Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

In nonlinear physics,it is very difficult to study interactions among different types of nonlinear waves.In this paper,the nonlocal symmetry related to the truncated Painleve′expansion of the(2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system.Then the corresponding group invariant solutions are found,from which interaction solutions among different types of nonlinear waves can be found.Furthermore,the Burgers equation is also studied by using the generalized tanh expansion method and a new Ba¨cklund transformation(BT)is obtained.From this BT,novel interactive solutions among different nonlinear excitations are found.     

Robust output feedback cruise control for high-speed train movement with uncertain parameters

In this paper,the robust output feedback cruise control for high-speed train movement with uncertain parameters is investigated.The dynamic of a high-speed train is modeled by a cascade of cars connected by flexible couplers,which is subject to rolling mechanical resistance,aerodynamic drag and wind gust.Based on Lyapunov’s stability theory,the sufficient condition for the existence of the robust output feedback cruise control law is given in terms of linear matrix inequalities(LMIs),under which the high-speed train tracks the desired speed,the relative spring displacement between the two neighboring cars is stable at the equilibrium state,and meanwhile a small prescribed H∞ disturbance attenuation level is guaranteed.One numerical example is given to illustrate the effectiveness of the proposed methods.     

Microwave-Assisted Synthesis,Crystal Structure and Magnetic Behavior of a Schiff Base Heptanuclear Cobalt Cluster

The reaction of Co(ClO₄)₂·6H₂O with 2-hydroxy-3-methoxy-benzaldehyde and an aqueous solution of methylamine in acetonitrile/MeOH under microwave irradiation and controlled temperature/pressure leads to formation of heptanuclear cobalt cluster [Co₇(mmp)₆(CH₃O)₆]·(ClO₄)₂ (1) (mmp is 2-methoxy-6-methyliminomethyl-phenol anion) in only 20 min and also results in higher yields in contrast to other synthesis methods. Complex 1 displays dominant ferromagnetic interactions through μ ₃-O and μ ₂-O (oxidophenyl) binding modes.     

Syntheses and Crystal Structures of Two New Pentaborates Templated by Transition-Metal Complexes

Two new pentaborates [M(dap)₃][B₅O₆(OH)₄]₂·H₂O (M = Co (1) and Ni (2); dap = 1,2-diaminopropane) have been hydrothermally synthesized. Both structures were determined by single crystal X-ray diffraction and further characterized by elemental analysis, FT-IR, thermogravimetric analysis and photoluminescence spectroscopy. Two compounds are isostructural and consist of isolated pentaborate [B₅O₆(OH)₄]^? anions and [M(dap)₃]²⁺ complex cations. The anionic [B₅O₆(OH)₄]^? groups are linked by extensive hydrogen bonds to form a 3-D supramolecular framework with large channels, in which the transition-metal complex templates are located. The luminescent properties of 1 and 2 were studied, and blue luminescence occurs with an emission maximum at 405 and 408 nm upon excitation at 332 and 328 nm respectively. Crystal data: 1, monoclinic, space group P2₁/c (No. 14), a = 9.7159(5) Å, b = 29.3372(19) Å, c = 11.5121(6) Å, β = 103.286(5)°, V = 3193.6(3) ų, Z = 4; 2, monoclinic, space group P2₁/c, a = 9.7264(4) Å, b = 29.3810(16) Å, c = 11.5185(6) Å, β = 103.249(4)°, V = 3204.0(3) ų, Z = 4.     

Hydroxo-Lanthanide Cluster Organic Framework Built by Hexanuclear Cluster Units

A novel hydroxo-lanthanide cluster organic framework, Sm₃L₈(μ ₃-OH)(H₂O)·H₂O (1), derived from the 4-pyridin-4-ylbenzoic acid (HL) has been hydrothermally made and structurally characterized by single crystal X-ray diffraction. Structure analysis shows the hexanuclear Sm₆ cluster unit is composed of inorganic tetranuclear hydroxo [Sm₄(OH)₂]¹⁰⁺ (Sm₄) cluster and dimeric [Sm₂(COO)₄]²⁺ (Sm₂) core. The Sm₆ cluster units are connected by L ligands to form a 2D Ln-based cluster organic framework. From the topological point of view, the layer architecture can be described as 4-connected sql net. Furthermore, the elemental analysis, PXRD, IR and TGA are also studied.     

Preparation of dendritic‐like CdS by hydrothermal method and its photocatalytic performance

In this article, dendritic‐like CdS has been prepared by a hydrothermal method using thiourea as the sulfur source, and the effects of experimental conditions on the morphologies of CdS have been investigated. The performances of CdS have been analyzed by X‐ray diffraction (XRD), field emission scanning electron microscopy (FESEM), and the fluorescence and photodegradation properties of CdS have also been investigated. The XRD result indicates that the dendritic‐like CdS are of hexagonal phase and they are highly crystallized. Also, the FESEM results show that the ratio of raw material affects the yield of CdS, the reaction time affects the morphology of CdS. The best morphology of CdS is dendritic structures and the length is about 6 μm. The fluorescence spectrum shows three peaks at 470 nm, 513 nm and 547 nm, which indicates that the dendritic‐like CdS mainly emits green and blue fluorescence. Moreover, the dendritic‐like CdS exhibits good photocatalytic activity and its photodegradation rate to methylene blue can reach 92%. The growth mechanism for the formation of CdS with dendritic structure is also described.     

Optical properties of flower‐like CdS prepared by a hydrothermal method with SDBS as surfactant

In this article, flower‐like CdS structures have been prepared by a hydrothermal method with SDBS as surfactant. The influences of different experimental conditions on the morphologies, UV‐Vis and fluorescence properties of CdS have been investigated. The performances of CdS have been analyzed by X‐ray diffraction (XRD), field emission scanning electron microscopy (FESEM), ultraviolet‐visible (UV–Vis) and room‐temperature photoluminescence (PL). The XRD result indicates that the flower‐like CdS structures are of hexagonal phase. The FESEM results indicate that the main role of SDBS is to make the CdS crystals assemble together to form the flower‐like structures. The UV–Vis results show CdS has a strong absorption in the ultraviolet region and visible‐light region. The PL results show CdS has two emission peaks, respectively at 461 nm and 553 nm. The growth mechanism for the formation of flower‐like CdS structures is also described.     

Selective etching of ZnTe in HF:H2O2:H2O solution: Interpretation of extended defect‐related etch figures

HF:H₂O₂:H₂O solution (40%wt.HF: 30wt.%H₂O₂: H₂O, 3:2:1 by volume) was used to reveal extended defects (line, face and volume defects) in bulk ZnTe crystals grown from Te solution. The etch patterns were analyzed based on their size, shape and distribution. The etch figures, both in the shape of pits and hillocks with high resolution, show forms controlled by the symmetries of the respective faces were produced. Two different sizes of pits were observed, the larger‐size pits correspond to dislocations penetrating the surface, however, the smaller‐size texture pits are produced on the defect‐free region, which serve as standard pits on respect faces. The face defects, such as grain boundaries, sub‐grain boundaries, dislocation walls, twins and stacking faults, can be all displayed clearly. Another essential feature of the etchant is that, it can effectively dissolve Te‐rich phase (Te inclusion/precipitates), which makes it promising to reveal the shape of this volume defect.