图的弱控制数及其束缚数

图的束缚数是图的控制数研究中一个很重要的方面,它在某种程度上反映了图的控制数对边数的敏感度.本文通过对图的结构特征的分析,研究了图的弱控制数及其束缚数,分别给出了紧的上界.     

行NA随机变量三角阵列的完全收敛性

令{Xm;1≤i≤n,n≥1}是行NA的随机变量三角阵列．利用NA随机变量序列的一个矩不等式,讨论了行NA的随机变量三角阵列在被随机变量X弱平均控制的条件下的完全收敛性．所得到的结果推广了行独立的随机变量三角阵列相应的结果．     

HNO二聚体蓝移氢键的理论研究

利用分子轨道从头算理论和密度泛函理论结合不同理论基组对于N-H…O蓝移氢键进行了详细的研究.利用标准方法和均衡校正方法对二聚体进行了几何优化,振动频率和相互作用能的计算.拓扑学和自然键轨道理论对于蓝移氢键的本质进行分析.自然键轨道(NBO)分析表明,σ*(N-H)轨道上电子密度降低是电子密度重排效应的结果.分子内电子重排、轨道再杂化和电子受体内部结构重组共同作用结果导致了N-H的振动频率大幅蓝移现象的出现.     

A位掺杂对La5/8(PrxCa1-x)3/8MnO3（x=0.25,0.5,0.75）相分离及输运性质的影响

采用固相反应法制备La5/8(PrxCa1-x)3/8MnO3(x=0.25,0.5,0.75)多晶样品,研究其磁性质和电磁输运特性.X射线衍射表明,La5/8(PrxCa1-x)3/8MnO3(x=0.25,0.5,0.75)多晶样品室温的晶体结构呈Pnma空间群的正交结构.磁化强度-电阻(M～T)关系显示,La5/8(PrxCa1-x)3/8MnO3(x=0.25,0.5,0.75)的居里温度TC随Pr掺杂量增加而逐渐降低,三种样品分别为160K、150K、100K.此外,随着Pr3+掺杂量增加,样品晶格畸变程度增大,铁磁相互作用减弱,并且三种成分均形成自旋玻璃态,其自旋冻结温度分别为150K、75K、70K.电阻-温度(ρ～T)关系表明,样品在x=0.25时出现电阻的双峰现象,这是由于样品中铁磁相与反铁磁相相互竞争造成的.结果表明,通过对钙钛矿锰氧化物的A位稀土掺杂,可对其CMR效应进行有效调控.     

2-F-环氧丁烷与几种生物小分子间的赝氢键结构

采用密度泛函B3LYP(Becke,three-parameter,Lee-Yang-PaH)/6-311++G**和HF(Hartree Fock)/6-311++G**方法,从理论上探讨了2-F-环氧丁烷分别与几种常见而重要的生物小分子咪唑(Iminazole)、噻唑(Thiazole)和恶唑(Oxazo1e)等分子间的弱相互作用,发现分子间同时存在N…H常规氢键和C-F…H-C赝氢键结构.弱相互作用能计算表明3个复合物的相对稳定性相当.计算结果表明,在C-F…H-C赝氢键结构中,与电子的直接供体F密切相关的共价键C-F键长增大,伸缩振动的频率红移,而作为电子受体的H-C基团,其C-H键伸缩振动光谱蓝移;另外,电子密度拓扑性质表明C-F…H-C赝氢键的共价性及离子性均与常规氢键相当.     

β-Hermite随机矩阵最大特征值精确渐近性的一般形式

对于相当广泛的边界函数和拟权函数,利用β-Hermite随机矩阵最大特征值的弱收敛定理、小偏差结论及广义βTracy-Wisdom分布的尾概率不等式,得到了其最大特征值的矩完全收敛性的精确渐近性的一般形式.     

Recyclable MoO3 nanobelts for photocatalytic degradation of Rhodamine B by near infrared irradiation

Molybdenum trioxide (MoO₃) represented an excellent photocatalytic performance with many applications, including degradation of organic contaminants and splitting of water. This paper presented a new route to synthesize MoO₃ nanobelts with high aspect ratios and crystallinity by a hydrothermal technique. This work showed that the as-synthesized nanobelts exhibited strong photocatalytic activity to degrade an organic dye of Rhodamine B (RhB) in aqueous solution under the exposure of the light source in the near infrared wavelength range, significantly improving the photocatalytic activity of the nanobelts. The results also showed that for a small concentration of RhB at 7.5 mg/L a complete photodegradation (for a given MoO₃ nanobelts quantity of 0.1 g) can be reached after exposing for 60 min. For all concentrations of the RhB solution, the photodegradation exhibited an exponential dependence on the exposure time followed by a sudden shutdown, but no complete photodegradation can be reached. Also, the residual quantity of RhB in solution after the photocatalytic reaction was determined by the initial RhB concentration. The photocatalytic degradation can be interpreted by the pseudo–first-order equation for the absorption of liquid/solid based on solid capacity; thus, photocatalytic degradation can be attributed to the interaction between the photoexcited electrons in the substrate and the antibonding orbital of the RhB in solution. The sudden shutdown was due to the inability of the photoexcited electrons in the substrate hopping to the antibonding orbital of RhB in the presence of the RhB intermediate products from the degraded RhB. In addition, this work showed that the photocatalytic reaction can be recovered after a thermal treatment of postreacted MoO₃ nanobelts, enhancing the utilization efficiency of the catalysis.     

Structural distortion,charge modulation and local anisotropies in magnetite below the Verwey transition using resonant X‐ray scattering

The pattern of charge modulations and local anisotropies below the Verwey transition has been determined and quantified in high‐quality Fe₃O₄ single crystals and thin films grown on MgO by using resonant X‐ray scattering at the Fe K‐edge. The energy, polarization and azimuthal angle dependencies of an extensive set of reflections with potential sensitivity to charge or local anisotropy orderings have been analyzed to explore their origins. A charge disproportion on octahedral B sites of 0.20 ± 0.05 e^? with [0 0 1] and cubic periodicities has been confirmed, while no significant charge disproportion has been obtained with [0 0 1/2] cubic periodicity. Additional charge modulations in the monoclinic a–b plane are also present. In addition, the occurrence of new forbidden (1, 1, 0) and (0, 0, 2n + 1/2) cubic reflections that arise from the anisotropy of the local structure around different tetrahedral and octahedral Fe atoms is shown. This complex pattern of weak charge modulations and local anisotropies is fully compatible with the low‐temperature crystal structure refined in the non‐polar C2/c space group and disproves any bimodal charge disproportion of the octahedral Fe atoms.     

Sulphur dioxide insertion into tin―carbon bonds: solvent effects and the nature of the transition state

Data describing the insertion of sulphur dioxide into the carbon―tin bond of a range of substituted phenyltrimethyltin compounds in methanol and benzene solvents have been reconsidered. The reaction in methanol is cleanly second order, but the reaction in benzene has both a second‐order and third‐order component, the latter ascribable to an initial equilibrium formation of a SO₂ complex with the phenyl ring followed by the insertion of a second SO₂ molecule into the carbon–tin bond. Molecular orbital calculations have identified the transition states (TS) and the favoured reaction pathways for the second‐order and third‐order reaction pathways in benzene. The effects of solvents on TS and enthalpies of reaction have also been examined. New insights into the types of TS involved in electrophilic substitution reactions are revealed. Copyright © 2013 John Wiley & Sons, Ltd.