O8h结构磁空间群C-G系数的计算

磁空间群相对于以往的空间群,在对物理图像的描述上更准确、更深刻。如它可在考虑晶体对称性的同时,也考虑到自旋磁矩的作用,因而它的C－G系数更加重要。本文利用本征函数法,计算了面心立方结构Oh^8磁空间群的C－G系数,以及波矢选择规则和C－G序列。     

简立方结构磁空间群耦合系数计算

利用本征函数法（EFM方法）计算了Oh^1结构磁空间群第一布里渊区部分点的C－G系数。     

D_(6h)~4结构空间群C-G系数的计算

在晶体拉曼散射张量的计算中 ,晶体空间群的C G系数具有重要作用 ,本文利用本征函数法[1] ,计算了六角密排结构D46h空间群的C G系数 ,同时给出波矢选择规则和C G序列。     

空间群O7h()O4()T2母分系数的计算

在群链G真包含G1真包含G2中，把两个子群的IR(不可约表示)基相乘，然后把乘积基耦合成IR基，耦合系数我们称之为母分系数。本文把陈金全创立的本征函数法^[1]用于计算空间群的群链Oh^7真包含O^4真包含T^2的母分系数，计算的结果显示母分系数是满足正交关系，同时也说明此方法是适用的。     

空间群O_h~7O~4T~2母分系数的计算

在群链G G_1 G_2中,把两个子群的IR(不可约表示)基相乘,然后把乘积基耦合成IR基,耦合系数我们称之为母分系数。本文把陈金全创立的本征函数法用于计算空间群的群链O_h~7 O~4 T~2的母分系数,计算的结果显示母分系数是满足正交关系,同时也说明此方法是适用的。     

D_（6h）~1结构空间群C－G系数的计算

在晶体拉曼散射张量的计算中，晶体空间群的Ｃ－Ｇ系数具有重要作用，本文利用本征函数法~［１］，计算了一大类光学材料的结构空间群的Ｃ－Ｇ系数，同时给出波矢选择定则和Ｃ－Ｇ序列。     

D46h结构空间群C-G系数的计算

在晶体拉曼散射张量的计算中,晶体空间群的Ｃ－Ｇ系数具有重要作用。本文利用本征函数法,计算了六角密排结构Ｄ６ｈ＾４空间各的Ｃ－Ｇ系数,同时给出波矢选择规则和Ｃ－Ｇ序列。     

D6h结构空间群C—G系数的计算

在晶体拉曼散射张量的计算中，晶体空间的Ｃ－Ｇ系数具有重要作用。本文利用本征函数法，计算了一大类光学材料的Ｄ６ｈ结构空间群的Ｃ－Ｇ系数，同时给出波矢选择定则和Ｃ－Ｇ序列。     

基于局部约束群稀疏的红外图像超分辨率重建

针对红外图像分辨率低、视觉质量差等问题,提出基于局部约束群稀疏模型的红外图像超分辨率重建方法.考虑到红外图像的纹理自相似性和原子系数的群结构稀疏性,首先建立了基于局部约束的群稀疏表示模型.然后,在假定低分辨率图像空间和高分辨率图像空间具有相似流形的前提下,联合局部约束群稀疏表示模型和K-SVD(K奇异值分解)方法,训练得到高低分辨率图像对应的群结构字典对.最后,通过高分辨字典和对应的红外图像群稀疏表示系数重建得到高分辨率的红外图像.实验结果表明,本文方法具有更好的超分辨率效果,无论是在客观评价指标还是主观视觉效果方面都有明显的提高.     

二十面体群C-G系数计算

本文简要介绍了计算Ｃ Ｇ系数的生群元矩阵方程法，给出计算二十面体群Ｃ Ｇ系数时采用的简化计算方法，并给出了Ⅰ群Ｃ Ｇ系数的计算结果。     

THE IRREDUCIBLE REPRESENTATIONS AND THEIR OCCUPATION NUMBER IN DIRECT MULTIPLICATION OF IRREDUCIBLE REPRESENTATIONS OF SU3 GROUP

In this paper, the C-G series of SU₃ group is studied using Racah-Speier theorem. A general formula which can be used to calculate irreducible representations and their occupation number in C-G series of SU₃ group is derived. The general formula is very straight forward and effective for actual calculation One can apply the formula to analyse the distribution rule of occupation number in C-G series of SU₃ group and to define the null space of Winger operator of SU₃ group, the latter is important to the calculation of Wigner coefficients when there is a multiplicity.     

Symmetry analysis in neutron diffraction studies of magnetic structures: 1. A phase transition concept to describe magnetic structures in crystals

On the basis of phase transition symmetry theory there has been developed an efficient method of calculating the possible magnetic structures liable to arise from the paramagnetic phase of the crystal. Every magnetic structure is described by the superposition of the basis functions of the irreducible representation incorporated in the magnetic representation of the crystal symmetry group. Convenient formulas are given to calculate the basis functions and composition of the magnetic representation. These formulas permit calculation by referring only to the tables of space group irreducible representations. The technique is illustrated on the example of magnetic structures in crystals with the symmetry group D⁶_3d.     

