LITTLEWOOD-PALEY THEOREM FOR SCHR(O)DINGER OPERATORS

Let H be a Schr(o)dinger operator on Rn. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.     

Weighted norm inequalities of Bochner-Riesz means

Let w be a Muckenhoupt weight and be the weighted Hardy spaces. We use the atomic decomposition of and their molecular characters to show that the Bochner-Riesz means are bounded on for 0<p?1 and δ>max{n/p−(n+1)/2,[n/p]rw⁻¹(rw−1)−(n+1)/2}, where rw is the critical index of w for the reverse Hölder condition. We also prove the boundedness of the maximal Bochner-Riesz means for 0<p?1 and δ>n/p−(n+1)/2.     

Hollow-fiber flow/hyperlayer field-flow fractionation for the size characterization of airborne particle fractions obtained by SPLITT fractionation

Hollow-fiber flow field-flow fractionation (HF FlFFF) was applied for the separation and size characterization of airborne particles which were collected in a municipal area and prefractionated into four different-diameter intervals >5.0, 2.5-5.0, 1.5-2.5, <1.5 microm) by continuous split-flow thin (SPLIIT) fractionation. Experiments demonstrated the possibility of utilizing a hollow-fiber module for the high-performance separation of supramicron-sized airborne particles at steric/hyperlayer operating mode of HF FlFFF. Eluting particles during HF FlFFF separation were collected at short time intervals (approximately 10 s) for the microscopic examination. It showed that particle size and size distributions of all SPLITT fractions of airborne particles can be readily obtained using a calibration and that HF FlFFF can be utilized for the size confirmation of the sorted particle fraction during SPLITT fractionation.     

Hydrodynamic assist and the dynamic contact angle in the coalescence of liquid drops

^** Email: decentsp{at}for.mat.bham.ac.uk The coalescence of two viscous liquid drops in an inviscid gasor in a vacuum is studied using the interface formation model.In the very early stages of coalescence during the formationof the ‘liquid-bridge’ connecting the two drops,this model predicts a moving contact line and a dynamic contactangle. This paper examines the dynamic evolution of this contactangle, and for small Reynolds number and small Capillary number,relevant particularly in micro-fluidics, a non-linear differentialequation is derived for the contact angle and solved computationally.It is found that the contact angle evolution can only be evaluatedby determining information about the flow away from the contactline. This is a manifestation of so-called hydrodynamic assist,studied experimentally in the context of curtain coating byBlake et al. (1999 Experimental evidence of non-local hydrodynamicinfluence on the dynamic contact angle. Phys. Fluids, 11, 1995–2007).For small Capillary number and small Reynolds number, the free-surfaceevolution is determined for the coalescence of two cylindersof equal radius. Finally, some comments are made on experimentsin coalescence, as well as on issues arising in a computationalsolution of the full model described here.     

Green's function in plane anisotropic bimaterials with imperfect interface

^** Email: lsudak{at}ucalgary.ca The fundamental solutions or Green's functions for 2D or 3Danisotropic media with imperfect interface remain a challengingproblem. In this paper, a general method is presented for therigorous solution for the 2D Green's function in an anisotropicelastic bimaterial subject to a line force or a line dislocation.Most significant is the fact that the bonding along the bimaterialinterface is considered to be homogeneous imperfect. Specifically,the tractions are continuous but the displacements are discontinuousand proportional, in terms of interface stiffness parameters,to their respective traction components. Using complex variabletechniques, the basic boundary-value problem for two analyticvector functions is reduced to a coupled linear first-orderdifferential equation for a single analytic vector functiondefined in the lower half space. The coupled linear differentialequation for the single analytic vector function can be subsequentlydecoupled into three independent linear first-order differentialequations for three newly defined analytic functions. Closed-formsolutions for the 2D Green's function are derived in terms ofthe exponential integral. Unlike previous works which involvesome sort of inverse transform method to obtain the physicalquantities from the transform domain, the key feature of thepresent method is that the physical quantities can be readilycalculated without the need to perform any inverse transformoperations.     

