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.     

羧基苯偶氮基杯[6]芳烃衍生物的合成及表征

近几年,随着对主客体化学研究的深入,杯芳烃的功能化修饰成为该领域的研究热点[1-6]。本文以邻、间、对氨基苯甲酸和杯[6]芳烃为原料,经重氮化 偶联反应合成了新型有色邻、间、对羧基苯偶氮基杯[6]芳烃,产物的结构经IR,1HNMR和元素分析表征;并研究了它们生色原理和光谱性能。结果表明它们是一类新型指示剂和具有新型配位空腔的主体分子。合成路线如下:图1　邻、间、对羧基苯偶氮基杯[6]芳烃的合成Fig.1　Fig1:Synthesisofp (o,m,p carboxylbenzeneazo)calix[6]arenes1　实验部分1 1　仪器与试剂Nicolet 460型傅里叶红外光谱仪(KBr…     

血卟啉衍生物的色谱分离

本文拟定的纸色谱法是以苯-乙酸乙酯-甲醇-乙酸(9:2:1:1)作展开剂,将血卟啉衍生物(HPD)分离为五部份,分别测定各部份浸取液的荧光发射光谱,作为一种对血卟啉衍生物组份作对比鉴定的参考方法。采用Ward的高效液相色谱程序对比研究结果表明,国产与美国产HPD的组份近似,均以血卟啉为主要组份,而前者血卟啉的含量较高;二者还均含有羟乙基乙烯基衍生物和羟基乙酸酯,初步研究了血卟啉衍生物在甲醇-水溶剂系统中的高效液相色谱行为,进一步将血卟啉衍生物分离为九部份,有利于单一组份研究。     

非螯合型手性双膦铑对脱氢苯丙氨酸的不对称催化加氢反应

报道从Ｄ－甘露醇出发合成手性双膦（２Ｓ，５Ｓ）－３，６－双（二苯膦）－１，４：３，６－双脱水－２，５－双去氧－Ｌ－艾杜醇，原位下ＢＤＰＩ与３种铑配合物作用生成手性非螯合型双膦铑催化剂，常压下对４种脱氢苯丙氨酸衍生物进行不对称催化化反主尖，对反应结果及ｅ．ｅ．值进行了讨论。     

Lewis acid promoted reactions of γ,γ-dialkoxyallylic zirconium species with various carbonyl compounds

The reactions of γ,γ-dialkoxyallylic zirconium species with carbonyl compounds in the presence of Lewis acid are reported. The reactivity of γ,γ-dialkoxyallylic zirconium species and reaction pathway were strongly dependent on the structure and electrostatic nature of the carbonyl compounds.     

Extending the scope of enantiomer separation by capillary supercritical fluid chromatography on immobilized polysiloxane-anchored permethyl-β-cyclodextrin (Chirasil-Dex)

Immobilized polysiloxane-anchored permethyl-β-cyclodextrin (Chirasil-Dex) with a cyclodextrin content of approximately 30 % by weight, previously employed as a versatile chiral stationary phase for the separation of enantiomers by GC, has been used for the separation of enantiomers by capillary supercritical fluid chromatography (SFC). A considerable number of racemates could be resolved, e.g. aromatic alcohols, amino alcohols (TFA derivatives), and underivatized acids. Many pharmaceutical compounds were among those analyzed, including several NSAIDs (e.g. ibuprofen and ketoprofen), a steroidal drug (nor-gestrel), a barbiturate (hexobarbital), and others. Among the racemates resolved were many which cannot be analyzed by GC owing to low volatility or decomposition at elevated temperatures. For two racemates, analysis temperature and mobile phase density were systematically varied to give constant analysis times or capacity factors k. Low temperatures (ca 60 °C) yielded the best separation in term of separation factor, α, or resolution, R_s, even though higher densities had to be used. In comparison with GC, capillary SFC was able to furnish higher separation factors and similar resolution. The applicability of capillary SFC for the analysis of mixtures of cyclodextrin derivatives, e.g. those used in the synthesis of Chirasil-Dex, was, furthermore, demonstrated.     

Structure of N-(1-silatranylmethyl) and N-(trimethoxysilyl-methyl) derivatives of nitrogen-containing heterocycles according to data of NMR, IR, and UV spectroscopy

The ¹H, ¹³C, ¹⁵N, and ²⁹Si NMR, IR, and UV spectra of N-(1-silatranylmethyl) and N-(trimethoxysilylmethyl) derivatives of nitrogen heterocycles have been studied. The dependence and interrelation of the chemical shifts of ²⁹Si and ¹⁵N nuclei of the silatranyl group in the spectra of N-(1-silatranylmethyl)-substituted nitrogen heterocycles are determined by the nature of the heterocyclic system. __________ Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 12, pp. 1857–1865, December, 2006.     

Enhanced chromatographic resolution of amine enantiomers as carbobenzyloxy derivatives in high-performance liquid chromatography and supercritical fluid chromatography

The carbobenzyloxy (cbz) protecting group is evaluated for it's potential to enhance the resolution of chiral amine enantiomers using high-performance liquid chromatography (HPLC) and supercritical fluid chromatography (SFC). A series of cbz derivatives of commercially available racemates was prepared and analyzed by enantioselective chromatography using a variety of mobile phases and polysaccharide and Pirkle-type chiral stationary phases (CSPs). The cbz-derivatized product consistently demonstrated enhanced chiral resolution under HPLC and SFC conditions. Improved selectivity and resolution combined with an automated preparative HPLC or SFC system can lead to the rapid generation of highly purified enantiomers of desirable starting materials, intermediates or final products.