Solvability of a nonlinear fifth‐order difference equation

Some formulas for well‐defined solutions to four very special cases of a nonlinear fifth‐order difference equation have been presented recently in this journal, where some of them were proved by the method of induction, some are only quoted, and no any theory behind the formulas was given. Here, we show in an elegant constructive way how the general solution to the difference equation can be obtained, from which the special cases very easily follow, which is also demonstrated here. We also give some comments on the local stability results on the special cases of the nonlinear fifth‐order difference equation previously publish in this journal.     

Single‐armed salamo‐like dioxime and its multinuclear Cu (II), Zn (II) and Cd (II) complexes: Syntheses,structural characterizations,Hirshfeld analyses and fluorescence properties

Three multinuclear Cu (II), Zn (II) and Cd (II) complexes, [Cu₂(L)(μ‐OAc)]·CHCl₂ ( 1 ), [Zn₂(L)(μ‐OAc)(H₂O)]·3CHCl₃ ( 2 ) and [{Cd₂(L)(OAc)(CH₃CH₂OH)}₂]·2CH₃CH₂OH ( 3 ) with a single‐armed salamo‐like dioxime ligand H₃L have been synthesized, and characterized by FT‐IR, UV–vis, X‐ray crystallography and Hirshfeld surfaces analyses. The ligand H₃L has a linear structure and C‐H···π interactions between the two molecules. The complex 1 is a dinuclear Cu (II) complex, Cu1 and Cu2 are all five‐coordinate possessing distorted square pyramidal geometries. The complex 2 also forms a dinuclear Zn (II) structure, and Zn1 and Zn2 are all five‐coordinate bearing distorted trigonal bipyramidal geometries. The complex 3 is a symmetrical tetranuclear Cd (II) complex, and Cd1 is a hexa‐coordinate having octahedral configuration and Cd2 is hepta‐coordinate with a pentagonal bipyramidal geometry, and it has π···π interactions inside the molecule. In addition, fluorescence properties of the ligand and its complexes 1 – 3 have also been discussed.     

The regularity of the multiple higher-order poles solitons of the NLS equation

Based on the inverse scattering method, the formulae of one higher-order pole solitons and multiple higher-order poles solitons of the nonlinear Schrödinger equation (NLS) equation are obtained. Their denominators are expressed as , where is a matrix frequently constructed for solving the Riemann-Hilbert problem, and the asterisk denotes complex conjugate. We take two methods for proving is invertible. The first one shows matrix is equivalent to a self-adjoint Hankel matrix , proving . The second one considers the block-matrix form of , proving . In addition, we prove that the dimension of is equivalent to the sum of the orders of pole points of the transmission coefficient and its diagonal entries compose a set of basis.     

Exceptionally Plastic/Elastic Organic Crystals of a Naphthalidenimine-Boron Complex Show Flexible Optical Waveguide Properties

The design of molecular compounds that exhibit flexibility is an emerging area of research. Although a fair amount of success has been achieved in the design of plastic or elastic crystals, realizing multidimensional plastic and elastic bending remains challenging. We report herein a naphthalidenimine–boron complex that showed size-dependent dual mechanical bending behavior whereas its parent Schiff base was brittle. Detailed crystallographic and spectroscopic analysis revealed the importance of boron in imparting the interesting mechanical properties. Furthermore, the luminescence of the molecule was turned-on subsequent to boron complexation, thereby allowing it to be explored for multimode optical waveguide applications. Our in-depth study of the size-dependent plastic and elastic bending of the crystals thus provides important insights in molecular engineering and could act as a platform for the development of future smart flexible materials for optoelectronic applications.     

Development of nanomaterial chemosensors for toxic metal ions sensing

Heavy metal ions are harmful to aquatic life and humans owing to their high toxicity and non‐biodegradability, so their removal from wastewater is an important task. Therefore, this work focuses on designing suitable, simple and economical nanosensors to detect and remove these metal ions with high selectivity and sensitivity. Based on this idea, different types of mesoporous materials such as hexagonal SBA‐15, cubic SBA‐16 and spherical MCM‐41, their chloro‐functionalized derivatives, as well as 4‐(4‐nitro‐phenylazo)‐naphthalen‐1‐ol (NPAN) azo dye have been synthesized, with the aim of designing some optical nanosensors for metal ions sensing applications. The mentioned azo dye has been anchored into the chloro‐functionalized mesoporous materials. The designed nanosensors were characterized using scanning and transmission electron microscopy as well as Fourier transform infrared and UV–visible spectral analysis, nitrogen adsorption–desorption isotherms, low‐angle X‐ray diffraction and thermogravimetric analyses. Their optical sensing to various toxic metal ions such as Cd (II), Hg (II), Mn (II), Fe (II), Zn (II) and Pb (II) at different values of pH (1.1, 4.9, 7 and 12) was investigated. The optimization of experimental conditions, including the effect of pH and metal ion concentration, was examined. The experimental results showed that the solution pH had a major impact on metal ion detection. The optical nanosensors respond well to the tested metal ions, as reflected by the enhancement in both absorption and emission spectra upon adding different concentrations of the metal salts and were fully reversible on adding ethylene diamine tetra acetic acid or citric acid to the formed complexes. High values of the binding constants for the designed nanosensors were observed at pHs 7 and 12, confirming the strong chelation of different metals to the nanosensor at these pHs. Also, high binding constants and sensitivity were observed for NPAN‐MCM‐41 as a nanosensor to detect the different metal ions. From the obtained results, we succeeded in transforming the harmful azo dye into an environmentally friendly form via designing of the optical nanosensors used to detect toxic metal ions in wastewater with high sensitivity.     

