一种新型芴类衍生物的光谱性质研究

合成了具有大π共轭性的对称型芴类衍生物9,9-二(2-乙基已基)-2,7-二(2-(4-甲氧基)苯-2,1-乙烯基)芴(简写为MO-Flu-MO)。通过元素分析、质谱、紫外-可见光谱和红外光谱对其进行了表征。测试了该染料在乙腈、二氯甲烷、四氢呋喃和正己烷4种不同极性溶剂中的线性吸收光谱和单光子荧光谱。结果发现溶剂效应对吸收光谱和荧光光谱表现出不同程度的影响,对产生这些光谱行为的主要原因进行了讨论。     

Fractional diffusion models of option prices in markets with jumps

Most of the recent literature dealing with the modeling of financial assets assumes that the underlying dynamics of equity prices follow a jump process or a Lévy process. This is done to incorporate rare or extreme events not captured by Gaussian models. Of those financial models proposed, the most interesting include the CGMY, KoBoL and FMLS. All of these capture some of the most important characteristics of the dynamics of stock prices. In this article we show that for these particular Lévy processes, the prices of financial derivatives, such as European-style options, satisfy a fractional partial differential equation (FPDE). As an application, we use numerical techniques to price exotic options, in particular barrier options, by solving the corresponding FPDEs derived.     

Simultaneous Determination of Acetylsalicylic Acid and Caffeine in Pharmaceutical Formulation by First Derivative Synchronous Fluorimetric Method

A sensitive, rapid, and specific assay has been developed for the simultaneous determination of acetylsalicylic acid and caffeine in commercial tablets based on their natural fluorescence. The mixture of these drugs was resolved by first derivative synchronous fluorimetric technique using two scans. At Δλ=106 nm, using first derivative synchronous scanning, only acetylsalicylic acid yields a detectable signal at 316 nm (peak to zero method) which is unaffected by caffeine. At Δλ=30 nm, the signal of caffeine at 288 nm (peak to zero method) is not affected by acetylsalicylic acid. The range of application is between 0.021 and 41.62 μg ml⁻¹ (correlation coefficient, R=0.9995) for acetylsalicylic acid and between 0.4486 and 44.86 μg ml⁻¹ (correlation coefficient, R=0.99786) for caffeine. The recovery range of 98.40–102% for acetylsalicylic acid and 90–100.5% for caffeine from their synthetic mixture was reported. Overall recovery of both compounds about 97–99% for acetylsalicylic acid and 97–98% for caffeine was obtained from real sample analysis. The detection limits are 0.0013 μg ml⁻¹ and 0.0306 μg ml⁻¹ for acetylsalicylic acid and caffeine, respectively. The relative standard deviation (n=10) for 20 μg ml⁻¹ of acetylsalicylic acid is 2.75% and for 2.2 μg ml⁻¹of caffeine is 1.7%.     

Fully HOC Scheme for Mixed Convection Flow in a Lid-Driven Cavity Filled with a Nanofluid

A fully higher-order compact (HOC) finite difference scheme on the 9-point two-dimensional (2D) stencil is formulated for solving the steady-state laminar mixed convection flow in a lid-driven inclined square enclosure filled with water-$Al_2O_3$ nanofluid. Two cases are considered depending on the direction of temperature gradient imposed (Case I, top and bottom; Case II, left and right). The developed equations are given in terms of the stream function-vorticity formulation and are non-dimensionalized and then solved numerically by a fourth-order accurate compact finite difference method. Unlike other compact solution procedure in literature for this physical configuration, the present method is fully compact and fully higher-order accurate. The fluid flow, heat transfer and heat transport characteristics were illustrated by streamlines, isotherms and averaged Nusselt number. Comparisons with previously published work are performed and found to be in excellent agreement. A parametric study is conducted and a set of graphical results is presented and discussed to elucidate that significant heat transfer enhancement can be obtained due to the presence of nanoparticles and that this is accentuated by inclination of the enclosure at moderate and large Richardson numbers.     

