Existence of multiple and sign-changing solutions for a second-order nonlinear functional difference equation with periodic coefficients

In the present paper, we apply the method of invariant sets of descending flow to establish a series of criteria to ensure that a second-order nonlinear functional difference equation with periodic boundary conditions possesses at least one trivial solution and three nontrivial solutions. These nontrivial solutions consist of sign-changing solutions, positive solutions and negative solutions. Moreover, as an application of our theoretical results, an example is elaborated. Our results generalize and improve some existing ones.     

Two novel Co (II)-coordination polymers as bifunctional materials for efficient photocatalytic degradation of dyes and electrocatalytic water oxidation

Two novel Co (II)- coordination polymers (CPs) based on 2,5-bis(4-carboxylpheny)-1,3,4-oxadiazole (bcpo), namely [Co/(bcpo)_0.5(tib)(H₂O)₂]_n (1) and [Co (bcpo)_0.5(bidpe)(H₂O)₂]_n (2) (tib = 1,3,5-tirs(1-imidazolyl)benzene, bidpe = 4,4′-bis (imidazolyl)diphenyl ether) have been synthesized under solvothermal conditions and characterized by powder X-ray diffraction (PXRD), single crystal X-ray diffraction, photochemistry as well as electrochemistry. The investigation of the photo-degradation methyl blue and methyl violet (MB, MV) properties of CPs 1–2 demonstrates that CP 1 shows great performance for the degradation of MB, and CP 2 could efficiently degrade MB/MV. Meanwhile, the possible photo-degradation mechanism has been proposed and explored. Simultaneously, electrochemistry studies show that both CPs 1 and 2 can catalyze water oxidation under an alkaline condition at the potential around 1.20 V vs. NHE with relatively low overpotential of 330–510 mV vs. NHE.     

Fabrication and Excellent Antibacterial Activity of Well-defined CuO/Graphdiyne Nanostructure

Copper oxide(CuO),due to its low cost,good chemical and physical stability,has recently been given special attention as a potential candidate for antibacterial agents.However,developing novel CuO nanocomposites with improved antibacterial property and unraveling the interface promotion mechanism has been a fundamental challenge for decades.Herein,well-defined CuO/graphdiyne(CuO/GDY)nanostructures with uniformly anchored CuO nanoparticles(ca.4.5 nm)have been fabricated.The CuO/GDY nanostructure exhibited superior E.coli inactivation efficiency,which is nearly 19 times and 7.9 times higher than the bare GDY and commercial CuO,respectively.The improved E.coli inactivation performance was mainly due to the increased reactive O2-species generated by the activation of molecular O2 over CuO/GDY surface.These findings demonstrate the efficient antibacterial activity of well-defined CuO/GDY nanostructures and provide insights on the development of efficient GDY-based antibacterial materials.     

金-石墨烯修饰电极电化学检测塑料瓶中双酚A

在离子液体碳糊电极(CILE)表面上采用一步电还原法制备了纳米金(nAu)-石墨烯(GR)复合膜修饰电极(nAu-GR/CILE)。研究了双酚A(BPA)在nAu-GR/CILE上的电化学行为,BPA的电极反应过程为受吸附控制的不可逆过程;采用示差脉冲伏安法研究了BPA氧化峰电流和浓度之间的关系,在0.08~400.0μmol/L范围内,检出限为0.021μmol/L(3σ)。将nAu-GR/CILE用于塑料瓶中BPA的检测,与采用高效液相色谱法(HPLC)进行对比,结果表明两种方法对BPA的检测结果相吻合。     

铜催化烯烃氰烷基化成环合成含氰吲哚酮

发展一种简单、高效的铜催化活泼烯烃氰烷基化成环合成吲哚酮的方法。 在CuI/DTBP(叔丁基过氧化物)催化作用下, N-芳基丙烯酰胺类化合物与α-氰基偶氮试剂发生自由基环化反应, 高效地合成了一系列含α-氰基季碳中心的吲哚酮, 并探讨了其反应机理。 该方法底物适用范围较广、反应体系温和, 催化体系廉价。     

Efficient Synthesis of Triarylamines Catalyzed by Copper(I) Diazabutadiene Complexes

Cuprous chloride was coordinated by diazabutadiene (DAB‐R) ligands to form Cu(I)‐(DAB‐R) complexes, most of which have a 1:1 ratio of Cu to DAB‐R as reported. In the case of a special DAB‐ⁱPP, N,N′‐bis(2,6‐diisopropylphenyl)‐1,4‐diaza‐1,3‐butadiene, an unexpected composition of complex was found with the formula Cu(I)Cl(DAB)₂. When employed as catalyst for triarylamine synthesis from the coupling of aryl halides with primary and secondary arylamines, the new Cu(I)‐(DAB‐ⁱPP) complex displayed high efficiency.     

Molecular dynamics studies on the local disordering of Σ3 and Σ11 grain boundaries in aluminium bicrystal

Molecular dynamics (MD) simulations using Morse interaction potential are performed in studies of [110] symmetrical tilt grain boundary (GB) structures with mis-orientation angles 50.5°(Σ11), 129.5°(Σ11), 70.5°(Σ3) and 109.5°(Σ3) at various tempratures. The GB structures are found to start local disordering at about 0.5T _m (T _m is the melting point of aluminium) for 50.5°(Σ11), 0.32T _m for 129.5° (Σ11) and 0.38T _m for 70.5°(Σ3), respectively. These results agree with conclusions deduced from the anelastic measurements. But, for twin-boundary structure 109.5°(Σ3), this disordering has not been found even when temperature increases up to 0.9T _m . The project supported by the National Natural Science Foundation of China and Laboratory for Non-linear Mechanics of Continuous Media, Institute of Mechanics, Academia Sinica.     

Topological Effect on the Structure of Self‐Assembled Aggregates from Amphiphilic Macromolecules in Solution

The self‐assembled morphologies of cyclic amphiphiles, which are composed of a long hydrophobic block and a short hydrophilic block, in selective solutions are studied by using a simulated annealing method. The morphological dependence of the aggregates on solvent quality is investigated. The topology effects are studied by comparing results from linear counterparts of the amphiphiles. It is observed that, in addition to spherical micelles, cylindrical micelles, disklike micelles, vesicles, and large compound micelles, muticompartment vesicles with several fluidic cores can be formed by the cyclic systems. The morphologies are regulated by the interaction parameter ε_AS between the hydrophobic block and solvents. Furthermore, it is revealed that the differences of characteristics of the self‐assembled aggregates originate from the difference in architectural constraint. The wide region of forming multicompartment vesicles suggests that cyclic amphiphilic macromolecules could be a suitable candidate for applications to deliver multiple functional components by compartmentalizing different components in different confined space of vesicles.     

刚体撞块撞击弹性长杆的二次撞击分析

本文采用应力波特征线方法详细分析了刚体撞击固支的弹性长杆的撞击过程，指出当撞块质量和长杆质量的比值满足一定条件时，在第一次撞击过程结束后会发生第二次撞击。