Generalized Brownian motion and elasticity

We introduce a family of stochastic processes which are a natural extension of Brownian motion to a tensor form. This allows us to solve a Dirichlet problem of linear elasticity obeying Lamé's equation, [1–(d– 1)]²V(x)+ [·V(x)]=0.     

Pressurized hot water extraction of berberine, baicalein and glycyrrhizin in medicinal plants

Pressurized hot water extraction (PHWE) using a laboratory made system was applied for the extraction of thermally labile and reasonably polar components such as berberine in coptidis rhizoma, glycyrrhizin in radix glycyrrhizae/liquorice and baicalein in scutellariae radix. PHWE was carried out dynamically at a flow of 1 ml/min, temperature between 95 and 140 °C, an applied pressure of 10-20 bar and extraction time of 40 min. Extraction by PHWE was found to give efficiencies comparable to Soxhlet extraction for baicalein in scutellariae radix and sonication for berberine in coptidis rhizoma, and glycyrrhizin in radix glycyrrhizae. Effects of ethanol added into the water used in PHWE were explored. Pressurized liquid extraction (PLE) with methanol as solvent was used for extraction of baicalein in scutellariae radix. The marker compounds present in the various medicinal plant extracts were determined by gradient elution HPLC.     

Polymer-coated hollow-fiber microextraction of estrogens in water samples with analysis by gas chromatography-mass spectrometry

A novel sorbent, dihydroxylated polymethylmethacrylate (DHPMM), coated on hollow-fiber membrane, is used for the polymer-coated hollow-fiber microextraction of trace amounts of natural and synthetic estrogens, such as diethylstilbestrol, estrone, 17beta-estradiol and 17alpha-ethynylestradiol, in aqueous samples. In this procedure, estrogens were extracted using the functionalized polar DHPMM polymer with derivatization using N-methyl-N-(trimethylsilyl)trifluoroacetamide followed by gas chromatography-mass spectrometric analysis. The detection limits for estrogens in aqueous sample were between 0.03 and 0.8 ng l(-1) and the calibration curves were linear over the concentration range 0.05-10 microgl(-1) and had correlation coefficients of >0.994. The relative standard deviations (RSDs) were <15% (n = 3). This simple, accurate, sensitive and selective analytical method is applicable to the determination of trace amounts of estrogens in reservoir and potable water samples.     

Filter Diagonalization with Finite Fourier Transform Eigenfunctions

Below, we briefly report on the progress in the development of the Filter Diagonalization technique when filtering is carried out with the aid of Finite Fourier Transform (FFT) eigenfunctions. During recent years interest in these functions, also known as ‘prolates’, or ‘slepians’, has increased among scientists doing research in the field of signal processing. The main explanation to this follows from the set of very special extremal and orthogonality properties exibited by the FFT eigenfunctions. Recent results of Walter and Shen on sampling with prolate spheroidal functions will necessary produce a new wave of interest. In the presented, Filter diagonalization machinery, we show that the sampling formula of Walter and Shen simplifies essentially the computation of matrix elements as certain 2D–integrals involving FFT eigenfunctions.     

Sixth algebraic order trigonometrically fitted predictor–corrector methods for the numerical solution of the radial Schrödinger equation

Our new trigonometrically fitted predictor–corrector (P–C) schemes presented here are based on the well known Adams–Bashforth–Moulton methods: the predictor is based on the fifth order Adams–Bashforth scheme and the corrector on the sixth order Adams–Moulton scheme. We tested the efficiency of our newly developed schemes against well known methods, with excellent results. The numerical experiments showed that at least one of our schemes is noticeably more efficient compared to other methods, some of which are specially designed for this type of problem. It is also worth mentioning that this is the first time that sixth algebraic order trigonometrically fitted Adams–Bashforth–Moulton P–C schemes are used to efficiently solve the radial Schrödinger equation.Active Member of the European Academy of Sciences and Arts     

Green Chemistry and Modern Technology

The basic principles, approaches, and early achievements of green chemistry are considered. The definition of green chemistry as a branch of chemistry that studies the laws of passing of chemical reactions and the properties of substances participating in such reactions, with the aim of acquiring basic knowledge that provides a basis for designing chemical technologies that eliminate (sharply curtail) the use and production of materials that pose a risk to the environment.     

Cyclizations via Palladium-Catalyzed Allylic Alkylations [New Synthetic Methods (79)]

The history of ring systems in organic chemistry parallels their synthetic accessibility. Transition-metal-catalyzed cyclizations offer a new opportunity to create carbo- and heterocyclic compounds with great facility. Among these methods, allylic alkylations catalyzed by palladium have proven unusually productive because of the extraordinary chemo-, regio-, and diastereoselectivity and the continuing possibility for the development of enantioselectivity. The rules for ring closure differ from those for non-transition-metal-catalyzed reactions. A major benefit is the ability to generate medium (eight-, nine-, ten-, and eleven-membered) and large rings in preference to normal (five-, six- and seven-membered) rings. With the appropriate substrate, efficient macrocyclizations are possible under conditions of normal concentrations. A second major benefit derives from the complementary stereochemistry of the metalcatalyzed substitution (net retention of configuration) compared to non-metal-catalyzed reactions (inversion of configuration). Further, the requirement for the substrate to conform to the transition-metal template may impose a stereochemical preference in the intermediate that ultimately translates into the thermodynamically less stable organic product regardless of the stereochemistry of the starting material. While more work has focused on carbocyclic synthesis, the possibilities for heterocyclic synthesis are just beginning to be tapped. In addition to forming heterocycles by C? C bond formation, use of a heteroatom as a nucleophile has already proven effective for oxygen and nitrogen, with other nucleophiles awaiting investigation. New dimensions for cyclization via allylic alkylation arise by generating the requisite π-allylpalladium intermediates by methods other than palladium(0)-initiated allylic ionizations. In addition, metals other than palladium will clearly expand the possibilities, but as yet remain untapped.     

化学专业生物化学课程教学内容和教学方法研究

本文是笔者在长期教学实践的基础上，对于化学专业生物化学课程教学内容和教学方法，研究的经济总结。其相关成果曾获陕西师范大学优秀教材一等奖及陕西省教学成果二等奖。     

Adaptive approach for nonlinear sensitivity analysis of reaction kinetics

We present a unified approach for linear and nonlinear sensitivity analysis for models of reaction kinetics that are stated in terms of systems of ordinary differential equations (ODEs). The approach is based on the reformulation of the ODE problem as a density transport problem described by a Fokker-Planck equation. The resulting multidimensional partial differential equation is herein solved by extending the TRAIL algorithm originally introduced by Horenko and Weiser in the context of molecular dynamics (J. Comp. Chem. 2003, 24, 1921) and discussed it in comparison with Monte Carlo techniques. The extended TRAIL approach is fully adaptive and easily allows to study the influence of nonlinear dynamical effects. We illustrate the scheme in application to an enzyme-substrate model problem for sensitivity analysis w.r.t. to initial concentrations and parameter values.