Oxidation of aqueous sulfur dioxide catalyzed by poly-4-vinylpyridine-Cu(II) complex. Part 1: Homogeneous phase oxidation

The oxidation of aqueous sulfur dioxide in the presence of polymer-supported copper(II) catalyst is also accompanied by homogeneous oxidation of aqueous sulfur dioxide catalyzed by leached copper(II) ions. Aqueous phase oxidation of sulfur dioxide of low concentrations by oxygen in the presence of dissolved copper(II) has therefore been studied. The solubility of SO2 in aqueous solutions is not affected by the concentration of copper(II) in the solution. In the oxidation reaction, only HSO3- is the reactive S(IV) species. Based on this observation a rate model which also incorporates the effect of sulfuric acid on the solubility of SO2 is developed. The rate model includes a power-law type term for the rate of homogeneous phase reaction obtained from a proposed free-radical chain mechanism for the oxidation. Experiments are conducted at various levels of concentrations of SO2 and O-2 in the gas phase and Cu(II) in the liquid phase. The observed orders are one in each of O-2, Cu(II) and HSO3-. This suggests a first-order termination of the free radicals of bisulfite ions.

Homogeneous isotropic turbulence: large momentum expansion

High temperature expansion is an effective tool for studying second order phase transitions. With this in mind, we have looked at a high momentum expansion for homogeneous isotropic turbulence. Combining our results with those of the inertial range, we give another view of extended self-similarity (ESS).

Axially homogeneous, zero mean flow buoyancy-driven turbulence in a vertical pipe

We report an experimental study of a new type of turbulent flow that is driven purely by buoyancy. The flow is due to an unstable density difference, created using brine and water, across the ends of a long (length/diameter = 9) vertical pipe. The Schmidt number Sc is 670, and the Rayleigh number (Ra) based on the density gradient and diameter is about 10(8). Under these conditions the convection is turbulent, and the time-averaged velocity at any point is `zero'. The Reynolds number based on the Taylor microscale, Re-lambda, is about 65. The pipe is long enough for there to be an axially homogeneous region, with a linear density gradient, about 6-7 diameters long in the midlength of the pipe. In the absence of a mean flow and, therefore, mean shear, turbulence is sustained just by buoyancy. The flow can be thus considered to be an axially homogeneous turbulent natural convection driven by a constant (unstable) density gradient. We characterize the flow using flow visualization and particle image velocimetry (PIV). Measurements show that the mean velocities and the Reynolds shear stresses are zero across the cross-section; the root mean squared (r.m.s.) of the vertical velocity is larger than those of the lateral velocities (by about one and half times at the pipe axis). We identify some features of the turbulent flow using velocity correlation maps and the probability density functions of velocities and velocity differences. The flow away from the wall, affected mainly by buoyancy, consists of vertically moving fluid masses continually colliding and interacting, while the flow near the wall appears similar to that in wall-bound shear-free turbulence. The turbulence is anisotropic, with the anisotropy increasing to large values as the wall is approached. A mixing length model with the diameter of the pipe as the length scale predicts well the scalings for velocity fluctuations and the flux. This model implies that the Nusselt number would scale as (RaSc1/2)-Sc-1/2, and the Reynolds number would scale as (RaSc-1/2)-Sc-1/2. The velocity and the flux measurements appear to be consistent with the Ra-1/2 scaling, although it must be pointed out that the Rayleigh number range was less than 10. The Schmidt number was not varied to check the Sc scaling. The fluxes and the Reynolds numbers obtained in the present configuration are Much higher compared to what would be obtained in Rayleigh-Benard (R-B) convection for similar density differences.

Solution of singular integral equations with logarithmic and Cauchy kernels

A direct method of solution is presented for singular integral equations of the first kind, involving the combination of a logarithmic and a Cauchy type singularity. Two typical cages are considered, in one of which the range of integration is a Single finite interval and, in the other, the range of integration is a union of disjoint finite intervals. More such general equations associated with a finite number (greater than two) of finite, disjoint, intervals can also be handled by the technique employed here.

Homogeneous precipitation from solution by urea hydrolysis: a novel chemical route to the a-hydroxides of nickel and cobalt

Homogeneous precipitation from solution by hydrolysis of urea at elevated temperatures (T=120 degrees C) yields novel ammonia-intercalated alpha-type hydroxide phases of the formula M(OH)(x)(NH3)(0.4)(H2O)(y)(NO3)(2-x) where x=2, y=0.68 for M=Ni and x=1.85, y=0 for M=Co. These triple-layered hexagonal phases (a=3.08+/-0.01 Angstrom, c=21.7+/-0.05 Angstrom) are more crystalline than similar phases obtained by chemical precipitation or electrosynthesis. This method can be adapted as a convenient chemical route to the bulk synthesis of alpha-hydroxides.

A Classification of Homogeneous Operators in the Cowen-Douglas Class

A complete list of homogeneous operators in the Cowen-Douglas class B-n(D) is given. This classification is obtained from an explicit realization of all the homogeneous Hermitian holomorphic vector bundles on the unit disc under the action of the universal covering group of the bi-holomorphic automorphism group of the unit disc.

