随机延迟微分方程的全隐式Euler方法

研究随机延迟微分方程数值解具有重要的意义,目前已有显式和半隐式两种数值方法,还没有全隐式的数值方法.本文构造了一种全隐式Euler方法,在该方法中用一些截断的随机变量代替维纳过程增量△W<,n>,接着证明了全隐式方法是1/2阶收敛的并通过数值实验验证了该方法的收敛性.最后,用数值实验表明在某些情况下全隐式方法的稳定性比半隐式方法好一些.     

漆酚铁聚合物的制备及性能研究

以生漆和三氯化铁反应制备漆酚铁聚合物,用红外光谱、涂膜鲜映性仪和光泽度仪等对聚合物结构和漆膜性能进行表征.结果表明,反应温度65℃,反应时间3h,漆酚和三氯化铁物质的量比为8∶1,所生成的漆酚铁聚合物性能较好.     

Different Hydrogen-Bonded Interactions in the Cocrystals of Nicotinamide with Two Aromatic Acids

Abstract  

Nicotinamide crystallizes with 3-hydroxy-2-naphthoic acid and 4-aminobenzoic acid to give rise to cocrystal 1 and 2, respectively. Cocrystal 1, [C₁₁H₈O₃][C₆H₆N₂O], crystallizes in the monoclinic space group C2/c with a = 25.810(4), b = 4.8932(5), c = 23.869(4) ?, β = 107.078(8)o, V = 2881.6(7) ?³, Z = 8, C₁₇H₁₄N₂O₄, M _r  = 310.30, D _c  = 1.431 g/cm³. Cocrystal 2, [C₇H₇NO₂][C₆H₆N₂O]·H₂O, crystallizes in the triclinic space group P-1 with a = 7.214(5), b = 7.326(5), c = 13.484(11) ?, α = 83.23(2), β = 77.189(18), γ = 80.35(2)o, V = 682.7(9) ?³, Z = 2, C₁₃H₁₅N₃O₄, M _r  = 277.28, D _c  = 1.349 g/cm³. Similar carboxylic acid···pyridine synthon R ₂²(7) can be observed in the two cocrystals. In 1, amide of nicotinamide forms a C(4) chain from the anti H to its carbonyl oxygen. In 2, the amide forms a R ₂²(8) homodimer which is linked into 2D layer by water molecule through different hydrogen-bonding interactions. The 3D hydrogen-bonded structure results from a synthon R ₄²(8) from amide, water and amino group of 4-aminobenzoic acid.     

载银sod基纳米分子筛的合成及抗菌性能

采用两步法合成了 sod 基系列分子筛(EMT、FAU、SOD),并通过离子交换法引入 Ag⁺得到载银分子筛,通过 X 射线衍射(XRD)、扫描电子显微镜(SEM)证明离子交换前后分子筛骨架结构和晶粒尺寸没有发生明显变化;通过红外光谱(IR)、热重(TG)证明制得的载银分子筛具有良好的稳定性;对获得的载银分子筛进行了Ag⁺释放实验与抗菌能力测试,考察了分子筛种类和晶粒尺寸对抗菌性能的影响。结果表明具有笼状结构的FAU与EMT分子筛因可储存更多的Ag⁺而具有更好的抗菌性能,而具有超笼结构的 FAU 分子筛抗菌性能最优。通过对比不同晶粒尺寸载银 FAU 分子筛抗菌数据发现,晶粒尺寸为 100 nm 的载银FAU分子筛因外表面丰富的抗菌活性位点以及其内部可以储存并不断释放 Ag⁺而具有最优的抗菌性能和抗菌寿命。而晶粒尺寸为10 nm的载银FAU分子筛由于晶粒尺寸较小、外比表面积大、扩散路径短,Ag⁺的释放速率最快,抗菌效率最高。     

可调谐光子晶体微环腔型光分叉复用器的设计*

提出了一种基于二维光子晶体微环腔的新型光分叉复用器,并可以通过改变环区的硅介质柱的折射率实现波长调谐.运用经典的微环自由光谱范围FSR和微环半径R的关系,证实新型的光子晶体微环腔也满足该关系.利用二维时域有限差分法系统分析了下路信号波长及相应效率随折射率的变化关系.结果表明,只需改变环区折射率0.005,下路波长就可以漂移1 nm,而有效微环半径还不足1.4 μm.     

基于圆柱型硅光子晶体的1×2光下路分束器

本文设计了一个基于圆柱型硅光子晶体自准直环形腔的1×2光下路分束器.该光下路分束器由三个分光镜和一个反射镜构成,其中窄光束依赖自准直效应进行传输.利用多光束干涉理论分析了光下路分束器中不同出口的理论透射谱,并且利用时域有限差分法对光下路分束器透射谱进行数值模拟计算,其结果与理论预测基本一致.当下路波长为1 550 nm时,光下路分束器的自由光谱范围约为30 nm,几乎涵盖了整个光通信C波段.由于其小尺寸和全硅材料,本文设计的1×2光下路分束器有望应用于未来的集成光路中.     

A global rigidity theorem for weakly Landsberg manifolds

In this paper we study a global rigidity property for weakly Landsberg manifolds and prove that a closed weakly Landsberg manifold with the negative flag curvature must be Riemannian.     

Crystal Structure of the Dihydrogen Phosphate Salt of Ozagrel (ozagrel=(E)-3-[4-(1H-Imidiazol-1-ylmethyl)phenyl]-2-Propenic Acid)

Abstract  Ozagrel, (E)-3-[4-(1H-Imidiazol-1-ylmethyl)phenyl]-2-propenic acid, crystallizes with phosphoric acid from aqueous solution to give the dihydrogen phosphate salt of ozagrel which crystallizes in the orthorhombic space group P2₁2₁2₁ with a = 4.6901(14), b = 8.929(4), c = 34.558(13) ?, V = 1447.2(9) ?³, Z = 4, C₁₃H₁₅N₂O₆P, M _r  = 326.24, D _c  = 1.497 g/cm³. In the crystal structure, phosphate anions interact with ozagrel through two kinds of hydrogen bonds forming a 1D hydrogen-bonded chain. Phosphate anions are hydrogen-bonded to each other through supramolecular synthon R₃³(12) forming a 1D double-chain structure which links ozagrel molecules into a 3D structure. Index Abstract  In crystal structure of the title compound, phosphate anions interact with ozagrel through two kinds of hydrogen bonds forming a 1D hydrogen-bonded chain. Phosphate anions are hydrogen-bonded to each other through supramolecular synthon R₃³(12) forming a 1D double-chain structure which links ozagrel molecules into a 3D structure.      

再论微分中值定理"中间点"ξ的性质

主要研究拉格朗日中值定理"中间点"ξ的单调性、连续性及可导性问题.     

Polarization beam splitter based on photonic crystal self-collimation Mach-Zehnder interferometer

A polarization beam splitter based on a self-collimation Mach-Zehnder interferometer (SMZI) in a hole-type silicon photonic crystal was proposed and numerically demonstrated. Utilizing polarization dependence of the transmission spectra of the SMZI and polarization peak matching (PPM) method, the SMZI can work as a polarization beam splitter (PBS) by selecting appropriate path length difference in the structure. Because of its intrinsic operating principle, the PBS possesses high polarization extinction ratios (PERs). As its dimensions are only several operating wavelengths, the PBS may have practical applications in photonic integrated circuits.