Extrapolation of accelerated thermooxidative tests to lower temperatures applying non-Arrhenius temperature functions

Extrapolations of the accelerated thermooxidative tests, based on the Arrhenius and two non-Arrhenius temperature functions, have been tested for 26 data sets. The data cover a wide range of materials from polyolefins and other polymers to biodiesel, edible oils and dried milk. It has been found that the extrapolation from high-temperature data to ambient temperature based on the Arrhenius temperature function leads to the estimations of unrealistically long durability. The best estimations corresponding most with experience are obtained for the extrapolation based on the temperature function k(T)=A _kexp(DT).     

LU implementation of the modified minimal polynomial extrapolation method for solving linear and nonlinear systems

We give an efficient implementation of the modified minimalpolynomial extrapolation (MMPE) method for solving linear andnonlinear systems. We will show how to choose the auxiliaryvectors in the MMPE method such that the resulting approximationsare always defined. This new implementation, which is basedon an LU factorization with a pivoting strategy, is inexpensiveboth in time and storage as compared with other extrapolationmethods.     

On non‐autonomous integro‐differential‐algebraic evolutionary problems

In this article, we show that a technique for showing well‐posedness results for evolutionary equations in the sense of Picard and McGhee [Picard, McGhee, Partial Differential Equations: A unified Hilbert Space Approach, DeGruyter, Berlin, 2011] established in [Picard, Trostorff, Wehowski, Waurick, On non‐autonomous evolutionary problems. J. Evol. Equ. 13:751‐776, 2013] applies to a broader class of non‐autonomous integro‐differential‐algebraic equations. Using the concept of evolutionary mappings, we prove that the respective solution operators do not depend on certain parameters describing the underlying spaces in which the well‐posedness results are established. Copyright © 2014 John Wiley & Sons, Ltd.     

Stokes问题Q_2-P_1混合元外推方法

考虑Stokes问题的有限元解与精确解插值的Q2-P1混合元的渐近误差展开和分裂外推.首先利用积分恒等式技巧确定了微分方程精确解与有限元插值之间积分式的主项,其次再借助插值后处理和分裂外推技术,得到了比通常的误差估计提高两阶的收敛速度.     

The Determination of Organic Compounds by Ther Oxidation with Permanganate

Abstract

The possibility of applying the graphical logarithmic ¹ extrapolation method of Siggia and co-workers to the analysis of mixtures of two organic subatences based on their redox reaction with permanganate has been verified. For this task, the oxidation of a mixture of formic and tartaric acids with pemanganate ir? a buffered medium was chosen.     

Numerical implementation of the Crank–Nicolson/Adams–Bashforth scheme for the time‐dependent Navier–Stokes equations

This article considers numerical implementation of the Crank–Nicolson/Adams–Bashforth scheme for the two‐dimensional non‐stationary Navier–Stokes equations. A finite element method is applied for the spatial approximation of the velocity and pressure. The time discretization is based on the Crank–Nicolson scheme for the linear term and the explicit Adams–Bashforth scheme for the nonlinear term. Comparison with other methods, through a series of numerical experiments, shows that this method is almost unconditionally stable and convergent, i.e. stable and convergent when the time step is smaller than a given constant. Copyright © 2009 John Wiley & Sons, Ltd.     

Some New Extrapolation Estimates for the Scale of Spaces

Using new extrapolation estimates for the - and -functionals of couples of limit spaces of the -scale , we introduce a class of extrapolation functors. A characterization of this class via the real interpolation method permits one to obtain new equivalent expressions for the norms in symmetric spaces close to and , which depend only on the -norms of a function.     

The Vector Epsilon Algorithm – a Residual Approach

We present an alternative to the vector -algorithm based on vector continued fractions and which is applicable when the sequence to be accelerated is generated by a one-point iteration function. These fractions are constructed in the language of Clifford algebras, which allow three-term recurrence relations. The new algorithm evidently has considerably greater numerical precision than the old one. Results from numerical experiments are reported.     

Nonlinear variation of sorption parameters of n-alkane homologsl in temperature-programmed gas chromatography (tpgc) and new equation for calculation of retention indixces

It has been demonstated that the considaerable difference in temperature increments of sorption parameters of n-alkanes under isothermal conditions is the main reason for nonlinear dependence of sorption parameters on molecular mass of homolog in temperaturre programmed gas chromatography (TPGC). A new nonlinear 4th parameter equation has been given for calculation of the retention indices. Coefficients of the equation are calculated from n-alkanes. The equation allows extrapolation and interpolation calculations of retention indices under TPGC conditions with experimental precision. The results obtained; for fatty acidkl methyl esters demonstrate the advantage of ovr equation in comparison with van den Dool and Kratz's equation.