Superconvergence of discontinuous Galerkin finite element method for the stationary Navier‐Stokes equations

This article focuses on discontinuous Galerkin method for the two‐ or three‐dimensional stationary incompressible Navier‐Stokes equations. The velocity field is approximated by discontinuous locally solenoidal finite element, and the pressure is approximated by the standard conforming finite element. Then, superconvergence of nonconforming finite element approximations is applied by using least‐squares surface fitting for the stationary Navier‐Stokes equations. The method ameliorates the two noticeable disadvantages about the given finite element pair. Finally, the superconvergence result is provided under some regular assumptions. © 2006 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 23: 421–436, 2007     

Generalization of a sharp Hölder's inequality and its application

In this paper, we generalize Hu Ke's sharpness of Hölder's inequality. As application, the obtained result is used to improve the well-known Opial-Olech inequality.     

Micromagnetic analysis of transition noise for high-density perpendicular recording

In this paper, specific issues related to high-density perpendicular magnetic recording processes, such as transition noise properties and cross-track correlation lengths, were investigated with the help of micromagnetic analysis. The effects of media parameters were taken into consideration, including intergranular exchange coupling, and exchange distribution, irregular grain shapes, magnetization saturation distribution, and anisotropy distribution. The micromagnetic simulation results showed that the effect of anisotropy distribution on transition noise is more significant than magnetization saturation distribution, and it is crucial to reduce this effect to achieve a high signal-to-noise ratio. Additionally, a new method to further estimate the partial erasure threshold was proposed to approximate the partial erasure effects, and the relation between the microtrack jitter and total track jitter was investigated.     

Effects of SnO2 addition on the magnetic properties of manganese zinc ferrites

SnO₂ was added to high-permeability MnZn ferrites and MnZn ferrites for high-frequency power supplies. The effects of the SnO₂ addition were studied. Sn⁴⁺ ions can dissolve into the spinel lattice and form stable Fe²⁺–Sn⁴⁺ pairs and hence can compensate the magneto-crystalline anisotropy constant K₁ and improve the initial permeability effectively. The initial permeability of ferrites is also improved as abnormal grain growth caused by ion vacancy is controlled with SnO₂ doping. In addition, the SnO₂ doping also leads to a decrease in the relative loss factor and an increase in density. The power loss and minimum power loss temperature decrease with SnO₂ doping.     

Hydrothermal synthesis of FeS2 for lithium batteries

Nanocrystalline FeS₂ cathode material of lithium cell was synthesized from cheap materials of FeSO₄, Na₂S₂O₃, and sulfur by a hydrothermal process. The scanning electron microscopy analysis showed the obtained material was nano-sized, about 500 nm. The X-ray powder diffraction analysis showed that the synthetic FeS₂ material had two phases of the crystalline structure, pyrite and marcasite. The phase of marcasite seems to have no negative effect on the electrochemical performance of the material. The synthetic FeS₂ showed a significant improvement of electrochemical performance for Li/FeS₂ cells.     

Concentration factors for functions with harmonic bounded mean variation

We discuss determination of jumps for functions with generalized bounded variation. The questions are motivated by A. Gelb and E. Tadmor [1], F. Móricz [5] and [6] and Q. L. Shi and X. L. Shi [7]. Corollary 1 improves the results proved in B. I. Golubov [2] and G. Kvernadze [3]. Supported by NSFC 10671062.     

A side-coupled photonic crystal filter with sidelobe suppression

This paper presents the theoretical model and the optimization method to suppress the sidelobes of side-coupled photonic crystal filters. Numerical verification shows a good agreement between the theoretical method and the finite-difference time-domain simulation, but the theoretic method does not involve the time-consuming computation. The theoretical method also presents a better physical image for choosing the critical parameters, such as the quality factor, phase shift and the number of resonators. Based on the theoretical model, two optimization methods (chirp and cascading) are proposed to deeply suppress the sidelobes. They also show more flexibility in controlling the bandwidth and steepness of the roll-off in the filter. PACS 42.70.Qs     

The Sheffer group and the Riordan group

We define the Sheffer group of all Sheffer-type polynomials and prove the isomorphism between the Sheffer group and the Riordan group. An equivalence of the Riordan array pair and generalized Stirling number pair is also presented. Finally, we discuss a higher dimensional extension of Riordan array pairs.     

Analysis of Metabolites in Allantoic Fluid of Chicken Embryo by 900 MHz NMR Spectroscopy

900 MHz ¹H NMR (nuclear magnetic resonance) spectroscopy was used to analyze metabolites in allantoic fluid of the chicken embryo in the 9th incubation day without any chemical or physical sample separation. The result showed that superhigh spectral dispersion and sensitivity at 900 MHz are useful in directly analyzing a complex mixture, particularly in resolving the overlapped NMR resonances. In this study, we had assigned 61 metabolites and 26 chemical fragments in the allantoic fluid. The relative concentrations of the major metabolites were also measured. Among the assigned metabolites, some were detected by NMR in chicken embryo allantoic fluids for the first time. The biological functions of these compounds were briefly discussed. Authors' address: Maili Liu, State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences, Wuhan 430071, People's Republic of China