On the Bavrin Integro-Differential Operators and Their Applications to Solution of Functional Equations

We construct a multiplicative group structure in the class of integro-differential operators specific for a polydisk which was introduced by I. I. Bavrin. We indicate two applications of these operators to solution of functional equations.     

On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation

A multidimensional version of the first Darboux problem is considered for a model second-order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.     

Quantitative evaluation of two-dimensional dynamic deformations using digital holography

An optical system for the parallel evaluation of in- and out-of-plane dynamical deformations will be described. A double pulse laser with pulse separation in the microsecond range is used for the investigations. Two separate interferograms of an object under test, in its undeformed and deformed state, are recorded in a few microseconds. The object is illuminated from two different directions and imaged onto a CCD sensor. This produces two sensitivity vectors. The reference beams have different directions in order to produce two directional spatial carriers. The Fourier method is used for quantitative evaluation, and the measurements along different sensitivity vectors are separated in the Fourier domain. The phases of the two interferograms are obtained from the complex amplitudes and the two dimensional deformation is calculated from the phases. Experimental results are presented.     

一类多元Gauss-Weierstrass 算子线性组合的加权Lp-逼近

本文研究一类多元Gauss-Weierstrass算子的线性组合加Jacobi型权逼近的性质,利用加权矩量不等式及加权K-泛函、光滑模等工具,建立了这类算子在Lp(1≤p≤∞)空间的正、逆定理和逼近阶的特征刻划.     

Identifying potential binding modes and explaining partitioning behavior using flexible alignments and multidimensional scaling

A method is described for the rapid and automatic analysis of flexible molecular alignments using multidimensional scaling and a normalized scoring scheme. A projection scheme was devised to separate orientational and conformational effects. It is shown that the approach can be utilized for the identification of common binding orientations or to the study of differences in partioning behavior. It is suggested that the method can be employed as a novel approach exploring molecular similarity as a dynamic property, so that it includes aspects of motion (by way of mutual orientations), conformations and molecular properties.     

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.     

多柱色谱技术进展

在色谱分析过程中，利用串联、并联或串并联结合的方式将多根色谱柱组合起来，可以实现高通量和高分辨的分离效果。相比于传统单柱色谱技术，多柱技术很好地满足了批量样品分析和复杂生物样品分离分析的需求，因此引起了广泛关注。该文对多柱技术在多维分离、芯片色谱、毛细管电泳、固定相筛选以及串联色谱等领域的应用进行了综述，并对其发展前景进行了展望。     

Optimal error estimates of a locally one-dimensional method for the multidimensional heat equation

For the multidimensional heat equation in a parallelepiped, optimal error estimates inL ₂(Q) are derived. The error is of the order of +¦h¦² for any right-hand sidef L ₂(Q) and any initial function ; for appropriate classes of less regularf andu ₀, the error is of the order of ((+¦h¦² ), 1/2<1.Translated fromMatematicheskie Zametki, Vol. 60, No. 2, pp. 185–197, August, 1996.     

On-line multidimensional chromatography using packed capillary liquid chromatography and capillary gas chromatography

The introduction of selected fractions from a liquid chromatograph into a gas chromatograph has been described; however, analyses were performed by off-line experiments requiring collection and reinjection of the separate fractions or by on-line procedures where disadvantageously, only a fraction of the separated peak or a well resolved component in a mixture could be introduced into a gas chromatograph. This disadvantage is overcome by the apparatus and method described in this paper, which utilizes a multidimensional chromatography system employing a high efficiency, packed capillary LC column coupled on-line to a capillary gas chromatograph. The liquid chromatograph (so designed) can act as a highly efficient clean-up or chemical class fractionation step prior to introduction into the gas chromatograph, significantly reducing sample preparation times in many applications. Thus minor components in a complex matrix can be determined without prior sample clean-up, an example of which is the determination of polychlorinated biphenyls in a complex hydrocarbon matrix.     

Advances of Chromatography in Analysis of Complex Samples

The separation and identification of complex samples is an urgent task that analytical chemistry has to face. Chromatography, as an important analysis technique, has been widely applied to many fields, such as life science, environment, medicine, food and petrochemical engineering.Recently, with the progress of science and tech-