有限群极大子群的θ-子群偶

N.P.Mukherjee和 P.Bhattacharya在“On theta pairs for a maximal sub-group”(Proc.Amer.Math.Soc,Vl09N3(1990))一文中定义了有限群的极大子群的θ-子群偶概念,研究了极大子群的极大θ-子群偶对群结构的影响,得到了一系列结果.本文在进一步探究θ-子群偶性质的基础上,对该文中一系列主要结果作出了本质性的改进,并给出了可解性、幂零性的一些新刻划.     

IMPACT MODEL RESOLUTION ON PAINLEVE’S PARADOX

Painlevé‘s paradox is one of the basic difficulties for solving LCP of dynamic systems subjected to unilateral constraints. A bi-nonlinear parameterized impact model, consistent with dynamic principles and experimental results, is established on the localized and quasi-static impact model theory. Numerical simulations are carried out on the dynamic motion of Painlevé‘s example. The results confirm ““““impact without collision““““ in the inconsistent states of the system. A ““““critical normal force““““ which brings an important effect on the future movement of the system in the indeterminate states is found. After the motion pattern for the impact process is obtained from numerical results, a rule of the velocity‘s jump that incorporates the tangential impact process is deduced by using an approximate impulse theory and the coefficient of restitution defined by Stronge. The results of the jump rule are quite precise if the system rigidity is big enough.     

Magnetic Properties of Pt-Based Nanoalloys: A Critical Review

In recent years, magnetic nanoalloys (MNAs) have attracted many attentions from all over the world, due to their potential applications in the broad fields of magneto-optics, data storage, engineering, and biology. Among these MNAs, Pt–M (M = Fe, Co, Ni) MNAs have been considered to be the most promising ones, due to their superparamagnetism and response to a magnetic field. Here, we firstly review the experimental work on the synthesis, characterization, and magnetic properties of Pt–Fe, Pt–Co, and Pt–Ni MNAs. Then, we discuss the recent theoretical work on Pt–Fe, Pt–Co, and Pt–Ni MNAs. Moreover, we also review the main applications of Pt–Fe, Pt–Co, and Pt–Ni MNAs in the fields of biology, information storage, and magnetic separation. It is found that the size, shape, and composition of Pt–Fe, Pt–Co, and Pt–Ni MNAs play a critical role on their fundamental magnetic properties from both the experimental and theoretical points of view. It is expected that this review could be a valuable resource for both experimental and theoretical researchers, who are interested in Pt-based MNAs.     

Enhanced slow light propagation in photonic crystal waveguides using angular properties of scatter elements

Applicability of the angular properties of scatter elements as a tool to achieve improved slow light performance with small group velocity dispersion and large bandwidth in photonic crystal waveguides is investigated. A polyatomic photonic crystal waveguide, including two scatter elements with different geometrical shapes in each primitive cell, is proposed to investigate the feasibility of our method. Numerical results show that a versatile control of the dispersion relation of slow light modes, with large normalized delay-bandwidth products ranging from 0.2085 to 0.3394, can be obtained using a unique geometrical parameter.     

Notable shift of ultraviolet intensity on Sn-doped ZnO nanostructure fabricated by sol–gel method

Sn-doped ZnO (SZO) thin films are deposited by sol–gel dip-coating method with Sn content at 0 at.% and 1–15 at.% with an increment of 2 at.%. The structure and luminescence of the films are investigated. X-ray diffraction results indicate that all the SZO samples show preferential orientation along the (002) direction, and the scanning electron microscope exhibits that the surface morphology of the films change from nanoparticles to nanorods with increasing Sn concentration. X-ray photoelectron spectroscopy reveals that Sn exists as valence of +4 in the matrix. The photoluminescence peaks at 381 and 398 nm are observed in all the samples. The ratio of intensity of peak at 381 nm to that of peak at 398 nm differed markedly. The intensity of peak at 398 nm might be due to the response for the Sn atoms, while the intensity of peak at 381 nm is probably related to the quantum size effect.     

Palladium‐Catalyzed Direct Cross‐Coupling of Carboranyllithium with (Hetero)Aryl Halides

A palladium‐catalyzed direct C‐arylation reaction of readily available cage carboranyllithium reagents with aryl halides has been developed for the first time. This method is applicable to a wide range of aryl halide substrates including aryl iodides, aryl bromides, and heteroaromatic halides.     

Preparation,characterization and photocatalytic performance of polyoxometalate / polyaniline / titania ternary composite

A new CoW₁₁Mn/PANI/TiO₂ ternary composite was synthesized with K₈[Co(H₂O)MnW₁₁O₃₉] (CoW₁₁Mn) and PANI/TiO₂ by electrostatic self-assembly. These catalysts were characterized using infrared (IR) spectroscopy, X-ray diffraction, scanning electron microscopy, ultraviolet–visible spectroscopy, and N₂ adsorption–desorption. CoW₁₁Mn/PANI/TiO₂ was used to photodegradate the example contaminant, gentian violet (GV). Under the optimum photodegradation conditions, 92.63% degradation was achieved, indicating that the introduction of polyoxometalate and polyaniline greatly enhanced the photocatalytic performance of the catalyst. Moreover, CoW₁₁Mn/PANI/TiO₂ exhibits stable performance with little loss in activity after three successive runs. Thus, CoW₁₁Mn/PANI/TiO₂ ternary composite could be a promising photocatalyst in photodegradation of organic pollutants.     

Quantum Correlations Induced by Local von Neumann Measurement

We study the total quantum correlation, semiquantum correlation and joint quantum correlation induced by local von Neumann measurement in bipartite system. We analyze the properties of these quantum correlations and obtain analytical formula for pure states. The experimental witness for these quantum correlations is further provided and the significance of these quantum correlations is discussed in the context of local distinguishability of quantum states.