Nonlocal boundary value problem for fractional differential equations with p‐Laplacian

In this paper, we are concerned with the existence of positive solutions for the following nonlocal BVP of fractional DEs with p‐Laplacian operator By using the fixed point theorem in a cone, multiplicity solutions of the BVP are obtained. An example is also given to show the effectiveness of the obtained result. Copyright © 2013 John Wiley & Sons, Ltd.     

异喹啉酰肼构筑锌配合物的合成、晶体结构及其性质

采用普通溶液法合成了配合物[Zn(eiqnthz)_2]·DMF(1)和[Zn3(piqnthz)_2Cl_2]·2H_2O(2)(Heiqnthz=N,N′-乙酰异喹啉甲酰肼,H2piqnthz=N,N′-丙酰异喹啉甲酰肼)。通过X射线单晶衍射分析、X射线粉末衍射分析、红外光谱分析、热重分析以及荧光光谱分析等分析方法对2个配合物进行结构测定和性质表征。结构分析表明配合物1是单核结构,单斜晶系,空间群为C2/c,锌离子周围有4个氮原子和2个氧原子与之配位,形成一个畸变的N4O2八面体构型。配合物2属于单斜晶系,C2/c空间群,三核结构。中心原子Zn(1)、Zn(2)、Zn(3)均为5配位,Zn(1)、Zn(3)位于分子两端并且是变形四角锥配位构型,Zn(2)位于中间形成三角双锥配位构型,整体呈V字型。荧光分析表明Heiqnthz、H2piqnthz与锌(Ⅱ)离子配位后其荧光都发生较大的红移。     

Reaction of 3-aminoquinoline-2,4-diones with isothiocyanic acid—an easy pathway to thioxo derivatives of imidazo[1,5-c]quinazolin-5-ones and imidazo[4,5-c]quinolin-4-ones

3-Amino-1H,3H-quinoline-2,4-diones react with thiourea or potassium thiocyanate in boiling acetic acid to give novel 2,3-dihydro-3-thioxoimidazo[1,5-c]quinazolin-5(6H)-ones in high yields. However, if the starting compounds are substituted with a benzyl group at position 3, a C-debenzylation proceeds to give 2,3-dihydro-2-thioxo-1H-imidazo[4,5-c]quinolin-4(5H)-ones. According to a proposed reaction mechanism, a molecular rearrangement of the primarily formed mono-substituted thiourea takes place. All compounds were characterized by ¹H, ¹³C and ¹⁵N NMR and IR spectroscopy as well as by mass spectrometry.     

分数导数型本构关系描述粘弹性梁的振动分析

本文研究粘弹性梁在周期激励作用下的受迫振动问题。梁的材料满足Kelvin-Volgt分数导数型本构关系。基于动力学方程、本构关系和应变－位移关系建立了小变形粘弹性梁的振动方程。采用分离变量法分析粘弹性梁的自由振动,导出模态坐标满足的常微分－积分方程和模态函数满足的常微分方程,对于两端简支的截面梁给出了固有频率和模态函数。对于简谐激励作用下粘弹性梁的受迫振动,利用模态叠加得到了稳态响应。最后给出数值算例说明本文方法的应用。     

Synthesis of Thiourea Derivatives on Soluble Polymeric Support

A modified poly(ethylene glycol) (PEG) has been developed as the soluble polymeric supports for liquid phase synthesis of novel thiourea derivatives.In each step of the sequence,the PEG-bound products were precipitated in cold Et2O and the unreacted materials and by-products were removed by simple filtration.The progress of reaction,purity of the isolation and the structure of the PEG-bound products were easily monitored by TLC,IR and ^1H NMR spectra.Representative thiourea derivatives were obtained in moderate yields with excellent purity from this modified PEG-bound product by the cleavage with 50% TFA/H2O.     

