Elliptic Reconstruction and a Posteriori Error Estimates for Fully Discrete Semilinear Parabolic Optimal Control Problems

This article studies a posteriori error analysis of fully discrete finite element approximations for semilinear parabolic optimal control problems. Based on elliptic reconstruction approach introduced earlier by Makridakis and Nochetto [25], a residual based a posteriori error estimators for the state, co-state and control variables are derived. The space discretization of the state and co-state variables is done by using the piecewise linear and continuous finite elements, whereas the piecewise constant functions are employed for the control variable. The temporal discretization is based on the backward Euler method. We derive a posteriori error estimates for the state, co-state and control variables in the $L^\infty(0,T;L^2(\Omega))$-norm. Finally, a numerical experiment is performed to illustrate the performance of the derived estimators.     

Trigonometric wavelets for Hermite interpolation

The aim of this paper is to investigate a multiresolution analysis of nested subspaces of trigonometric polynomials. The pair of scaling functions which span the sample spaces are fundamental functions for Hermite interpolation on a dyadic partition of nodes on the interval . Two wavelet functions that generate the corresponding orthogonal complementary subspaces are constructed so as to possess the same fundamental interpolatory properties as the scaling functions. Together with the corresponding dual functions, these interpolatory properties of the scaling functions and wavelets are used to formulate the specific decomposition and reconstruction sequences. Consequently, this trigonometric multiresolution analysis allows a completely explicit algorithmic treatment.

     

An Arithmetic Reduction of Finite Rank 3 Geometries with Linear Spaces as Plane Residues and with Dual Linear Spaces as Point Residues

Let be a rank three incidence geometry of points, lines and planes whose planes are linear spaces and whose point residues are dual linear spaces (notice that we do not require anything on the line residues). We assume that the residual linear spaces of belong to a natural class of finite linear spaces, namely those linear spaces whose full automorphism group acts flag-transitively and whose orders are polynomial functions of some prime number. This class consists of six families of linear spaces. In the amalgamation of two such linear spaces imposes an equality on their orders leading, in particular, to a series of diophantine equations, the solutions of which provide a reduction theorem on the possible amalgams of linear spaces that can occur in .We prove that one of the following holds (up to a permutation of the words point and plane):A) the planes of and the dual of the point residues belong to the same family and have the same orders,B) the diagram of is in one of six families,C) the diagram of belongs to a list of seven sporadic cases.Finally, we consider the particular case where the line residues of are generalized digons.     

Intermolecular contact interactions and their temperature dependence

A model, based on inverse gas chromatography experiments, has been developed for intermolecular interaction and its temperature dependence. The model ascribes to each substance a four-component solubility parameter; the four components reflect the van der Waals, polar, electron donor, and electron acceptor interactive properties. Their values depend on temperature in the same manner as does the cohesive energy. The latter was found to depend only on the critical temperature, the acentric factor, and the reduced temperature. The model was used for evaluation of the solubility parameters from polymer-solvent interaction coefficients and their temperature dependence with high accuracy. For binary solventsolvent mixtures, the free energy of mixing and its temperature dependence, as well as enthalpy of mixing can be derived from this model with a good accuracy.     

Volumetric studies and thermodynamics of viscous flow of hydroxamic acids in acetone + water solvent at temperatures 303.15 and 313.15 K

Densities ρ and viscosities η of two hydroxamic acids, N-phenyl-2-chlorobenzo- and N-o-tolyl-4-chlorobenzo-, have been determined as a function of their concentration in aqueous acetone solution at temperatures 303.15 and 313.15 K. Apparent molar volumes, standard-state partial molar volumes and relative viscosities have been calculated. The viscosity data have been analyzed using Jones-Dole equation. The activation thermodynamic parameters of viscous flow have been evaluated using Feakins equation. These were obtained to throw light on the mechanism of viscous flow. Thermodynamic interactions in solutions have been studied in terms of a number of excess functions calculated from the experimental data. The effect of hydroxamic acid concentration and temperature on these parameters has been discussed. The results were interpreted in the light of solute-solvent interactions in aquo-organic media.     

稀土元素在钢中的热力学参数及应用

综合报道了通过采用几种不同的高温金属溶液实验方法，研究所得到的稀土元素在金属溶液冶炼温度范围内分别与硫、氧、氧 硫、碳、氮、低熔点铜、磷、钛、铌、钒等重要元素相互作用规律及有关的一系列热力学参数和温度函数式，并简要地讨论了这些热力学参数在含稀土钢中的应用。     

Evaluation of the limit of performance of an analytical method based on a statistical calculation of its critical concentrations according to ISO standard 11843: Application to routine control of banned veterinary drug residues in food according to European Decision 657/2002/EC

Traceability of the measurement of analytical parameters capable of evaluating the performance of methods is an important concept for the assessment of quality for the routine control, especially for residue monitoring of non-authorized medicinal substances in food from animal origin. The European Decision no. 657/2002/EC recommends to calculate two statistical limits, CCα and CCβ, which allow to evaluate the critical concentrations above which the method reliably distinguish and quantify a substance taking into account the variability of the method and the statistical risk to take a wrong decision. The calculation, which can be derived from the ISO standard no. 11843 is applied on a routine basis. An example displays a very simple way for evaluating the performance of an LC-MSMS method which has been validated a few years ago and is qualified onto a Micromass Quattro LCZ tandem mass spectrometer to monitor and confirm the nitrofuran metabolite residues in food from animal origin. Community Reference Laboratory for Antimicrobial Veterinary Drug Residue Control in Food from Animal Origin     

将A-L理论推广到无限维李代数

为使由Alhassid与Levine所提出的动力学李代数方法（简称A－L理论）能适用于更多的散射体系，在h(∞)中引入了有效集合C（有限维）的概念．按照微扰理论的意义，C中的代数元所对应的群参量是较低次微扰的结果，而不属于C的代数元所对应的群参量则相当于较高次做扰所产生的修正结果．因此可以近似地利用C来代替h(∞)．这样，不仅简化了计算程序并且对于很多具有现实意义的散射过程的计算成为可能．     

The effect of injection procedures on efficiency in micellar electrokinetic capillary chromatography

Summary Micellar electrokinetic capillary chromatography (MECC) involves the application of a high voltage (10–30 KV) across a capillary column (75μm i.d.) which is filled with a solution containing micelles. The mobile phase in this work consisted of sodium dodecyl sulfate in an aqueous borate/phosphate buffer system. Injection parameters in MECC were investigated to minimize the contribution to band-broadening resulting from the injection process. Efficiencies as high as 240,000 theoretical plates/meter are reported.     

Aa1Dd1-Aa2Dd2型氢键体系的网络结构参数

利用溶胶-凝胶分配理论对氢键溶液的模型体系进行研究, 给出了体系的凝胶化条件以及凝胶点后氢键网络中各类结构参数的计算方案, 并进行了相应的数值计算. 结果表明, 当两类质子受体基团的活性不同时, 质子受体基团的竞争作用对网络结构有一定影响. 这为控制氢键网络结构特征提供了可能的理论线索.