Densest packings of eleven congruent circles in a circle

In 1969 Pirl provided the densest packings ofn equal circles in a circle forn 10. We will prove the optimality for the packings that were conjectured forn=11. The proof is based on elementary combinatorial and analytical techniques.     

Shock fluctuations in the asymmetric simple exclusion process

Summary We consider the one dimensional nearest neighbors asymmetric simple exclusion process with ratesq andp for left and right jumps respectively;q<p. Ferrari et al. (1991) have shown that if the initial measure isv _, , a product measure with densities and to the left and right of the origin respectively, <, then there exists a (microscopic) shock for the system. A shock is a random positionX _t such that the system as seen from this position at timet has asymptotic product distributions with densities and to the left and right of the origin respectively, uniformly int. We compute the diffusion coefficient of the shockD=lim _t t ^–1(E(X _t )²–(EX _t )²) and findD=(p–q)(–)^–1((1–)+(1–)) as conjectured by Spohn (1991). We show that in the scale the position ofX _t is determined by the initial distribution of particles in a region of length proportional tot. We prove that the distribution of the process at the average position of the shock converges to a fair mixture of the product measures with densities and . This is the so called dynamical phase transition. Under shock initial conditions we show how the density fluctuation fields depend on the initial configuration.     

Zero cycles on conic fibrations and a conjecture of Bloch

Let X be a smooth projective surface over a number field k. Let (CH₀(X)) denote the Chow group of zero-cyles modulo rational equivalence on X. Let CH₀(X) be the subgroup of CH ₀(X) consisting of classes which vanish when going over to an arbitrary completion of k. Bloch put forward a conjecture asserting that this group is isomorphic to the Tate-Shafarevich group of a certain Galois module atttached to X. In this paper, we disprove this general conjecture. We produce a conic bundle X over an elliptic curve, for which the group (CH₀(X) is not zero, but the Galois-theoretic Tate-Shafarevich group vanishes.     

海芋凝集素的理化性质鉴定

采用葡聚糖凝胶１００（ＳｅｐｈａｄｅｘＧ－１００）从天南星科植物海芋（Ａｌｏｃａｓｉａｏｄｏｒａ（Ｒｏｘｂ）Ｃ．Ｋｏｃｈ）中分离出了一种凝集素（简称ＡＯＬ）．ＡＯＬ对兔血有较强的凝集效果,而对各类型人血的凝集活力较弱,在３种糖蛋白中,猪甲状腺球蛋白对ＡＯＬ的凝血活力抑制最强;ＡＯＬ对培养人外周血白细胞的转化率高达７９％,超过对照ＰＨＡ的转化率;用ＳｅｐｈａｄｅｘＧ－２００柱测得ＡＯＬ的相对分子质量为３１５００;用癌细胞体外培养的方法证明了ＡＯＬ对肺腺癌细胞株Ｐ１８具有较强的直接杀伤能力．此外还发现ＡＯＬ对温度（８０℃以下）、变性剂（盐酸胍和脲）有较高的稳定性,在ｐＨ６～１０的范围内相当稳定．     

Photoconductivity of fullerene derivatives

Two fullerene derivatives (compounds 1 and 2) have been synthesized. Their redox properties have been measured by cyclic voltammetry. The photoconductivities of poly(N_vinylcarbazo_le) (PVK) doped with fullerene and with their derivatives have been studied to explore the possible relationship between the reductibility of fullerenes and the photoconductivity of fullerenes_doped PVK. The charge generation efficiencies of PVK doped with fullerene and with its derivatives have changed remarkably: the diversity of charge generation efficiency is obvious in different doping systems. The result indicates that there is charge transfer between fullerenes and PVK.     

THE TYPE OF A CLASS OF VILENKIN CONVOLUTION OPERATORS

在满足第二个数公理的零紧Ａｂｅｌ群Ｇ的空间Ｌ（Ｇ）中研究了一类Ｖｉｌｅｎｋｉｎ卷积算子的性质．该类算子包括Ｖｉｌｅｎｋｉｎ－Ｆｏｕｒｉｅｒ级数的部份和、Ｆｅｊｅｒ平均等作为特例．文中证明了这类算子是弱（１,１）型和强（ｑ,ｑ）型的,１＜ｑ＜∞．     

电动势负反馈直流调速系统研究

在分析了电压负反馈直流调速系统的优缺点基础上,本文提出了电动势负反馈调速方法,并给出了该方法的系统图、框图和静特性。对电动势负反馈双直流电动机调速系统也进行了探讨。文中还对电动势负反馈直流调速系统的优缺点和应用范围加以了分析。     

C^＊—代数中的正逼近

讨论了Ｃ＊－代数中的正元逼近问题,研究了逼近度的一系列性质;应用Ｃ＊－代数的万有表示和Ｈａｌｍｏｓ关于正算子逼近的结果,证明了Ｃ＊－代数中的任一元都存在最佳正逼近并且给出了最佳正逼近的表达式。     

Theq-harmonic oscillator and the Al-Salam and Carlitz polynomials

One more model of aq-harmonic oscillator based on theq-orthogonal polynomials of Al-Salam and Carlitz is discussed. The explicit form ofq-creation andq-annihilation operators,q-coherent states and an analog of the Fourier transformation are established. A connection of the kernel of this transform with a family of self-dual biorthogonal rational functions is observed.     

土壤中碳酸钙和有机碳测定的一种新方法

利用阿曼苏丹国的一千多个土壤样品,对土壤中碳酸钙和有机碳测定的实验方法进行了研究。发现实际碳酸钙的含量可由“亚稳态”时碳酸钙含量乘以适当的因子代替,从而大大提高了工作效率。而利用有机碳/全氮(C/N)的特殊规律,则可建立一个确定“有机碳”实验中所需土壤样品量的新方法。