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.     

Analysis of combined conduction and radiation heat transfer in presence of participating medium by the development of hybrid method

The current study addresses the mathematical modeling aspects of coupled conductive and radiative heat transfer in the presence of absorbing, emitting and isotropic scattering gray medium within two-dimensional square enclosure. A blended method where the concepts of modified differential approximation employed by combining discrete ordinate method and spherical harmonics method, has been developed for modeling the radiative transport equation. The gray participating medium is bounded by isothermal walls of two-dimensional enclosure which are considered to be opaque, diffuse and gray. The effect of various influencing parameters i.e., radiation-conduction parameter, surface emissivity, single scattering albedo and optical thickness has been illustrated. The adaptability of the present method has also been addressed.     

0+ analogue state in 118Sb from 117Sn(p,nγ) reaction

The analogue of the 0⁺ ground state in ¹¹⁸Sn has been observed in the compound nucleus ¹¹⁸Sb through ¹¹⁷Sn(p,n γ) ¹¹⁷Sb reaction. The neutron decays of this analogue resonance have been studied from the deexciting γ-rays of the residual nucleus ¹¹⁷Sb. From off resonance excitation functions, spin assignments have been made to states in ¹¹⁷Sb, on the basis of Hauser-Feshbach formalism. The resonance parameters of the isobaric analogue resonance have been determined, including the total, proton and neutron decay widths.     

Solubilization Site of Organic Perfume Molecules in Sodium Dodecyl Sulfate Micelles: New Insights from Proton NMR Studies

The site of incorporation of solubilizates in sodium dodecyl sulfate (SDS) micellar systems has been investigated by proton NMR spectroscopy. The solubilizate molecules chosen for the present study are phenol, 4-methylphenol, 4-allyl-2-methoxyphenol, anisole, 4-methylanisole, 4-propenylanisole, 1,8-cineole, and limonene. These molecules possess a wide variety of functional groups with different degrees of hydrophilic/hydrophobic character and are thereby solubilized at different micellar locations. Aromatic compounds, especially those having a phenolic-OH group, showed a large upfield shift of SDS methylene protons that are closely linked to the terminal sulfate groups. Additionally, in the case of phenolic compounds, the unresolved signals of the nine straight-chain bulk methylene protons of SDS are split into a broad doublet with uneven intensity. This splitting of methylene protons was found to be dependent on the concentration of the substrate. Based on these observations, probable solubilization sites and orientation of the substrate molecule within the micelles are discussed. Phenolic compounds, being the most hydrophilic among the present set, reside at the hydrophilic/hydrophobic boundary of micelle-water interface and thus influence the resonances of SDS protons the most. Aromatic methoxy and aliphatic compounds, being relatively more hydrophobic in nature, reside inside the micellar core and thereby result in smaller shifts. Copyright 2000 Academic Press.     

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.     

Remarkable impact of intermode couplings on multimode vibronic dynamics: the photoelectron spectrum of CH3F

Electronic and nuclear motions on intersecting potential energy surfaces are often intricately mixed and the spectrum can become very complex. Here we choose the strongly coupled Jahn-Teller system CH3F+ as a prototype example, and establish the importance of intermode coupling terms on multimode vibronic dynamics. The theoretical approach consists of a full second-order diabatic vibronic Hamiltonian, constructed from high-quality electronic structure calculations. Our results compare amazingly well with the experimental data. This highlights the success of the present theoretical approach in explaining the complex structure of vibronic spectra, ubiquitous in molecular systems.     

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.     

Is there any three-center CBC bond in 1, 5-C2B3H5 and 1,5-C2B3H3?

Localized molecular orbitals, two- and three-center bond indices of 1,5-dicarba-closo-pentaborane ( 5 ) and 1,5-dicarba-closo-pentaborane ( 3 ) and their hydrocarbon analogs bicyclo [1,1,1]-pentane and [1,1,1] propellane, respectively, have been calculated using a suitable basis set. No previously reported three-center CBC bond has been found. However, a new three-center BCB bond has been observed in 1,5-dicarba-closo-pentaborane ( 5 ). © 1995 John Wiley & Sons, Inc.     

Removal of Cr(VI) from Aqueous Solution Using Activated Cow Dung Carbon

Removal of hexavalent chromium from aqueous medium by using activated cow dung carbon was studied. Cow dung was carbonized and activated by treating with concentrated H(2)SO(4) followed by heating for 24 h at 120 degrees C. The extent of adsorption was studied as a function of pH, contact time, amount of adsorbent, concentration of adsorbate, and temperature. At lower pH (<3.5), the prepared sorbent was capable of removing approximately 90% Cr(VI) at 5 ppm concentration from aqueous synthetic solution. The dynamics of migration of the sorbate ions from the bulk onto the sorbent surface was studied and the results obtained under various experimental conditions were found to follow standard adsorption isotherms. The reaction kinetics was found to be of first order. Copyright 2000 Academic Press.     

Sequential cross-metathesis/phosphorus-based olefination: stereoselective synthesis of 2,4-dienoates

A variety of stereodefined 2,4-dienoates have been prepared in a stereoselective manner by sequencing olefin cross-metathesis (CM) with phosphorus-based olefination reactions (Wittig and Horner-Wadsworth-Emmons) in good yield using commercially available reagents.