Vector subdivision schemes and multiple wavelets

We consider solutions of a system of refinement equations written in the form

where the vector of functions is in and is a finitely supported sequence of matrices called the refinement mask. Associated with the mask is a linear operator defined on by . This paper is concerned with the convergence of the subdivision scheme associated with , i.e., the convergence of the sequence in the -norm.

Our main result characterizes the convergence of a subdivision scheme associated with the mask in terms of the joint spectral radius of two finite matrices derived from the mask. Along the way, properties of the joint spectral radius and its relation to the subdivision scheme are discussed. In particular, the -convergence of the subdivision scheme is characterized in terms of the spectral radius of the transition operator restricted to a certain invariant subspace. We analyze convergence of the subdivision scheme explicitly for several interesting classes of vector refinement equations.

Finally, the theory of vector subdivision schemes is used to characterize orthonormality of multiple refinable functions. This leads us to construct a class of continuous orthogonal double wavelets with symmetry.

     

三例基于5-(二甲基氨基)间苯二甲酸的锌(Ⅱ)/铜(Ⅱ)配合物的合成、晶体结构、Hirshfeld表面分析和荧光性质

利用配体 5-(二甲基氨基)间苯二甲酸(H₂dia)和咪唑(mdz)分别与锌(Ⅱ)和铜(Ⅱ)金属盐反应,制备了 3 例过渡金属配合物[Zn(dia)(mdz)₂]·2H₂O (1)、[Cu(dia)(mdz)₂(DMF)] (2)和[Cu(dia)(mdz)₂]·H₂O (3)。利用单晶 X射线衍射、元素分析、红外光谱、热重和Hirshfeld表面分析对其进行了结构表征。结果表明配合物1和2为一维线状链,1中每个四配位的Zn(Ⅱ)处于变形四面体中心,2中Cu(Ⅱ)中心拥有五配位的三角双锥几何构型。改变合成溶剂条件得到锯齿形一维链状配合物3,其四配位Cu(Ⅱ)中心展现出对称平面四边形构型。上述结果说明,金属离子几何构型以及合成溶剂可能对配合物结构具有重要影响。丰富的分子间氢键帮助3例配合物形成稳定的三维超分子结构。热重分析表明,3例配合物均具有良好的热稳定性。固体荧光分析表明配合物1具有较强荧光性,而配合物2和3荧光强度均远低于配体。     

单轴拉伸下氧化锆纳米柱相变机理的分子动力学研究

通过分子动力学模拟,观察到[001]取向的四方氧化锆纳米柱在拉伸载荷下具有两个线弹性变形的应力-应变关系.这一现象是四方结构向单斜结构相变的结果 .为了进一步阐明应力-应变曲线,进行了包括晶体结构分析和原子应变计算在内的详细研究.晶格取向强烈影响塑性变形机制,即[001]和[111]取向的纳米柱在拉伸载荷下经历相变,而沿[110]取向的纳米柱导致脆性断裂.观察到显著的温度效应,随着温度从300K升高到1500K,弹性模量从573.45GPa线性降低到482.65GPa.此外,还用轻推弹性带(NEB)理论估算了相变能垒,观察到相变能垒随温度的升高而降低.这一工作将有助于加深对氧化锆的四方相到单斜相转变和纳米尺度力学行为的理解.     

反铁磁链中Dzyaloshinskii–Moriya机制驱动矢量自旋手征束缚态的研究

Dzyaloshinskii-Moriya(DM)相互作用驱动的矢量自旋手征态,能和声子发生耦合,具备非常丰富的物理现象.本论文以一维反铁磁链中自旋手征-声子耦合模型为基础,研究不同声子环境下,耦合强度对自旋手征动力学演化过程的影响规律.结果表明,对自旋S=1/2的系统,在不同的声子浴(sub-Ohmic(0 1))中,均会在非相干到相干自旋涨落过程中产生无能隙一级相变,其来源是自旋手征束缚态的形成.相变发生的临界自旋-声子耦合强度正比于自旋涨落大小,反比于系统德拜频率.当自旋-声子耦合强度超过其临界值时,自旋手征束缚态的产生将极大地抑制非相干自旋涨落.     

Nonlinear transport in p-type SiGe quantum well structure containing Ge quantum dots

We use magneto-transport spectroscopy to study a dramatic instability between a low and high conductivity mode in Si/SiGe-based resonant tunneling diodes with an embedded layer of self-assembled Ge hut cluster quantum dots in the Si barrier. In the low current regime a simple activation-type behavior with an astonishingly low activation energy in the order of 0.1 meV is determined. In the high current regime a region of negative differential conduction can be observed. We discuss the influence of different layer structures and magnetic fields.     

