Laplace-Beltrami operator on symmetric space X ≡ SOo(2, 3)/SO(2) × SO(3) of rank 2 and the related 2-body one dimensional quantum systems

The explicit form of the Laplace-Beltrami operator Δ_LB on symmetric space X  SO₀(2,3)/SO(2) xSO(3) of rank 2 is given. Using the representation of SO₀(2,3) the eigenfunctions of δ_LB, i.e. plane waves on X are constructed. The integral representation of the zonal spherical functions of the group SO_o(2, 3) is presented and the related 2-body one-dimensional quantum systems are considered.     

基于互相关算法的飞机导线故障诊断与定位系统设计

以飞机导线短路故障和断路故障为研究对象,目的在于寻求一种测试方法能够提高应用时域反射测量原理进行故障诊断与定位的精度。按照实际机场工程应用背景,设计了以便携式工控机为控制核心、以LabVIEW为驱动软件的飞机导线故障诊断与定位系统。根据信号传播特性,提出了基于互相关算法的故障定位方法,消除了系统误差的影响。计算机仿真和实物测试结果表明该系统具有测试过程方便、准确性高的优点,为提高民航机务维修质量具有促进作用。     

Effects of electron correlation and spin-orbit coupling on the electronic and magnetic properties of TbCu3Mn4O12

Electronic and magnetic properties of the three magnetic-sublattice double perovskite TbCu₃Mn₄O₁₂ (TCMO) are investigated by performing first-principles density-functional theory calculations. Our electronic structure calculations show that TCMO is half-metallic and its half-metallicity can only be correctly described when the electron correlation on Tb³⁺ 4f⁸ electrons are considered. The energies of different magnetic configurations among the three magnetic sublattices are also calculated, revealing that the magnetic configuration with Mn and Cu spins in the antiparallel arrangement and with the Tb magnetic moments ferromagnetically/antiferromagnetically (FM/AFM) coupled to Cu/Mn spins (that is Tb^↓Cu₃^↓Mn₄^↑O₁₂) is the lowest energetic magnetic state, which is consistent with recent experimental results. The magnetic anisotropy is further calculated for the [1 1 1], [1 1 0], and [0 0 1] spin quantization directions. It is found that the [1 1 1]-direction is more stable than the [1 1 0]- and [0 0 1]-directions by 123 and 135 meV per formula unit, respectively, indicating a significant magnetic anisotropy. Our detailed projected partial density of states analysis finally shows that Cu and Mn are antiferromagnetically coupled by superexchange interaction and Tb is expected to interact FM with A-site Cu and AFM with B-site Mn sublattices by way of 4f-2p-3d.