基于EKF的水下LD通信精对准控制算法

高速激光通信中接收机与光斑中心很难处于精对准状态,导致水下光通信链路难以稳定建立.首先采用蒙特卡洛仿真统计法分析激光光子在海水中传输的接收光强分布规律,再通过实验对接收端的光斑图像进行采样分析,利用曲线拟合得到接收器位置与接收光强的关系.仿真与实验结果表明:光束经过25 m的水下传输,接收光强分布仍近似为高斯分布.采用非线性估计算法(扩展卡尔曼滤波)与基本状态控制反馈理论,根据接收光强度估计接收器当前位置与最大光强处的距离,通过反馈算法实现接收端与光斑中心的主动跟踪对准.算法仿真结果显示,接收端对准误差在2 mm以下,稳定后接收效率超过98%.     

Synthesis,Properties, and Applications of 2-D Materials: A Comprehensive Review

Recent advances in atomically thin two-dimensional (2-D) materials have led to a variety of promising future technologies for post-CMOS nanoelectronics and energy generation. This review is an attempt to thoroughly illustrate the current status and future prospects for 2-D materials other than graphene (e.g., BN nanosheets, MoS₂, NbSe₂, WS₂, etc.), which have already been contemplated for both low-end and high-end technological applications. An overview of the different synthesis techniques for 2-D materials is presented here, with an exploration of the potential for developing methods of controllable large scale synthesis. Furthermore, we summarize the underlying theories which correlate the structural and physical properties of 2-D materials with their state-of-the-art applications. Finally, we show that utilizing the unprecedented properties arising from these materials would lead to innovative devices. Such devices would significantly reduce both device dimensions and power consumption, as necessary for the creation of tomorrow's sustainable technology.     

石墨烯/正十八烷微胶囊的制备与及其热性能研究

以石墨烯/正十八烷为芯材,三聚氰胺-尿素-甲醛树脂(MUF)为壁材,苯乙烯马来酸酐共聚物(SMA)为乳化剂,采用乳液聚合法制备相变微胶囊.系统研究了石墨烯对于正十八烷微胶囊性能的影响.采用场发射扫描电子显微镜(FE-SEM)、傅里叶变换红外光谱分析仪(FTIR)、拉曼光谱仪、X射线衍射仪(XRD)、Hot Disk热常数分析仪、示差扫描量热仪(DSC)和热重分析仪(TGA)对相变微胶囊的外貌形态、晶型结构和热性能进行表征和分析.结果表明,微胶囊呈圆球形且光滑,粒径约为1~30μm.当石墨烯添加量为0.1 g时,微胶囊的形貌无明显变化.当加入过量石墨烯时,微胶囊出现了明显的团聚现象.XRD测试表明,包覆于微胶囊中的石墨烯没有使微胶囊的结晶峰位置发生明显的偏移,这对于微胶囊的实际应用是有利的.微胶囊的相变热焓和包覆率随着石墨烯的加入而不断减小,但芯材的过冷现象得到了明显的改善.石墨烯对于微胶囊传热性能的提升有着显著的效果.当石墨烯的添加量为0.2 g时,微胶囊的导热系数为0.092 W·m-1·K-1,与纯微胶囊相比提高了约51%,这说明石墨烯改善了传统相变微胶囊的传热性能,提升了相变微胶囊的应用性能.     

Competing energy scales in high‐temperature superconductors: Ultrafast pump–probe studies

We present a review of photoexcited quasiparticle dynamics of cuprate and pnictide high‐temperature superconductors in regimes (temperature, doping) where different phases such as superconductivity, spin‐density‐wave (SDW) and pseudogap phases coexist or compete with one another. We start with the overdoped cuprate superconductor Y_1–xCa_x Ba₂Cu₃O_7–δ, where the superconducting gap and pseudogap coexist in the superconducting state. In another cuprate Tl₂Ba₂Ca₂Cu₃O_y, we ob‐ serve a competition between SDW and superconducting orders deep in the superconducting state. Finally, in the underdoped iron pnictide superconductor (Ba,K)Fe₂As₂, SDW order forms at 85 K, followed by superconductivity at 28 K. We also find the emergence of a normal‐state order that suppresses SDW at a temperature T * ～ 60 K and argue that this normal‐state order is a precursor to superconductivity. (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Painlev′e Prop erty and Integrability of Polynomial Dynamical Systems

The main purpose of this paper is to investigate the connection between the Painlev′e property and the integrability of polynomial dynamical systems. We show that if a polynomial dynamical system has P...