Extremal ranks of matrix expression of A − BXC with respect to Hermitian matrix

The extremal ranks of matrix expression of A − BXC with respect to X^H = X have been discussed by applying the quotient singular value decomposition Q-SVD and some rank equalities of matrices in this paper.     

Superconvergence analysis of FEMs for the Stokes–Darcy system

We consider a superconvergence analysis for quadratic finite element approximations of the Stokes–Darcy system. The superclose property of an extra half order is proven for uniform triangular meshes. Based on the result of the superclose property, global superconvergence is derived by applying a postprocessing technique. In addition, some numerical examples are presented to demonstrate our theoretical results. Copyright © 2010 John Wiley & Sons, Ltd.     

The Structure of Finite Non-Nilpotent Groups in Which Every 2-Maximal Subgroup Permutes with all 3-Maximal Subgroups

The structure of finite non-nilpotent groups in which every 2-maximal subgroup permutes with every 3-maximal subgroup is described.     

Complex dynamics of a diffusive epidemic model with strong Allee effect

In this paper, we investigate the dynamics of a diffusive epidemic model with strong Allee effect in the susceptible population. We show some properties of solutions of the model, the asymptotic stability of the equilibria. Especially, we show that there exists a separatrix curve that separates the behavior of trajectories of the system, implying that the model is highly sensitive to the initial conditions. Furthermore, we give the conditions of Turing instability and determine the Turing space in the parameters space. Based on these results, we perform a series of numerical simulations and find that the model exhibits complex pattern replication: spots, spot–stripe mixtures and stripes patterns.     

Influence of tungsten doping concentration on the electronic and optical properties of anatase TiO2

The structural, electronic and optical properties of tungsten-doped TiO₂ have been investigated using density functional theory with plane wave basis sets and ultrasoft pseuodopotential. Substitutional W doping at Ti sites create W 5d states just below the conduction band minimum while interstitial W doping gives isolated W 5d states in the middle of forbidden region. Averaged bond lengths show that W doping at Ti sites produce minimum structural distortion as compared to the interstitial W-doped TiO₂. Substitutional W-doped TiO₂ has better visible light absorption compared to interstitial W-doped TiO₂ and has stable configuration which provide reasonable explanation for the experimental findings. Tungsten doping in TiO₂ with different doping concentrations is investigated as an enabling concept for enhancing the visible light absorption. Optical properties show that optimal W doping concentration would improve the visible light absorption. 2.08% W doping concentration gives strong visible and ultraviolet light absorption among all doped models found consistent with experiments.     

Octagonal dual-concentric-core photonic crystal fiber for C-band dispersion compensation with low confinement loss

A novel kind of octagonal dual-concentric-core photonic crystal fiber （PCF） is calculated with the finite element method （FEM） and proposed for broadband compensation. In order to realize highly negative dispersion, the hole diameter of the second ring is reduced relative to conventional PCFs. Numerical simulation results show that when the diameters of large holes and small holes are 0.77 pm and 0.5 #m, respectively, and the pitch of the adjacent rings is 1.1 μm, the negative dispersion can achieve about 840 ps.nm^-1.km^-1 at 1 550 nm and the dispersion slope can match with single mode fiber （SMF-28） perfectly. This PCF can compensate the positive dispersion and also its slope of about 50 times its length of SMF-28 fiber, which is suitable for C-band optical fiber telecommunication as a dispersion compensation fiber.     

Temperature dependent exchange bias effect in polycrystalline BiFeO3/FM (FM = NiFe, Co) bilayers

Extensive studies on the temperature (T) dependent exchange bias effect were carried out in polycrystalline BiFeO₃(BFO)/NiFe and BFO/Co bilayers. In contrast to single-crystalline BFO/ferromagnet (FM) bilayers, sharp increase of the exchange bias field (H _E ) below 50 K were clearly observed in both of these two bilayers. However, when T is higher than 50 K, H _E increases with T and decreases further when T is larger than 230 K (for BFO/NiFe) or 200 K (for BFO/Co), which is similar to those reported in single-crystalline BFO/FM bilayers. After the exploration of magnetic field cooling, the temperature dependent exchange bias can be explained considering two contributions from both the interfacial spin-glass-like frustrated spins and the polycrystalline grains in the BFO layer. Moreover, obvious exchange bias training effect can be observed at both 5 K and room temperature and the corresponding results can be well fitted based on a recently proposed theoretical model taking into account the energy dissipation of the AFM layer.     

Synthesis of mesoporous-silica coated multi-branched gold nanoparticles for surface enhanced Raman scattering evaluation of 4-bromomethcathinone

Mesoporous silica-coated multi-branched gold nanoparticles (bAu@mesoSiO₂) aiming for enhanced Raman sensing for 4-bromomethcathinone (4-BMC) detection is reported. In this work, we present an effective strategy to probe the Raman signal of 4-MBC. Morphologies and optical properties of the synthesized materials with different [Au³⁺]/[Au⁰] ratios are characterized utilizing transmission electron microscopy (TEM), UV–vis and mid-infrared spectroscopy. Both experimental and theoretical (simulation) studies were investigated. Taking advantages of gold core branches that provide highly localized and strongly enhanced electromagnetic fields due to plasmon resonance, surface-enhanced Raman scattering (SERS) is observed. The experimental results show that the SERS intensity exhibits a 100-fold increase with the increased average length and quantity of gold branches (nano tips). The analytical performance yielded a detection limit of 0.1?mg/ml for the 4-MBC target within 5?mins. The sensing method will likely find further improvement and broad use in the forensic science. Besides rapid detection and portability, the combination of the Raman effect and enhanced materials imparts other notable advantages, such as its non-contact and free of reagents.