Some upper bounds for sums of eigenvalues of the Neumann Laplacian

Let be the th Neumann eigenvalue of a bounded domain with piecewisely smooth boundary in . In 1992, P. Kröger proved that , where the upper bound is sharp in view of Weyl's asymptotic formula. The aim of this paper is twofold. First, we will improve this estimate by multiplying a factor in terms of to its right-hand side which approaches strictly from below to 1 as tends to infinity. Second, we will generalize Kröger's estimate to the case when is a compact Euclidean submanifold.

     

SOME MULTIPLIER THEOREMS FOR ANISOTROPIC HARDY SPACES ——In Memory of Professor Yongsheng Sun

Let A be a symmetric expansive matrix and Hp(Rn) be the anisotropic Hardy space associated with A. For a function m in L∞(Rn), an appropriately chosen function η in Cc∞(Rn) and j ∈ Z define mj(ξ) = m(Ajξ)η(ξ). The authors show that if 0 ＜ p ＜ 1 and (m)j belongs to the anisotropic nonhomogeneous Herz space K11/p-1,p(Rn), then m is a Fourier multiplier from Hp(Rn) to Lp(Rn). For p = 1, a similar result is obtained if the space K10,1(Rn) is replaced by a slightly smaller space K(w).Moreover, the authors show that if 0 ＜ p ≤ 1 and if the sequence {(mj)V} belongs to a certain mixednorm space, depending on p, then m is also a Fourier multiplier from Hp(Rn) to Lp(Rn).     

Three-dimensional GaN-Ga2O3 core shell structure revealed by x-ray diffraction microscopy

In combination of direct phase retrieval of coherent x-ray diffraction patterns with a novel tomographic reconstruction algorithm, we, for the first time, carried out quantitative 3D imaging of a heat-treated GaN particle with each voxel corresponding to 17 x 17 x 17 nm3. We observed the platelet structure of GaN and the formation of small islands on the surface of the platelets, and successfully captured the internal GaN-Ga2O3 core shell structure in three dimensions. This work opens the door for nondestructive and quantitative imaging of 3D morphology and 3D internal structure of a wide range of materials at the nanometer scale resolution that are amorphous or possess only short-range atomic organization.     

Quantum size effect on surface photovoltage spectra: alpha-Fe(2)O(3) nanocrystals on the surface of monodispersed silica microsphere

A new method for the preparation of Fe(2)O(3) nanoparticle/SiO(2) microsphere composites is described, in which fine alpha-Fe(2)O(3) nanocrystals were prepared by forced hydrolysis of FeCl(3) aqueous solution. The structure and optical spectra of these alpha-Fe(2)O(3) nanocrystals have been studied. Their visible optical absorption can be enhanced by their adsorptions on the surface of SiO(2) microspheres and thereafter simple packing of these microspheres to the aggregated structures. The size-dependent photogenerated surface photovoltage spectra (SPS) of these composites were studied, and quantum confinement effects of the SPS properties were observed. The transport of photoinduced charges between nanocrystals with intrinsic electronic nature of confined states accounts for this phenomenon. These results are helpful in understanding the relationship among d-d transition and charge-transfer transition in transition metal oxides and find applications in photovoltaic devices.     

Rapid analysis of the essential oils from dried Illicium verum Hook. f. and Zingiber officinale Rosc. by improved solvent-free microwave extraction with three types of microwave-absorption medium

A new method of extracting essential oils from dried plant materials has been studied. By adding a microwave-absorption medium (MAM) to a reactor, solvent-free microwave extraction (SFME) was improved and can be used to extract essential oils from dried plant material without pretreatment. With a microwave irradiation power of 85 W it took only approximately 30 min to extract the essential oils completely. The whole extraction process is simple, rapid, and economical. Three types of MAM, iron carbonyl powder (ICP), graphite powder (GP), and activated carbon powder (ACP), and two types of dried plant material, Illicium verum Hook. f. and Zingiber officinale Rosc., were studied. The results were compared with those obtained by use of conventional SFME, microwave-assisted hydrodistillation (MAHD), and conventional hydrodistillation (HD), and the conclusion drawn was that improved SFME was a feasible means of extracting essential oils from dried plant materials, because there were few differences between the composition of the essential oils extracted by improved SFME and by the other methods.     

