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.     

Electrocatalytic activity of binary Palladium Ruthenium anode catalyst on Ni-support for ethanol alkaline fuel cells

In search for a cheaper anode catalyst for the oxidation of ethanol for development of direct alcohol fuel cells, Pd has been considered here as an interesting substitute for Pt in Pt Ru binary electrodeposite. The binary catalyst when co-deposited on nickel support has been found to increase the current density and decrease the anodic overvoltage significantly with respect to pure Pt, Pd and Ni. Its electrocatalytic capability is also comparable with that of the Pt-Ru binary electrocatalyst on Ni-support, when studied in 1 M EtOH containing 1 M NaOH solution. The effect of loading of Pd Ru electrocatalyst on Ni support has also been tested. The electrocatalytic activity of the electrodes for oxidation of ethanol has been explained by studies of cyclic voltammetry, chronopotentiometry, steady-state polarization, and conjugated scanning electron microscopy–energy dispersion X-ray spectroscopy. It has been found that electrode containing the higher amount of deposit are less affected by carbonaceous poisons.     

Schiffer variation of complex structure and coordinates for Teichmüller spaces

Schiffer variation of complex structure on a Riemann surfaceX ₀ is achieved by punching out a parametric disc \(\bar D\) fromX ₀ and replacing it by another Jordan domain whose boundary curve is a holomorphic image of \(\partial \bar D\) . This change of structure depends on a complex parameter ε which determines the holomorphic mapping function around \(\partial \bar D\) . It is very natural to look for conditions under which these ε-parameters provide local coordinates for Teichmüller spaceT(X ₀), (or reduced Teichmüller spaceT ^#(X₀)). For compactX ₀ this problem was first solved by Patt [8] using a complicated analysis of periods and Ahlfors' [2] τ-coordinates. Using Gardiner's [6], [7] technique, (independently discovered by the present author), of interpreting Schiffer variation as a quasi conformal deformation of structure, we greatly simplify and generalize Patt's result. Theorems 1 and 2 below take care of all the finitedimensional Teichmüller spaces. In Theorem 3 we are able to analyse the situation for infinite dimensionalT(X ₀) also. Variational formulae for the dependence of classical moduli parameters on the ε's follow painlessly.     

Metal complexes of sulphur-nitrogen chelating agents. Part 14. Nickel(II), palladium(II), copper(II), cobalt(II), and cobalt(III) complexes of the tetradentate schiff bases having ONNS donor sites

Summary Complexes of nickel(II), palladium(II), copper(II), cobalt(II), and cobalt(III) with methyl-2-(-salicylaldiminoethyl)-cyclopent-1-en-dithiocarboxylate (H₂L¹) and methyl-2-(-salicylaldiminoisopropyl)cyclopent-1-en-dithiocarboxylate (H₂L²) have been prepared. They contain the donor sites ONNS. The metal(II) ions from neutral, monomeric square planar chelate complexes. The cobalt(III) complexes [CoL¹-(H₂O)₂]X (X=Cl or ClO₄) appear to betrans-diaqua-species. All compounds have been characterized by a number of physico-chemical methods.     

Thermal noise in Hg0.795Cd0.205Te detectors for large biasing fields

Thermal noise in Hg_0.795Cd_0.205Te detectors is estimated for large biasing fields at a lattice temperature of 77 K, by computing the correlation functions of the velocity fluctuations with the Monte Carlo technique. The noise temperature for current components transverse to the field is almost independent of the field, but that corresponding to the parallel component increases by a factor of about 1.3 at 50 V/cm and by a factor of 3.0 at 300V/cm. The thermal noise voltage for a detector of 85 resistance increases from 0.6nV/Hz^1/2 at low biasing fields to about 3nV/Hz^1/2 at a field of 300 V/cm. The noise power is also found to remain constant up to about 75 GHz, and it decreases thereafter by a factor of 0.25 for doubling of the frequency.     

