有限差分格式在偏微分方程初边值问题中的应用

利用Taylor级数推导了一元函数的差商公式,进而得到多元函数的偏差商公式,并构造出显式和隐式两种有限差分格式.根据不同的偏差商形式,把有限差分格式应用于偏微分方程的初边值问题中,通过不同差分格式的截断误差精度分析合理地选择出有效的差分方程.     

3-芳亚甲基联氨羰基-5-(对位取代苯基)-吡唑衍生物的 合成、结构和生物活性

以4-取代苯乙酮及草酸二乙酯为起始原料, 设计合成了20个新的3-芳亚甲基联氨羰基-5-(对位取代苯基)-吡唑衍生物, 产率较高. 所合成的化合物经元素分析, IR, 1H NMR对其结构进行了表征, 化合物4b, 4h还通过X-ray单晶衍射进一步确证了其结构. 初步生物活性实验结果表明, 所合成的化合物对绿豆发芽过程有着较好的生长调节作用.     

N-（5-取代-1,3,4-噻二唑-2-基）-酰胺类化合物的合成、结构表征及其生物活性研究

为了寻找高效生物活性的化合物,笔者设计合成了一系列同时含有1,3,4-噻二唑、酰胺及芳氧亚甲基等活性基团的化合物.首先以取代羧酸和氨基硫脲为起始原料,三氯氧磷为脱水剂,脱水环化得到2-氨基-5-取代-1,3,4-噻二唑,然后再将所得到的产物与酰氯进行酰胺化反应,合成出12个新的N-(5-取代-1,3,4-噻二唑-2-基)-酰胺类化合物.将所合成的化合物通过元素分析、红外光谱、核磁共振氢谱等测试手段进行分析,确证结构.初步观察了所合成的目标化合物在10 ppm浓度下对小麦胚鞘发芽的影响,测试结果表明,所合成的目标化合物中大部分对小麦芽鞘生长具有抑制作用.     

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random interfacial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order asymptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen （2006） as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song （2005） for second-order solutions for random interfacial waves with steady uniform currents if N = 2.     

三层密度分层流体界面内波三阶Stokas解的研究

以小振幅波理论为基础,利用摄动方法研究了三层密度分层流体的界面内波,给出了各层流体速度势的三阶渐近解及界面内波波面位移的三阶Stokes波解.结果表明:界面内波波面位移的三阶Stokes波解描述了界面波的三阶非线性修正及两界面波之间的三阶非线性相互作用;波速不仅取决于波数和各层流体的厚度,而且还与波幅有关.     

5-苯基-1,3,4-噻二唑/噁二唑-2-硫基乙酸铜配合物的合成及其晶体结构

合成了新的2个双核铜配合物,经元素分析、红外光谱和X-射线单晶衍射对其结构进行表征.配合物A(分子式C44H44Cu2N8O16S4,Mr=1196.25),属于三斜晶系,空间群P-1,晶胞参数a=8.3893(14),b=11.580(2),c=13.919(2),β=91.717(2)°,Z=1,V=1263.6(4),Dc=1.572g/cm3,μ=1.084mm-1,F(000)=614,R1=0.0509,wR2=0.1406.配合物B(分子式C42H40Cu2N8O12S8,Mr=1232.48),属于单斜晶系,空间群P2(1)/c,晶胞参数a=8.9557(13),b=9.7814(14),c=28.914(4),β=95.419(2)°,Z=2,V=2521.6(6)3,Dc=1.623g/cm3,μ=1.243mm-1,F(000)=1260.0,R1=0.0402,wR2=0.1042.     

Third-order Stokes wave solutions for interfacial internalwaves in three-layer dendity-stratified fluid

<正>Interfacial internal waves in a three-layer density-stratified fluid are investigated using a singular perturbation method,and third-order asymptotic solutions of the velocity potentials and third-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory.As expected,the third-order solutions describe the third-order nonlinear modification and the third-order nonlinear interactions between the interfacial waves.The wave velocity depends on not only the wave number and the depth of each layer but also on the wave amplitude.     

三层密度分层流体界面内波三阶Stokes解的研究

以小振幅波理论为基础,利用摄动方法研究了三层密度分层流体的界面内波,给出了各层流体速度势的三阶渐近解及界面内波波面位移的三阶Stokes波解。结果表明：界面内波波面位移的三阶Stokes波解描述了界面波的三阶非线性修正及两界面波之间的三阶非线性相互作用;波速不仅取决于波数和各层流体的厚度,而且还与波幅有关。     

浅谈数学建模中常微分模型在教学活动中的应用

数学建模是数学学习的一种新方式,它可以培养学生的多种数学能力,使学生学会运用数学思维方式去观察、分析现实社会,去解决日常生活中的问题。数学建模是运用数学思想和方法解决实际问题的过程,也是一个不断探索、不断创新．不断完善和提高的过程。     

Syntheses and Crystal Structures of Two Novel Cobalt(Ⅱ) Complexes with 2-Amino-5-substituted-1,3,4-thiadiazole as Ligands

Two novel cobalt(Ⅱ) compounds were obtained and characterized by X-ray single-crystal diffraction,IR,1H NMR and elemental analysis.Compound 1 crystallizes in monoclinic,space group P21/n,with a = 18.046(4),b = 11.335(3),c = 19.157(5) ,β = 92.707(3)o,Z = 4,V = 3914.4(16) 3,Mr = 968.56,Dc = 1.644 g/cm3,μ = 1.378 mm-1,F(000) = 1960,the final R = 0.0367 and wR = 0.0895.The crystal of compound 2 is of monoclinic,space group P21/c with a = 8.7253(10),b = 10.9031(13),c = 18.235(2) ,β = 93.2210(10)o,Z = 4,V = 1732.0(3) 3,Mr = 464.21,Dc = 1.780 g/cm3,μ = 1.560 mm-1,F(000) = 932,the final R = 0.0322 and wR = 0.0743.