逆p·n·p·矩阵的表征

一个n阶实方阵A,若其各阶主子式皆非正,则称A为p.n.p.矩阵,记作A∈PNP;特别地,若A∈NP且各阶主子式皆负,则称A为p.n.矩阵,记作A∈PN进一步,若n阶实方阵A非奇异,且A^-1∈PNP,则称A为逆p.n.p.矩阵,记作A∈IPNP;特别地,若A^-1∈PN,则称A为逆p.n.矩阵,记作A∈IPN。     

广义严格对角占优矩阵的判定

１引言设Ａ＝（ａｉｊ）Ｃｎｘｎ,若对每一ｉＮ＝｛１,２,…,ｎ｝都有则称Ａ为对角占优矩阵,记为ＡＤυ;若（１）式中每一不等号都是严格的,则称Ａ为严格对角占优矩阵,记为ＡＤ．若存在正对角阵Ｘ使ＡＸＤυ（或ＡＸＤ）,则称Ａ为广义（或广义严格）对角占优矩阵;记为ＡＤΥ（或ＡＤ）．广义严格对角占优矩阵的判定在计算数学和矩阵论的研究中占有重要的地位,文［１］和［２］分别定义了α－对角占优矩阵和双对角占优矩阵,讨论了广义严格对角占优矩阵的判定及性质,本文引进了α双对角占优矩阵的概念,得到了广义严格对角占优矩…     

The crystal and molecular structure of spiro[1-(S)-Br-3-(S)-H-4-(R)-l-(1′ R,2′ S,5′R)-menthyloxy-5-oxo-6-oxa-bicyclo[3.1.0]hexane-2,3′-(R)-(4′-(R)-diphenylmethoxy-5′-l-(1′ R,2′ S,5′ R)-menthyloxy-butyrolactone)]

Crystal structure of C₄₁H₅₃O₇Br has been determined by single-crystal X-ray diffraction. The compound crystalline in the orthorhombic space group P2₁2₁2₁, with a = 11.264(2), b = 12.058(2), c = 29.337(6) Å, Z = 4. The bond angles of cyclopropane moiety in the molecule are approximate to 60° and agree with theoretic values of the internal angles in a cyclopropane, and two chiral menthyloxy groups are located above and under the whole chiral molecule, respectively. The configuration of the pentacyclic lactone is shown as envelope form.     

几种多取代吡咯的NMR研究(Ⅱ)

吡咯的多取代物中,许多具有生理活性。本文测定了下列化合物的¹³CNMR谱:Ⅰ、Ⅶ:R=H;Ⅱ、Ⅷ:R=o-CH₃;Ⅲ、Ⅸ:R=m-CH₃;Ⅳ、Ⅹ:R=p-CH₃;Ⅴ、Ⅺ:R=p-COOCH₂CH₃;Ⅵ、Ⅻ:R=m-NO₂。     

Optical Absorption Study on the Conversion and Restoration of Color Centers in Pure KCI Crystals

The conversion and restoration processes of colour centers in pure KCI crystals were studied by optical absorption measurements. When the sample is heated the aggregative centers in it begin to dissolve to F centers, and the opposite process will take place, i.e. F centers will aggregate to form F₂, F₃, F₄centers if the samples are cooled down. It was found that the conversion and restoration processes are dependent on the annealing temperature and time. In our experiment, the samples were treated at various temperatures and time. In addition the restoration process for the 350°C treated sample was studied live. We found that the higher the annealing temperature is the slower the restoration in the samples proceed, and the conversion process maintained for a few minutes even after annealing treatment.     

三角域上Bernstein—Bézier曲面的一种推广

本文给出了三角域上Bernstein—Bezier曲面的一种推广,并研究了这种曲面的性质和算法。     

Cassini卵形谱包含域的改进及应用

本文给出了改进的Cassini卵形谱包含域,讨论了相应的隔离定理及边界问 题,所得结果推广了文[1-4]的相应定理.作为应用得到了M-矩阵的一个新表征.     

广义对角占优矩阵的充分条件

广义对角占优势矩阵及M-矩阵是计算数学和矩阵理论研究的重要课题之一。本文利用α-对角占优矩阵给出了判定广义对角占优及非异M-矩阵的若干充分条件，改进了文[1]及文[2]的相应的结果，作为应用，利用矩阵分块又给矩阵非奇异若干判定条件。     

关于2n阶常微分方程两点边值问题解的存在性与唯一性

本文利用Leray－Schauder度理论建立了一类2n阶非线性常微分方程两点边值问题解的存在性与唯一性定理，以及利用Fredholm择一原理与Fourier展式，建立了一类2n阶线性常微分方程两点边值问题解的存在性唯一性定理．     

多取代吡咯的合成及其性质(Ⅱ)

前文已报导1-芳基-2-甲基-3-乙酰基-5-对氯苯基吡咯。本文用间硝基-ω-溴代苯乙酮与乙酰丙酮作用,得到1-间硝基苯基-3-乙酰基-1,4-戊二酮(1),(1)与各种不同的芳香族伯胺在冰醋酸存在下进行环合反应,生成1,2,3,5-四取代吡咯(2)至(10)。后者与氨基脲反应得到相应的缩氨脲。