On AB Bond Percolation on the Square Lattice and AB Site Percolation on Its Line Graph

We prove that AB site percolation occurs on the line graph of the square lattice when $p \in (1 - \sqrt {1 - p_c } ,\sqrt {1 - p_c } )$ , where p _c is the critical probability for site percolation in $\mathbb{Z}^2$ . Also, we prove that AB bond percolation does not occur on $\mathbb{Z}^2$ for p = $\frac{1}{2}$ .     

Photonic-band-gap structures and guide modes in two-dimensional magnetic photonic crystal heterostructures

We first investigate the band gap structures of two-dimensional magnetic photonic crystals (MPC) composed of rectangular (square) magnetic cylinders embedded in a host dielectric material in the rectangular (square) lattice, and we then study guide modes at interface of MPC heterostructures (MPCHs) by use of plane wave expansion method in combination with supercell technique. We find that both the mirror-symmetric MPCHs and the mixed-type MPCHs composed of square cylinders in a square lattice can produce the TM guide modes even without any lattice distortions. This feature is quite different from that of the non-magnetic PC heterostructures, in which the occurrence of the guide modes requires the relatively longitudinal gliding or transverse displacement of lattices. It may provide a new way to generate guide modes and apply to the device of light wave guides.Received: 26 August 2003, Published online: 2 April 2004PACS: 42.70.Qs Photonic bandgap materials - 78.67.-n Optical properties of low-dimensional, mesoscopic, and nanoscale materials and structures - 63.20.Pw Localized modes - 42.79.Gn Optical waveguides and couplers     

Characterization of the classical domains by Carathèodory volume elements and Eisenman-Kobayashi volume elements

We give a sufficient and necessary condition that a domain is biholomorphic to the classical domain.     

跳跃非线性项依赖于导数的二阶微分方程周期解的存在性

本文研究二阶微分方程χ"+aχ+-bχ-+f(χ)g(χ'=p(t)周期解的存在性,这里χ+=max{χ,0},χ-=max{-χ,0},a,6是正常数并且点(a,b)位于某一条Fucik谱曲线上.当g(χ)的极限lim.g(χ)=g(+∞),lim g(χ)=g(-∞)和f(χ)的极限lim,g(χ)=f(+∞),lim f(χ)=f(-∞)都存在且有限时,给出了此方程存在周期解的充分条件.     

On the Action of a Groupoid on a Manifold

In this paper,some properties of reduction for symplectic F-spaces are discussed.The properties of stable subgroups are discussed.We find that the symplectic action of a symplectic groupoid on a symplectic manifold can induce a symplectic map between reduced symplectic manifolds.This symplectic action can be characterized by the action of its induced symplectic groupoid on a symplectic manifold.Lastly,we shall discuss Poisson reduction and give a Poisson reduction theorem.     

Summability of Product Jacobi Expansions

Orthogonal expansions in product Jacobi polynomials with respect to the weight function W_α, β(x)=∏^d_j=1 (1−x_j)^α_j (1+x_j)^β_j on [−1, 1]^d are studied. For α_j, β_j>−1 and α_j+β_j−1, the Cesàro (C, δ) means of the product Jacobi expansion converge in the norm of L^p(W_{α, β}, [−1, 1]^d), 1p<∞, and C([−1, 1]^d) if

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Moreover, for α_j, β_j−1/2, the (C, δ) means define a positive linear operator if and only if δ∑^d_i=1 (α_i+β_i)+3d−1.     

催化剂组分对制备单壁碳纳米管的影响

利用柠檬酸法制备出了Mo-Fe-MgO，Mo-Co-MgO和W-Co-MgO催化剂，在小型流化床中，以Ar气为载气，在1123 K下催化裂解CH₄来制备单壁碳纳米管(SWCNTs).利用透射电子显微镜和拉曼光谱方法研究了催化剂组分对SWCNTs制备的影响，并对SWCNTs的生长机理进行了探索，研究结果表明，柠檬酸法是一种制备负载型SWCNTs催化剂的有效方法，三种催化剂都能够得到质量较好的SWCNTs,在1123 K左右，SWCNTs在三种催化剂上的生长过程可能类似于“微液相模型”.催化剂的组分对SWCNTs的管径分布影响较小，不同催化剂所得到的SWCNTs在内部结构上存在一定的差异.催化剂中加入第二组分Mo和W能有效提高产物的碳产率. 关键词： 单壁碳纳米管 催化化学气相沉积法 生长机理 拉曼光谱     

Reduced-temperature ordering of FePt nanoparticle assembled films by Fe30Pt70/Fe3O4 core/shell structure

In this paper, Fe30Pt70/Fe3O4 core/shell nanoparticles were synthesized by chemical routine and the layered polyethylenimine （PEI）-Fe30Pt70/Fe3O4 structure was constructed by molecule-mediated self-assembly technique. The dimension of core/shell structured nanoparticles was that of 4nm core and 2 nm shell. After annealing under a flow of forming gas （50%Ar2＋30%H2） for 1 h at or above 400℃, the iron oxide shell was reduced to Fe and diffused to Pt-rieh core, which leaded to the formation of L1. phase FePt at low temperature. The x-ray diffraction results and magnetic properties measurement showed that the chemical ordering temperature of Fe30Pt70/Fe3O4 core/shell nanoparticles assembly can be reduced to as low as 400℃. The sample annealed at 400℃ showed the eoereivity of 4KOe with the applied field of 1.5T. The core/shell structure was suggested to be an effective way to reduce the ordering temperature obviously.[第一段]     

RESERVOIR DESCRIPTION BY USING A PIECEWISE CONSTANT LEVEL SET METHOD

We consider the permeability estimation problem in two-phase porous media flow. We try to identify the permeability field by utilizing both the production data from wells as well as inverted seismic data. The permeability field is assumed to be piecewise constant, or can be approximated well by a piecewise constant function. A variant of the level set method, called Piecewise Constant Level Set Method is used to represent the interfaces between the regions with different permeability levels. The inverse problem is solved by minimizing a functional, and TV norm regularization is used to deal with the ill-posedness. We also use the operator-splitting technique to decompose the constraint term from the fidelity term. This gives us more flexibility to deal with the constraint and helps to stabilize the algorithm.     

Multi-Channel Optical Device for Solar-Driven Bacterial Inactivation under Real-Time Temperature Feedback

Solar-driven photothermal antibacterial devices have attracted a lot of interest due to the fact that solar energy is one of the cleanest sources of energy in the world. However, conventional materials have a narrow absorbance band, resulting in deficient solar harvesting. In addition, lack of knowledge on temperature change in these devices during the photothermal process has also led to a waste of energy. Here, we presented an elegant multi-channel optical device with a multilayer structure to simultaneously address the above-mentioned issues in solar-driven antibacterial devices. In the photothermal channel, semiconductor IrO₂-nanoaggregates exhibited higher solar absorbance and photothermal conversion efficiency compared with nanoparticles. In the luminescence channel, thermal-sensitive Er-doped upconversion nanoparticles were utilized to reflect the microscale temperature in real-time. The bacteria were successfully inactivated during the photothermal effect under solar irradiation with temperature monitoring. This study could provide valuable insight for the development of smart photothermal devices for solar-driven photothermal bacterial inactivation in the future.