A posteriori error analysis of a quadratic finite volume method for nonlinear elliptic problems

In this article, we construct and analyze a residual-based a posteriori error estimator for a quadratic finite volume method (FVM) for solving nonlinear elliptic partial differential equations with homogeneous Dirichlet boundary conditions. We shall prove that the a posteriori error estimator yields the global upper and local lower bounds for the norm error of the FVM. So that the a posteriori error estimator is equivalent to the true error in a certain sense. Numerical experiments are performed to illustrate the theoretical results.     

On s-hamiltonian line graphs of claw-free graphs

For an integer $s\ge 0$, a graph $G$ is $s$-hamiltonian if for any vertex subset $S?V\left(G\right)$ with $\left|S\right|\le s$, $G?S$ is hamiltonian, and $G$ is $s$-hamiltonian connected if for any vertex subset $S?V\left(G\right)$ with $\left|S\right|\le s$, $G?S$ is hamiltonian connected. Thomassen in 1984 conjectured that every 4-connected line graph is hamiltonian (see Thomassen, 1986), and Ku?zel and Xiong in 2004 conjectured that every 4-connected line graph is hamiltonian connected (see Ryjá?ek and Vrána, 2011). In Broersma and Veldman (1987), Broersma and Veldman raised the characterization problem of $s$-hamiltonian line graphs. In Lai and Shao (2013), it is conjectured that for $s\ge 2$, a line graph $L\left(G\right)$ is $s$-hamiltonian if and only if $L\left(G\right)$ is $(s+2)$-connected. In this paper we prove the following.(i) For an integer $s\ge 2$, the line graph $L\left(G\right)$ of a claw-free graph $G$ is $s$-hamiltonian if and only if $L\left(G\right)$ is $(s+2)$-connected.(ii) The line graph $L\left(G\right)$ of a claw-free graph $G$ is 1-hamiltonian connected if and only if $L\left(G\right)$ is 4-connected.     

影响单摆实验的因素及改进方法

用单摆测定当地的重力加速度和单摆振动定律的验证,很容易做.下面谈谈影响单摆实验的几个因素及其解决方法.1 用单摆测定当地重力加速度 可见,g的测定主要取决于l和T.因此,为了提高实验的精度,在测量过程中必须注意以下几个方面.     

Convex functions, subdifferentiability and renormings

This paper through discussing subdifferentiability and convexity of convex functions shows that a Banach space admits an equivalent uniformly [locally uniformly, strictly] convex norm if and only if there exists a continuous uniformly [locally uniformly, strictly] convex function on some nonempty open convex subset of the space and presents some characterizations of super-reflexive Banach spaces. Supported by NSFC     

非傍轴平顶高斯光束M2因子两种定义的比较研究

基于功率密度的二阶矩方法,推导出了非傍轴平顶高斯(FG)光束束宽和远场发散角的解析表达式·研究表明,当w0/λ→0时,远场发散角趋于渐近值θmax=63.435°,与阶数无关·使用非傍轴高斯光束代替傍轴高斯光束作为理想光束,研究了非傍轴FG光束的M2因子,并与传统定义的M2因子作了比较·在非傍轴范畴,非傍轴FG光束的M2因子不仅与阶数N有关,而且与w0/λ有关·按照定义,当w0/λ→0时,非傍轴FG光束的M2因子不等于0,对阶数N=1,2,3时,M2因子分别趋于0.913,0.882和0.886·当N→∞时,M2因子取最小值M2min=0.816·     

Hamiltonian N2‐locally connected claw‐free graphs

A graph G is N₂‐locally connected if for every vertex ν in G, the edges not incident with ν but having at least one end adjacent to ν in G induce a connected graph. In 1990, Ryjá?ek conjectured that every 3‐connected N₂‐locally connected claw‐free graph is Hamiltonian. This conjecture is proved in this note. © 2004 Wiley Periodicals, Inc. J Graph Theory 48: 142–146, 2005     

