Isometries and additive mapping on the unit spheres of normed spaces

In this paper, we investigate isometric extension problem in general normed space. We prove that an isometry between spheres can be extended to a linear isometry between the spaces if and only if the natural positive homogeneous extension is additive on spheres. Moreover, this conclusion still holds provided that the additivity holds on a restricted domain of spheres.     

Inclined Substrate Deposition of Nanostructured TiO2 Thin Films for DSSC Application

Nanostructured TiO₂ films were deposited onto Indium Tin Oxide (ITO) and glass substrates by dc reactive magnetron sputtering at different substrate inclination angles. The structural and optical properties of the deposited films were studied by X-ray diffraction, scanning electron microscopy and UV–Vis spectrophotometer, respectively. Dye-sensitized solar cells (DSSC) were assembled using these TiO₂ films as photoelectrodes and the effect of the substrate inclination angle in the preparing process of TiO₂ films on the DSSC conversion efficiency was studied.     

Cauchy problems for Hilfer fractional evolution equations on an infinite interval

It is well known that the classical Ascoli-Arzelà theorem is powerful technique to give a necessary and sufficient condition for investigating the relative compactness of a family of abstract continuous functions, while it is limited to finite compact interval. In this paper, we shall generalize the Ascoli-Arzelà theorem on an infinite interval. As its application, we investigate an initial value problem for fractional evolution equations on infinite interval in the sense of Hilfer type, which is a generalization of both Riemann-Liuoville and Caputo fractional derivatives. Our methods are based on the Hausdorff theorem, classical/generalized Ascoli-Arzelà theorem, Schauder fixed point theorem, Wright function, and Kuratowski measure of noncompactness. We obtain the existence of mild solutions on an infinite interval when the semigroup is compact as well as noncompact.     

Manipulating Nonlinear Photocurrent from Interlayer Coupling in Bilayer Metamaterials for Polarized Terahertz Generation

Polarized terahertz (THz) wave generation is of great significance for chiral and anisotropic sensing applications. However, how to manipulate amplitude, polarization, and ellipticity of the THz generation is still a fundamental challenge. Herein, polarized THz wave generation is achieved from a bilayer metamaterial consisting of T-shaped structure (TSS) and split resonator rings (SRRs) by combining Maxwell and hydrodynamic equations. The elliptically polarized THz wave can be synthetized directly from horizontally and vertically polarized THz components due to the orthogonal nonlinear photocurrents along the arm-directions of TSS and SRRs, respectively. Besides, the ellipticity and the orientation angle of the THz polarization ellipse can be modulated by the twist angle between the SRRs and TSS layers. The maximum ellipticity can reach 0.34 while the orientation angle is tunable from −0.45 to 0.48π by tuning the twist angle. This work proposes an interlayer coupling method for the polarized THz sources based on metamaterials in potential circular dichroism and chiral sensing applications.     

Flexibly Enhanced Photonic Spin Hall Effect via Selective Brewster Angle

The manipulating of photonic spin Hall effect (SHE) plays a crucial role for development of spin-dependent nanodevices and systems. Since the photonic SHE is generally enhanced near the Brewster angle, the choice of incident angle usually has low flexibility with natural materials due to their dielectric constants. Herein, an efficient method to flexibly enhance the photonic SHE by utilizing selective Brewster angle in an anisotropic metamaterial is proposed. Through adjusting the thickness ratio of two media in metamaterial, the Brewster angle can be flexibly adjusted in a broad range (nearly 0–90°). With the selective Brewster angle, the spin-dependent transverse shift can be enhanced at nearly arbitrary incident angles. Furthermore, based on this structure, a binary encoding system is demonstrated, realizing information conversion around incident angles. This research work provides more possibilities for applications in manipulating photonic SHE.     

Improving Data Quality in Traditional Low-Dose Scanning Transmission Electron Microscopy Imaging

It has become very important to study and find optimal conditions for imaging electron-beam (e-beam) sensitive materials in scanning transmission electron microscopy under low electron-dose with high signal-to-noise ratio (SNR). Convergence and collection angles and electron-probe current are essential parameters. However, these parameters have rarely been discussed in a systematic way. In this paper, the illumination and collection conditions are optimized according to the resolution requirement of different materials by adjusting the condenser and intermediate lenses in a commercial transmission electron microscope. To demonstrate the significance of optimizing these parameters, two examples, zeolite MFI and metal–organic framework (MOF) MIL-101, are taken among the sensitive materials, with the most important electron incidences along the [010] and <110> directions, respectively. High SNR atomic resolution images of MFI are obtained with e-beam current as low as 0.50 pA, reaching information transfer for reflection up to 18 0 2 corresponding to d-spacing of 0.11 nm, close to the resolution limit of 0.098 nm from resolvable diffraction limit. MOF MIL-101 is characterized under an even lower e-beam 0.2 pA to avoid severe beam damage. High-quality annular dark and bright field images are obtained, which proves the wide applicability of this method on more e-beam sensitive materials.     

俯仰振荡三角翼前缘涡破碎的流动显示

前缘后掠角为６５°和７０°的两个平板三角翼作俯仰振荡运动，前缘涡破碎的流动显示实验研究在南京航空航天大学１米低速风洞中进行。俯仰振荡运动的攻角范围为０°～６０°，折合频率为０．０３和０．０６。采用四氯化钛发烟技术显示前缘涡核轨迹及涡破碎位置。流动显示图形采用相位锁定照相记录。实验结果表明大幅俯仰振荡三角翼的动态涡破碎的弦向位置明显滞后于相应攻角下的静态位置，此滞后量随折合频率增加而增大。本文也根据测得的涡破碎位置随攻角变化曲线讨论了涡破碎位置的传播速度     

聚晶立方氮化硼刀具切削高锰钢的磨损机制

在半精加工试验条件(切削深度ap=0．5mm，进给量f=0．3mm／r，干切)下研究了聚晶立方氮化硼刀具切削奥氏体高锰钢时的磨损机制，用WDH-Ⅱ型光电温度计测量了切削温度，用工具显微镜测量后刀面磨损量，进而考察了切削时间和切削速度对后刀面磨损量的影响，采用S-250MK型扫描电子显微镜观察刀具前、后刀面的磨损形貌和组成变化．结果表明：当切削温度为400～750℃时，聚晶立方氮化硼刀具同高锰钢中的γ相及其析出相(Fe，Mn)3C之间产生严重的机械磨损；当切削温度超过800℃时，聚晶立方氮化硼刀具同高锰钢单一γ相之间产生扩散磨损；聚晶立方氮化硼刀具适合于高速切削.     

细长体背风面横向非对称分离的研究

用数值模拟方法研究了超声速情况下，无限长细长体背风面的涡结构。数值模拟的出发方程和计算格式分别为全Ｎ－Ｓ方程和二阶空间精度的ＴＶＤ格式。数值结果给出了圆锥、半球柱体和椭圆锥在不同攻角下的流场结果。结果表明圆锥在攻角α＝１５°，２０°和２５°时背风面呈现明显的稳定非对称横向分离，而半球柱体和椭圆锥在３２．５°和２５°时背风面均未出现非对称的横向分离结构。     

不确定非线性结构动力响应的区间分析方法

研究多自由度非线性不确定参数系统的动力响应问题. 以区间数学为基础，将不确定 性参数用区间进行定量化，借助一阶Taylor级数，给出了近似估计非线性振动系统动力响 应范围的区间分析方法. 从数学证明和数值算例两方面，将其与概率摄动有限元法进行了比 较，结果显示区间分析方法对不确定参数先验信息具有要求较少、精度较高的优点.