Co-cliques and star complements in extremal strongly regular graphs

Suppose that the positive integer μ is the eigenvalue of largest multiplicity in an extremal strongly regular graph G. By interlacing, the independence number of G is at most 4μ² + 4μ − 2. Star complements are used to show that if this bound is attained then either (a) μ = 1 and G is the Schläfli graph or (b) μ = 2 and G is the McLaughlin graph.     

Higher order bad loci

Zero-schemes on smooth complex projective varieties, forcing all elements of ample and free linear systems to be reducible, are studied. Relationships among the minimal length of such zero-schemes, the positivity of the line bundle associated with the linear system, and the dimension of the variety are established. Bad linear spaces are also investigated.     

Inherited LU-factorizations of matrices

Various types of LU-factorizations for nonsingular matrices, where L is a lower triangular matrix and U is an upper triangular matrix, are defined and characterized. These types of LU-factorizations are extended to the general m × n case. The more general conditions are considered in the light of the structures of [C.R. Johnson, D.D. Olesky, P. Van den Driessche, Inherited matrix entries: LU factorizations, SIAM J. Matrix Anal. Appl. 10 (1989) 99-104]. Applications to graphs and adjacency matrices are investigated. Conditions for the product of a lower and an upper triangular matrix to be the zero matrix are also obtained.     

SOLUTIONS OF THE EQUATION x^m＋y^m=z^m IN SL2z

This paper solves an open problem of Vaserstein. The main result is: the equation x^m y^m=z^m has a solution in SL2z if and only if m is not divisible by 4 or 6 and m is not congruent to 3 modulo 6.     

Hybrid organosilazane/organosilylamine telechelic oligomers—I. Two-dimensional NMR spectroscopy characterization of dimethylsilylethylenediamine oligomers

The detailed characterization of multifunctional hybrid organosilazane/organosilylamine telechelic oligomers by IR and ¹H, ¹³C and ²⁹Si NMR spectroscopy in one and two dimenions has been undertaken. The specific multifunctional oligomers, comprising NH/NH₂ or SiCl functionalities depending on the monomer feed-ratio, were prepared from mono- and di-functionally reacted dichlorodimethylsilane (DDS) and mono-, di-, tri- and tetra-functionally reacted ethylenediamine (EDA). Varying the feed-ratio afforded control of the microstructures of the oligomers and the preparation of oligomers with, in some cases, conterminously located silicon–chlorine (SiCl) groups. The combination of the NMR methods with the IR technique has enabled the detailed microstructural characterization of the oligomers and the identification of the functionalities therein. This approach and the knowledge gained from the DDS/EDA system has been applied to the microstructural characterization of other hybrid organosilazane/silylamine preceramic telechelic oligomers.     

深紫外无机非线性光学晶体硼铍酸锶及其分子工程学探索方法

阐述了紫外无机非线性光学晶体分子工程学探索方法的基本特点，具体分析深紫外无机非线性光学晶体硼铍酸锶（ＳＢＢＯ）以氟硼铍酸钾（ＫＢＢＦ）为主要参考晶体的分子设计方法，随后根据晶体结构研究、单晶培养、和非线性光学性能测定等实验结果讨论ＳＢＢＯ作为新型深紫外无机晶体的主要优点，即它既具有更短的紫外吸收边（接近１５５ｎｍ）和较大的非线性光学系数（ｄ２２（ＳＢＢＯ）＝０６×ｄ２２（ＢＢＯ）＝１３８ｐｍ／Ｖ），同时晶体无明显层状习性，并肯有良好的化学稳定性和机械性能     

Asymptotics in the random assignment problem

Summary We show that, in the usual probabilistic model for the random assignment problem, the optimal cost tends to a limit constant in probability and in expectation. The method involves construction of an infinite limit structure, in terms of which the limit constant is defined. But we cannot improve on the known numerical bounds for the limit.Research supported by NSF Grant MCS90-01710     

Formation of lead pyrophosphate glass and the role of anion disproportionation

Thermal, spectroscopic and electrical properties of lead pyrophosphate glass prepared by melt quenching have been examined. A model based on the structural disproportionation of the P₂O ₇ ⁴⁻ ions has been proposed and is shown to consistently explain all the observations. The equilibrium of various anionic species has been discussed on the basis of their electronegativities which are in turn related to their basicities. Communication No. 129 from the Materials Research Centre     

金催化化学发光新体系——苯并吡喃化学发光分析法测定金矿中的痕量金

本文提出了一种测定矿样中痕量金的化学发光分析法,氯化6,7-二羟基-2,4-二甲基苯并吡喃-H_2O_2化学发光体系,方法的检出限为7ppb。工作曲线线性范围是10～1000ppbAu,测定的相对标准偏差小于7％。应用本法测定矿样中的金,结果良好。     

Remarks on a theorem of Taskinen on spaces of continuous functions

We clarify and prove in a simpler way a result of Taskinen about symmetric operators on C(Kⁿ), K an uncountable metrizable compact space. To do this we prove that, for any compact space K and any n ∈ ?, the symmetric injective n–tensor product of C(K), , is complemented in C(B_C(K)*), a result of independent interest. The techniques we develop allow us to extend the result in several directions. We also show that the hypothesis of metrizability and uncountability cannot be removed.