Efficient stochastic FEM for flow in heterogeneous porous media. Part 1: random Gaussian conductivity coefficients

This paper is concerned with the development of efficient iterative methods for solving the linear system of equations arising from stochastic FEMs for single‐phase fluid flow in porous media. It is assumed that the conductivity coefficient varies randomly in space according to some given correlation function and is approximated using a truncated Karhunen–Loève expansion. Distinct discretizations of the deterministic and stochastic spaces are required for implementations of the stochastic FEM. In this paper, the deterministic space is discretized using classical finite elements and the stochastic space using a polynomial chaos expansion. The highly structured linear systems which result from this discretization mean that Krylov subspace iterative solvers are extremely effective. The performance of a range of preconditioned iterative methods is investigated and evaluated in terms of robustness with respect to mesh size and variability of the conductivity coefficient. An efficient symmetric block Gauss–Seidel preconditioner is proposed for problems in which the conductivity coefficient has a large standard deviation.The companion paper, herein, referred to as Part 2, considers the situation in which Gaussian random fields are transformed into lognormal ones by projecting the truncated Karhunen–Loève expansion onto a polynomial chaos basis. This results in a stochastic nonlinear problem because the random fields are represented using polynomial chaos containing terms that are generally nonlinear in the random variables. Copyright © 2013 John Wiley & Sons, Ltd.     

Conformational properties of propargyloxy-calix[4]arene tricarboxamides: NMR and DFT studies on the O-through-the-annulus rotation

The size limit of substituents allowing O-through-the-annulus rotation of substituted calix[4]arenes was further extended to the propargyloxy group in 24-propargyloxy-25,26,27-tris(N,N-dimethylcarbamoylmethoxy)-p-tert-butylcalix[4]arene by demonstrating its free but slow motion affording equilibrium between the partial cone and 1,2-alternate conformers. The effect of solvent and upper rim substituents R¹ on the conformational inversion was investigated by means of ¹H NMR. The rotational isomerisation of the parent (R¹ = H) analogue could not unambiguously be detected. The experimental results were supported by comprehensive density functional theory studies.     

Two optimal Dai–Liao conjugate gradient methods

Two adaptive choices for the parameter of Dai–Liao conjugate gradient (CG) method are suggested. One of which is obtained by minimizing the distance between search directions of Dai–Liao method and a three-term CG method proposed by Zhang et al. and the other one is obtained by minimizing Frobenius condition number of the search direction matrix. Global convergence analyses are made briefly. Numerical results are reported; they demonstrate effectiveness of the suggested adaptive choices.     

Octahedral Chiral‐at‐Metal Iridium Catalysts: Versatile Chiral Lewis Acids for Asymmetric Conjugate Additions

Octahedral iridium(III) complexes containing two bidentate cyclometalating 5‐tert‐butyl‐2‐phenylbenzoxazole ( IrO ) or 5‐tert‐butyl‐2‐phenylbenzothiazole ( IrS ) ligands in addition to two labile acetonitrile ligands are demonstrated to constitute a highly versatile class of asymmetric Lewis acid catalysts. These complexes feature the metal center as the exclusive source of chirality and serve as effective asymmetric catalysts (0.5–5.0 mol % catalyst loading) for a variety of reactions with α,β‐unsaturated carbonyl compounds, namely Friedel–Crafts alkylations (94–99 % ee), Michael additions with CH‐acidic compounds (81–97 % ee), and a variety of cycloadditions (92–99 % ee with high d.r.). Mechanistic investigations and crystal structures of an iridium‐coordinated substrates and iridium‐coordinated products are consistent with a mechanistic picture in which the α,β‐unsaturated carbonyl compounds are activated by two‐point binding (bidentate coordination) to the chiral Lewis acid.     

一类变号(k,n-k)共轭边值问题正解的存在性

通过构造一个特殊的锥,利用范数形式的锥拉伸锥压缩不动点定理,在允许非线性项变号无下界且没有任何单调性假设的条件下,得出了一类高阶(k,n-k)共轭两点边值问题方程组正解的存在性结论.     

Contingent derivatives and regularization for noncoercive inverse problems

Abstract

We study the inverse problem of parameter identification in noncoercive variational problems that commonly appear in applied models. We examine the differentiability of the set-valued parameter-to-solution map using the first-order and the second-order contingent derivatives. We explore the inverse problem using the output least-squares and the modified output least-squares objectives. By regularizing the noncoercive variational problem, we obtain a single-valued regularized parameter-to-solution map and investigate its smoothness and boundedness. We also consider optimization problems using the output least-squares and the modified output least-squares objectives for the regularized variational problem. We give a complete convergence analysis showing that for the output least-squares and the modified output least-squares, the regularized minimization problems approximate the original optimization problems suitably. We also provide the first-order and the second-order adjoint method for the computation of the first-order and the second-order derivatives of the output least-squares objective. We provide discrete formulas for the gradient and the Hessian calculation and present numerical results.     

Isatindolignanoside A,a glucosidic indole-lignan conjugate from an aqueous extract of the Isatis indigotica roots

A glucosidic indole-lignan conjugate with a novel carbon skeleton, named isatindolignanoside A (1), was isolated from an aqueous extract of the Isatis indigotica roots “ban lan gen”. Its structure was determined by comprehensive analysis of spectroscopic data, enzyme hydrolysis, and electronic CD calculations. Compound 1 is active against Coxsackie virus B3 and represents the first example of natural product having a structural feature of conjugation between indole and lignan, and its plausible biosynthetic pathway is postulated.