Determination of human complement factor C4 using resonance light-scattering technique with sodium dodecylbenzene sulphonate probe

Based on the interaction between human complement factor C4 (human C4) and sodium dodecylbenzene sulphonate (SDBS) and the resonance light-scattering (RLS) technique, a highly sensitive assay for human C4 using resonance light-scattering technique was developed. At pH 2.8 Na2HPO4-citric acid buffer solution, the RLS intensities of SDBS system at 283, 503 and 600 nm were obviously enhanced in the presence of human C4. The effects of surfactant, pH, incubation time, concentration of SDBS and foreign substances on the enhanced RLS intensity of system were investigated. Under the optimum conditions, the enhanced RLS intensity is directly proportional to the concentration of human C4 in the range of (0.5-120)x10(-6)gl-1 and the linear regression equation was obtained with high correlation coefficient. This RLS technique was applied to the determination of human C4 in some synthetic samples with good recovery. Moreover, it was found that the electrostatic interaction is the main binding force between SDBS and human C4.     

分离结晶Bridgman法晶体生长过程的影响因素

本文采用全局数值模拟方法探讨了微重力条件下温度梯度对分离结晶Bridgman法晶体生长系统的作用规律。同时,在常重力条件下研究了坩埚半径对晶体生长系统的影响。结果发现,在微重力条件下随着温度梯度的增加,晶体生长系统内部的流动强度随之增加,且由于晶体生长系统低温区温度不断降低,使得结晶界面位置不断上升;在常重力条件下,重力的作用随着坩埚半径的增加而增强,导致晶体生长系统内部的流动强度增加,最大流函数增大。     

Fabrication and Properties of Double-Side Tl2Ba2CaCu2O8 Thin Film on CeO2 Buffered Sapphire Substrate

The double-side Tl2Ba2 CaCu2O8 （Tl-2212） superconducting thin films were fabricated on CeO2 buffered sapphire substrates. The reactive magnetron sputtering technique was used to grow CeO2 buffer thin films on sapphire substrates. Making use of the metal cerium as a sputtering source, the depositing rate is much higher compared with the CeO2 target. The Ti-2212 thin films on CeO2 buffered sapphire substrates were fabricated by adc magnetron sputtering and post-annealing process. The x-ray diffraction indicates that the thin film is pure Tl-2212 phase with the e-axis perpendicular to the substrate surfaces, and epitaxially grown on the CeO2 buffered sapphire. The critical transition temperature Tc is around 106K, the critical current density Jc is around 3.5 MA/cm^2 at 77K, and the microwave surface resistance R8 at 77K and 10 CHz of the film is as low as 390μ Ω.     

White Emitting ZnS Nanocrystals： Synthesis and Spectrum Characterization

Spherical organic-bonded ZnS nanocrystals with 4.0 4-0.2 nm in diameter are synthesized by a liquid-solid-solution method. The photoluminescence spectrum of sample （[S^2-]/[Zn^2＋] = 1.0） shows a strong white emission with a peak at 490nm and - 170 nm full widths at half maximum. By Gauss fitting, the white emission is attributed to the overlap of a blue emission and a green-yellow emission, originating from electronic transitions from internal S^2- vacancies level to valence band and to the internal Zn^2＋ vacancy level, respectively. After sealingZnS nanocrystals onto InGaN chips, the device shows CIE coordinates of （0.29,0.30）, which indicates their potential applications for white light emitting diodes.     

Transverse momentum distribution of the Z produced at the Large Hadron Collider and related phenomena

From the recent theoretical result on the production of the Higgs boson at the Large Hadron Collider, it follows that other particles will also be produced with small transverse momentum, of the order of 1 GeV/c$1\text{GeV}/c$. The leptonic decay mode of the Z is especially suited for a first observation of this phenomenon. Other related effects, such as paired jets, are also discussed.