高效液相色谱分析食品罐内涂料中双酚A和双酚F环氧衍生物残留

建立了高效液相色谱分析食品罐内涂料中双酚A(BPA)和双酚F(BPF)环氧衍生物的方法.样品经乙腈提取后,旋转蒸发浓缩至干,以V(乙腈)∶ V(水)=50∶ 50混合液溶解并定容;采用Lichrospher C18柱,以乙腈/水为流动相梯度洗脱,进行高效液相色谱分离;荧光检测器检测,激发波长230 nm,发射波长301 nm.在2.3～230 μg/L浓度范围内,各BPA和BPF环氧衍生物的响应峰面积与其相应浓度呈良好相关性,检出限为0.57～6.55 μg/L;在80～400 μg/L添加水平范围内,平均添加回收率为85%～107%;相对标准差小于7.4%.结果表明,本方法适用于食品罐内涂料中BPA和BPF环氧衍生物残留分析.     

Quantum Correlations in Werner Derivatives

Quantum correlations in Werner derivatives are studied with two diferent approaches,i.e.,measurementinduced disturbance(MID)[Phys.Rev.A 77(2008)022301]and ameliorated MID(AMID)[J.Phys.A 44(2011)352002].They are derived via strict deductions with MID while numerically calculated via the measurement optimization with AMID.Interestingly,quantum correlations captured with both approaches are completely coincident.Moreover,some distinct features of the quantum correlations and their underlying physics are exposed via analyses and discussions.     

分数维Vasicek利率模型下的欧式期权定价公式

假定股票价格和利率的运动过程服从几何分数维布朗运动,利用风险对冲技术,分数维布朗运动随机分析理论与偏微分方程方法,得到了分数维Vasicek随机利率下欧式期权所满足的定价方程,获得了波动率是对间函数的情形下欧式看涨和看跌期权的一般定价公式以及它们的平价公式.     

B‐spline spectral method for constrained fractional optimal control problems

In this paper, we present a direct B‐spline spectral collocation method to approximate the solutions of fractional optimal control problems with inequality constraints. We use the location of the maximum of B‐spline functions as collocation points, which leads to sparse and nonsingular matrix B whose entries are the values of B‐spline functions at the collocation points. In this method, both the control and Caputo fractional derivative of the state are approximated by B‐spline functions. The fractional integral of these functions is computed by the Cox‐de Boor recursion formula. The convergence of the method is investigated. Several numerical examples are considered to indicate the efficiency of the method.     

烷氧基取代聚对苯乙炔三阶非线性光学性能

通过双醚化反应、氯甲基化反应以及在强碱性条件下进行的脱氯化氢反应制备聚（2-甲氧基-5-丁氧基）对苯乙炔（PMOBOPV）、聚（2-甲氧基-5-己氧基）对苯乙炔（PMOHOPV）、聚（2,5-二丁氧基）对苯乙炔（PDBOPV）和聚（2,5-二己氧基）对苯乙炔（PDHOPV）等四种可溶性聚对苯乙炔（PPV）衍生物,通过紫外-可见吸收光谱对产物分子结构进行表征.结果显示,PMOBOPV、PMOHOPV、PDBOPV和PDHOPV的共轭π电子发生π → π* 跃迁的吸收峰分别位于491 nm、495nm、504nm和510nm处,相应的光学禁带宽度分别为2.23eV、2.18eV、2.12eV和2.07eV.利用简并四波混频技术测量PPV衍生物的三阶非线性光学性能,探讨了分子结构对PPV衍生物三阶非线性极化率（χ(3)）的影响.研究发现,激发波长为532 nm时,PMOBOPV、PMOHOPV、PDBOPV和PDHOPV的共振χ(3)值分别为3.45×10－10、5.13×10－10、7.15×10－10和9.61×10－10 esu;激发波长为1064 nm时,它们的非共振χ(3)值分别为1.09×10－11、1.42×10－11、1.62×10－11和2.14×10－11 esu.