On-line arbitrarily vertex decomposable trees

A tree T is arbitrarily vertex decomposable if for any sequence τ of positive integers adding up to the order of T there is a sequence of vertex-disjoint subtrees of T whose orders are given by τ. An on-line version of the problem of characterizing arbitrarily vertex decomposable trees is completely solved here.     

Orthonormal polynomial bases in function spaces

We construct polynomial orthonormal bases in various function spaces. Our bases have linear order of growth of degrees of polynomials. We show that this order is optimal.     

On the Neighbour-Distinguishing Index of a Graph

A proper edge colouring of a graph G is neighbour-distinguishing provided that it distinguishes adjacent vertices by sets of colours of their incident edges. It is proved that for any planar bipartite graph G with Δ(G)≥12 there is a neighbour-distinguishing edge colouring of G using at most Δ(G)+1 colours. Colourings distinguishing pairs of vertices that satisfy other requirements are also considered.     

氙灯泵浦新型晶体Nd∶S－VAP调Q激光器腔内倍频研究

采用氙灯泵浦晶体Ｎｄ∶Ｓ－ＶＡＰ，ＫＴＰ晶体腔内倍频，实现了Ｎｄ∶Ｓ－ＶＡＰ晶体０．５３２５μｍ绿光激光ＢＤＮ染料片调Ｑ运转。测量了输出绿光激光的特性及不同腔长和染料片小信号透过率情况下的输出能量及脉冲宽度，给出了染料片调Ｑ腔内倍频的耦合波方程组，数值求解方程组，所得的理论数据与实验结果很好地相符     

SYNTHESIS AND CATALYTIC PROPERTY OF POLYSTYRENE SUPPORTED GLUTAMIC ACID SCHIFF BASE COMPLEX OF Mn（ Ⅱ ） IN AEROBIC OXIDATION OF CYCLOHEXENE

The polystyrene supported glutamic acid Schiff base complex of Mn （ Ⅱ ） （PS-Sal-Glue-Mn） was prepared with chloromethylated styrene polymer beads, 2,4-dihydroxybenzaldehyde, L-glutamic acid and manganese （ Ⅱ ） acetate tetrahyrate. The polymeric ligand and the complex were characterized by FT-IR, small area X-ray photoelectron spectroscopy （XPS） and 1CP-AES. In the presence of the manganese complex, cyclohexene （1） was effectively oxidized by molecular oxygen without reductant. The major products of the reaction were 2-cyclohexen-l-ol （2）, 2-cyclohexen-l-one （3） and 2-cyclohexen-1- hydroperoxide （4）, which was different with typical oxidation of cyclohexene. The influence of reaction temperature and additive for oxidation had been studied. The selectivity of 2-cyclohexen-1-hydroperoxide varied with reaction time and different additives. The mechanism of cyclohexene oxidation had also been discussed.     

一类2(1H)-喹喔啉衍生物的电子轰击质谱分析

以邻苯二胺为原料合成表征了一类喹喔啉衍生物；1-烷基-3-甲基-2（1H）-喹喔啉-2-酮（1-alkyl-3-methly-2(1H)-quinoxalin-2-one，简称AMQ，其中alky=H、CH3、Et、n-C3H5、n-C5H11、n-C16H33)。用电子轰击电离质谱（EI-MS）和核磁共振谱图（^1H-NMR)鉴定了AMQ，研究了不同取代基对这类化合物EI-MS谱图的影响，分析得到一些裂解规律。结果表明：所有样品谱图中均有芳香化合物的特征CnHn^ 系列峰m/z78，65，52，39和（或）m/z77、76、64、63、51、50、38、37。对于末取代的样品及低级烷烃取代的样品，谱图中的基峰为分子离子峰，对于取代基中碳数大于等于3的样品。谱图中的基峰不是分子离子峰，分子离子峰强度随着碳数的增加而降低。这些样品一般容易发生骨架重排，丢失一分子CO，生成1-烷基-2-甲基苯并哒唑正离子。此外，还讨论了谱图中其它的一些碎片离子峰。这对于研究和指导喹喔啉衍生物 的合成，探讨它们在药效及结构特征与生理活性的关系等方面具有重要的应用价值和理论意义。     

Is Gauss quadrature optimal for analytic functions?

Summary We consider the problem of optimal quadratures for integrandsf: [–1,1] which have an analytic extension to an open diskD _r of radiusr about the origin such that 1 on . Ifr=1, we show that the penalty for sampling the integrand at zeros of the Legendre polynomial of degreen rather than at optimal points, tends to infinity withn. In particular there is an infinite penalty for using Gauss quadrature. On the other hand, ifr>1, Gauss quadrature is almost optimal. These results hold for both the worst-case and asymptotic settings.This research was supported in part by the National Science Foundation under Grants MCS-8203271 and MCS-8303111This research was supported in part by the National Science Foundation under Grant MCS-8923676     

Formation of (E) 1-alkoxy-1,3-butadienes from corresponding propargyl ethers; vicarious nucleophilic substitution in alkoxyallenes

Propargyl ethers treated with dimsyl anion in DMSO at 80-100°C undergo terminal methylenation to afford corresponding (E) 1-alkoxy-1,3-butadienes. The reaction proceeds via an alkoxy-allene.     

H-bonding dependent structures of (NH4+)3H+(SO4 2-)2. Mechanisms of phase transitions

The role of different H-bonds in phases II, III, IV, and V of triammonium hydrogen disulfate, (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2), has been studied by X-ray diffraction and (1)H solid-state MAS NMR. The proper space group for phase II is C2/c, for phases III and IV is P2/n, and for phase V is P onemacr;. The structures of phases III and IV seem to be the same. The hydrogen atom participating in the O(-)-H(+).O(-) H-bond in phase II of (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2) at room temperature is split at two positions around the center of the crucial O(-)-H(+).O(-) H-bonding, joining two SO(4)(2)(-) tetrahedra. With decreasing temperature, it becomes localized at one of the oxygen atoms. Further cooling causes additional differentiation of possibly equivalent sulfate dimers. The NH(4)(+) ions participate mainly in bifurcated H-bonds with two oxygen atoms from sulfate anions. On cooling, the major contribution of the bifurcated H-bond becomes stronger, whereas the minor one becomes weaker. This is coupled with rotation of sulfate ions. In all the phases of (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2), some additional, weak but significant, reflections are observed. They are located between the layers of the reciprocal lattice, suggesting possible modulation of the host (NH(4)(+))(3)H(+)(SO(4)(2)(-))(2) structure(s). According to (1)H MAS NMR obtained for phases II and III, the nature of the acidic proton disorder is dynamic, and localization of the proton takes place in a broader range of temperatures, as can be expected from the X-ray diffraction data.