Photocyclisierung von 1-[3-(Chloracetylamino)propyl]-3-methylindol. 12. Mitteilung über synthetische Indol-Verbindungen

Photochemical cyclization of 1-[3-(chloroacetylamino)propyl]-3-methyl-indole . Photochemical cyclization of 1-[3-(chloroacetylamino)propyl]-3-methyl-indole involving loss of HCl leads to the three isomers 2, 3 and 4 , the structures of which have been determined by physical and chemical methods.     

An Investigation of the Tea Aroma. Part I. New volatile black tea constituents

A total of 68 constitutents, mainly aldehydes, ketones and esters, have been identified for the first time in a black tea aroma concentrate using coupled gas-chromatography/mass spectrometry.     

Determination of the Relative Configurations in the Side Chains of the Antibiotics Hedamycin and Pluramycin A; Synthesis and NMR. Data of Suitable Model Compounds

Several diepoxyhexanoates and epoxyhexenoates were prepared by epoxidation of methyl 2-methyl-2,4-hexadienoate or by Darzens condensation. Their ¹ H- and ¹³C-NMR. spectra were measured and assigned. Comparison of these data with the spectra of the antibiotics hedamycin ( 1 ) and pluramycin A ( 2 ) allowed the determi-nation of the relative configurations in the side chains of these antibiotics. They were found to be (14R*,16S*,17R*,18S*) for hedamycin ( 1 ) and (14R*,16S*,17Z) for pluramycin A ( 2 ).     

双波长光学低相干干涉术用于血氧饱和度测量的数值分析

提出了采用双波长光学低相干干涉仪（Optical low coherence interferometer，OCI）来测量人体视网膜血管中血氧饱和度（Oxygen Saturation，SO2）的方法．详细阐述了双波长光学低相干干涉术用于血氧饱和度测量的基本原理，并分析了OCI中双波长的选择原则．基于内径为200μm的毛细玻璃管的简易人眼视网膜血管模型，分别模拟了光源中心波长为680nm和820nm时血液血氧饱和度由40％提高到60％时对应干涉信号的变化．数值分析表明，要判别20％的血氧饱和度变化，0CI系统灵敏度至少要达到70dB．     

Mobile and immobile fluid transport: Coupling framework

We introduce a solver method for mobile and immobile transport regions. The motivation is driven by transport processes in porous media (e.g. waste disposal, chemical deposition processes). We analyze the coupled transport‐reaction equation with mobile and immobile areas. We apply analytical methods, such as Laplace‐transformation, and for the numerical methods we apply Godunov's scheme, see (Mat. Sb. 1959; 47 :271–306; Finite Volume Methods for Hyperbolic Problems. Cambridge University Press: Cambridge, 2002). The method is based numerically on flux‐based characteristic methods and is an attractive alternative to the classical higher‐order TVD methods, see (J. Comput. Phys. 1993; 49 :357–393). In this paper, we will focus on the derivation of analytical solutions for general and special solutions of the characteristic methods that are embedded in a finite‐volume method. At the end of the paper, we illustrate the higher‐order method for different benchmark problems. Copyright © 2010 John Wiley & Sons, Ltd.     

Consistency of iterative operator‐splitting methods: Theory and applications

In this article, we describe a different operator‐splitting method for decoupling complex equations with multidimensional and multiphysical processes for applications for porous media and phase‐transitions. We introduce different operator‐splitting methods with respect to their usability and applicability in computer codes. The error‐analysis for the iterative operator‐splitting methods is discussed. Numerical examples are presented. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

John Napiers Trigonometrie – ein Blick zurück

Zusammenfassung  Dieser Artikel gibt einen überblick über Napiers Beitr?ge zur sph?rischen Trigonometrie, wobei die dafür notwendigen sachlichen und historischen Grundlagen weitgehend bereitgestellt werden. Da diese Beitr?ge in der Literatur trotz ihrer erheblichen Bedeutung ganz im Schatten von Napiers Logarithmen stehen, erscheint eine solche Zusammenschau gerechtfertigt. Auch kommen einige neue oder kaum bekannte Einzelheiten zur Sprache. Mathematics subject classification (2000)  01A45 · 51-03     

Iterative operator-splitting methods with higher-order time integration methods and applications for parabolic partial differential equations

In this paper we design higher-order time integrators for systems of stiff ordinary differential equations. We combine implicit Runge–Kutta and BDF methods with iterative operator-splitting methods to obtain higher-order methods. The idea of decoupling each complicated operator in simpler operators with an adapted time scale allows to solve the problems more efficiently. We compare our new methods with the higher-order fractional-stepping Runge–Kutta methods, developed for stiff ordinary differential equations. The benefit is the individual handling of each operator with adapted standard higher-order time integrators. The methods are applied to equations for convection–diffusion reactions and we obtain higher-order results. Finally we discuss the applications of the iterative operator-splitting methods to multi-dimensional and multi-physical problems.