On noncommutative piecewise Noetherian rings

We extend the definition of a piecewise Noetherian ring to the noncommutative case, and investigate various properties of such rings. In particular, we show that a ring with Krull dimension is piecewise Noetherian. Certain fully bounded piecewise Noetherian rings have Gabriel dimension and exhibit the Gabriel correspondence between prime ideals and indecomposable injective modules.     

Approximating exponential and logarithmic functions using polynomial interpolation

This article takes a closer look at the problem of approximating the exponential and logarithmic functions using polynomials. Either as an alternative to or a precursor to Taylor polynomial approximations at the precalculus level, interpolating polynomials are considered. A measure of error is given and the behaviour of the error function is analysed. The results of interpolating polynomials are compared with those of Taylor polynomials.     

Mixed multiplicities,Hilbert polynomials and homaloidal surfaces

We investigate the relationship among several numerical invariants associated to a (free) projective hypersurface V : the sequence of mixed multiplicities of its Jacobian ideal, the Hilbert polynomial of its Milnor algebra, and the sequence of exponents when V is free. As a byproduct, we obtain explicit equations for some of the homaloidal surfaces in the projective 3‐dimensional space constructed by C. Ciliberto, F. Russo and A. Simis.     

High-resolution semi-discrete Hermite central-upwind scheme for multidimensional Hamilton–Jacobi equations

We introduce a high resolution fifth-order semi-discrete Hermite central-upwind scheme for multidimensional Hamilton–Jacobi equations. The numerical fluxes of the scheme are constructed by Hermite polynomials which can be obtained by using the short-time assignment of the first derivatives. The extensions of the proposed semi-discrete Hermite central-upwind scheme to multidimensional cases are straightforward. The accuracy, efficiency and stability properties of our schemes are finally demonstrated via a variety of numerical examples.     

Iterative process acceleration of calculation of unsteady,viscous, compressible,and heat‐conductive gas flows

In this paper, extrapolation technique is introduced in the Semi‐Implicit Method for Pressure‐Linked Equations ‐ Time Step (SIMPLE‐TS) finite volume iterative algorithm for calculation of compressible Navier–Stokes–Fourier equations subject of slip and jump boundary conditions. The initial state, required by the iterative solver in simulation of unsteady flow problems, is approximated in time by Lagrange polynomial extrapolation in each node. The approach is applicable to a parallel code in a straightforward way due to algorithmic independence of the neighboring nodes in the computational grid. A criterion is proposed to determine the order of extrapolation polynomial and stop the extrapolation execution, when the local steady state is reached. The approach is tested on different microflow problems: Couette flow, flow past a square in a microchannel at subsonic and supersonic speeds, and convective Rayleigh–Bénard flow of a rarefied gas. The acceleration varies from 1.14‐fold to 2.8‐fold. Copyright © 2014 John Wiley & Sons, Ltd.     

Introducing nonlinear,multivariate ‘Predictor Surfaces’ for quantitative modeling of chemical systems with higher-order,coupled predictor variables

Innovations in chemometrics are required for studies of chemical systems which are governed by nonlinear responses to chemical parameters and/or interdependencies (coupling) among these parameters. Conventional and linear multivariate models have limited use for quantitative and qualitative investigations of such systems because they are based on the assumption that the measured data are simple superpositions of several input parameters. ‘Predictor Surfaces’ were developed for studies of more chemically complex systems such as biological materials in order to ensure accurate quantitative analyses and proper chemical modeling for in-depth studies of such systems. Predictor Surfaces are based on approximating nonlinear multivariate model functions by multivariate Taylor expansions which inherently introduce the required coupled and higher-order predictor variables.     

Finding optimal finite field strengths allowing for a maximum of precision in the calculation of polarizabilities and hyperpolarizabilities

The finite field method, widely used for the calculation of static dipole polarizabilities or the first and second hyperpolarizabilities of molecules and polymers, is thoroughly explored. The application of different field strengths and the impact on the precision of the calculations were investigated. Borders could be defined and characterized, establishing a range of feasible field strengths that guarantee reliable numerical results. The quality of different types of meshes to screen the feasible region is assessed. Extrapolation schemes are presented that reduce the truncation error and allow to increase the precision of finite field calculations by one to three orders of magnitude. © 2013 Wiley Periodicals, Inc.     

溶剂热法制备立方状ITO粉体及其电性能

以乙二醇、乙醇为溶剂通过溶剂热法制备出立方状ITO纳米粉体,研究了反应时间、NaOH浓度对ITO纳米粉体形貌的影响,并讨论了溶剂体积比、NaOH浓度对ITO粉体导电性的影响及机理。结果表明：采用乙二醇与乙醇做溶剂,V_EG：V_EtOH=4：1时,制备出分散性良好的立方状ITO纳米粉体,平均粒径为10.7 nm,且其XRD衍射峰强度比I₄₀₀/I₂₂₂最高为0.380;乙二醇与乙醇做溶剂,V_EG：V_EtOH=4：1,且NaOH浓度为0.275 mol·L^-1时,粉体电导率最高为46.75 mS·cm^-1。     

二氧化钛含量对铈稳定立方氧化锆陶瓷的性能影响

本文用无压烧结法成功制备了高硬度的立方氧化锆陶瓷,研究了氧化锆陶瓷的物相,Vickers硬度,显微结构,相对密度等性能,主要分析了TiO2添加量对Zr0.8Ce0.2O2陶瓷硬度和相对密度的影响。结果表明:烧结助剂TiO2可以有效抑制陶瓷晶粒异常生长,加快气孔排除,促进氧化锆陶瓷烧结致密化,提高陶瓷硬度。最高维氏硬度为20.2 GPa,最高相对密度达到了99.8%。     

New q‐Hermite polynomials: characterization,operators algebra and associated coherent states

This paper addresses a construction of new q‐Hermite polynomials with a full characterization of their main properties and corresponding raising and lowering operator algebra. The three‐term recursive relation as well as the second‐order differential equation obeyed by these new polynomials are explicitly derived. Relevant operator actions, including the eigenvalue problem of the deformed oscillator and the self‐adjointness of the related position and momentum operators, are investigated and analyzed. The associated coherent states are constructed and discussed with an explicit resolution of the induced moment problem. The phase collapse in a q‐deformed boson system is studied.