Theoretical study of the reaction of H2 with a Cu2Pt2 cluster

The study of the interaction of a pyramidal tetramer of Cu₂Pt₂ with the H₂ is reported here through ab initio multiconfigurational self-consistent field (MC-SCF) calculations, plus extensive multireference configuration interaction (MR-CI), variational and perturbative calculations. The lowest three electronic states X ¹A′, a ³A′ and a ¹A′ of the bare cluster were considered in order to study this interaction. For the H₂ C_s approaching a Pt vertex, results show that the Cu₂Pt₂ pyramid cluster in its X ¹A′ and a ¹A′ states can spontaneously capture and dissociate the H₂. For the H₂ C_s approaching a Cu vertex, where H₂ is located in the C_s reflecting plane, the Cu₂Pt₂ cluster in its X ¹A′ electronic state shows capture of the hydrogen molecule after surmounting an energy barrier; moreover, in this approach the Cu₂Pt₂ cluster in its a ¹A′ electronic state shows spontaneous capture of the hydrogen molecule. For the H₂ approaching a Cu vertex, where the C_s reflecting plane bisects the H₂ molecule, the Cu₂Pt₂ cluster in its three lowest-lying states is able to capture the hydrogen molecule after surmounting a small barrier. The Cu₂Pt₂+H₂ C_s face-on interactions show a lower H₂ activation than that which was obtained in the equivalent Pt₄+H₂ interactions.     

Correlation between phosphorus concentration and opto-electrical properties of doped a-Si:H films

Phosphorus doped hydrogenated amorphous silicon (a-Si:H) films were prepared by decomposition of silane using RF plasma glow discharge. Both DC dark conductivity measurements, and spectrophotometric optical measurements through the range 200–3000 nm were recorded for the prepared films. The DC conductivity activation energy E_a decreased from 0.8 eV for the undoped sample to 0.34 eV for the highest used doping value. The optical energy gap E_g decreased ranging from 1.66 eV to 1.60 eV. The refractive index n, the density of charge carriers N/m* and the plasma frequency ω_p showed an opposite behavior, i.e. an increase in value with doping. Fitting the dispersion values to Sellmeier equation led to the determination of the material natural frequency of oscillating particles. A correlation between the changes in these parameters with the doping has been attempted.     

The row–column multiplication of high dimensional rhotrices

This paper presents the row–column multiplication of rhotrices that are of high dimension. This is an extension of the same multiplication carried out on rhotrices of dimension three, considered to be the base rhotrices.     

Conversion of a rhotrix to a ‘coupled matrix’

In this note, a method of converting a rhotrix to a special form of matrix termed a ‘coupled matrix’ is proposed. The special matrix can be used to solve various problems involving n?×?n and (n?–?1)?×?(n?–?1) matrices simultaneously.     

Hochschild cohomology of partial relation extensions

We show how to compute the low Hochschild cohomology groups of a partial relation extension algebra.     

The fundamental groups of a triangular algebra

A finite dimensional algebra A (over an algebraically closed field) is called triangular if its ordinary quiver has no oriented cycles. To each presentation (Q I) of A is attached a fundamental group π₁(Q I), and A is called simply connected if π₁(Q I) is trivial for every presentation of A. In this paper, we provide tools for computations with the fundamental groups, as well as criteria for simple connectedness. We find relations between the fundamental groups of A and the first Hochschild cohomology H ¹ (A A).     

Toward a solution of a class of non-linear stochastic perturbed PDEs using automated WHEP algorithm

This paper introduces a generalization and automation of the Wiener Hermite expansion with perturbation (WHEP) technique to solve a class of stochastic nonlinear partial differential equations with a perturbed nonlinearity. The automated algorithm generates the deterministic resultant linear equations according to the application of a general linear differential operator and the input parameters. Sample output with different nonlinearities, orders and corrections are presented. The resultant equations are solved numerically and the ensemble average and variance are computed and compared with previous research work. Higher order solutions with higher corrections are computed to show the importance of the generalization of the WHEP technique. The current work extends the use of WHEP for solving stochastic nonlinear differential equations.     

A New Stable Bubble Element for Incompressible Fluid Flow Based on a Mixed Petrov–Galerkin Finite Element Formulation

A new mixed Petrov–Galerkin formulation employing the MINI element with a non-confirming bubble function for an incompressible media governed by the Stokes equations, which is equivalent to the stabilized finite element by P ¹-P ¹ approximation, is proposed. The new formulation possesses better stability properties than the conventional Bubnov–Galerkin formulation employing the MINI element. In this aspect, the stabilizing effect of this formulation is evaluated by a stabilizing parameter determined by both shapes of the trial and the weighting bubble functions.     

Ring transformation of chromone-3-carboxamide

4-Hydroxycoumarin-3-carboxaldehyde (5) was obtained from chromone-3-carboxaldehyde (1) via chromone-3-carboxamide (2) and 3-aminomethylene-2H-chroman-2,4-dione (3). 3-Alkylaminomethylenechroman-2,4-diones (7,8) were obtained from the reaction of primary aliphatic amines with chromone-3-carboxamide (2). Treatment of chromone-3-carboxamide with sodium methoxide gives 3-(2-hydroxybenzoyl)-2H-chromeno[2,3-b]pyridine-2,5(1H)-dione (9).