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.     

On concepts of directional differentiability

Various definitions of directional derivatives in topological vector spaces are compared. Directional derivatives in the sense of Gâteaux, Fréchet, and Hadamard are singled out from the general framework of -directional differentiability. It is pointed out that, in the case of finite-dimensional spaces and locally Lipschitz mappings, all these concepts of directional differentiability are equivalent. The chain rule for directional derivatives of a composite mapping is discussed.     

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).     

壳聚糖衍生物的制备及其吸附性能

壳聚糖衍生物的制备及其吸附性能曲荣君，马千里，郑秀丽，孙言志（烟台师范学院化学系烟台２６４０２５）关键词壳聚精衍生物，制备，吸附壳聚糖（ＣＴＳ）是重金瞩离子的吸附剂￣［１，２］，由于壳聚精分子中的－ＮＨ＿２在ｐＨ较低的水溶液易形成而使ＣＴＳ溶于水，造...     

5-氨基-1,3-二氢-1,3-二氧-异吲哚-2-丙酸类衍生物的合成及抗血管生成活性研究

根据RGD序列肽的构效关系, 设计并合成了一系列以5-氨基-1,3-二氢-1,3-二氧-异吲哚-2-丙酸为分子骨架的新化合物. 其中间体和目标物的化学结构经¹H NMR, MS和元素分析确证. 体外初步生物活性筛选结果表明, 目标物在10^－5 mol/L浓度下对bFGF诱导的鸡胚绒毛尿囊膜新生血管生成有显著抑制活性.     

KF－Al2O3催化下3，4－二氢－2H－吡喃[3,2-h]喹啉衍生物的合成

芳醛、8－羟基喹啉与丙二腈或氰乙酸乙酯KF－Al2O3催化下反应生成一系列新 的3，4－二氢－2H－吡喃[3,2-h]喹淋衍生物，产物的结构通过单晶X射线确证。     

氮硫杂冠醚及其衍生物的合成

以噻吩、水杨醛、二胺、溴乙酸、烯丙基氯和丙烯腈为原料合成了 4,5 :14 ,15 二苯 3 ,16 二氧 2 1 硫 7,12 二氮双环[16.2 .1]二十一环 1( 2 0 ) ,18 二烯 (简称氮硫杂冠醚 )及其 5种衍生物 ,经元素分析 ,IR ,1 HNMR和MS谱表征了这些化合物的结构 .