<Emphasis Type="Italic">L</Emphasis><Subscript><Emphasis Type="Italic">m</Emphasis></Subscript> Extemal Polynomials Associated with Generalized Jacobi Weights

Asymptotic estimations of the Christoffel type functions for Lm extremal polynomials with an even integer m associated with generalized Jacobi weights are established. Also, asymptotic behavior of the zeros of the Lm extremal polynomials and the Cotes numbers of the corresponding Turan quadrature formula is given.     

基于核心素养的“V型函数”模型教学

数学模型是培育学生数学核心素养的有效载体,更是高中数学教学中一种有效的教学方式.本文以“V型函数模型”的教学为例,针对如何破解一类绝对值函数题型,在教学中提升学生的模型意识,落实学科核心素养的问题,进行了实践探索,并给出一些反思与感悟.     

可数Fuzzy紧集的性质

讨论可数Fuzzy紧集在L值Zadeh型函数下的逆不变性,证明可数Fuzzy紧集与Fuzzy紧集的乘积是可数Fuzzy紧的。     

正弦型函数解析式的确定

由正弦型函数的解析式 ,作出函数的图象是现行高中代数课本的重要知识点 .反之 ,由正弦型函数的图象 ,求出正弦型函数的解析式 ,能强化训练学生的逆向思维能力 ,加深理解正弦型函数的有关概念 ,巩固掌握正弦型函数的性质 .因此 ,许多课外辅导读物上都列有这类题型对学生进行逆向训练 .如在全国范围内影响较大的 ,《数学通报》编辑部组织专家编写的《数学高考研究与复习》(97年理科版 )Ｐ2 8例 6,Ｐ31 5(1 3) ,Ｐ352 (6)等就是这类题型 .在全国高考试题中 ,已知正弦型函数的图象求解析式也成为保命题热点 .如 1 990年全国高考理科试题 (5) :…     

Zienlkiewicz元的分层形式

本文给出了Zienkiewicz元的分层形式,由此极易得到其表达式的系数估计并可直接引出Zienkiewicz元的表达式.     

光谱线型函数的四种形式及其变换关系

从理论上研究了光谱线型函数的四种形式及其关系,以多普勒展宽导致的线型函数为例,分析了光子数、能量按频率及波长分布函数的最大值和半高全宽。结果表明,光子数、能量按频率的分布函数近似相等,光子数、能量按波长的分布函数也近似相等。通过对多普勒线型函数的分析,建立了根据两条光谱线的线型函数的最大值比值求得光子数比值的方法。     

半平面解析的无穷级Laplace-Stieltjes变换

应用一个无穷级的型函数,研究右半平面解析的Laplace-Stieltjes变换的增长性和值分布,推广了Dirichlet级数的相关结论.     

关于Fermat 型函数方程的亚纯解

本文研究了三项Fermat 型函数方程亚纯解的存在性问题, 证明了: 如果(1/n) + (1/m) + (1/k) < (25/72) ; 则不存在非常数亚纯函数f, g, h 满足函数方程fⁿ + g^m + h^k ≡ 1:     

Utility of Raman Data in Studying Substituted Amines and Hydrazines

By utilizing the Raman spectra of gases, it is frequently possible m provide sufficient data to unequivocally assign the fundamental and several hot bands of the two torsional modes of two coupled methyl rotors which is illustrated by the Raman spectrum of gaseous dimethylamine. From these data V03 = V30, V33 and V‘33 terms have been obtained and their values are compared to those obtained from MP2/6 - 31G(d) ab initio calculations. Also if one of the conformers of an amine or hydrazine has a plane of symmetry and another one has no symmetry, it can be possible to determine the origin of the observed amino torsional mode with excited states from the Raman spectrum, i.e., ethylamine is an example. Since the NH stretches of substituted amines and hydrazines are frequently very weak in the infrared spectrum, the Raman spectra are necessary for the assignment of these fundamentals. Studies are in progress to use the “isolated” NH stretching frequencies to obtain the r0 distances for amines and hydrazinest