例析递推数列与数学建模

数学建模是高中数学新课标的一个新内容,为学生提供了自主学习的空间,有助于学生体验综合运用数学知识和方法解决实际问题的过程,增强应用意识、创新意识和实践能力,但目前也是数学教学中的一个薄弱点.本文就几个实际问题结合常见的递推数列作简单的分析.     

新外推完全多重网格法北大核心

使用新外推公式和高阶插值算子,为相邻细层提供好的初值,对初值使用磨光算子磨光几次后,再调用V型多重网格法求得该层数值解,构造了基于四阶紧致差分格式的新外推完全多重网格法.数值实验表明,与对比算法相比,新算法迭代次数少、计算时间短、稳健性强.     

β-环糊精的双官能化

通过两条路线对β-环糊精进行双官能化合成了3个带双官能团的β-环糊精--叠氮基对甲苯磺酰基β-环糊精(3), 二对甲苯磺酰基β-环糊精(4)和二叠氮基β-环糊精(5).对甲苯磺酰基β-环糊精(1)的对甲苯磺酰基被叠氮基取代制得单叠氮基β-环糊精(2);2与对甲苯磺酰咪唑反应得到3.1先与对甲苯磺酰咪唑反应生成4;4的对甲苯磺酰基被叠氮基取代得到5.3～5的结构经1H NMR, IR和元素分析表征.     

克伦特罗包被原及其抗体作用的电化学阻抗研究

电化学阻抗免疫传感器技术结合了电化学阻抗的高灵敏性和免疫分析的高特异性,可响应修饰有生物分子的电极界面的电子转移速率的信号变化,具有简便、快速、灵敏、不需示踪物等优点,为生化的免疫测定提供了新的检测平台.     

THE ASSOCIATION OF LIVING POLYSTYRYLLITHIUM IN BENZENE

The effects of the chain length,active end group and concentration on the association of living polystyryllithium (PS~-Li~+)chains in benzene were examined by a combination of static and dynamic laser light scattering in a cuvette equipped with a high-vacuum stopcock.The results show that long PS~-Li~+ chains(M_w>1×10~4)usually form dimers in the solution. In contrast,shorter PS~-Li~+ chains exhibit two relaxation modes,where the fast mode is related to the translational diffusion of the living chain dim...     

制备条件对Au/LaCoO_3催化氧化CO性能的影响

采用溶胶-凝胶法制备了钙钛矿型复合氧化物LaCoO_3, 并用沉积-沉淀法(DP法)制备了Au/LaCoO_3催化剂. 考察了制备条件对催化剂催化氧化CO活性的影响. 结果表明, 制备过程中, 溶液pH、 pH调节顺序及催化剂焙烧温度对催化剂活性均有一定影响. Au/LaCoO_3催化剂的最佳制备条件为: 沉积过程中在HAuCl4溶液中先加入载体后, 再调节溶液pH=8, 得到的催化剂经250 ℃焙烧后可提高催化剂稳定性.     

Revisiting the thermosensitivity of poly(acrylamide-co-diacetone acrylamide)

The lower critical solution temperature （LCST） behavior of poly（acrylamide-co-diacetone acrylamide） （poly（AM-co-DAM）） copolymer in aqueous solutions was studied. The results demonstrate the LCST linearly decreases as the molar fraction of DAM （fDAM） increases. In the range of fDAM 〈 0.36, the transmittance increases as fDAM decreases because the more hydrophilic copolymer chains can form looser aggregates with a lower refractive index. The transmittance exhibits a minimum when fDAM is less than 0.28 as the chains form micelle-like structure with a size smaller than the wavelength. The LCST decreases with the initial polymer concentration, but it levels off when the polymer concentration is high enough. Moreover, no hysteresis can be observed in the change of transmittance during the heating-cooling process because no additional hydrogen bonds are formed in the collapsed state due to the steric hindrance of the large side groups in DAM units.     

Three-dimensional simulation method of multipactor in microwave components for high-power space application

Based on the particle-in-cell technology and the secondary electron emission theory, a three-dimensional simulation method for multipactor is presented in this paper. By combining the finite difference time domain method and the panicle tracing method, such an algorithm is self-consistent and accurate since the interaction between electromagnetic fields and particles is properly modeled. In the time domain aspect, the generation of multipactor can be easily visualized, which makes it possible to gain a deeper insight into the physical mechanism of this effect. In addition to the classic secondary electron emission model, the measured practical secondary electron yield is used, which increases the accuracy of the algorithm. In order to validate the method, the impedance transformer and ridge waveguide filter are studied. By analyzing the evolution of the secondaries obtained by our method, multipactor thresholds of these components are estimated, which show good agreement with the experimental results. Furthermore, the most sensitive positions where multipactor occurs are determined from the phase focusing phenomenon, which is very meaningful for multipactor analysis and design.     

运用反例基于识别的手写数字串分割

采用基于识别的分割方法进行手写数字串分割.在识别的过程中,运用反例样本估计分类器参数,实验数据表明,这种运用反例样本训练的分类器与没有经过反例样本训练的分类器相比,将提高拒识率到19%左右,从而保证了较高的识别率,验证了只有经过反例训练的分类器的输出结果才是可信赖的.     

基于平均场支持向量机的混沌时间序列预测

提出了一种新的基于支持向量机的混沌时间序列预测方法，该方法利用平均场理论使支持向量机的学习过程变得简单高效。同时由于该方法将支持向量机的参数近似为高斯分布的，因此采用平均场理论能够容易的求解这些参数，这样获得的支持向量机的参数比传统的基于二次规划的算法更加精确，而且学习速度更快。最后利用该方法对嵌入维数与模型的泛化能力关系进行了探讨，并利用Mackey-Glass时间序列对该方法进行了验证，结果表明：该预测方法能精确地预测混沌时间序列,而且在混沌时间序列的嵌入维数未知时也能取得比较好的预测效果.这一结论预示着平均场支持向量机是一种研究混沌时间序列的有效方法.