Maximal <Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">p</Emphasis></Superscript>‐regularity for elliptic operators with VMO‐coefficients

In this paper we show that the parabolic problem associated with elliptic operators A having coefficients in has the property of maximal -regularity. RID="h1" ID="h1"In Memoriam Philippe Bénilan     

Symbolic Computation of Newton Sum Rules for the Zeros of Polynomial Eigenfunctions of Linear Differential Operators

A symbolic algorithm based on the generalized Lucas polynomials of first kind is used in order to compute the Newton sum rules for the zeros of polynomial eigenfunctions of linear differential operators with polynomial coefficients.     

Can a finite element method perform arbitrarily badly?

In this paper we construct elliptic boundary value problems whose standard finite element approximations converge arbitrarily slowly in the energy norm, and show that adaptive procedures cannot improve this slow convergence. We also show that the -norm and the nodal point errors converge arbitrarily slowly. With the -norm two cases need to be distinguished, and the usual duality principle does not characterize the error completely. The constructed elliptic problems are one dimensional.

     

Data and modeling of negative ion transport in gases of interest for production of integrated circuits and nanotechnologies

We review techniques to prepare, evaluate and apply sets of cross section and transport data for negative ions that are required for the modeling of collisional non-equilibrium plasmas used for processing of microelectronic circuits. We collect and discuss the transport coefficients and cross section sets.We have compiled data for negative ions in CF₄ and CF₄-related negative ions in rare gases. In addition, we consider data for F⁻ and CF₃⁻ in rare gases. Furthermore, we analyze the cross sections of halogen negative ions in rare gases and other molecules. This is followed by the data for SF₆ related ions in SF₆ and in rare gases. The cross section for scattering of O⁻ in O₂ has been derived from the transport data and used to make calculations of the transport properties. Finally we give a brief discussion of the availability of the data for H⁻ ions in H₂. We have derived cross sections in several cases but the basic aim is to show the basic features of transport coefficients. In particular we discuss the need to represent properly some details such as the non-conservative nature of transport coefficients and the anisotropy of diffusion. Application of approximate theories and representations of cross sections are also discussed.     

N2-broadening coefficients in the ν2 and ν4 bands of PH3 at low temperature

N₂-broadening coefficients have been measured for 41 transitions of PH₃ at −100 °C in the ^QR branch of the ν₂ band and the ^PP, ^RP, and ^SP branches of the ν₄ band, using a tunable diode-laser spectrometer. The recorded lines with J values ranging from 1 to 13 and K from 0 to 10 are located between 1026 and 1093 cm⁻¹. The collisional widths are determined by fitting each spectral line with a Voigt profile, a Rautian profile, and a speed-dependent Rautian profile. The latter models provide larger broadening coefficients than the Voigt model. These coefficients have also been calculated on the basis of a semiclassical model of interacting linear molecules by considering an atom-atom Lennard-Jones potential in addition to the electrostatic contributions. By comparing broadening coefficients at room and low temperatures, the temperature dependence of these broadenings has been determined both experimentally and theoretically.     

On the structure of the class A(ϕ)

In this paper, we study whether the set A(?) is closed under multiplication f · g, where f and g belong to the class A(?). We also study the problem of the existence of a solution of the equation Bx = C (where B,C ∈ A(?) and B ≠ 0) on the set A(?).     

Effect of Alkyl Side Chain on the Conformational Properties of Polysulfones with Quaternary Groups

Modification of intrinsic viscosity, temperature coefficient, and preferential adsorption coefficient of polysulfones with different alkyl side groups in N,N-dimethylformamide/methanol and N,N-dimethylformamide/water was investigated at different compositions and temperatures. The specific interactions, such as hydrogen bonding and polyelectrolyte effect induced by an enhanced dissociation of the ionizable groups, determine both the modification of the solvation power of the polymer coil and the difference in the composition of the mixed solvent inside and outside the coil.     

基于改进的语音参数提取的线性预测

根据语音发生基本原理和线性预测编码原理，针对自相关法需要加窗从而降低了解的精度，而协方差法不能保证保证解所重构出系统的稳定性的特点，提出了一种改进的Cholesky分解的方法求解协方差方程组以产生声道模型参数的方法，实践证明，这种方法既保证了系统的稳定性，又提高了解的精度。     

Elution profiles of lanthanides with α‐hydroxyisobutyric acid by ion exchange chromatography using fine resin

Experiments were carried out using a strong acid cation exchange resin with a particle size of 75–150 μm, termed as “fine resin” in hydrogen ion form for the elution of individual lanthanides Sm, Eu, Gd, Tb, and Dy that are produced as fission products in the spent nuclear fuel and generated in the effluent during reprocessing of spent nuclear fuel. Batch experiments were carried out to study the effect of concentration of nitric acid on distribution coefficient. The distribution coefficient values for these individual lanthanides were determined in nitric acid medium in the concentration range of 0.01–4.0 N. Uptake of each individual lanthanide by resin was increased with increased nitric acid concentration from 0.01 to 0.5 N and remained similar from 0.5 to 1.0 N and decreased thereafter up to 4.0 N. Column experiments were also carried out using the same resin to study the parameters like pH of the eluent, flow rate, and resin bed height under isocratic elution conditions for eluting lanthanide elements using α‐hydroxyisobutyric acid as eluent. The results of this study have indicated the possibility for the elution of individual lanthanides.     

Numerical integration of ordinary differential equations on manifolds

Summary This paper is concerned with the problem of developing numerical integration algorithms for differential equations that, when viewed as equations in some Euclidean space, naturally evolve on some embedded submanifold. It is desired to construct algorithms whose iterates also evolve on the same manifold. These algorithms can therefore be viewed as integrating ordinary differential equations on manifolds. The basic method “decouples” the computation of flows on the submanifold from the numerical integration process. It is shown that two classes of single-step and multistep algorithms can be posed and analyzed theoretically, using the concept of “freezing” the coefficients of differential operators obtained from the defining vector field. Explicit third-order algorithms are derived, with additional equations augmenting those of their classical counterparts, obtained from “obstructions” defined by nonvanishing Lie brackets.