Surfaces of revolution in the Heisenberg group and the spectral generalization of the Willmore functional

We study the generalization of the Willmore functional for surfaces in the three-dimensional Heisenberg group. Its construction is based on the spectral theory of the Dirac operator entering into theWeierstrass representation of surfaces in this group. Using the surfaces of revolution we demonstrate that the generalization resembles the Willmore functional for the surfaces in the Euclidean space in many geometrical aspects. We also observe the relation of these functionals to the isoperimetric problem.     

用光栅衍射法测试液体表面张力

利用π型直线状振源，在待测液面产生正弦形表面驻波，将其作为一种理想的反射式光栅，通过对激光束的衍射，形成线阵衍射光斑．借助LCCD等硬件测试系统及相应的数据采集与处理系统，实时准确地测量液体表面张力。     

绝缘表面和气体导电与湿度的关系

湿度对绝缘体表面电导和气体电导有一定的影响，但通常在湿度传感器的研究中忽略了气体电导的贡献。本文通过特殊设计装置来区分表面电导和气体电导，并分别从实验和理论上进行了定性的研究。     

First-principle studies on the electronic structure of Fe3O4(110) surface

The first-principle was employed to study the six possible models for the Fe₃O₄(110) surface, namely the AB-terminated surface (AB model), the AB-terminated with Fe_A vacancy (AB-Fe_A vac model), the AB-terminated with Fe_B vacancy (AB-Fe_B vac model), the B-terminated surface (B model), the B-terminated surface with Fe_B vacancy (B-Fe_B vac model) and the B-terminated surface with O vacancy (B-O vac model). The stability, the electronic structure and the magnetic properties of the six surface models were also calculated. The results predict that the B-O vac model is more stable than other types of surface models. The half-metallic property remain in the AB and B models, while the other four surface models exhibit metallic properties. At the same time, the AB, AB-Fe_A vac, AB-Fe_B vac, B and the B-Fe_B vac models have ferrimagnetic properties, while the B-O vac model has antiferromagnetic property.      

On the Patterson–Sullivan Measure for Geometrically Finite Groups Acting on Complex or Quaternionic Hyperbolic Space

The goal of this paper is to provide a tool, the Global Measure Formula, that will facilitate the study of the limit set of discrete geometrically finite groups of isometries of the rank one symmetric spaces. We consider the shadow of a ball from a fixed reference point onto the boundary, and prove a formula that describes the measure of the shadow in terms of the center of the shadowed ball, generalizing a result from real hyperbolic geometry.     

用玻色子组态混合和玻色子表面δ相互作用研究核谱

用玻色子组态混合波函数和玻色子表面δ相互作用研究了三玻色子核⁴⁶Ti和⁵⁴Cr的sdgIBMI的能谱和E2跃迁概率,理论计算结果令人满意,比sdIBMI能拟合出更多的能级和E2跃迁概率,而且它们的误差更小. 说明g玻色子在振动区也起着重要的作用,同时进一步证明了这种玻色子组态混合模型是成功的.     

BRST invariance and the conical pendulum

The Hamiltonian formulation of the BRST method for quantizing constrained systems developed recently by Nemeschanskyet al is applied to the well-known problem of the conical pendulum in classical mechanics. The similarity of the system to a gauge theory wherein the two constraints serve as generators of local Abelian gauge transformations is also pointed out. The definition of the physical states of the system as a gauge theory and also as a BRST invariant theory is then discussed in some detail.     

The Investigation of Bulk and Surface Polariton Modes in Ga1?xNxAs by Using Infrared Magneto Spectroscopy

We present and discuss infrared magnetoplasma reflectivity and surface polariton modes in Ga_1–xN_xAs. It assumed that the sample is characterized by a magnetoplasma dielectric tensor. Surface polariton dispersion for two component magnetoplasma was calculated from reflectivity spectra data. We detect transverse optic phonon of GaN sublattice in 470 cm^-1. The origin of sharp feature in p-polarization reflectivity about 300 cm^–1 as well as LO phonon frequency of GaAs sublattice is due to Brewster mode. An interesting feature of surface modes in Voigt geometry is nonreciprocalicity, which means that the frequency changes when the direction of propagation is reversed. Also, the infrared magnetoplasma reflectivity of GaNAs should be providing determination of the electrons and heavy holes effective mass and carrier's concentration.     

用于曲面精密检测的新型光纤三角传感器研究

基于光纤传感技术和三角测量方法，提出了一种用于曲面检测的新型光纤三角传感器。根据所设计的轮辐式接收光纤结构，可以在测量曲面与传感头间位移时，首先获取被测点处微面元的倾斜信息，以便对传感器测量值进行实时误差修正，从而解决了被测表面倾斜对坐标测量带来的影响。该传感器还能有效地消除环境光干扰、光源波动、表面反射率变化等对测量带来的影响。建立了传感器测量的数学模型。理论分析和初步的实验结果证明了系统的有效性和实用性。该传感器系统不稳定性好于0.3%，横向分辨率好于8μm，高度分辨率好于0.1μm。     

On the Solvability of the Multidimensional Version of the First Darboux Problem for a Model Second-Order Degenerating Hyperbolic Equation

A multidimensional version of the first Darboux problem is considered for a model second-order degenerating hyperbolic equation. Using the technique of functional spaces with a negative norm, the correct formulation of this problem in the Sobolev weighted space is proved.