Taylor公式在判断级数敛散性时的应用

在一些证明级数敛散性的问题中，Taylor公式的应用有时能起到关键作用．通过实例说明如何运用这一思想，讨论级数的敛散性问题．     

注重函数模型构建,探究实际应用问题

随着社会科技的发展,数学与其他学科的联系日趋密切,数学的应用越来越广泛,因此构建数学模型、解决实际问题已成为近几年的考试热点之一.这类问题贴近生活,贴近社会,有利于体现数学的人文价值和社会价值,有利于考查学生分析、猜想、建模和综合应用等各方面的能力.     

自然数幂方和用二项系数表示的系数公式

得到了自然数幂方和由二项系数表示的系数a_i~(k)的公式,和由排列数表示的系数b_i~(k)的公式,证明了系数存在唯一性及系数间的若干重要性质,给出了计算系数的C-语言程序.     

Intramolecular Aldol Condensation ofα- Oxo Ketene Dibenzylthioacetals: A Facile Route to Substituted Thiophenes

As a kind of intermediates, a-oxo ketene dithioacetals I are important in organicsynthesis"'. In our recent studies, we found that the difference of dialkythio group canbestow various properties on these kinds of compounds"'. To exploit the reactivityadjusted by the dialkythio groups in l, a-oxo ketene dibenzylthioacetals 2 were chosenand studied. Some interesting new results were obtained in these experiments. Here wereport the new results.When studying the reaction of a-oxo ketene dibenzylt…     

OPTIMAL ERROR ESTIMATE IN L~∞(J;L~2(Ω)) NORM OF FEM FOR A MODEL FOR COMPRESSIBLE MISCIBLE DISPLACEMENT IN POROUS MEDIA

We'll study the FEM for a model for compressible miscible displacement in porous media which includes molecular diffusion and mechanical dispersion in one-dimensional space.A class of vertices-edges-elements interpolation operator ink is introduced.With the help of ink(not elliptic projection),the optimal error estimate in L∞(J;L2(Ω)) norm of FEM is proved.     

具有次亚B性质的ω_（α＋1）－紧T_1空间是ω_α－LindelOf空间

在本文中，我们证明了具有次亚Ｂ性质的ω＿（α＋１－）紧Ｔ＿１空间是ω＿α－Ｌｉｎｄｅｌｏｆ空间，此结果改进并推广了［１］中的主要结果。     

Local generalized empirical estimation of regression

Let f(x) be the density of a design variable X and m(x) = E[Y\X = x] the regression function. Then m(x) - G(x)/f(x), where G(x) = m(x)f(x). The Dirac δ-function is used to define a generalized empirical function Gn (x) for G(x) whose expectation equals G(x). This generalized empirical function exists only in the space of Schwartz distributions, so we introduce a local polynomial of order p approximation to Gn(.) which provides estimators of the function G(x) and its derivatives. The density f(x) can be estimated in a similar manner. The resulting local generalized empirical estimator (LGE) of m(x) is exactly the Nadaraya-Watson estimator at interior points when p = 1, but on the boundary the estimator automatically corrects the boundary effect. Asymptotic normality of the estimator is established. Asymptotic expressions for the mean squared errors are obtained and used in bandwidth selection. Boundary behavior of the estimators is investigated in details. We use Monte Carlo simulations to show that the     

石墨炉原子吸收光谱法测定土壤中离子交换态的镉

本文研究了石墨炉原子吸收光谱法测定土壤中离子交换态的镉的适宜条件.试样经MgCl2溶液震荡提取离心后,以10%的磷酸二氢铵做基体改进剂,方法检出限为0.03840 μg/L,相对标准偏差(n=6)为0.9231%.本方法具有准确、简便之优点,可用于土壤样品中镉的测定.     

无溶剂顶空气相色谱法测定盐酸左氧氟沙星残留溶剂

采用无溶剂-顶空-气相色谱直接测定盐酸左氧氟沙星中残留溶剂乙醇、甲苯、二甲基亚砜(DMSO)等.各残留溶剂的检出限分别在0.007-0.032 μg,6次测定的相对标准偏差RSD在1.84%-1.92%,加标回收在90.9%-110%.方法简便、快速、灵敏,可应用于其他药品中残留溶剂的分析.     

高效液相色谱法测定金菊泡腾片中绿原酸的含量

采用Nucleosil C18(250mm×4.6mm,4.5μm)色谱柱,以甲醇-磷酸水溶液(pH=3.0)为流动相,其比例为25∶75,检测波长为327 nm,流速1.0 mL/min,柱温29 ℃,建立金菊泡腾片和双黄连口服液中绿原酸含量的高效液相色谱(HPLC)测定方法.绿原酸浓度在0.02-0.1 mg/mL与峰面积积分值呈良好的线性关系,A=0.9394C 0.3674(r=0.9991).该方法灵敏、简便、重现性好、结果准确,可用于金菊泡腾片中绿原酸含量的测定和产品质量控制.