Asymptotic Expansions of Posterior Distributions in Nonregular Cases

We study the asymptotic behaviour of the posterior distributions for a one-parameter family of discontinuous densities. It is shown that a suitably centered and normalized posterior converges almost surely to an exponential limit in the total variation norm. Further, asymptotic expansions for the density, distribution function, moments and quantiles of the posterior are also obtained. It is to be noted that, in view of the results of Ghosh et al. (1994, Statistical Decision Theory and Related Topics V, 183-199, Springer, New York) and Ghosal et al. (1995, Ann. Statist., 23, 2145-2152), the nonregular cases considered here are essentially the only ones for which the posterior distributions converge. The results obtained here are also supported by a simulation experiment.     

Working group report: Flavor physics and model building

This is the report of flavor physics and model building working group at WHEPP-9. While activites in flavor physics have been mainly focused on B-physics, those in model building have been primarily devoted to neutrino physics. We present summary of working group discussions carried out during the workshop in the above fields, and also briefly review the progress made in some projects subsequently.     

Intramolecular nitrone cycloaddition reaction on carbohydrate-based precursors: application in the synthesis of spironucleosides and spirobisnucleosides

A simple synthesis of chiral spironucleosides and spirobisnucleosides is described. Intramolecular 1,3-dipolar nitrone cycloaddition reaction of d-glucose-derived precursors having olefin at C-3 and nitrone at C-5, C-1, or C-2 (in nor-series) furnished bisisoxazolidinospirocycles 4-7, 11, and 12 in good yields. Reductive ring opening of the isoxazolidine moieties in 4-6 followed by construction of a nucleoside base upon the generated amino groups smoothly yielded spirobisnucleosides 17 and 18 and spironucleosides 20 and 21.     

Processable heat-resistant polymers. XI. Synthesis and characterization of unsaturated polyamideimides

Polycondensation of the diacid chloride of 2-(3-carboxy vinyl)phenyl-1,3-dioxoisoindoline-5-carboxylic acid with m-phenylenediamine and the diacid chloride of 2-(4-carboxy phenyl)-1,3-dioxoisoindoline-5-carboxylic acid with 1,5-bis(3-aminophenyl)1,4-pentadien-3-one was carried out in polar solvents to produce new unsaturated polyamide–imides. The solution and the thermal, electrical, and a few other properties of the polymers were studies. The polymers were soluble in highly polar solvents. The solubility parameter of the polymers was calculated from the Small's group contribution. The polymers were fairly thermostable and underwent crosslinking creaction when heated, preferably in the presence of a suitable catalyst. The crosslinked polymers were in soluble even in highly polar solvents and possessed higher thermal stability. The swelling behavior of the polymers was studied and the molecular weight between two consecutive crosslinks was determined. X-ray diffraction and the dielectric properties of the polymers and their crosslinked products were also studied.     

More Efficient Palladium Catalyst for Hydrogenolysis of Benzyl Groups

Organic halides absorbed without solvent onto sodium phenylsulfinate on alumina (1) gave phenylsulfones (2) under microwave or ultrasound activation.     

Grafting Vinyl Monomers onto Poly(ethylene Terephthalate) (PET). IV. Graft Copolymerization of Methyl Methacrylate onto PET Fibers Using Acetyl Acetonate Complexes of Mn(III), Co(III), and Fe(III)

The graft copolymerization of methyl methacrylate onto poly-(ethylene terephthalate) using metal complexes of Mn³⁺, Co³⁺, and Fe³⁺ as initiators was studied. The rate of polymerization, R_p, increased with increasing complex concentrations.

The rate of polymerization was also studied by varying monomer concentrations. Increasing monomer concentrations, the rate of polymerization increases significantly. The graft yield increases with increasing temperature within the range 60–75°C. The graft yield is medium dependent. A suitable kinetic scheme has been pictured and rate equations have been derived.     

A Facile One‐Pot Synthesis of Pyrrolo[1, 2‐a] Indoles by Intramolecular 1,3‐Dipolar Cycloaddition under Neat‐Microwave Irradiation

A straightforward and general approach for the stereoselective synthesis of fused pyrrolo[1,2‐a] indoles frameworks from>intramolecular 1,3‐dipolar cycloaddition using N‐alkylated Baylis–Hillman derivatives is presented. It was found that the cycloaddition proceeded efficiently under microwave irradiation in solvent‐free condition to afford highly stereoselective cycloadducts in good yield.     

Linear {NiII–LnIII–NiII} Complexes Containing Twisted Planar Ni(μ‐phenolate)2Ln Fragments: Synthesis,Structure, and Magnetothermal Properties

Sequential reaction of a multisite LH₄ ligand {2‐[2‐hydroxy‐3‐(hydroxymethyl)‐5‐methylbenzylideneamino]‐2‐methylpropane‐1,3‐diol} with appropriate lanthanide salts followed by the addition of Ni(NO₃)₂ ? 6 H₂O in a 4:1:2 stoichiometric ratio in the presence of triethylamine afforded four heterobimetallic trinuclear complexes [Ni₂Gd(LH₃)₄] ? 3 NO₃ ? 3 MeOH ? H₂O ? CH₃CN ( 1 ), [Ni₂Tb(LH₃)₄] ? 3 NO₃ ? 3 MeOH ? CH₃CN ( 2 ), [Ni₂Dy(LH₃)₄] ? 3 NO₃ ? 3 MeOH ? H₂O ? CH₃CN ( 3 ), and [Ni₂Ho(LH₃)₄] ? 3 NO₃ ? 3 MeOH ? H₂O ? CH₃CN ( 4 ). Complexes 1 – 4 possess linear trimetallic cores with a central lanthanide ion. Magnetic studies revealed a predominant ferromagnetic interaction between the Ni and Ln centers. Alternating current susceptibility measurements of complex 3 showed a small frequency dependence of the out‐of‐phase signal, χ′′_M , under zero direct current field, but without achieving a net maximum above 2 K. Magnetic studies on 1 revealed that it has a significant magnetocaloric effect.     

Approximation of the Posterior Distribution in a Change-Point Problem

We consider a family of models that arise in connection with sharp change in hazard rate corresponding to high initial hazard rate dropping to a more stable or slowly changing rate at an unknown change-point . Although the Bayes estimates are well behaved and are asymptotically efficient, it is difficult to compute them as the posterior distributions are generally very complicated. We obtain a simple first order asymptotic approximation to the posterior distribution of . The accuracy of the approximation is judged through simulation. The approximation performs quite well. Our method is also applied to analyze a real data set.