Effect of local variations of the laminar flame speed on the global finger-flame acceleration scenario

Numerous formulations describing the dynamics and morphology of corrugated flames, including the scenarios of flame acceleration, are based on a “geometrical consideration”, where the wrinkled-to-planar flame velocities ratio, S_w /S_L , is evaluated as the scaled flame surface area, while the entire combustion chemistry is immersed into the planar flame speed S_L , which is assumed to be constant. However, S_L may experience noticeable spatial/temporal variations in practice, in particular, due to pressure/temperature variations as well as non-uniform distribution of the equivalence ratio and/or that of combustible or inert dust impurities. The present work initiates the systematic study of the impact of the local S_L -variations on the global flame evolution scenario. The variations are assumed to be imposed externally, in a manner being a free functional of the formulation. Specifically, the linear, parabolic and hyperbolic spatial S_L -distributions are incorporated into the formulations of finger flame acceleration in pipes, and they are compared to the case of constant S_L . Both two-dimensional channels and cylindrical tubes are considered. The conditions promoting or moderating flame acceleration are identified, and the revisited equations for the flame shape, velocity and acceleration rate are obtained for various S_L -distributions. The theoretical findings are validated by the computational simulations of the reacting flow equations, with agreement between the theory and modelling demonstrated.     

Gas chromatography-mass spectrometry of the trimethylsilyl (oxime) ether/ester derivatives of cholic acids: their presence in the aquatic environment

This paper presents a derivatization, mass fragmentation study relating to the most common six cholic acids, such as cholic, lithocholic, chenodeoxycholic, ursodeoxycholic, 3-hydroxy,7-ketocholanic and dehydrocholic acids, identified and quantified as pollutants in the aquatic environment at the first time. Derivatizations have been performed with the two-step process (1: oximation, 2: silylation) varying the time and temperature of both reactions. Optimum responses have been obtained after 30 min oximation with hydroxylamine.HCl and 90 min silylation with hexamethyldisilazane and trifluoroacetic acid at 70 degrees C. Fragmentation patterns of the trimethylsilyl (oxime) ether/ester derivatives of all six cholic acids provided the theoretically expected, fully derivatized compounds. Reproducibility/linearity of derivatives calculated on the basis of the corresponding selective fragment ions, characterized by the relative standard deviation percentages of measurements, proved to be < or =4.9 (RSD%). The practical utility of the method was shown by the identification and quantification of cholic acids as pollutants in the aquatic environment. Subsequently to a solid phase extraction study varying the pH of extractions (pH 2, pH 4 and pH 7), applying the OASIS cartridges, it has been confirmed that the recoveries for all six cholic acids are acceptable, varying between 77% and 104%, and are independent on the pH. The total cholic acid content of a Hungarian wastewater plants' influent wastewater varied between 184 microg/L and 356 microg/L, while the Danube rivers' cholic acid content was 4.1 microg/L, only.     

Simulating electron spin resonance spectra of nitroxide spin labels from molecular dynamics and stochastic trajectories

Simulating electron spin resonance spectra of nitroxide spin labels from motional models is necessary for the quantitative analysis of experimental spectra. We present a framework for modeling the spin label dynamics by using trajectories such as those from molecular dynamics (MD) simulations combined with stochastic treatment of the global protein tumbling. This is achieved in the time domain after two efficient numerical integrators are developed: One for the quantal dynamics of the spins and the other for the classical rotational diffusion. For the quantal dynamics, we propagate the relevant part of the spin density matrix in Hilbert space. For the diffusional tumbling, we work with quaternions, which enables the treatment of anisotropic diffusion in a potential expanded as a sum of spherical harmonics. Time-averaging arguments are invoked to bridge the gap between the smaller time step of the MD trajectories and the larger time steps appropriate for the rotational diffusion and/or quantal spin dynamics.     

A new heuristic for learning Bayesian networks from limited datasets: a real-time recommendation system application with RFID systems in grocery stores

Bayesian networks (BNs) are a useful tool for applications where dynamic decision-making is involved. However, it is not easy to learn the structure and conditional probability tables of BNs from small datasets. There are many algorithms and heuristics for learning BNs from sparse datasets, but most of these are not concerned with the quality of the learned network in the context of a specific application. In this research, we develop a new heuristic on how to build BNs from sparse datasets in the context of its performance in a real-time recommendation system. This new heuristic is demonstrated using a market basket dataset and a real-time recommendation model where all items in the grocery store are RFID tagged and the carts are equipped with an RFID scanner. With this recommendation model, retailers are able to do real-time recommendations to customers based on the products placed in cart during a shopping event.     

The Noether map II

Let be a faithful representation of a finite group . In this paper we proceed with the study of the image of the associated Noether map

In our 2005 paper it has been shown that the Noether map is surjective if is a projective -module. This paper deals with the converse. The converse is in general not true: we illustrate this with an example. However, for -groups (where is the characteristic of the ground field ) as well as for permutation representations of any group the surjectivity of the Noether map implies the projectivity of .

     

Oxidative polymerization of N-substituted carbazoles

Poly(N-vinylcarbazole), poly(N-carbazole) and poly(N-ethylcarbazole) powders were chemically synthesized by the reaction of ceric ammonium nitrate (CAN) with N-vinylcarbazole carbazole and N-ethylcarbazole in acetonitrile. Products were characterized by elemental analysis, Fourier transform infrared spectroscopy, scanning electron microscopy and viscosity, X-ray fluorescence and four-probe conductivity measurement. It is found that when a suitable concentration of CAN is used in the polymerization process, the conductivity of chemically synthesized polymers can be improved further by controlling the CAN addition. © 1997 John Wiley & Sons, Ltd.     

Legendre polynomial solutions of high-order linear Fredholm integro-differential equations

In this study, a Legendre collocation matrix method is presented to solve high-order Linear Fredholm integro-differential equations under the mixed conditions in terms of Legendre polynomials. The proposed method converts the equation and conditions to matrix equations, by means of collocation points on the interval [−1, 1], which corresponding to systems of linear algebraic equations with Legendre coefficients. Thus, by solving the matrix equation, Legendre coefficients and polynomial approach are obtained. Also examples that illustrate the pertinent features of the method are presented and by using the error analysis, the results are discussed.     

A collocation approach for solving linear complex differential equations in rectangular domains

In this paper, a collocation method is presented to find the approximate solution of high‐order linear complex differential equations in rectangular domain. By using collocation points defined in a rectangular domain and the Bessel polynomials, this method transforms the linear complex differential equations into a matrix equation. The matrix equation corresponds to a system of linear equations with the unknown Bessel coefficients. The proposed method gives the analytic solution when the exact solutions are polynomials. Numerical examples are included to demonstrate the validity and applicability of the technique and the comparisons are made with existing results. The results show the efficiency and accuracy of the present work. All of the numerical computations have been performed on a computer using a program written in MATLAB v7.6.0 (R2008a). Copyright © 2012 John Wiley & Sons, Ltd.