The local ultraconvergence of high‐order finite element method for second‐order elliptic problems with constant coefficients over a rectangular partition

In this article, we will discuss the local ultraconvergence of high‐degree finite element method based on a rectangular partition for the second‐degree elliptic problem with constant coefficients in Ω ? ?² , u( y ) = 0 on ?Ω . Based on suitable regularity, ultraconvergence of the displacement of the extrapolated kth (k ≥ 3) degree finite element solution has been obtained by an extrapolation technique. Finally, numerical experiments are applied to demonstrate our theoretical findings.     

Asymptotic Behavior of Solutions to the Difference Equation Using the Second Differences of a Liapunov Function

We introduce the concept of the second Liapunov differences in difference equations and show that, in the autonomous case, the second variations can guarantee the existence of solutions tending to zero while others starting arbitrarily near 0 go to ∞. These are based on Yorke's results for ordinary differential equations.     

ON CERTAIN CLASS OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

In the present investigation we define a new class of meromorphic functions on the punctured unit disk △*:= {z ∈ C : 0 < |z| < 1} by making use of the generalized Dziok-Srivastava operator H l m [α1 ]. Coefficient inequalities, growth and distortion inequalities, as well as closure results are obtained. We also establish some results concerning the partial sums of meromorphic functions and neighborhood results for functions in new class.     

Diffusion Mechanism of As‐spun Polyacrylonitrile Fiber in a Dimethyl Sulfoxide‐Water Coagulation Bath

In this paper, the diffusion mechanism of as‐spun PAN fiber was investigated in dimethyl sulfoxide‐water by determining the dynamic compositions of the fibers and the diffusion coefficients of solvent and nonsolvent during coagulation. The diffusion process could be divided into two stages. Results showed that the first stage of the diffusion process was the most important during the whole process, which was fundamental to further study on the formation mechanism. Also, compared with wet spinning, the dry‐jet wet spinning method had the advantage of mild coagulating at a high jet‐stretch. At high concentrations, the diffusion coefficients increased and the ratio of solvent diffusion coefficient to nonsolvent diffusion coefficient decreased; an increasing temperature resulted in the increase of both diffusion coefficients with a decrease in their ratios. To some extent, for the PAN‐DMSO‐water system, the more the ratios D_s*/D_n* tended to 1, the more the cross‐section shapes of as‐spun PAN fiber tended to be circular.     

Implementation of depth-dependent soil concentrations in multimedia mass balance models

In standard multimedia mass balance models, the soil compartment is modeled as a box with uniform concentrations, which often does not correspond with actual field situations. Therefore, the theoretically expected decrease of soil concentrations with depth was implemented in the multimedia model SimpleBox 3.0. The effects of this implementation on the model outcomes were explored for nine compounds in four environmental compartments. For compounds with a low penetration depth, the new model predicts substantially higher or lower concentrations in the vegetation compartment than the old model. For those compounds, predicted concentrations in surface water and air were higher in the new model, but the deviations from the old model were smaller than in the vegetation compartment. For compounds with a large penetration depth, the model adaptations show little effect. No field study was carried out to validate the results of the model calculations, but we did collect measured data on concentrations in vertical soil profiles from literature. According to those data, we concluded that the implementation of depth dependent soil concentrations might be a useful extension for steady state multimedia mass balance models. More field study has to be carried out to validate the model outcomes.     

Limit distribution of the coefficients of polynomials with only unit roots

We consider sequences of random variables whose probability generating functions have only roots on the unit circle, which has only been sporadically studied in the literature. We show that the random variables are asymptotically normally distributed if and only if the fourth central and normalized (by the standard deviation) moment tends to 3, in contrast to the common scenario for polynomials with only real roots for which a central limit theorem holds if and only if the variance is unbounded. We also derive a representation theorem for all possible limit laws and apply our results to many concrete examples in the literature, ranging from combinatorial structures to numerical analysis, and from probability to analysis of algorithms. © 2013 Wiley Periodicals, Inc. Random Struct. Alg., 46,707–738, 2015     

Automatic kinetic model generation and selection based on concentration versus time curves

The goal of the paper is to automatize the construction and parameterization of kinetic reaction mechanisms that can describe a set of experimentally measured concentration versus time curves. Using the framework and theorems of formal reaction kinetics, first, we build a set of possible mechanisms with a given number of measured and unmeasured (real or fictitious) species and reaction steps that fulfill some chemically reasonable requirements. Then we fit all the corresponding mass-action kinetic models and offer the best one to the chemist to help explain the underlying chemical phenomenon or to use it for predictions. We demonstrate the use of the method via two simple examples: on an artificial, simulated set of data and on a small real-life data set. The method can also be used to do a kind of lumping to generate a model that can reproduce the simulation results of a detailed mechanism with less species and thereby can largely accelerate spatially inhomogeneous simulations.     

Diffusion of Quinine with Ethanol as a Co-Solvent in Supercritical CO2

This study aims at contributing to quinine extraction using supercritical CO₂ and ethanol as a co-solvent. The diffusion coefficients of quinine in supercritical CO₂ are measured using the Taylor dispersion technique when quinine is pre-dissolved in ethanol. First, the diffusion coefficients of pure ethanol in the supercritical state of CO₂ were investigated in order to get a basis for seeing a relative change in the diffusion coefficient with the addition of quinine. We report measurements of the diffusion coefficients of ethanol in scCO₂ in the temperature range from 304.3 to 343 K and pressures of 9.5, 10 and 12 MPa. Next, the diffusion coefficients of different amounts of quinine dissolved in ethanol and injected into supercritical CO₂ were measured in the same range of temperatures at p = 12 Mpa. At the pressure p = 9.5 MPa, which is close to the critical pressure, the diffusion coefficients were measured at the temperature, T = 343 K, far from the critical value. It was found that the diffusion coefficients are significantly dependent on the amount of quinine in a small range of its content, less than 0.1%. It is quite likely that this behavior is associated with a change in the spatial structure, that is, the formation of clusters or compounds, and a subsequent increase in the molecular weight of the diffusive substance.