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.     

Effect of secondary electrons from latent tracks created in YBCO by swift heavy ion irradiation

Swift heavy ions (SHI) with electronic energy loss exceeding a value of 14.4 keVnm⁻¹ create amorphized latent tracks in YBCO type superconductors. In the low fluence regime of an ion beam where tracks do not overlap, a decrease of the superconducting transition temperature as probed through resistivity studies, is not expected due to availability of percolating current paths. The present study however shows T_c decrease by about 1–3 K in thin films of YBCO when irradiated by 250 MeVAg ions at 79 K at a fluence of 5×10¹⁰–1×10¹² ionscm⁻². The highest fluence used in the present study is three times less than the fluence where track overlapping becomes significant. The T_c tends to increase towards the preirradiation value on annealing the films at room temperature. To explain this unusual result, we consider the effect of ion irradiation in inducing materials modification not only through creation of amorphized latent tracks along the ion path, but also through creation of atomic disorder in the oxygen sublattice in the Cu–O chains of YBCO by the secondary electrons. These electrons are emitted radially from the tracks during the passage of the SHI. Considering the correlation between the charge state of copper and its oxygen coordination, we show in particular that the latter process is a consequence of the inelastic interaction of the SHI induced low-energy secondary electrons with the YBCO lattice, which result in chain oxygen disorder and T_c decrease.     

Kinetics and mechanism of the reactions of hexaaqua rhodium (III) with sulphur (IV) in aqueous medium

An O-bonded sulphito complex, Rh(OH₂)₅(OSO₂H)²⁺, is reversibly formed in the stoppedflow time scale when Rh(OH₂) ₆ ³⁺ and SO₂/HSO ₃ ⁻ buffer (1 <pH< 3) are allowed to react. For Rh(OH₂)₅OH₂₊+ SO₂ □ Rh(OH₂)₅(OSO₂H)²⁺ (k₁/k_-1), k₁ = (2.2 ±0.2) × 10³ dm³ mol⁻¹ s⁻¹, k₋1 = 0.58 ±0.16 s⁻¹ (25°C,I = 0.5 mol dm⁻³). The protonated O-sulphito complex is a moderate acid (K _d = 3 × 10⁻⁴ mol dm⁻³, 25°C, I= 0.5 mol dm⁻³). This complex undergoes (O, O) chelation by the bound bisulphite withk= 1.4 × 10⁻³ s⁻¹ (31°C) to Rh(OH₂)₄(O₂SO)⁺ and the chelated sulphito complex takes up another HSO ₃ ⁻ in a fast equilibrium step to yield Rh(OH₂)₃(O₂SO)(OSO₂H) which further undergoes intramolecular ligand isomerisation to the S-bonded sulphito complex: Rh(OH₂)₃(O₂SO)(OSO₂)^- → Rh(OH₂)₃(O₂SO)(SO₃)⁻ (k _iso = 3 × 10⁻⁴ s⁻¹, 31°C). A dinuclear (μ-O, O) sulphite-bridged complex, Na₄[Rh₂(μ-OH)₂(OH)₂(μ-OS(O)O)(O₂SO)(SO₃) (OH₂)]5H₂O with (O, O) chelated and S-bonded sulphites has been isolated and characterized. This complex is sparingly soluble in water and most organic solvents and very stable to acid-catalysed decomposition     

Canonical measures on the moduli spaces of compact Riemann surfaces

We study some explicit relations between the canonical line bundle and the Hodge bundle over moduli spaces for low genus. This leads to a natural measure on the moduli space of every genus which is related to the Siegel symplectic metric on Siegel upper half-space as well as to the Hodge metric on the Hodge bundle.     

Diff (S 1) and the Teichmüller spaces

Precisely two of the homogeneous spaces that appear as coadjoint orbits of the group of string reparametrizations, , carry in a natural way the structure of infinite dimensional, holomorphically homogeneous complex analytic Kähler manifolds. These areN=Diff(S ¹)/Rot(S ¹) andM=Diff(S ¹)/Möb(S ¹). Note thatN is a holomorphic disc fiber space overM. Now,M can be naturally considered as embedded in the classical universal Teichmüller spaceT(1), simply by noting that a diffeomorphism ofS ¹ is a quasisymmetric homeomorphism.T(1) is itself a homomorphically homogeneous complex Banach manifold. We prove in the first part of the paper that the inclusion ofM inT(1) iscomplex analytic.In the latter portion of this paper it is shown that theunique homogeneous Kähler metric carried byM = Diff (S ¹/SL(2, ) induces preciselythe Weil-Petersson metric on the Teichmüller space. This is via our identification ofM as a holomorphic submanifold of universal Teichmüller space. Now recall that every Teichmüller spaceT(G) of finite or infinite dimension is contained canonically and holomorphically withinT(1). Our computations allow us also to prove that everyT(G), G any infinite Fuchsian group, projects out ofM transversely. This last assertion is related to the fractal nature ofG-invariant quasicircles, and to Mostow rigidity on the line.Our results thus connect the loop space approach to bosonic string theory with the sum-over-moduli (Polyakov path integral) approach.     

