数学软件在高等数学研究型教学中的应用

这些年来,我们积极尝试将数学软件应用在高等数学课程的教学中,获得了一些可喜的成绩.起到了启发学生思维,增强学生主动参与,教会学生发现问题并使用工具来解决问题的能力.本文以一种特殊曲线的性质分析为例讲述了数学软件在研究性教学中的应用.     

一种分解指数算符的简洁方法

提出一种新的分解指数算符的方法,这种方法不仅简单易懂,而且有助于找到更多的算符恒等式.     

Evolution from Diffuse Ferroelectric to Relaxor Ferroelectric in Pb1-xBax（Fe1/2Nb1/2）O3 Solid Solutions

Dielectric and ferroelectric characteristics for Pb1-xBax（Fe1/2Nh/2）O3 （x = 0,0.05,0.1,0.15, and 0.2） ceramics are determined together with their structures. X-ray diffraction （XRD） analysis confirms the solid solutions with the cubic structure. The dielectric nature changes from diffuse ferroelectric to relaxor ferroelectric with increasing x, while the phase transition temperature Tc （or Tm） decreases monotonously. The diffuse ferroelectric phase transition is observed in the solid solutions with 0≤x ≤0.05. For Pbl-xBax（Fe1/2Nb1/2）O3 with 0.1≤ x≤0.2, relaxor ferroelectric behavior is determined, and the Vogel-Fulcher equation is used to describe the relaxor behavior. The 1/ε versus T plots reveal the diffusion dielectric characteristics in both diffuse and relaxor ferroelectrics.     

LED微阵列投影系统设计

为满足便携式投影仪的市场需求,设计了一种基于LED微型阵列的投影系统。该系统由显示单元和投影物镜构成。采用尺寸为12 mm×9 mm的自发光LED微型阵列作为系统的显示单元,利用光学设计软件设计了投影物镜。投影物镜采用反远距光学结构,全视场角为80°,焦距为8 mm,属于强光、广角镜头。在空间频率20 lp/mm处,该物镜的调制传递函数大于0. 85,畸变小于2%,符合投影系统的设计要求。该投影系统具有体积小,结构简单,投影效果好,易加工等诸多优势,可为第三代投影技术的发展提供参考。     

三次Gauss和及二项指数和的混合均值

我们用三角和的性质研究一类三次Gauss和与两项指数和混合均值的计算问题,并给出一个精确的计算公式.     

Preparation of SiO2-TiO2 mesoporous inorganic hybrid capillary open tubular column and the separation for amino acid mixtures

采用溶胶-凝胶法制备了SiO2/TiO2混溶胶.把溶胶抽入柱中,通过溶剂热反应和高温焙烧制得无机杂化毛细管电色谱开管柱.采用扫描电子显微镜(SEM)、能谱(EDS)、N2吸附-脱附(BET)对开管柱的结构形貌、成分和孔径分布进行了表征.以三种混合氨基酸作为分析物,获得了较好分离.     

Preparation of PEO-b-PPO-b-PEO/α-cyclodextrin supramolecular hydrogels hybridized with exfoliated graphite nanoplates

Abstract

In this work, an effective method was developed to prepare novel PEO-b-PPO-b-PEO (EPE)/α-cyclodextrin (α-CD) supramolecular hydrogels containing exfoliated graphite nanoplates (xGNPs) by mixing an aqueous solution of α-CD with an aqueous dispersion of xGNPs at the presence of amphiphilic EPE copolymer. The EPE copolymer played three important roles in the preparation process: (1) as an exfoliating agent to break expanded graphites into xGNPs under ultrasonication, (2) as a dispersant to stabilize xGNPs in the aqueous solution, and （3）as a component to form the inclusion complexes with α-CD. The resultant xGNPs/EPE/α-CD hybridized hydrogels were characterized by scanning electron microscopy, wide-angle X-ray diffraction, differential scanning calorimetry, and Fourier transform infrared spectroscopy, which confirmed not only the formation of supramolecular hydrogel structure but also the homogenous dispersion of xGNPs in the hydrogel matrix. It was found that the existence of xGNPs can accelerate the speed of gel formation in comparison with that of the native EPE/α-CD hydrogel. Additionally, the water-retention ability and the release behavior of vancomycin hydrochloride for the xGNPs/EPE/α-CD hybridized hydrogels were investigated.     

衍生化气相色谱法检测3-氨基-1,2-丙二醇

冰水冷却下将3-氨基-1,2-丙二醇加入到衍生化试剂三氟乙酸酐中,充分振荡,50℃反应30min,冷至室温后直接进气相色谱检测,面积归一法定量。在选定的实验条件下,加标回收率大于99%,测定峰面积的相对标准偏差为0.6%。该方法也可应用于3-氯-1,2-丙二醇、2-氨基-1,3-丙二醇、1,3-二氨基-2-丙醇等其它高粘度物质的检测。     

中药柴胡总皂苷急性肝毒性的代谢组学研究

运用UPLC-MS联用技术对空白对照组、柴胡总皂苷(SS)组大鼠在给药后第3天和第5天的尿液样本进行分析检测,获得了以质荷比和保留时间为变量的矩阵数据。据此建立各组大鼠的尿液代谢轮廓图,并利用主成分分析(PCA)建立了SS的代谢组学毒性模型。结合肝组织病理,探讨了柴胡总皂苷的急性肝毒性。对于SS组与正常组,大鼠尿液代谢轮廓图表现出了一定的差异。在代谢组学毒性模型中,给药第3天和第5天的PCA分类均偏离正常组,而第5天的偏离程度强于第3天。同时,在第5天的肝组织病理切片中发现了组织病变。由此表明,给药组大鼠的代谢组偏离了正常组,这种偏离正是肝急性毒性的表现,且给药到第5天的肝毒性强于第3天,表明肝毒性与给药累积剂量呈正相关,表现出了明显的急性和累积肝毒性。     

A Trinuclear Ni(Ⅱ) Mixed-ligand Complex Containing Pentadentate N-butylsalicylhydrazide and Monodentate Imidazole:Synthesis, Characterization and Crystal Structure

A novel trinuclear nickel(Ⅱ) complex [Ni3(bushz)2(Himdz)2(H2O)2]?2DMF (1, bushz=N-butylsalicylhydrazide, Himdz=imidazole, DMF=N,N-dimethyl-formamide) has been synthesized and characterized by X-ray single-crystal diffraction characterization. Complex 1 crystallizes in the monoclinic system, space group P21/c with a=7.706(7), b=14.882(6), c=18.639(6) , β=108.08(2)o, V=2032(1) 3, Dc=1.525 g/cm3, Mr=932.95, Z=2, F(000)=972, μ=1.442 mm-1, the final R=0.0359 and wR=0.0771. The three nickel(Ⅱ) atoms in 1 are arranged in a strictly linear structure and exhibit alternating square-planar and octahedral geometries. The complex is connected to form a supramolecule with an infinite three-dimensional network through intermolecular hydrogen bonds. The electrochemical studies reveal that redox of Ni3+/Ni2+ in the complex is a quasi-reversible process. The thermal stability of the title complex was also studied.