Mean Square Estimates for Coefficients of Symmetric Power <Emphasis Type="Italic">L</Emphasis>-Functions

Let L(sym ^j f,s) be the jth symmetric power L-function attached to a holomorphic Hecke eigencuspform f(z) for the full modular group, and \(\lambda_{\mathrm{sym}^{j}f}(n)\) denote its nth coefficient. In this paper we are able to prove that

$\int_{1}^{x}\bigg|\sum_{n\leq y}\lambda_{\mathrm{sym}^{3}f}(n)\bigg|^{2}dy=O\bigl(x^{2}\bigr),$

and

$\int_{1}^{x}\bigg|\sum_{n\leq y}\lambda_{\mathrm{sym}^{4}f}(n)\bigg|^{2}dy=O\bigl(x^{\frac{11}{5}}\log x\bigr).$

     

A new finding of the existence of Feigenbaum’s constants in the fractional-order Chen–Lee system

This paper examines the universal quantitative properties of the fractional- and integer-order Chen?CLee systems. A?series of bifurcation diagrams of the system were generated in order to measure Feigenbaum??s constants. It was found that the measured values of the integer-order system were accurately approaching their universal constants, while the errors between measured values of the fractional-order system and the universal constants were not very large. The results showed that both the fractional- and integer-order Chen?CLee systems belonged to a quadratic map. To the authors?? knowledge, this is the first paper to measure Feigenbaum??s constants in fractional-order systems.     

Characterization of cubic phase MgZnO/Si(1 0 0) interfaces

The microstructural properties of the Mg_xZn_1−xO/Si(1 0 0) interface were investigated using transmission electron microscopy (TEM) and chemical states of the heterostructure were studied by high resolution X-ray photoelectron spectroscopy (XPS). By analyzing the valence band spectra of thin Mg_xZn_1−xO/Si(1 0 0) heterostructures, the valence band offset between such Mg_0.55Zn_0.45O and Si(1 0 0) was obtained to be 2.3 eV. Using the cubic ternary thin films as insulators, metal-insulator-semiconductor (MIS) capacitors have been fabricated. Leakage current density lower than 3 × 10⁻⁷ A/cm² is obtained under the electrical field of 600 kV/cm by current-voltage (I-V) measurement. Frenkel-Poole conduction mechanism is the main cause of current leakage under high electrical field.     

Nanowire as pico-gram balance at workplace atmosphere

The mechanical resonance behavior of a ZnO nanowire/nanorod at ambient condition has been studied under optical microscope by cutting its length using focused ion beam microscopy. Nanobalance using a ZnO nanowire as the cantilever has been demonstrated for measuring the mass in the order of pico-grams in working atmosphere (see optical microscopy images). The measurement limit of the balance is estimated to be ∼1 pg. The technique demonstrated here has potential for commercial applications in general laboratories, especially for measuring the mass of wet biological cells or species.     

山东省主栽果树生殖器官中稀土与微量营养元素的相关性研究

通过对山东省5大类主栽果树20余个树种的花粉、种子和果实稀土与微量元素自然含量进行分析比较, 认为稀土(RE)与微量元素在各树种花粉中平均含量顺序为Fe＞Zn＞B＞Cu＞Mn＞RE, 种子中B＞Fe＞Zn＞Mn＞Cu＞RE, 果实中Fe＞B＞Zn＞Cu＞Mn＞RE. 各元素在各生殖器官中的自然分布因树种而有很大差异. 但基本规律类同, 即花粉＞种子＞果实. 花粉富集各种微量营养元素的能力都很强. 花粉和果实稀土与微量元素之间绝大多数呈正相关, 种子大多呈负相关, 但相关性均不显著.     

Crystallization of amorphous SiC and superhardness effect in TiN/SiC nanomultilayers

TiN/SiC nanomultilayers with various constituent layer thicknesses were prepared by magnetron sputtering using TiN and SiC ceramic targets. X-ray diffractometer, scanning electron microscope, energy dispersive spectrometer, high-resolution transmission electron microscope, atomic force microscope and nanoindenter were employed to study the growth, microstructure and mechanical properties of these films. Experimental results revealed that amorphous SiC, which is more favorable under normal sputtering conditions, was forced to crystallize and grew epitaxially with TiN layers at thicknesses of less than 0.8 nm. The resultant films were found to form strong columnar structures, accompanied with a remarkable hardness increment. Maximal nanoindentation hardness as high as 60.6 GPa was achieved when SiC thickness was ∼0.6 nm. A further increase of SiC thickness caused the formation of amorphous SiC, which blocked the epitaxial growth of the multilayers, resulting in the decline of film's hardness. Additionally, investigations on multilayers different in TiN layer thicknesses showed that they are insensitive in both microstructure and hardness to the fluctuation of TiN layer thickness. The formation of epitaxially grown structure between crystalline SiC and TiN layers was found to be responsible for the obtained superhardness in multilayers.     

刻蚀改变InGaN/AIGaN应变多量子阱发光特性

为了分析干法刻蚀对应变多量子阱(SMQWs)发光特性的影响,采用感应耦合等离子体(ICP)刻蚀技术对金属有机物化学气相沉积(MOCVD)生长的InGaN/AlGaN应变多量子阱覆盖层表面刻蚀了约95 nm.通过光致发光(PL)特性表征发现,干法刻蚀后量子阱光致发光强度较未刻蚀量子阱光致发光强度提高了近3倍.干法刻蚀后,量子阱表面呈现高低起伏状形貌,粗糙度提高,出射光在起伏状粗糙形貌表面反复散射,从而逃逸概率增大,有助于光致发光强度增强.理论计算结果得出表面形貌变化引起的量子阱光致发光强度增强因子约为1.3倍.另外,由于所采用的感应耦合等离子体功率较小,刻蚀损伤深度几乎不会达到量子阱阱层,然而干法刻蚀过程中Ar离子隧穿到量子阱阱层内部可能形成新的发光中心,从而使量子阱的发光强度得到提高.