Magnetostriction of a single crystal of nickel observed with an X-ray four-circle goniometer

We proposed a technique to observe magnetostrictive coefficients of a single crystal specimen with X-ray diffraction. An angle between a direction of crystallographic orientation and a direction of magnetic field could be estimated with two kinds of diffraction peaks which were found with an X-ray four-circle goniometer. The magnetostriction was measured by a shift of Bragg angle. This technique was suitable for a case to observe the magnetostrictive coefficient which varied as a function of the magnetic field direction. We applied the technique to a single crystal specimen of nickel and showed dependences of the magnetostriction on the magnetic field strength and its direction around an axis of easy magnetization at room temperature.     

U_q（sl（2））的二维循环表示，C—G系数和一个自由费米子八顶角模型

明确地构造了量子代数Ｕｑ（Ｓｌ（２））当ｑ＝ｉ和ｚ中心扩张时的两维循环表示，此表示是既约的；给出了张量表示的Ｃ—Ｇ规则和Ｃ—Ｇ系数以及不同次序张量表示的扭结子（Ｉｎｔｅｒｔｗｉｎｅｒ）．此扭结子是一个满足自由费米子条件的八顶角Ｒ矩阵，因此给出了一个可积顶角模型．     

The symmetry of three-electron states in a quantized magnetic field

The states of itinerant electrons on the finite square lattice in a quantized magnetic field are discussed. The single-electron states are classified by irreducible representations (IRs) of the magnetic translation group.The representation correspond to the Landau level, whereas its basis functions are analogs of the cyclotronic orbits. The filling factor of the Landau level is considered in the frame of multi-electron functions. Corresponding states are classified by the IR of MTG as well as by the irreducible representation of a symmetric group (permuting the electrons) and a unitary group (permuting electron states). The discussion is restricted to the case when the magnetic flux per unit cell of the two-dimensional square lattice is a rational number in terms of magnetic flux quanta. The additional parameter of the model is the Hubbard interaction between electrons.     

Classical diffusion in strong random media

We study classical diffusion of particles in random media. Although many of our results are general, we focus on the case of an ion in a three-dimensional medium with random, quenched charge centers obeying bulk charge neutrality. Within a functional-integral framework, we calculate the effective diffusion coefficients by first-order and second-order self-consistent perturbation theory (with a Gaussian reference in both cases). We also carry out a one-loop order momentum space renormalization group calculation. The self-consistent methods are complicated numerically and fail beyond intermediate disorder strengths. In contrast, the renormalization group calculation gives an analytical result that appears valid even to high disorder strengths. The methodology, generally applicable to a quantitative calculation of effective diffusion coefficients in disordered media, resolves deficiencies in self-consistent perturbation theory approaches to this class of problems.     

Symmetry analysis of magnetic structures and spin-waves on the basis of a stabilizer concept

The common scheme for the group theory analysis of a crystal magnetic structure and a spin-wave spectrum is developed. This scheme is based on the representation theory of a crystal space group G (for magnetic structure analysis) and on the co-representation theory of the Shubnikov group M of a magnetically ordered crystal (for spin wave analysis).Unlike the standard calculation, the procedure proposed in this paper is based on the conception of the stabilizer-the symmetry group of single atoms, and this considerably symplified the calculation work, reducing it to the work with the elements of the stabilizer and with the representatives of the expansion of the G or M groups with respect to the group of the stabilizer. It is enough to calculate the components of the basic functions only at one atom, as for the other atoms they may be found by the action of the representatives.For the symmetrization of the spin wave Hamiltonian matrix a new mathematical procedure is used the expansion of group G over the double coset classes. It lets us easily find the symmetric relations between the different matrix elements. The method is illustrated in the example of the complicated magnetic structure of a garnet Dy₃Al₅O₁₂. The advantages of the new method are especially obvious in the case of structures with a great number of magnetic atoms in a primitive cell.     

Electronic and magnetic properties of the rare earth intermetallic compounds RRu4Sn6 (R=Nd, Sm, Gd, Tb, Dy and Ho)

A number of compounds of structural formula RRu₄Sn₆ (R=rare-earth element) have previously been reported to form in the tetragonal crystal structure with space group I4¯2m. In this structure the R atoms are well isolated from each other. We embarked on this study to investigate the physical properties and to compare with earlier results obtained on the strongly correlated, low charge-carrier density compound CeRu₄Sn₆. Here we report our results of crystallographic, electrical resistivity, and magnetic studies on this family of compounds. In contrast to the behaviour in CeRu₄Sn₆, magnetic ordering is evident at low temperatures in the compounds with R=Sm, Gd, and Dy, as is evidenced by well-resolved anomalies in the temperature dependence of the electrical resistivity and static magnetic susceptibility.