State Dependent Attempt Rate Modeling of Single Cell IEEE 802.11 WLANs with Homogeneous Nodes and Poisson Arrivals

Analytical models of IEEE 802.11-based WLANs are invariably based on approximations, such as the well-known mean-field approximations proposed by Bianchi for saturated nodes. In this paper, we provide a new approach for modeling the situation when the nodes are not saturated. We study a State Dependent Attempt Rate (SDAR) approximation to model M queues (one queue per node) served by the CSMA/CA protocol as standardized in the IEEE 802.11 DCF. The approximation is that, when n of the M queues are non-empty, the attempt probability of the n non-empty nodes is given by the long-term attempt probability of n saturated nodes as provided by Bianchi's model. This yields a coupled queue system. When packets arrive to the M queues according to independent Poisson processes, we provide an exact model for the coupled queue system with SDAR service. The main contribution of this paper is to provide an analysis of the coupled queue process by studying a lower dimensional process and by introducing a certain conditional independence approximation. We show that the numerical results obtained from our finite buffer analysis are in excellent agreement with the corresponding results obtained from ns-2 simulations. We replace the CSMA/CA protocol as implemented in the ns-2 simulator with the SDAR service model to show that the SDAR approximation provides an accurate model for the CSMA/CA protocol. We also report the simulation speed-ups thus obtained by our model-based simulation.

Homogeneous hydrogenations ofα, β-unsaturated compounds using pentacyanocobaltate (II) anion as catalyst system

Hydrogenation of someα, β-unsaturated carbonyl compounds using potassium pentacyanocobaltate (II), K3Co(CN)5, as a homogeneous catalyst has been investigated. Thus, hydrogenation of 1-carvone (I), mesityl oxide (4), 2-cyclohexenone (8) and benzalacetone (6) afforded the corresponding dihydrocompounds. Hydrogenation ofβ-ionone (10) afforded a mixture of theα, β-dihydrocompounds (14) and (15). In all these cases, it was observed that the reaction proceeded to completion only in the presence of added base. Hydrogenation of 5α-androst-l-en-17β-ol-3-one acetate (19) afforded the saturated compound, 5α-androst-17β-ol-3-one (20) in 60% yield. It was found that other steroid enones and dienones were not reduced by this catalyst system.

Relation between Chandrasekhar's X-function and the eigenvalues of integral operators with difference kernels

Abstract is not available.

The curvature invariant for a class of homogeneous operators

For an operator T in the class B-n(), introduced by Cowen and Douglas, the simultaneous unitary equivalence class of the curvature and the covariant derivatives up to a certain order of the corresponding bundle E-T determine the unitary equivalence class of the operator T. In a subsequent paper, the authors ask if the simultaneous unitary equivalence class of the curvature and these covariant derivatives are necessary to determine the unitary equivalence class of the operator T is an element of B-n(). Here we show that some of the covariant derivatives are necessary. Our examples consist of homogeneous operators in B-n(). For homogeneous operators, the simultaneous unitary equivalence class of the curvature and all its covariant derivatives at any point w in the unit disc are determined from the simultaneous unitary equivalence class at 0. This shows that it is enough to calculate all the invariants and compare them at just one point, say 0. These calculations are then carried out in number of examples. One of our main results is that the curvature along with its covariant derivative of order (0, 1) at 0 determines the equivalence class of generic homogeneous Hermitian holomorphic vector bundles over the unit disc.

Kernels for large margin time-series classification

In this paper we propose a novel family of kernels for multivariate time-series classification problems. Each time-series is approximated by a linear combination of piecewise polynomial functions in a Reproducing Kernel Hilbert Space by a novel kernel interpolation technique. Using the associated kernel function a large margin classification formulation is proposed which can discriminate between two classes. The formulation leads to kernels, between two multivariate time-series, which can be efficiently computed. The kernels have been successfully applied to writer independent handwritten character recognition.

An exact analysis for vibration of simply-supported homogeneous and laminated thick rectangular plates

A three-dimensional linear, small deformation theory of elasticity solution by the direct method is developed for the free vibration of simply-supported, homogeneous, isotropic, thick rectangular plates. The solution is exact and involves determining a triply infinite sequence of eigenvalues from a doubly infinite set of closed form transcendental equations. As no restrictions are placed on the thickness variation of stresses or displacements, this formulation yields a triply infinite spectrum of frequencies, instead of only one doubly infinite spectrum by thin plate theory and three doubly infinite spectra by Mindlin's thick plate theory. Further, the present analysis yields symmetric thickness modes which neither of the approximate theories can identify. Some numerical results from the two approximate theories are compared with those from the present solution and some important conclusions regarding the effect of the assumptions made in the approximate theories are drawn. The thickness variations of stresses and displacements are also discussed. The analysis is readily extended for laminated plates of isotropic materials. Numerical results are also given for three-ply laminates, and are used to assess the accuracy of thin plate theory predictions for laminates. Extension to general lateral surface conditions and forced vibrations is indicated.

Hydrolytic reactions of tetrasulphur tetranitride in a homogeneous medium

The hydrolytic reactions of tetrasulphur tetranitride are studied in a homogeneous medium. Alkaline hydrolysis gives sulphite, thiosulphate, sulphate and sulphide whereas the products in acid hydrolysis are mainly sulphur dioxide, elemental sulphur and hydrogen sulphide, with traces of polythionates. Under optimum conditions, tetrasulphur tetranitride reacts with sulphite consuming 2 moles of sulphite per mole of sulphur nitride to give 2 moles of trithionate. The reaction of sulphur nitride with thiosulphuric acid gives pentathionate and tetrathionate.

Hydrolytic reactions of esters and amides of thiosulphurous acid in a homogeneous medium

The hydrolytic reactions of esters and amides of thiosulphurous acid are investigated in a homogeneous medium. The esters are hydrolysed by alkali to give sulphide, sulphite and thiosulphate whereas the amides are resistant towards alkali. Both the esters and amides are hydrolysed by acids giving hydrogen sulphide, sulphur dioxide, polythionates and elemental sulphur. The hydrolysis of these esters and amides in presence of sulphurous acid and thiosulphuric acid gives tetrathionate and hexathionate, respectively.