成分和厚度的依赖

通过调整Mn的成分，系统地研究了Ni81Fe19/Ni100-xMnx双层膜的磁学性质，特别是交换偏置场(Hex)的变化.当Ni100-xMnx中Mn的原子百分比在534%到600%之间时，对于150nm的Ni81Fe19，得到了最大的交换偏置场175kA/m，同时由于Mn对Ni81Fe19层的扩散所造成的磁矩的降低小于20%；高角x射线衍射证明Ni100-xMnx的晶格常数随着Mn成分的改变而变化，Mn含量越多，其晶格常数越大；制备态Ni100-xMnx膜晶格常数与θ相NiMn膜晶格常数的接近程度与NiMn膜θ相形成的容易程度相对应.也研究了交换偏置场随着Ni１００-xMnx厚度的变化，第一次得到了当Ni100-xMnx中Mn的原子百分比为706%时，Ni81Fe19(150nm)/Ni100-xMnx(90nm)双层膜在经过240℃，5h退火后，可以有80kA/m的交换偏置场，此时铁磁层磁矩的大小几乎不变. 关键词： Ni81Fe19/Ni100-xMnx 交换偏置场     

Highly strained InxGa(1−x)As−InyAl(1−y)As (x>0.8,y<0.3) layers for short wavelength QWIP and QCL structures grown by MBE

Highly strained quantum cascade laser (QCL) and quantum well infrared photodetector (QWIPs) structures based on In_xGa_(1−x)As−In_yAl_(1−y)As (x>0.8,y<0.3) layers have been grown by molecular beam epitaxy. Conditions of exact stoichiometric growth were used at a temperature of 420°C to produce structures that are suitable for both emission and detection in the 2–5 μm mid-infrared regime. High structural integrity, as assessed by double crystal X-ray diffraction, room temperature photoluminescence and electrical characteristics were observed. Strong room temperature intersubband absorption in highly tensile strained and strain-compensated In_0.84Ga_0.16As/AlAs/In_0.52Al_0.48As double barrier quantum wells grown on InP substrates is demonstrated. Γ–Γ intersubband transitions have been observed across a wide range of the mid-infrared spectrum (2–7 μm) in three structures of differing In_0.84Ga_0.16As well width (30, 45, and 80 Å). We demonstrate short-wavelength IR, intersubband operation in both detection and emission for application in QC and QWIP structures. By pushing the InGaAs–InAlAs system to its ultimate limit, we have obtained the highest band offsets that are theoretically possible in this system both for the Γ–Γ bands and the Γ–X bands, thereby opening up the way for both high power and high efficiency coupled with short-wavelength operation at room temperature. The versatility of this material system and technique in covering a wide range of the infrared spectrum is thus demonstrated.     

Combined effects of clay modifications and compatibilizers on the formation and physical properties of melt‐mixed polypropylene/clay nanocomposites

The melt mixing technique was used to prepare various polypropylene (PP)‐based (nano)composites. Two commercial organoclays (denoted 20A and 30B) served as the fillers for the PP matrix, and two different maleated (so‐called) compatibilizers (denoted PP‐MA and SMA) were employed as the third component. The results from X‐ray diffraction (XRD) and transmission electron microscope (TEM) experiments revealed that 190 °C was an adequate temperature for preparing the nanocomposites. Nanocomposites were achieved only if specific pairs of organoclay and compatibilizer were simultaneously incorporated in the PP matrix. For example, PP/20A(5 wt %)/PP‐MA(10 wt %) and PP/30B(5 wt %)/SMA(5 wt %) composites exhibited nanoscaled dispersion of 20A or 30B in the PP matrix. Differential scanning calorimetry (DSC) results indicated that the organoclays served as nucleation agents for the PP matrix. Generally, their nucleation effectiveness increased with the addition of compatibilizers. The thermal stability enhancement of PP after adding 20A was confirmed with thermogravimetric analysis (TGA). The enhancement became more evident as a suitable compatibilizer was further added. However, for the 30B‐included composites, thermal stability enhancement was not evident. The dynamic mechanical properties (i.e., storage modulus and loss modulus) of PP increased as the nanocomposites were formed; the properties increment corresponded to the organoclay dispersion status in the matrix. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 4139–4150, 2004