Synthesis by organic molten salt method and characterization of chalcopyrite AgInS2 nanorods

In this paper, chalcopyrite AgInS₂ nanorods were synthesized for the first time by a one‐step, ambient pressure, environment friendly organic molten salt (OMS) method at 200 °C. The as‐synthesized products were characterized by X‐ray diffraction (XRD), scanning electron microscopy (SEM) and energy dispersive spectroscopy (EDS), respectively. The XRD results reveal that the as‐synthesized products at 120–160 °C under ambient pressure contain AgIn₅S₈ which will decrease with the increase of growth temperature. A sample containing only the chalcopyrite AgInS₂ phase is successfully obtained at 200 °C. Furthermore, the elemental compositions are found to become increasingly stoichiometric with increasing temperature. UV‐Vis and photoluminescence (PL) spectra are utilized to investigate the optical properties of AgInS₂ nanorods. By testing on UV‐Vis spectra, it is concluded that the limiting wavelength of the AgInS₂ nanorods is 661 nm and the band gap is 1.88 eV. A broad red emission band peak centered at about 1.874 eV (662 nm) is clearly observed at room temperature, and the intensity of the emission increases with excitation wavelength. In addition, the photoluminescence quantum yield (PLQY) of the nanocrystals at the excitation wavelength of 250 nm was determined to be 13.2%. A possible growth mechanism of AgInS₂ nanorods was discussed. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

矩形毛细微槽横截面上气液分界面形状理论分析

对背面有热流输入的矩形毛细微槽群横截面上的气液分界面形状进行了理论分析,在一定条件下对Wayner蒸发模型进行简化,根据等壁温条件推出蒸发薄液膜区域热流密度近似为定值,通过流体动力学理论推导出了微槽横截面薄液膜区域液膜厚度变化的关系式,并与Wayner蒸发模型的计算结果进行了比较。进一步提出了全新的交界线区域长度的判定方法,根据蒸发薄液膜区域总换热量计算得到蒸发薄液膜区域的长度,交界处接触角,以及固有弯月面区域的曲率半径,从而最终得出了微槽横截面整个气液分界面的形状曲线,理论分析表明:槽宽、热流密度、过热度等因素对蒸发薄液膜区域长度、接触角以及固有弯月面曲率半径等参数有较大的影响。     

Synthesis and characterization of Ni-Zn ferrite nanoparticles

Nickel zinc ferrite nanoparticles Ni_xZn_1−xFe₂O₄ (x=0.1, 0.3, 0.5) have been synthesized by a chemical co-precipitation method. The samples were characterized by X-ray diffraction, Fourier transform infrared spectroscopy, electron paramagnetic resonance, dc magnetization and ac susceptibility measurements. The X-ray diffraction patterns confirm the synthesis of single crystalline Ni_xZn_1−xFe₂O₄ nanoparticles. The lattice parameter decreases with increase in Ni content resulting in a reduction in lattice strain. Similarly crystallite size increases with the concentration of Ni. The magnetic measurements show the superparamagnetic nature of the samples for x=0.1 and 0.3 whereas for x=0.5 the material is ferromagnetic. The saturation magnetization is 23.95 emu/g and increases with increase in Ni content. The superparamagnetic nature of the samples is supported by the EPR and ac susceptibility measurement studies. The blocking temperature increases with Ni concentration. The increase in blocking temperature is explained by the redistribution of the cations on tetrahedral (A) and octahedral (B) sites.     

3D graphical representation of protein sequences and their statistical characterization

Based on three physicochemical properties of amino acid side chains, we proposed a novel unique 3D graphical representation of protein sequences. Then, we constructed two vectors of three components as mathematical objects to characterize protein sequences numerically. The similarity/dissimilarity analysis among nine ND5 protein sequences proved the utility of our approach. A correlation and significance analysis have been provided to compare our results and the sequence homology.