On the concept and existence of solutions for fractional impulsive systems with Hadamard derivatives

In this paper, a class of nonlinear fractional order differential impulsive systems with Hadamard derivative is discussed. First, a reasonable concept on the solutions of fractional impulsive Cauchy problems with Hadamard derivative and the corresponding fractional integral equations are established. Second, two fundamental existence results are presented by using standard fixed point methods. Finally, two examples are given to illustrate our theoretical results.     

Positive numerical splitting method for the Hull and White 2D Black–Scholes equation

We consider the locally one‐dimensional backward Euler splitting method to solve numerically the Hull and White problem for pricing European options with stochastic volatility in the presence of a mixed derivative term. We prove the first‐order convergence of the time‐splitting. The parabolic equation degenerates on the boundary x = 0 and we apply a fitted finite volume scheme to the equation to resolve the degeneracy and derive the fully discrete problem as we also investigate the discrete maximum principle. Numerical experiments illustrate the efficiency of our difference scheme. © 2014 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 31: 822–846, 2015     

变时滞Hopfield神经网络的全局吸引性和全局指数稳定性

对一类具时滞的Hopfeild型神经网络模型,在非线性神经元激励函数只要求满足Lipschitz连续的条件下,利用推广的Halanay时延微分析不等式、Dini导数以及泛函微分析技术,给出了这类模型的平衡点全局指数稳定性和全局吸引性的充分条件,这些条件易于检验,且改进和推广了前人的结论.此外,此文给出了研究神经网络模型的全局吸引性的微分不等式比较方法.     

三嗪类化合物的合成及其产酸性能研究

合成了一系列的三嗪类光生酸剂1a—1e,确定了它们的结构,并对1e在乙腈溶剂中365和405nm光下的曝光分解产酸性能进行了初步的定量研究.结果表明,在测定浓度范围内分解量子产率和产酸量子产率基本上都不随浓度的变化而变化,在405nm光下比在365nm光下有更高的分解和产酸量子效率.有关这类化合物的光生酸性能与曝光波长的关系正在进一步研究中.     

Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation

In this paper, we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation, namely BurgersKadomtsev-Petviashvili equation(Burgers-K-P) that arises in shallow water waves.Furthermore, using the residual power series method(RPSM), approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package. We also presented a few graphical illustrations for some surfaces. The fractional derivatives were considered in the conformable sense. All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method. The numerical outcomes confirmed that both methods are simple, robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations.     

一种新型三角架罗丹明B荧光探针对Cu～（2＋）识别性能研究

设计、合成了一种新颖的三角架结构罗丹明B衍生物（2）.在乙醇-水（8/1,V/V）介质中,用Tris-HCl控制体系pH为6.8,观察到Cu^2＋对化合物2的荧光及紫外-可见吸收增强性能,同时化合物2对Cu^2＋具有较高的选择性响应.选择最大激发和发射波长为557/577nm,测定了探针2（1.00×10^-5mol·L^-1）对Cu^2＋响应的校准曲线,线性范围为0.10～10.00×10^-5mol·L^-1,相关系数R^2=0.9964（n=15）,检出限为1.129×10^-7mol·L^-1,平行测定5次的相对标准偏差（R.S.D.）为2.2%;以557nm为最大吸收波长测定紫外吸收,Cu^2＋响应的浓度线性范围为0.50～25.00×10^-5mol·L^-1,相关系数R^2=0.9948（n=13）,检出限为3.338×10^-7mol·L^-1.     

Syntheses, Crystal Structures and Fluorescence Properties of Two Triazolyl Derivatives with Biphenyl Links

Two novel triazolyl derivatives with biphenyl links, namely 4,4-bis（1,2,4-triazol-1-ylmethyl）biphenylene 1 and 4,4-bis（3,5-dimethyl-1,2,4-triazol-1-ylmethyl）biphenylene 2, have been synthesized and structurally characterized by single-crystal X-ray diffraction. Compounds 1·H2O·HCl and 2·2H2O·2HCl crystallize in the monoclinic system with space group C2/c and P21/c, respectively. The dihedral angles of the two phenyl rings are 30.26（6）° in 1·H2O·HCl, while co-planar （0.00（7）°） in 2·2H2O·2HCl. In 1·H2O·HCl, the N-H…O hydrogen bonds link 1 to form chain-like structures which are further connected by O-H…Cl, C-H…Cl, C-H…O and π-π supramolecular interactions. The hydrogen bonds of O-H…Cl in 2·2H2O·2HCl provide distinguishing P/M helical chains along the b axis, and these chains are further connected by N-H…O hydrogen bonds to generate a 2D structure. Compounds 1 and 2 in methanol solution show much stronger emission bands at 319 nm than biphenyl at 316 nm under excitation at 260 nm.     

9,10⁃二(N⁃苯基吲哚⁃3⁃乙烯基)蒽的合成及聚集诱导荧光和压致荧光变色性质

通过简单的Wittig反应合成了一个荧光化合物9,10-二(N-苯基吲哚-3-乙烯基)蒽(IA-Ph); 通过核磁共振和质谱对其结构进行了确认; 利用荧光发射光谱和紫外吸收光谱对其光物理性质进行了表征. 结果表明, 化合物IA-Ph兼具聚集诱导荧光(AIE)和压致荧光变色性质, 在相同浓度下, 该化合物在THF/H₂O(体积比1∶9)混合溶液中的荧光强度比在纯四氢呋喃(THF)溶液中增加了12倍, 具有明显的AIE效应. 通过简单而有效的机械力研磨, 化合物可以从初始的发绿光转变为研磨后的橙红光, 光谱红移约68 nm; 而且在加热或溶剂熏蒸条件下, 化合物的颜色可以回复到起始的绿光, 具有完全可逆性.     

Performance enhancement of a DC-operated micropump with electroosmosis in a hybrid nanofluid: fractional Cattaneo heat flux problem

The purpose of this investigation is to theoretically shed some light on the effect of the unsteady electroosmotic flow (EOF) of an incompressible fractional second-grade fluid with low-dense mixtures of two spherical nanoparticles, copper, and titanium. The flow of the hybrid nanofluid takes place through a vertical micro-channel. A fractional Cattaneo model with heat conduction is considered. For the DC-operated micropump, the Lorentz force is responsible for the pressure difference through the microchannel. The Debye-Hükel approximation is utilized to linearize the charge density. The semi-analytical solutions for the velocity and heat equations are obtained with the Laplace and finite Fourier sine transforms and their numerical inverses. In addition to the analytical procedures, a numerical algorithm based on the finite difference method is introduced for the given domain. A comparison between the two solutions is presented. The variations of the velocity heat transfer against the enhancements in the pertinent parameters are thoroughly investigated graphically. It is noticed that the fractional-order parameter provides a crucial memory effect on the fluid and temperature fields. The present work has theoretical implications for biofluid-based microfluidic transport systems.