Implementation and use of the method of prudent ascent in conformational analysis using molecular mechanics

In two-dimensional conformational analysis the current practice is to perform an energy minimization for all possible combinations of two dihedral angles in the molecule, in a fixed order, and apply a certain dihedral angle step-size. A newly developed method is presented in which the order of the evaluation points on the energy-surface is not fixed, but is dependent on all previous results in a way which we call “the method of prudent ascent.” In this method the most promising calculation is carried out first, thus minimizing the risk of atomic collisions. In order to be able to take care of the many additional degrees of conformational freedom present in, e.g., carbohydrate molecules, all minimizations are performed using a set of different promising starting conformations on the basis of previous calculations, and only the lowest energy result for each point is saved. An application of the method to conformational analysis of methyl-cellobiose and the artificial sweetener trichlorogalactosucrose is also presented.     

Immunoaffinity-based extraction of phenylurea herbicides using mixed antibodies against isoproturon and chlortoluron

Summary The analysis of several phenylurea herbicides in different waters is described using an immunoaffinity column clean-up and determination by high performance liquid chromatography. The pesticides were selectively retained on a solid phase extraction column containing antibodies to chlortoluron and to isoproturon immobilised onto silica. Selected phenylureas were eluted using a simple phosphate buffered saline/ethanol mixture at low pH. The immunoaffinity approach gave extracts free of interfering substances and allowed detection limits comparable to those required for pesticides in water in the European Community. The proposed method was successfully applied to the determination of chlortoluron, isoproturon, linuron and chlorbromuron in tap and river water. Presented at the 21^st ISC held in Stuttgart, Germany, 15^th–20^th September, 1996     

Thermal relaxation in poled non-linear optical sidechain polymers: Influence of annealing

The influence of different annealing treatments has been investigated on the stability of the Electro-Optic coefficient in a poled DANS (4-dimethylamino-4′-nitrostilbene) sidechain polymer, which was poled near its T_g-onset of 140°C. The annealing treatments and the EO relaxation experiments were performed at 120°C. The EO stability can be significantly increased both by an annealing treatment after poling and by annealing before poling. This latter effect is concluded from the reduction of the EO relaxation rates in successive relaxation cycles performed in the same polymer sample - completely depoled and repoled in between the cycles. The effect from the different annealing treatments on the time-dependence of the EO relaxation process is different and is analyzed in terms of a Debye-like model with a single, time-dependent Debye relaxation time r(t)=r_i+C. t³. The time-dependence of r and the observed effects from annealing are attributed to the parallel relaxation process of physical ageing.     

The derivatization of fatty acids by (chloro)alkyl chloroformates in non-aqueous and aqueous media for GC analysis

Fatty acids can be conveniently derivatized in less than one minute with (chloro)alkyl chloroformates such as methyl chloroformate, 2-chloroethyl chloroformate and 2,2,2-trichloroethyl chloroformate. 2,2,2-Trichloroethyl chloroformate is the most reactive reagent, and yields a reaction product which can be sensitively detected by GC ECD (detection limit 50 ng/ml, i.e. 25 pg/injection, for C⁸, C¹⁰, and C¹² acids). In non-aqueous media 3-picoline, N-methylpiperidine, and dimethylaminopyridine show catalytic activity comparable with that of pyridine and can, therefore, replace it. N-methylpiperidine is the best basic catalyst in aqueous media (i.e. media containing up to 40 % water).     

Inherent Ethyl Acetate Selectivity in a Trianglimine Molecular Solid

Ethyl acetate is an important chemical raw material and solvent. It is also a key volatile organic compound in the brewing industry and a marker for lung cancer. Materials that are highly selective toward ethyl acetate are needed for its separation and detection. Here, we report a trianglimine macrocycle ( TAMC ) that selectively adsorbs ethyl acetate by forming a solvate. Crystal structure prediction showed this to be the lowest energy solvate structure available. This solvate leaves a metastable, “templated” cavity after solvent removal. Adsorption and breakthrough experiments confirmed that TAMC has adequate adsorption kinetics to separate ethyl acetate from azeotropic mixtures with ethanol, which is a challenging and energy-intensive industrial separation.     

The completion of locally refined simplicial partitions created by bisection

Recently, in [Found. Comput. Math., 7(2) (2007), 245-269], we proved that an adaptive finite element method based on newest vertex bisection in two space dimensions for solving elliptic equations, which is essentially the method from [SINUM, 38 (2000), 466-488] by Morin, Nochetto, and Siebert, converges with the optimal rate.The number of triangles in the output partition of such a method is generally larger than the number of triangles that in all intermediate partitions have been marked for bisection, because additional bisections are needed to retain conforming meshes.A key ingredient to our proof was a result from [Numer. Math., 97(2004), 219-268] by Binev, Dahmen and DeVore saying that for some absolute constant , where is the number of triangles from the initial partition that have never been bisected. In this paper, we extend this result to bisection algorithms of -simplices, with that generalizing the result concerning optimality of the adaptive finite element method to general space dimensions.

     

Computation of differential operators in wavelet coordinates

In [Found. Comput. Math., 2 (2002), pp. 203-245], Cohen, Dahmen, and DeVore proposed an adaptive wavelet algorithm for solving general operator equations. Assuming that the operator defines a boundedly invertible mapping between a Hilbert space and its dual, and that a Riesz basis of wavelet type for this Hilbert space is available, the operator equation is transformed into an equivalent well-posed infinite matrix-vector system. This system is solved by an iterative method, where each application of the infinite stiffness matrix is replaced by an adaptive approximation. It was shown that if the errors of the best linear combinations from the wavelet basis with terms are for some , which is determined by the Besov regularity of the solution and the order of the wavelet basis, then approximations yielded by the adaptive method with terms also have errors of . Moreover, their computation takes only operations, provided , with being a measure of how well the infinite stiffness matrix with respect to the wavelet basis can be approximated by computable sparse matrices. Under appropriate conditions on the wavelet basis, for both differential and singular integral operators and for the relevant range of , in [SIAM J. Math. Anal., 35(5) (2004), pp. 1110-1132] we showed that , assuming that each entry of the stiffness matrix is exactly available at unit cost.

Generally these entries have to be approximated using numerical quadrature. In this paper, restricting ourselves to differential operators, we develop a numerical integration scheme that computes these entries giving an additional error that is consistent with the approximation error, whereas in each column the average computational cost per entry is . As a consequence, we can conclude that the adaptive wavelet algorithm has optimal computational complexity.

     

Optimality of a Standard Adaptive Finite Element Method

In this paper an adaptive finite element method is constructed for solving elliptic equations that has optimal computational complexity. Whenever, for some s > 0, the solution can be approximated within a tolerance ε > 0 in energy norm by a continuous piecewise linear function on some partition with O(ε^-1/s) triangles, and one knows how to approximate the right-hand side in the dual norm with the same rate with piecewise constants, then the adaptive method produces approximations that converge with this rate, taking a number of operations that is of the order of the number of triangles in the output partition. The method is similar in spirit to that from by Morin, Nochetto, and Siebert, and so in particular it does not rely on a recurrent coarsening of the partitions. Although the Poisson equation in two dimensions with piecewise linear approximation is considered, the results generalize in several respects.