Computation of limit periodic continued fractions. A survey

Over the last 20 years a large number of algorithms has been published to improve the speed and domain of convergence of continued fractions. In this survey we show that these algorithms are strongly related. Actually, they essentially boil down to two main principles.We also prove some results on asymptotic expansions of tail values of limit periodic continued fractions.Dedicated to Luigi Gatteschi on his seventieth birthdayThis research was partially supported by The Norwegian Research Council and by the HMC project ROLLS, under contract CHRX-CT93-0416.     

On the group extension of the transformation associated to non-archimedean continued fractions

Summary Let F_q be a finite field with q elements. We consider formal Laurent series of F_q -coefficients with their continued fraction expansions by F_q -polynomials. We prove some arithmetic properties for almost every formal Laurent series with respect to the Haar measure. We construct a group extension of the non-archimedean continued fraction transformation and show its ergodicity. Then we get some results as an application of the individual ergodic theorem. We also discuss the convergence rate for limit behaviors.     

Enantioselective separations by capillary GC on derivatized cyclodextrins. Part 2: Determination of enantiomeric excess of some racemic 2,3-isopropylidene-1,2,3-cyclohexanetriol derivatives on permethyl α-, β-, and γ-cyclodextrins

Capillary GC on permethyl α-, β-, and γ-cyclodextrins has been applied to separate and quantify the enantiomers of some 2,3-iso-propylidene-1,2,3-cyclohexanetriol derivatives. Quantitative CGC data are compared to those obtained with chiral shift ¹H NMR.     

用铜（Ⅱ）—L—精氨酸配体交换薄层色谱拆分氨基酸对映体

报道了一种新的配体交换薄层色谱拆分氨基酸对映体的方法。以醋酸铜－Ｌ－精氨酸的络合物为配体交换剂，用浸渍的方法吸附在硅胶薄层板上，制成配体交换薄层，用ＰＲＩＳＭＡ优化法选择出展开剂的最佳组成为：甲醇／乙腈／四氢呋喃／水＝８０：８．２：５．８：６，在此色谱条件下，十对氨基酸对映体得到良好的分离，Ｄ－和Ｌ－氨基酸的相对比移值在１．０９－２．４０之间。文中对配体交换薄层的制备方法，样品的分子结构及色谱行为     

Determination of the Enantiomeric Purity of l-Carnitine and Acetyl-l-Carnitine by Chiral Liquid Chromatography

A chiral liquid chromatographic method for determination of the enantiomeric purity of both l-carnitine and acetyl-l-carnitine is described. Separation of the enantiomers of dl-carnitine and acetyl-dl-carnitine was achieved on a commercial chiral column (Chiralcel OD-R) after derivatization with (alpha-bromo)methyl phenyl ketone. Introduction of this lipophilic UV chromophoric group to the carnitine and acetylcarnitine molecules improved their retention, resolution, and UV detection. The mobile phase was 74:26 (v/v) 0.5 mol L^-1 sodium perchlorate–acetonitrile, pH 3.8, and the flow rate was 0.4 mL min^-1. Detection was performed at 235 nm. The method is selective and reliable for determination of the enantiomeric purity of bulk drug substances l-carnitine and acetyl-l-carnitine.     

Biphenyl-tricarbonylchrom-komplexe, 9. Mitt.: Synthesen,chromatographische Enantiomerentrennung,Circulardichroismus und Chiralität von mono- und bis-(Tricarbonylchrom)-Komplexen di- und tetrasubstituierter sowie überbrückter Biphenyle

Chiral title compounds have been resolved by medium pressure liquid chromatography (MPLC) on triacetylcellulose in ethanol. Whereas a quantitative separation was achieved for16 and20, a recycling technique had to be applied to1,4,6,10 and15 leading to a 100% e.e. for1,6 and15 and to ca. 60% e.e. for4 and10.An unambiguous assignment of the chirality (+)-(R) _a -(S) _m for tricarbonylchromium-6,6-dimethyl-diphenicacid dimethylester (4) was deduced both from the photochemical decomplexation to (-)-5 with the known chirality (R) _a (whose e.e. was determined by MPLC on triacetylcellulose) and by comparison of the¹H-n.m.r. spectra of4 and5 thereby proving the structure 4 for the former.Other chiralities both for mono and bis(tricarbonylchromium)biphenyl complexes were established by chemical correlations and comparison of the CD spectra with those of key compounds.

Herrn Prof. Dr.H. Tuppy mit besten Wünschen zum 60. Geburtstag gewidmet.     

柴油烃族组成分布的GC-MS测定

应用GC－MS测定柴油烃族组成按沸点的分布，通过柱色 谱分离后的柴油饱和烃和芳烃组分分别进入气相色谱－质谱联用仪分析，采集其每一扫描的质谱图后，按ASTM－D2425方法计算其每一扫描的烃族组成，因为每一扫描与保留时间对应，所以可将两部分烃族组成加和后应用ASTM－D2887方法计算柴油烃族组成按沸点的分布规律；实验结果表明，该法与ASTM－D2887和ASTM－D2425的实验结果吻合，并能给出有关柴油烃族组成的详尽分布规律。     

Gel permeation chromatographic characterization of sodium hyaluronate and its fractions prepared by ultrasonic degradation

Summary High-molecular-weight sodium hyaluronate isolated from rooster combs was degraded by ultrasonication. The molecular weight of hyaluronate and its polydispersity was determined by gel-permeation chromatography. During 75-min treatment the molecular weight value decreased from 1.39×10⁶ Da to 2.25×10⁵ Da while the polydispersity of the molecular weight increased from 1.29 to 2.36. The reciprocal value of the square of the hyaluronate's molecular weight was linearly proportional to the time of ultrasonication.     

Size exclusion chromatographic characterization of sodium hyaluronate fractions prepared by high energetic sonication

Summary A high molecular weight sodium hyaluronate isolated from rooster combs was degraded by ultrasonication. High-performance size exclusion chromatography allowed rapid and accurate determination of molecular weight parameters (M_z, M_w, M_n) and distributions. The time dependence of hyaluronan ultrasonication to the molecular characteristics of the polymer was investigated. A non-random nature of the degradation process was demonstrated and the reciprocal M_n value was found to be linearly proportional to the time of ultrasonication.