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.     

An observation of electron phase transition in SmB6 at low temperatures

In order to reveal the nature of the ground state of archetypal intermediate-valence compound SmB₆, a comprehensive study of its transport and magnetic properties was carried out on high-quality single crystals at temperatures of 1.8-300 K in magnetic fields up to 7 T. A drastic enhancement of negative magnetoresistance was observed below 14 K, with the maximum absolute value of Δρ/ρB²∼2.2×10⁻³ T⁻² at T≈5.2 K. This effect seems to be attributable to anomalous magnetic scattering of many-body (exciton-polaronic) complexes induced by fast valence fluctuations on Sm sites. The observed anomalies of magnetotransport, thermoelectric and magnetic characteristics are discussed in terms of electron phase transition to the coherent state of interacting many-body complexes occurring at T^*∼5 K.     

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.     

2-硝基丙烯热解反应的理论研究

利用MO-AM1方法研究了2-硝基丙烯热解的反应途径。结果表明, 2-硝基丙烯可能首先热解产生一个四元环状中间体。该中间体依照分步过程继续分解时, 存在两种可能的途径, 其中先断N—O键的反应过程比先断C—C键的过程从能量上更为有利。反应过程中电荷无明显转移, 具有双自由基反应特点。     

7种中位—四取代苯基卟啉化合物的合成

卟啉是一类结构与生命物质(如血红素和维生素B_(12))相似的化合物,近年来曾被用于人体肿瘤的光动力学治疗;此外,在电化学、光物理学和光化学、放射医学、微量元素测定、纺织品漂洗等领域中的应用也相当广泛,已受到科技工作者的普遍关注和重视。本文按Rothemond法将相应的取代苯甲醛与新蒸吡咯在丙酸中缩合,制得具有酸性、中性和碱     

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.     

Characterizations of generalized Hermite and sieved ultraspherical polynomials

A new characterization of the generalized Hermite polyno-
mials and of the orthogonal polynomials with respect to the measure
is derived which is based on a ``reversing property" of the coefficients in the corresponding recurrence formulas and does not use the representation in terms of Laguerre and Jacobi polynomials. A similar characterization can be obtained for a generalization of the sieved ultraspherical polynomials of the first and second kind. These results are applied in order to determine the asymptotic limit distribution for the zeros when the degree and the parameters tend to infinity with the same order.