Geometric Algebra in Linear Algebra and Geometry

This article explores the use of geometric algebra in linear and multilinear algebra, and in affine, projective and conformal geometries. Our principal objective is to show how the rich algebraic tools of geometric algebra are fully compatible with and augment the more traditional tools of matrix algebra. The novel concept of an h-twistor makes possible a simple new proof of the striking relationship between conformal transformations in a pseudo-Euclidean space to isometries in a pseudo-Euclidean space of two higher dimensions. The utility of the h-twistor concept, which is a generalization of the idea of a Penrose twistor to a pseudo-Euclidean space of arbitrary signature, is amply demonstrated in a new treatment of the Schwarzian derivative.     

基于单端半导体光放大器的可调谐超短光脉冲源理论与实验研究

超短光脉冲源是光时分复用(OTDM)系统中的关键器件.提出了一种基于单端半导体光放大器(SOA)的注入型主动锁模光纤激光器产生超短光脉冲的方案，建立了该方案的理论模型.实验实现了高消光比稳定的重复频率10—40GHz皮秒级光脉冲的输出，输出波长在30nm范围内连续可调. 关键词： 超短光脉冲 单端半导体光放大器 主动锁模     

Preparation and characterization of optically active polystyrene via a chiral nitroxide‐mediated polymerization

2,2,6,6‐Tetramethyl‐4‐[d‐(+)‐10‐camphorsulfonyl]‐1‐piperidinyloxy was synthesized and used as a chiral nitroxide for the bulk polymerizations of styrene initiated with benzoyl peroxide (BPO), tetraethylthiuram disulfide (TETD), and thermal initiation. The results showed that the polymerizations proceeded in a controlled/living way; that is, the kinetics presented approximately first‐order plots, and the number‐average molecular weights of the polymers with narrow molecular weight distributions (weight‐average molecular weight/number‐average molecular weight) increased with the monomer conversion linearly. The molecular weight distributions in the case of thermal initiation were narrower than those in the case of BPO and TETD, whereas the polymerization rate with BPO or TETD as an initiator was obviously faster than that with thermal initiation. In addition, successful chain‐extension reactions were carried out, and the structures of the obtained polymers were characterized by gel permeation chromatography and ¹H NMR. The specific rotations of the polymers were also measured by polarimetric analysis. © 2006 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 44: 1522–1528, 2006     

The energy exchange and the optimum length of the sample tube of opfirl

The energy exchange between the pumping laser and FIR signal in the optically pumped FIR laser (OPFIRL) system was studied. The iteration method has been used to calculate the power density of the pumping and FIR signals at any point along the optical axis of the sample tube. It was found that the power density of the FIR signal did not always increase along the length of the laser tube. There was a maximum FIR power density at the appropriate point in the sample tube. If the distance of maximum power point from the entrance of the OPFIRL tube was taken as the length of sample tube Z_opt, the maximum FIR laser output should be obtained. This was the optimum length of OPFIRL tube. The value of Z_opt was closely related to the parameter of OPFIRL such as the pumping power density, the pumping detuning and the frequency of the FIR laser. The energy-exchange and the maximum output of the fir laser were calculated under the ideal condition.     

高分子阳离子絮凝剂用于炼油废水处理研究

用聚二甲基二烯丙基氯化铵型高分子阳离子絮凝剂处理炼油废水考察了险油和化学耗氧量的动态变化规律。对产生的浮渣性质及滤饼的成份进行了研究。并且与聚合铝的处理效果进行对照。研究结果表明，ＨＣＡ除油和化学耗管氧量的性能优于ＰＡＣ，ＨＣＡ产生的浮渣是ＰＡＣ的三分之一，而浮渣中的含油量则是ＰＡＣ的三倍。     

Active set algorithms for isotonic regression; A unifying framework

In this and subsequent papers we will show that several algorithms for the isotonic regression problem may be viewed as active set methods. The active set approach provides a unifying framework for studying algorithms for isotonic regression, simplifies the exposition of existing algorithms and leads to several new efficient algorithms. We also investigate the computational complexity of several algorithms.In this paper we consider the isotonic regression problem with respect to a complete order where eachw _i is strictly positive and eachy _i is an arbitrary real number. We show that the Pool Adjacent Violators algorithm (due to Ayer et al., 1955; Miles, 1959; Kruskal, 1964), is a dual feasible active set method and that the Minimum Lower Set algorithm (due to Brunk et al., 1957) is a primal feasible active set method of computational complexity O(n ²). We present a new O(n) primal feasible active set algorithm. Finally we discuss Van Eeden's method and show that it is of worst-case exponential time complexity.This work was supported by the National Science and Engineering Research Council of Canada under Research Grant A8189 and an Ontario Graduate Scholarship.     

The upper and lower second order directional derivatives of a sup-type function

The purpose of this paper is to give a formula for expressing the second order directional derivatives of the sup-type functionS(x) = sup{f(x, t); t T} in terms of the first and second derivatives off(x, t), whereT is a compact set in a metric space and we assume thatf, f/x and ² f/x ² are continuous on ⁿ × T. We will give a geometrical meaning of the formula. We will moreover give a sufficient condition forS(x) to be directionally twice differentiable.     

比光谱-导数吸光光度法及其应用与进展

综述了比光谱－导数吸光光度法的基本原理、主要试验条件的选择及其在多组分混合物同时测定中的应用与进展。全文共引用了参考文献50篇。     

取代硫脲化合物对作物的生长调节作用

取代脲类化合物已广泛用作除草剂、杀虫剂、杀鼠剂。根据结构活性关系,亦对烯丙基、甲基、二芳基取代硫脲衍生物的植物生长调节活性进行了研究。本文合成了3类取代硫脲化合物:R_1NHCSNHR_2,其中:R_1=苯基,α-萘基,叔丁基,R_2=α-苯基乙     

Synthesis and structure of anhydrodimers of salicylaldehydes

Anhydrodimers have been synthesized by reactions of salicylaldehyde and 3,5-di-tert-butylsalicylaldehyde with SOCl₂ or PCl₅. A mechanism of condensation has been proposed, and the molecular structure of dibenzo-2,6,9-trioxabicyclo[3.3.1]nona-3,7-diene has been determined by X-ray structural analysis.Deceased.Translated fromIzvestiya Akademii Nauk. Seriya Khimicheskaya, No. 8, pp. 1549–1551, August, 1995.The work was supported by the Russian Foundation for Basic Research (Project No. 94-03-08653).