Evaluation of the stability and analysis of halogenated furanones in disinfected drinking waters

A refined method for the sub-nanomolar analysis of 13 halogenated furanones in chlorinated drinking water is proposed which uses liquid-liquid extraction, methylation where necessary, gas chromatographic separation, and either micro-electron capture or ion trap mass spectrometric detection. Liquid-liquid extraction with methyl tert-butyl ether was demonstrated to be effective for recovery of halogenated furanones. Confirmation of the halogenated furanones identity and reduction of natural organic matter interference were achieved by ion trap tandem mass spectrometry. Compound stabilities and procedural efficiencies were evaluated to permit optimization of the method for reasonable sample volumes and a 1000:1 pre-concentration factor that would permit feasible sample collection in the field. Both chlorinated and brominated analogues of MX (3-chloro-4-(dichloromethyl)-5-hydroxy-2(5H)-furanone) were included in a suite of compounds targeted in a national occurrence study of disinfection by-products.     

Mixed finite element approximation of the vector potential

Summary We consider a mixed finite element approximation of the three dimensional vector potential, which plays an important rôle in the simulation of perfect fluids and in the calculation of rotational corrections to transonic potential flows. The central point of our approach is a saddlepoint formulation of the essential boundary conditions. In particular, this avoids the wellknown Babuka paradox when approximating smooth domains by polyhedrons. Using piecewise linear/piecewise constant elements for the vector potential/the boundary terms, we obtain optimal error estimates under minimal regularity assumptions for the solution of the continuous problem.     

The average a posteriori error of numerical methods

Summary The definition of the average error of numerical methods (by example of a quadrature formula to approximateS(f)= f d on a function classF) is difficult, because on many important setsF there is no natural probability measure in the sense of an equidistribution. We define the average a posteriori error of an approximation by an averaging process over the set of possible information, which is used by (in the example of a quadrature formula,N(F)={(f(a ₁), ...,f/fF} is the set of posible information). This approach has the practical advantage that the averaging process is related only to finite dimensional sets and uses only the usual Lebesgue measure. As an application of the theory I consider the numerical integration of functions of the classF={f:[0,1]/f(x)–f(y)||x–y|}. For arbitrary (fixed) knotsa _i we determine the optimal coefficientsc _i for the approximation and compute the resulting average error. The latter is minimal for the knots . (It is well known that the maximal error is minimal for the knotsa _i .) Then the adaptive methods for the same problem and methods for seeking the maximum of a Lipschitz function are considered. While adaptive methods are not better when considering the maximal error (this is valid for our examples as well as for many others) this is in general not the case with the average error.     

An asymptotic finite element method for improvement of solutions of boundary layer problems

Summary A scheme that uses singular perturbation theory to improve the performance of existing finite element methods is presented. The proposed scheme improves the error bounds of the standard Galerkin finite element scheme by a factor of O(ⁿ⁺¹) (where is the small parameter andn is the order of the asymptotic approximation). Numerical results for linear second order O.D.E.'s are given and are compared with several other schemes.     

A priori-Schranken für diskrete Lösungen monotoner Operatorgleichungen und Anwendungen

Summary Operator equationsTu=f are approximated by Galerkin's method, whereT is a monotone operator in the sense of Browder and Minty, so that existence results are available in a reflexive Banach spaceX. In a normed spaceY error estimates are established, which require a priori bounds for the discrete solutionsu _h in the norm of a suitable space . Sufficient conditions for the uniform boundedness u _{h Z} =O(1) ash0 are proved. Well-known error estimates in [3] for the special caseX=Y=Z are generalized by this. The theory is applied to quasilinear elliptic boundary value problems of order 2m in a bounded domain . The approximating subspaces are finite element spaces. Especially the caseX=W ₀ ^{m, p} (), 1<p<,Y=W ₀ ^{m. 2} (),Z=W ₀ ^{m. max (2,p)} ()W^m, () is treated. Some examples for 1<p<2 are considered. Forp2 a refined technique is introduced in the author's paper [7].

     

变分过渡态理论对OCS,CO2,CS2体系的研究

本文用变分过渡态理论,首次对无鞍点的释能反应O+CS→CO+S、O+CO→CO+O和S+CS→CS+S进行了动力学研究,考察了反应动力学瓶颈区性质,计算了反应的速度常数,并将O+CS反应的速度常数值与实验值及经典轨迹计算结果进行了比较,三者基本相符.     

醋酸十二铵的吸附和SiO2悬浮液的稳定性

（1）测定了醋酸十二烷基铵（DAA）在CAB－O－SIL上的吸附，其等温线属双平台或LS型[1－3，5]；（2）NaCl的存在使DAA的吸附增加．但不影响其低浓度下第一平台的吸附量；HCl的存在则在全浓度范围内抑制了DAA的吸附，（3）测定了CAB－O－SIL颗粒在上述各溶液中的悬浮液的稳定性；（4）根据表面形成小胶团的吸附理论（即二步模型产）[2，3，5，]，并借助电导跟踪溶液中发生的变化，满意地解释了吸附和聚沉的实验结果．     

Synthesis, crystal structure and magnetic properties of a novel complex [Cu(NIT2Py)(PDA)(H2O)]·(CH3OH)(H2O)

A novel complex [Cu(NIT2Py)(PDA)(H₂O)]·(CH₃OH)(H₂O) has been synthesized and structurally characterized by X-ray diffraction methods. It crystallizes in the monoclinic space group P2(1)/c. The structure consists of [Cu(NIT2Py)(PDA)(H₂O)] moiety, one solvent methanol molecule and one water molecule. The copper(II) ion is in a distorted octahedral environment: one nitrogen atom and one oxygen atom from the NIT2Py, one nitrogen atom from the PDA (2,6-pyridine dicarboxylic acid) and one oxygen atom from the aqueous in the basal plane; two oxygen atoms from the PDA in the axial position. The units of [Cu(NIT2Py)(PDA)(H₂O)] were connected as one dimension chain by the intermolecular hydrogen bonds. The complex exhibits intramolecular antiferromagnetic interactions between the Cu(II) ion and the NIT2Py.