances and were combined with vicinal ³J(F,H) and ³J(H,H) scalar coupling constants to analyse the ring conformations. Where possible the derived solution‐phase structural data have been compared with those of the crystalline state. The results demonstrate the influence of the gauche effect in stabilising C^γ‐exo conformations of the fluorinated pyrrolidines. It was further shown that when steric interactions were also present, this conformational bias was diminished and the contribution of the alternative C^γ‐endo conformation was seen to increase in solution at lower sample temperatures.     

NMR Investigation of Ring Conformation in Substituted Dihydronaphthalenes

Vicinal J_HH couplings were investigated for a series of substituted dihydronaphthalenes allowing the conformation of the non-aromatic ring to be evaluated. It was found that the substitution of bromine for hydrogen increases the total puckering amplitude of the non-aromatic ring. Different formulations of the Karplus equation were investigated and the influence on the observed results are discussed.     

NMR Studies of Drugs. Application of Achiral and Chiral Lanthanide Shift Reagents to α-Ethyl-α-Phenylsuccinimide

The 60 MHz ¹H NMR spectra of 3-ethyl-3-phenylpyrrolidine-2,5-dione, 1, were studied in CDCl₃ at 28° using the achiral lanthanide shift reagent (LSR) tris(6,6,7,7,8,8,8-heptafluoro-2,2-dimethyl-3,5-octanedionato)europium(III), Eu(FOD)₃ 2, for spectral simplification, and the chiral LSR, tris[3-heptafluoropropylhydroxymethylene)-(+)-camphorato]-europium(III), Eu(HFC)₃ 3, to induce enantiomeric shift differences (δδδ) for several nuclei. A non-racemic sample of 1 was treated with 3 to determine the sense of magnetic nonequivalence of selected nuclei. Significant δδδ is seen for the signals of the methyl and aryl ortho protons. Modest δδδ can also be seen for the NH signal and for one of the H-4 protons, although LSR-induced broadening for the two latter signals is severe. The (-) enantiomer appeared to exhibit an upfield sense of magnetic nonequivalence (3:1 molar ratio ca. 0.15—0.35) for the methyl signal but a downfield sense for H_ortho (3:1 ratio ca. 0.6).     

Synthesis of a new water-soluble C(2)-symmetric chiral diamine: preliminary investigation of its catalytic properties for asymmetric hydrogenation under biphasic conditions

A water-soluble version of N,N'-dimethyl-1,2-diphenylethane-1,2-diamine was prepared by introduction of phosphonic acid moieties on the para position of the aromatic rings. Preliminary investigation of the catalytic properties of the iridium complex of this ligand under biphasic conditions showed that this system compared well with the homogeneous counterpart for the asymmetric hydrogenation of ketones but with noticeably higher reaction rates for the biphasic system.     

Some unusual features of the electrochemistry of silver in aqueous base

Multilayer oxide films were grown on silver in base by repetitive potential cycling; however, the type of oxide obtained, as assessed on the basis of its reduction behaviour, was dependent on the lower limit of the oxide growth cycles. Using limits of 1.03–2.60 V (RHE) the oxide film produced was assumed to be predominantly Ag₂O; reduction of the latter yielded a cathodic peak at ca. 0.8 V and a surface layer of silver microparticles of diameter ranging from ca. 100 to 227 nm which, although relatively stable, were prone to rapid, extensive reoxidation. Altering the oxide growth limits to 0.7–2.60 V resulted in the growth of a different type of oxide deposit which is assumed to be AgOH; reduction of the latter occurred in a negative sweep in a random manner, i.e. in the form of cathodic spikes extending to potentials as low as ca. –0.5 V. Both types of silver oxide species are assumed to be involved in premonolayer oxidation and electrocatalysis at silver in base and the nature of the former process is discussed in some detail. Electronic Publication