一类非线性发展方程的精确解

利用hirota双线性法,得到(3+1)维孤子方程、(3+1)维KP-Boussinesq方程、(2+1)维修正Caudrey-Dodd-Gibbon-Kotera-S awada方程、Hirota-Satsuma浅水波方程的精确解,并做出一部分解的图形,进一步研究解的结构和性质.     

两个基于2,5-二甲氧基对苯二甲酸和咪唑衍生物的超分子钴配位聚合物的结构及光催化反应

本文以咪唑衍生物为配体,通过水热合成法与钴离子制备出两个配位聚合物:{[Co(DTA)(1,4-DIB)(H₂O)]·H₂O}_n(1)和[Co(DTA)(1,3-BMIB)]_n(2)(1,4-DIB=1,4-二(1H-咪唑-1-基)苯; 1,3-BMIB=1,3-二(4-甲基-1H-咪唑-1-基)苯;H₂DTA=2,5-二甲氧基对苯二甲酸)。利用X射线单晶衍射、粉末衍射、热失重、元素分析、红外光谱以及固体紫外-可见光谱等对两个配合物进行了表征。结构分析证实配合物1和2是通过二维结构堆积成的三维超分子化合物。粉末衍射测试则显示两个配合物在水中有很好的稳定性。固体紫外-可见光谱显示两个配合物属半导体材料,对紫外-可见光有很强的吸收作用。在光催化实验中,配合物1和2可加快亚甲基蓝的降解速度。     

Synthesis and optical properties of new chalcones containing 4-[bis(2-hydroxyethyl)amino]phenyl fragment

New chalcones with 4-[bis(2-hydroxyethyl)amino] phenyl fragment were obtained from 4-[bis(2-acetoxyethyl) amino]- benzaldehyde by the Claisen–Schmidt reaction. From their UV-VIS absorption and emission spectra, optical band gap values were calculated based on the Stokes shifts as well as the molar absorption coefficients and fluorescence quantum yields were estimated. The dependence of the absorption and emission maxima on solvent polarity and pH was evaluated.     

Generalized Jacobi spectral Galerkin method for fractional pantograph differential equation

This work is concerned with the extension of the Jacobi spectral Galerkin method to a class of nonlinear fractional pantograph differential equations. First, the fractional differential equation is converted to a nonlinear Volterra integral equation with weakly singular kernel. Second, we analyze the existence and uniqueness of solutions for the obtained integral equation. Then, the Galerkin method is used for solving the equivalent integral equation. The error estimates for the proposed method are also investigated. Finally, illustrative examples are presented to confirm our theoretical analysis.     

Highly sensitive perylene tetra-(alkoxycarbonyl) based colorimetric and ratiometric probes for fluorine detection

Fluoride anion (F^?) affects environmental, biological, and chemical processes significantly. Therefore, its detection has received increasing attention, and sensitive, effective, and convenient probes for F^? detection need to be developed urgently. In this work, two perylene tetra-(alkoxycarbonyl) (PTAC) based colorimetric and ratiometric probes, P1 and P2, were developed for the detection of F^?. The interactions between F^? and these two probes were investigated by absorption, electrochemistry, ¹H NMR, and density functional methods. Both the two probes were complexed with F^? with a ratio of 1:1. The detection limits of P1 and P2 were 0.22 μM and 0.87 μM, respectively. It was worth noting that the absorption peak of P1 showed a 190 nm red shift when sensing F^?, and P1 is the largest red shift value reported in F^? probes based on PTAC derivatives. This phenomenon was resulted from the unique configuration and deprotonation of P1 that can promote the intramolecular charge transfer (ICT). This strategy provides an example for the development of other ion probes based on D-A type ICT mechanism.     

Penicillilactone A,a novel antibacterial 7-membered lactone derivative from the sponge-associated fungus Penicillium sp. LS54

One novel 7-membered lactone derivative, penicillilactone A (1), together with two known compounds, rugulosin A (2) and rugulosin (3) were isolated from the sponge-derived fungus Penicillium sp. LS54. Their structures were elucidated on the basis of spectroscopic analysis and comparison with literature data. Remarkably, penicillilactone A (1) is the first natural product containing a 7-membered lactone ring fused with a furan core. Penicillilactone A (1) exhibited moderate antibacterial activity against aquatic pathogen Vibrio harveyi with an MIC value of 8 μg/mL.     

Thermoelastic solutions for thermal distributions moving over thin slim rod under memory-dependent three-phase lag magneto-thermoelasticity

Abstract

Enlightened by the Caputo fractional derivative, the present study deals with a novel mathematical model of generalized thermoelasticity to investigate the transient phenomena due to the influence of magnetic field and moving heat source in a rod in the context of three-phase lag (TPL) theory of thermoelasticity. Both ends of the rod are fixed and heat insulated. Employing Laplace transform as a tool, the problem has been transformed into the space-domain and solved analytically. Finally, solutions in the real-time domain are obtained by applying the inverse Laplace transform. Numerical calculation for stress, displacement, and temperature within the rod is carried out and displayed graphically. The effect of moving heat source speed on temperature, stress, and temperature is studied. It is found from the distributions that the temperature, thermally induced displacement and stress of the rod are found to decrease at large source speed. For the better understanding of the effect of moving heat source on all the distributions, three animations are added.     

逻辑函数高阶布尔e偏导数求解算法的实现

针对已有方法在求解布尔e偏导数时只能解决小规模电路的问题,提出了一种基于逻辑函数不相交运算的大函数高阶布尔e偏导数的求解算法.该方法将逻辑函数转化为不相交乘积项的集合,用逻辑函数的不相交运算替代布尔e导数运算中的逻辑"与"运算;并将不包含待求导变量的乘积项拆分出来,不参与布尔e导数运算,以达到降低算法复杂度、提高算法速度的目的.提出的算法用C语言编程实现,并用MCNC测试电路进行了测试.实验结果显示,本算法能快速实现大函数高阶布尔e偏导数的求解,求解效率与参与不相交运算的乘积项数量有关,但对输入变量的数量不敏感.     

二元函数四条性质之间的关系

二元函数的连续性,偏导数存在性,偏导数连续性以及可微性是二元函数的四条经典性质,它们之间的关系一直是学生的疑惑点,本文结合严格的证明和典型的反例给出四条性质之间关系的详尽阐释.     

Sharper uncertainty principles associated with Lp-norm

Motivated by the well-established phase derivative embedded technique, this study devotes to sharper uncertainty principles related to the L^p-norm type of uncertainty product, giving rise to two kinds of uncertainty inequalities that improve the classical result through providing tighter lower bounds. The conditions that truly reach these better estimates are obtained. Examples and simulations are carried out to verify the correctness of the derived results, and finally, possible applications in time-frequency analysis are also given.