Modulation of the lowest metal-to-ligand charge-transfer state in [Ru(bpy)2(N-N)]2+ systems by changing the N-N from hydrazone to azine: photophysical consequences

Two Ru(II) complexes, [Ru(bpy)2L](ClO4)2 (1) and [Ru(bpy)2L'](BF4)2 (2), where bpy is 2,2'-bipyridine, L is diacetyl dihydrazone, and L' 1:2 is the condensate of L and acetone, are synthesized. From X-ray crystal structures, both are found to contain distorted octahedral RuN(6)(2+) cores. NMR spectra show that the cations in 1 and 2 possess a C2 axis in solution. They display the expected metal-to-ligand charge transfer (1MLCT) band in the 400-500 nm region. Complex 1 is nonemissive at room temperature in solution as well as at 80 K. In contrast, complex 2 gives rise to an appreciable emission upon excitation at 440 nm. The room-temperature emission is centered at 730 nm (lambda(em)(max)) with a quantum yield (Phi(em)) of 0.002 and a lifetime (tau(em)) of 42 ns in an air-equilibrated methanol-ethanol solution. At 80 K, Phi(em) = 0.007 and tau(em) = 178 ns, with a lambda(em)(max) of 690 nm, which is close to the 0-0 transition, indicating an 3MLCT excited-state energy of 1.80 eV. The radiative rate constant (5 x 10(4) s(-1)) at room temperature and 80 K is almost temperature independent. From spectroelectrochemistry, it is found that bpy is easiest to reduce in 2 and that L is easiest in 1. The implications of this are that in 2 the lowest (3)MLCT state is localized on a bpy ligand and in 1 it is localized on L. Transient absorption results also support these assignments. As a consequence, even though 2 shows a fairly strong and long-lived emission from a Ru(II) --> bpy CT state, the Ru(II) --> L CT state in 1 shows no detectable emission even at 80 K.     

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.     

Breathers in ferrimagnetic systems

Breathers in discrete nonlinear ferrimagnetic spin lattices are investigated for both easy-axis and easy-plane configurations. The region in frequency space of the formation of breathers is determined and the anticontinuum limit discussed. The monochromatic and the coloured breathers are found out numerically for different parameters and different conditions of excitations.     

MWCNTs-ZrO2 as a reusable heterogeneous catalyst for the synthesis of N-heterocyclic scaffolds under green reaction medium

A simple, efficient, and facile heterogeneous multi-walled carbon nanotubes-zirconia nanocomposite (MWCNTs-ZrO₂) has been synthesized using natural feedstock coconut juice (água-de-coco do Ceará). The synthesized catalyst was characterized by Fourier transform infrared spectroscopy, X-ray diffraction, field emission scanning electron microscopy, and X-ray photoelectron spectroscopy analysis. The heterogeneous nanocomposite has been used for one-pot synthesis of various N-heterocyclic compounds like pyrazoles, 1,2-disubstituted benzimidazoles, 2-arylbenzazoles, and 2,3-dihydroquinazolin-4(1H)-ones under green reaction medium at room temperature. This novel method has several advantages, such as short reaction time, simple work-up, excellent yield, and green reaction conditions. The catalyst was recycled up to four times without significant loss in catalytic activity.     

Synthesis,Crystal Structure and Thermal Behavior of Gadolinium Dicyanamide Dihydrate Gd[N(CN)2]3 · 2 H2O

Gadolinium dicyanamide dihydrate Gd[N(CN)₂]₃ · 2 H₂O was prepared by ion exchange in aqueous solution followed by evaporation of the solvent at room temperature. Gd[N(CN)₂]₃ · 2 H₂O was characterized by single‐crystal structure analysis, FTIR spectroscopy and DSC analysis. In the crystal there are three crystallographically independent [N(CN)₂]^? ions and Gd³⁺ which are coordinated by six N atoms from six different [N(CN)₂]^? ions and two O atoms from two water molecules forming an irregular quadratic antiprism. Four H bonds have been identified in the structure of Gd[N(CN)₂]₃ · 2 H₂O, two of them running to terminal N atoms and two to the bridging N atoms of dicyanamide ions (Gd[N(CN)₂]₃ · 2 H₂O: P2₁/n (no. 14), a = 7.4845(15) Å, b = 11.529(2) Å, c = 13.941(3) Å, β = 93.98(3)°, Z = 4, 1948 reflections, 175 parameters, R1 = 0.0493). The DSC analysis indicates that Gd[N(CN)₂]₃ · 2 H₂O looses the crystal water at temperatures around 130 – 140 °C forming anhydrous Gd[N(CN)₂]₃, the structure of which has been refined by the Rietveld method based on X‐ray powder diffraction data. Gd[N(CN)₂]₃ was found to be isotypic with Ln[N(CN)₂]₃ (Ln = La, Ce, Pr, Nd, Sm and Eu) which previously have been described in the literature.