Reactions of sulfur(IV) with an octahedral manganese(IV) complex of 1,8-bis(2-hydroxy benzamido)-3,6-diaza octane: the role of phenolate–amide–amine coordination

The Mn^IV complex of tetra-deprotonated 1,8-bis(2-hydroxybenzamide)-3,6-diazaoctane (Mn^IVL) engrossed in phenolate-amido-amine coordination is reduced by HSO₃⁻ and SO₃²⁻ in the pH range 3.15–7.3 displaying biphasic kinetics, the Mn^IIIL⁻ being the reactive intermediate. The Mn^IIIL⁻ species has been characterized by u.v.–vis. spectra {λ _max, (ε, dm³ mol⁻¹ cm⁻¹): 285(15 570), 330 sh (7570), 469(6472), 520 sh (5665), pH=5.42}. SO₄²⁻ was the major oxidation product of S^IV; dithionate is also formed (18 ± 2% of [Mn^IV]_T) which suggests that dimerisation of SO₃^−• is competitive with its fast oxidation by Mn^IV/III. The rates and activation parameters for Mn^IVL + HSO₃⁻ (SO₃²⁻) → Mn^IIIL⁻; Mn^IIIL⁻ + HSO₃⁻ (SO₃²⁻) → Mn^IIL²⁻ are reported at 28.5–45.0 °C (I=0.3 mol dm⁻³, 10% (v/v) MeOH + H₂O). Reduction by SO₃²⁻ is ca. eight times faster than by HSO₃⁻ both for Mn^IVL and Mn^IIIL⁻. There was no evidence of HSO₃⁻/SO₃²⁻ coordination to the Mn centre indicating an outer sphere (ET) mechanism which is further supported by an isokinetic relationship. The self exchange rate constant (k₂₂) for the redox couple, Mn^IIIL⁻/Mn^IVL (1.5 × 10⁶ dm³ mol⁻¹ s⁻¹ at 25 °C) is reported.     

Kinetics and mechanism of the complex formation between oxalatopentaamminecobalt(III) and aluminium(III) and gallium(III); a comparative study

Summary The reversible complex formation between oxalatopentaammine cobalt(III), aluminium(III) and gallium(III) was investigated by the stopped flow technique at 30 ± 0.1 °C and I = 1.0 mol dm^–3. The reactivity sequence: Ga^III > Al^III is observed, however, the major path for gallium(III) was (NH3)₅CoC₂O₄H²⁺ + GaOH²⁺ (NH₃)₅CoC₂O₄-Ga⁴⁺ + H₂O. The formation and dissociation rate constants of the binuclear species have been compared with the analogous data for iron(III) and nickel(II) reported earlier. The results reflect the fact that the half-bonded exalato moiety of (NH₃)₅CoC₂O _inf4 ^p+ acts as a chelating agent for the metal ions.Author to whom all correspondence should be directed.     

Determination of trace metallic impurities in high-purity quartz by ion chromatography

A method has been developed for the determination of relevant trace impurities (alkali, alkaline and transition metals) in high purity quartz by ion-chromatography. In situ reagent (HF) purification and simultaneous sample dissolution was achieved in a multichannel vapour phase digestion assembly. Twenty-one samples can be digested at a time in this vapour phase system. Significant decrease in the process blank levels for all the analytes was observed. Drastic reduction (250 times) of NH4+ blank was achieved in the described vapour phase digestion, which enables the determination of trace concentration of sodium in high purity quartz. After volatilisation of the matrix and unreacted HF, the clear water leached solutions were injected into an ion-chromatograph equipped with conductivity detector for the determination of alkali and alkaline earth metals. In the case of transition metals, the trace residues were leached with 10 mM HCl and after separation on a mixed bed analytical column (IonPac CS5) were detected by spectrophotometry after post column derivatisation using 4-(2-pyridylazo)resorcinol (PAR). The accuracy of the result was checked by their comparison with those obtained by independent methods like inductively coupled plasma (ICP) MS and ICP atomic emission spectrometry. The achievable detection limits are between 0.4 ng/g (Li) and 22 ng/g (Mn). The application of the method to the determination of the above trace metals in two high-purity-grade quartz samples is demonstrated.     

A novel and expeditious approach to unusual spirolactam building blocks

A rapid access to 7-azaspiro[4.5]decan-6-ones 1 involving three regio- and chemoselective reactions starting from tetrabromonorbornyl derivatives is described. The alkaline H(2)O(2) cleavage reaction of monosubstituted alpha-diketones 9 furnished the potential bridged bicyclic lactones 10in a highly regio- and stereoselective manner. The radical-mediated, intermolecular bridgehead C-C bond formation of the versatile bridged lactones 10 with acrylonitrile followed by LAH reduction of the adduct 13 intriguingly leads to the formation of novel spirolactam building blocks 1.