一个分数阶忆阻器模型及其简单串联电路的特性

忆阻器是具有时间记忆特性的非线性电阻. 经典HP TiO₂忆阻器模型的忆阻值为此前通过忆阻器电流的时间积分, 即记忆没有损失. 而最近研究证实HP TiO₂ 线性忆阻器掺杂层厚度不能等于零或者器件整体厚度, 导致器件的记忆有损失. 基于此发现, 本文首先提出了一个阶数介于0 与1间的分数阶HP TiO₂ 线性忆阻器模型, 研究了当受到周期外激励时, 分数阶导数的阶数对其忆阻值动态范围和输出电压动态幅值的影响规律, 推导出了磁滞旁瓣面积的计算公式. 结果表明, 分数阶导数阶数对磁滞回线的形状及所围成区域面积有重要影响. 特别地, 在外激频率大于1时, 分数阶忆阻器的记忆强度达到最大. 然后讨论了此分数阶忆阻器与电容或电感串联组成的单口网络的伏安特性. 结果表明, 在周期激励驱动时, 随着分数阶导数阶数的变化, 此分数阶忆阻器与电容的串联电路呈现出纯电容电路与忆阻电路的转换, 而它与电感的串联电路则呈现出纯电感电路与忆阻电路的转换.     

A new operational vector approach for time-fractional subdiffusion equations of distributed order based on hybrid functions

This research study deals with the numerical solutions of linear and nonlinear time-fractional subdiffusion equations of distributed order. The main aim of our approach is based on the hybrid of block-pulse functions and shifted Legendre polynomials. We produce a novel and exact operational vector for the fractional Riemann–Liouville integral and use it via the Gauss–Legendre quadrature formula and collocation method. Consequently, we reduce the proposed equations to systems of equations. The convergence and error bounds for the new method are investigated. Six problems are tested to confirm the accuracy of the proposed approach. Comparisons between the obtained numerical results and other existing methods are provided. Numerical experiments illustrate the reliability, applicability, and efficiency of the proposed method.     

Cauchy problems for Hilfer fractional evolution equations on an infinite interval

It is well known that the classical Ascoli-Arzelà theorem is powerful technique to give a necessary and sufficient condition for investigating the relative compactness of a family of abstract continuous functions, while it is limited to finite compact interval. In this paper, we shall generalize the Ascoli-Arzelà theorem on an infinite interval. As its application, we investigate an initial value problem for fractional evolution equations on infinite interval in the sense of Hilfer type, which is a generalization of both Riemann-Liuoville and Caputo fractional derivatives. Our methods are based on the Hausdorff theorem, classical/generalized Ascoli-Arzelà theorem, Schauder fixed point theorem, Wright function, and Kuratowski measure of noncompactness. We obtain the existence of mild solutions on an infinite interval when the semigroup is compact as well as noncompact.     

A numerical technique based on B-spline for a class of time-fractional diffusion equation

This paper presents an efficient numerical technique for solving a class of time-fractional diffusion equation. The time-fractional derivative is described in the Caputo form. The L1 scheme is used for discretization of Caputo fractional derivative and a collocation approach based on sextic B-spline basis function is employed for discretization of space variable. The unconditional stability of the fully-discrete scheme is analyzed. Two numerical examples are considered to demonstrate the accuracy and applicability of our scheme. The proposed scheme is shown to be sixth order accuracy with respect to space variable and (2 − α)-th order accuracy with respect to time variable, where α is the order of temporal fractional derivative. The numerical results obtained are compared with other existing numerical methods to justify the advantage of present method. The CPU time for the proposed scheme is provided.     

The Cubic B-Spline Method for a Class of Caputo-Fabrizio Fractional Differential Equations北大核心CSCD

基于分数阶微积分基本定理和三次B样条理论,构造了求解线性Caputo-Fabrizio型分数阶微分方程数值解的三次B样条方法,利用分数阶微积分基本定理将初值问题转化为关于解函数的表达式,再使用三次B样条函数逼近表达式中积分项的被积函数,进而计算了一类Caputo-Fabrizio型分数阶微分方程的数值解.给出了所构造的三次B样条方法的误差估计、收敛性和稳定性的理论证明.数值实验表明,该文数值方法在求解一类Caputo-Fabrizio型分数阶微分方程数值解时具有一定的可行性和有效性,且计算精度和计算效率优于现有的两种数值方法.