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.     

A Characterization of Graphs without Even Factors

In this paper, we first reduce the problem of finding a minimum parity (g,f)-factor of a graph G into the problem of finding a minimum perfect matching in a weighted simple graph G*. Using the structure of G*, a necessary and sufficient condition for the existence of an even factor is derived. This paper was accomplished while the second author was visiting the Center for Combinatorics, Nankai University. The research is supported by NSFC     

因子分析在企业竞争力评价中的应用

根据因子分析原理,建立了企业竞争力的规模因子、效益因子和成长因子得分模型。通过现实竞争力和潜在竞争力分析,实现了企业竞争力和可持续发展的评价。     

On the Statistics of Partial Quotients of Finite Continued Fractions

We refine the remainder estimate in the asymptotic formula, earlier obtained in a joint paper with V. A. Bykovskii, for Arnold's problem about Gauss-Kuzmin statistics.     

具有平整表面的定向纳米碳管膜的制备

为了获得表面平整的定向纳米碳管，通过化学及物理的方法将纳米碳管膜进行反转，使其原来的AAO模板底面成为新的表面，用溶液逐步去除表面的铝和氧化铝后，获得了平整的定向纳米碳管膜表面，从而可将其作为工作面使用. 还比较了5％NaOH和6%H₃PO₄＋1.8%H₂CrO₄溶液去除氧化铝的效果.     

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.     

Two-point Padé approximants for formal Stieltjes series

We prove that certain two-point Padé approximants occupying the diagonal of the Padé table form monotone sequences of lower and upper bounds uniformly converging to a Stieltjes function. The results can be applied to the theory of inhomogeneous media for the calculation of the bounds on the effective transport coefficients of heterogeneous materials.