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.     

Amorphous Fe–Mg alloy thin films: magnetic properties and atomic vibrational dynamics

Amorphous (a-) Fe _x Mg_1?x alloys are interesting materials for the investigation of non-Debye-like low-energy vibrational excitations. We have prepared a-Fe _x Mg_1?x alloy thin films (0.3 ≤ × ≤0.7) by vapour quenching. The amorphous state was confirmed by conversion electron Mössbauer spectroscopy between 4.2–300 K, and the x- and temperature-dependence of the isomer shift and hyperfine magnetic field was measured. For x= 0.6 and 0.7, magnetic ordering occurs below ~150 K. The atomic vibrational density of states, g(E), was determined by nuclear resonant inelastic scattering, providing clear evidence for the non-Debye-like low-energy vibrational excitations.     

On the absolute matrix summability of Fourier series and some associated series

The object of the paper is to study the absolute matrix summability problem of Fourier series, conjugate series and some associated series under a new set of conditions on matrix methods, generalising many known results in the literature.     

Manifestation of diamagnetic chemical shifts of proton NMR signals by an anisotropic shielding effect of nitrate anions

A remarkable upfield shift of the py_α protons of complexed 2,2′-bipyridine in [cis-Pd(bpy)(NO₃)₂] is observed which is considered to originate from the anisotropic influence of suitably positioned coordinated nitrate anions around the Pd(II) centre of the molecule. A typical complexation-induced downfield shift is observed for the NH₂ protons in [cis-Pd(en)(NO₃)₂] where ‘en’ stands for ethylenediamine.     

Alkenyl- and aryl[2-(hydroxymethyl)phenyl]dimethylsilanes: an entry to tetraorganosilicon reagents for the silicon-based cross-coupling reaction

Alkenyl- and aryl[2-(hydroxymethyl)phenyl]dimethylsilanes, highly stable tetraorganosilicon reagents, are found to react with aryl and alkenyl iodides in the presence of a palladium catalyst and K2CO3 as a base, significantly milder conditions compared with those ever reported for the silicon-based cross-coupling reactions. The reaction tolerates a wide range of functional groups, including silyl protectors, and allows a gram-scale synthesis to recover and reuse the silicon residue.     

Conformational effects on vibronic spectra and excited state dynamics of 3-fluorobenzoic acid dimer

Two conformational isomers of 3-fluorobenzoic acid dimer (3-FBA(2)) have been identified in a supersonic jet expansion by use of laser-induced fluorescence excitation (FE), UV-UV hole-burning, and dispersed fluorescence (DF) spectroscopic methods. In the FE spectrum, the S(1) origins of the two isomeric species appear at a frequency gap of only 24 cm(-1), and the vibronic intensities of the redshifted dimer (dimer I) are about two times weaker than those of dimer II. However, ab initio quantum chemistry calculations at the MP2/6-31G(**) level of theory predict that all the isomeric species of 3-FBA(2) have almost the same binding energy (approximately 17 kcal/mol) in the ground state. Furthermore, unlike benzoic acid dimer, the present system shows intense activity for a low-frequency mode in both the FE and DF spectra. With the aid of DFT (B3LYP/6-311G(**)) predicted normal mode frequencies, we have assigned the mode to the in-plane gear (cogwheel) vibration of the cyclic hydrogen-bonded frame of the dimer. The Franck-Condon profiles for vibronic excitation of the mode indicate that the distortion of the cyclic hydrogen bond frame as a result of S(1)<--S(0) excitation is larger for dimer I than dimer II. Moreover, the fluorescence lifetime at the S(1) zero-point level of the former is also significantly smaller than the latter. Using the predictions of configuration interaction singles calculations, we have proposed that the spectral and dynamical differences between the two isomeric species observed in this study are manifestations of the different characteristics of their S(1) surfaces. By measuring FE, DF, and hole-burning spectra of a mixed dimer between 3-fluobenzoic acid and benzoic acid we have shown that the isomeric features in the homodimer spectra are due to two locally excited rotamers of the 3-fluorobenzoic acid moiety.     

Gold nanoshells on polystyrene cores for control of surface plasmon resonance

A method is presented for synthesizing core-shell structures consisting of monodisperse polystyrene latex nanospheres as cores and gold nanoparticles as shells. Use of polystyrene spheres as the core in these structures is advantageous because they are readily available commercially in a wide range of sizes, and with dyes or other molecules doped into them. Gold nanoparticles, ranging in size from 1 to 20 nm, are prepared by reduction of a gold precursor with sodium citrate or tetrakis(hydroxymethyl)phosphonium chloride (THPC). Carboxylate-terminated polystyrene spheres are functionalized with 2-aminoethanethiol hydrochloride (AET), which forms a peptide bond with carboxylic acid groups on their surface, resulting in a thiol-terminated surface. Gold nanoparticles then bind to the thiol groups to provide up to about 50% coverage of the surface. These nanoparticles serve as seeds for growth of a continuous gold shell by reduction of additional gold precursor. The shell thickness and roughness can be controlled by the size of the nanoparticle seeds as well as by the process of their growth into a continuous shell. By variation of the relative sizes of the latex core and the thickness of the gold overlayer, the plasmon resonance of the nanoshell can be tuned to specific wavelengths across the visible and infrared range of the electromagnetic spectrum, for applications ranging from the construction of photonic crystals to biophotonics. The position and width of the plasmon resonance extinction peak are well-predicted by extended Mie scattering theory.     

Studies on alkaline protease produced by Bacillus sp. NG312

An alkalophilic hyperproducer of alkaline protease, Bacillus sp. NG312, was isolated, and the enzyme showed maximum activity at pH 11.0 and 60°C. The temperature optimum was increased by 10°C in presence of Ca²⁺. The crudeenzyme was found to have half-life of 11 d at 37°C and maximum stability at pH 9.0–10.0. It also exhibited very good stability in presence of detergent components and some locally available commericial detergent powders.     

Impact of extended pi conjugation on methyl rotor-induced IVR in aromatic molecules

Laser-induced fluorescence excitation and resolved fluorescence spectra following excitations of the single vibronic levels (SVL) of p-vinyltoluene (p-VT) and p-vinylfluorobenzene (p-VFB) have been measured in a seeded supersonic free-jet expansion. A complete vibronic assignment of the fluorescence spectrum measured following excitation of the 0(0)0-band of p-VT has been presented. Normal vibrational modes in the S0 and S1 states of the molecule have been calculated by CASSCF method, and the correlation between the two set of modes is made by expressing the excited-state normal modes in terms of those of the ground state. The calculations predict that in the excited state methyl and vinyl torsional motions of p-VT are extensively mixed with many of the out-of-plane modes of the aromatic ring. Our resolved fluorescence spectral data measured following SVL excitations essentially agree with such predictions. In the excited state, the molecule exhibits a dramatically low threshold for the rotor-induced IVR in a supersonic jet expansion. Several mechanisms have been discussed to explain the phenomenon.     

3 + 2]-cycloaddition of nonstabilized azomethine ylides. 10. An efficient strategy for the construction of x-Azatricyclo[m.n.0. 0

Various new structural entities related to x-azatricyclo[m.n.0. 0(a)()(,)(b)()]alkanes are constructed by the intramolecular [3 + 2] dipolar cycloaddition of nonstabilized cyclic azomethine ylides. The ylide is generated by the sequential double desilylation of N-alkyl alpha,alpha'-bis(trimethylsilyl)cyclic amines using Ag(I)F as a one-electron oxidant.