渐变段倾角对渐变复合腔特性影响的分析

利用模式耦合理论,在考虑多模耦合的情况下,对渐变结构复合腔进行了冷腔分析,计算了H51-H52模式对下,各个模式的耦合及场幅值分布情况,分析了渐变段的倾角对渐变复合腔的Q值及场幅值分布的影响。研究表明：渐变段的倾角对渐变结构复合腔的高频特性有很大的影响,特别是各模式的场分布及Q值,合适地选择渐变角度,能使场幅值放大率比较大,这将有利于提高注-波互作用效率。     

Near-infrared emission bands of Er-doped YAP and LSO crystals

The ground state absorption (GSA), photoluminescence (PL) and photoluminescence excitation (PLE) spectra for Er(1.0 at%):YAP and Er(0.5 at%):LSO were measured at room temperature. Based on the GSA spectra, the radiative transition rates and luminescence branch ratios of erbium ions were determined by the Judd-Ofelt (J-O) method. In the range of 1400-1700 nm Er(1.0 at%):YAP has intense absorption at 1509 nm (0.96×10⁻²⁰ cm²), which is almost two times larger than the peak absorption of Er(0.5 at%):LSO. From the PL and PLE spectra, four intense emission bands around 850 nm (⁴S_3/2→⁴I_13/2), 980 nm (⁴I_11/2→⁴I_15/2), 1230 nm (⁴S_3/2→⁴I_11/2) and 1520 nm (⁴I_13/2→⁴I_15/2) were observed. The stimulated emission cross-sections of the four bands were calculated by the Fuchtbauer-Ladenberg (F-L) equation. The results suggest that Er(1.0 at%):YAP has potential to realize laser oscillation at 858 nm because of the relatively large simulated emission cross-section (1.76×10⁻²⁰ cm²). The temperature dependences of the PL spectra for the two crystals were also investigated in the range of 290-12 K. The ∼1520 nm emission presents continuous increase with temperature, while the emissions around 850, 1230 and 980 nm firstly increase with temperature, then reach their own largest values at the transition temperatures (about 100 K), and finally decrease with temperature. These results were well interpreted by the temperature dependence of multi-phonon process.     

Raman polarization analysis of highly crystalline polyethylene fiber

The complex orientation dependence in space of Raman active vibrations in the orthorhombic structure of polyethylene (PE) is discussed in terms of Raman tensor elements as intrinsic physical parameters of the lattice. Building upon the symmetry assignment of these vibrational modes, we systematically studied, from both theoretical and experimental viewpoints, the changes of polarized intensity for the A_g and the B_2g + B_3g vibrational modes with respect to PE molecular orientation. After explicitly expanding the Raman selection rules associated with the A_g and the B_2g + B_3g modes, introducing them into general expressions of the orientation distribution function, and validating them by means of a least‐square fitting procedure on experimental data, we compare here two mesostructural models for a highly crystallized and self‐aligned PE fiber structure. Stereological arguments are shown concerning the arrangement of orthorhombic fibrils in such a sample that unfold the correct values of five independent Raman tensor elements for orthorhombic PE. Copyright © 2010 John Wiley & Sons, Ltd.     

Third-Order Optical Nonlinearity in Two-Dimensional Transition Metal Dichalcogenides

We present a detailed calculation of the linear and nonlinear optical response of four types of monolayer twodimensional (2D) transition-metal dichalcogenides (TMDCs), having the formula MX₂ with M=Mo, W and X=S, Se. The calculations are based on 6-band tight-binding model of TMDCs, and then performing a semi-classical perturbation analysis of response functions. We numerically calculate the linear χ_μν⁽¹⁾ (-ω;ω) and nonlinear surface susceptibility tensors χ_μνζη⁽³⁾(-ω_Σ; ω_r; ω_s; ω_t) with ω_Σ=ω_r+ω_s+ω_t. Both non-degenerate and degenerate cases are studied for thirdharmonic generation and nonlinear refractive index, respectively. Computational results obtained with no external fitting parameters are discussed regarding two recent reported experiments on MoS₂, and thus we can confirm the extraordinarily strong optical nonlinearity of TMDCs. As a possible application, we demonstrate generation of a π/4-rotated squeezed state by means of nonlinear response of TMDCs, in a silica micro-disk resonator covered with the 2D material. Our proposed method will enable accurate calculations of nonlinear optical response, such as four-wave mixing and highharmonic generation in 2D materials and their heterostructures, thus enabling study of novel functionalities of 2D photonic integrated circuits.