耗散KDV型方程的渐近吸引子

摘 要:本文考虑了耗散KDV型方程 的渐近吸引子,即构造了一个有限维解序列.首先利用数学归纳法证明了该解序列不会远离方程的整体吸引子；其次，证明了它在长时间后无限趋于方程的整体吸引子, 并且给出了渐近吸引子的维数估计.     

Splitting Quantum Information with Five-Atom Cluster State in Cavity QED

A realizable scheme is proposed for implementing quantum information splitting with five-atom cluster state in cavity QED, where we explicitly illustrate the procedure. The scheme does not involve Bell-state measurement and is insensitive to the cavity and the thermal field.     

Crystalline phase of Y_2O_3 :Eu particles generated in a substrate-free flame process

In this study, factors affecting the crystal structure of flame-synthesized Y 2 O 3 :Eu particles were inves- tigated, especially the particle size effect and its interaction with Eu doping concentration. Polydisperse Y 2 O 3 :Eu (size range 200 nm to 3 m) powder samples with Eu doping concentrations from 2.5 mol% to 25 mol% were generated in either H 2 /air or H 2 /O 2 substrate-free flames. The crystal structure of the powder samples was determined by powder X-ray diffraction (XRD), which was complemented...     

Exciton effects in armchair graphene nanoribbons

We have studied the exciton effects in armchair graphene nanoribbons systematically, using the nonorthogonal tight-binding model supplement by the long-range Coulomb interactions. It is found from our calculations that the excitation energies, the exciton binding energies and the exciton wave function sizes of the E ₁₁ and E ₂₂ excitons all exhibit oscillation as a function of the ribbon width. And there is a phase shift of π between the oscillation of the E ₁₁ and E ₂₂ excitons.     

Path-following interior point algorithms for the Cartesian <Emphasis Type="Italic">P</Emphasis><Subscript>*</Subscript>(κ)-LCP over symmetric cones

In this paper, we establish a theoretical framework of path-following interior point algorithms for the linear complementarity problems over symmetric cones (SCLCP) with the Cartesian P _*(κ)-property, a weaker condition than the monotonicity. Based on the Nesterov-Todd, xy and yx directions employed as commutative search directions for semidefinite programming, we extend the variants of the short-, semilong-, and long-step path-following algorithms for symmetric conic linear programming proposed by Schmieta and Alizadeh to the Cartesian P _*(κ)-SCLCP, and particularly show the global convergence and the iteration complexities of the proposed algorithms. This work was supported by National Natural Science Foundation of China (Grant Nos. 10671010, 70841008)     

Group IV M‐POSS (M=Zr,Hf) Coordination Polymers

The synthesis and characterization of Zr‐POSS and Hf‐POSS coordination polymers were reported. The IR data and the solid‐state ²⁹Si MAS NMR indicated the existence of Si? O? M linkage. The polarized optical microscopy images and the XRD data suggested their crystalline nature.     

Construction of dsDNA biosensor based on dendritic SiO2 nanoparticle and investigation on its interaction with benzo[a]pyrene

In this work, a new dsDNA biosensor was constructed to monitor the interaction of DNA and benzo[a]pyrene (BaP). Firstly, dendritic SiO₂ nanoparticles were synthesized by silanization of SiO₂ nanoparticles with (??-(methacryloyloxy)propyl) trimethoxysilane and polymerization with acrylic acid. Then, due to the rich carboxyl groups of these nanoparticles, they were associated with the amino groups of a self-assembly membrane formed on the gold electrode by a sulfur-containing compound, 5-amino-3-mercapto-1,2,4-triazole. Finally, dsDNA was immobilized on the electrode surface by static adsorption with the aid of metallic ion. The whole immobilization steps were characterized by cyclic voltammogram and electrochemical impedance spectrum. After that, using methylene blue as a probe, the interaction of BaP with dsDNA was investigated. A linear relationship between the percentages of current decrease with the logarithm of BaP concentrations was found in the range from 0.33 to 133???M.     

Fluorinated star‐shaped block copolymers: Synthesis and optical properties

Tetrakis(4‐(1‐bromoethyl)phenyl)silane is synthesized and utilized to initiate the atom transfer radical polymerization (ATRP) of methyl methacrylate (MMA) to generate bromo‐terminated four‐armed PMMA macroinitiators, which further initiate the ATRP of methylacryloyloxyl‐2‐hydroxypropyl perfluorooctanoate (FGOA) to create fluorinated star‐shaped block copolymers PMMA‐b‐poly(FGOA)s with fluorine content ranging from 0 to 31.7 wt %. The polymerizations are well controlled with the polydispersity indices <1.30. The polymers readily dissolve in common organic solvents and show good film‐formation. Compared with the nonfluorinated sample, the fluorinated films exhibit significantly increased water contact angles owing to the enrichment of fluorine on the surface. The enhanced hydrophobicity is advantageous for the optical stability when the devices work under a moist environment. Moreover, the films possess high thermo‐optic coefficients, tunable refractive indices, and extremely low birefringence coefficients because of the presence of bulky and rigid tetraphenylsilane core and star‐shaped topological structure, showing potential application in optical waveguide devices. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2016 , 54, 1969–1977