Tauberian theorem for m‐spherical transforms on the Heisenberg group

In this paper we prove a Tauberian type theorem for the space L ( H _n ). This theorem gives sufficient conditions for a L ( H _n ) submodule J ? L ( H _n ) to make up all of L ( H _n ). As a consequence of this theorem, we are able to improve previous results on the Pompeiu problem with moments on the Heisenberg group for the space L^∞( H _n ). In connection with the Pompeiu problem, given the vanishing of integrals ∫ z ^m L _g f ( z , 0) dσ ( z ) = 0 for all g ∈ H _n and i = 1, 2 for appropriate radii r₁ and r₂, we now have the (improved) conclusion f ≡ 0, where = · · · and form the standard basis for T^(0,1)( H _n ). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Structures of the reduced niobium oxides Nb12O29 and Nb22O54

The crystal structure of Nb₂₂O₅₄ is reported for the first time, and the structure of orthorhombic Nb₁₂O₂₉ is reexamined, resolving previous ambiguities. Single crystal X-ray and electron diffraction were employed. These compounds were found to crystallize in the space groups P2/m (, , , β=102.029(3)^°) and Cmcm (, , ), respectively and share a common structural unit, a 4×3 block of corner sharing NbO₆ octahedra. Despite different constraints imposed by symmetry these blocks are very similar in both compounds. Within a block, it is found that the niobium atoms are not located in the centers of the oxygen octahedra, but rather are displaced inward toward the center of the block forming an apparent antiferroelectric state. Bond valence sums and bond lengths do not show the presence of charge ordering, suggesting that all 4d electrons are delocalized in these compounds at the temperature studied, T=200 K.     

The mutual responses of higher plants to environment: physiological and microbiological aspects

Higher plants are different from animals in many aspects, but the important difference may be that plants are more easily influenced by environment. Plants have a series of fine mechanisms for responding to environmental changes, which has been established during their long-period evolution and artificial domestication. The relationship between higher plants and environment is influenced mutually. The component in environment provides higher plants with nutrients for shaping themselves and higher plants simultaneously bring photosynthetic products and metabolites to surroundings, which is the most important part of natural circle. Photosynthetic products are realized mainly by physiological mechanisms, and microbiological aspects in environment (for instance, soil environment) impact the above processes greatly. The complete understanding of the relationship will extremely promote the sustainable utilization of plant resources and make the best use of its current potential under different scales.     

Matrix coefficients and coadjoint orbits of compact Lie groups

Let be a compact Lie group. We use Weyl functional calculus (Anderson, 1969) and symplectic convexity theorems to determine the support and singular support of the operator-valued Fourier transform of the product of the -function and the pull-back of an arbitrary unitary irreducible representation of to the Lie algebra, strengthening and generalizing the results of Cazzaniga, 1992. We obtain as a consequence a new demonstration of the Kirillov correspondence for compact Lie groups.

     

Low-energy excitations of Yb As in a magnetic field

We discuss the effects of an applied magnetic field on the low-energy excitations in the low temperature phase of Yb₄As₃. We show also why the magnetic interaction of the Yb³⁺ ions is nearly of an isotropic Heisenberg spin-1/2 type. A small anisotropy due to an intrachain dipolar interaction leads to the opening of a gap when a magnetic field is applied. The model agrees with available experimental data. Simple experiments are suggested in order to further test the present theory. Received 3 February 1999     

Magnetic impurities in gapless Fermi systems: perturbation theory

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, with r>0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U>0case: it exhibits both strong coupling (SC) states (for r<1) and local moment states (for r>1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U>0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon familiar in the normal r=0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for and r>1 but not for . Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength. Received 26 August 1999     

空间矩亚像素细分算法的研究

本文首先介绍了空间矩亚像素细分算法的基本原理、计算模板及公式,然后着重分析该方法的原理误差的起因,并推导了原理误差公式;本文利用实验对方法的有效性、线性及精度进行了研究,给出了方法的亚像素定位的标准差、直线边缘检测的坐标图、补偿后的直线边缘坐标图及实测尺寸对比结果     

Incommensurability in the magnetic excitations of the bilinear-biquadratic spin-1 chain

We study the magnetic excitation spectrum of the spin-1 chain with Hamiltonian .We focus on the range where the spin chain is in the gapped Haldane phase. The excitation spectrum and static structure factor is studied using direct Lanczos diagonalization of small systems and density-matrix renormalization group techniques combined with the single-mode approximation. The magnon dispersion has a minimum at until a critical value is reached at which the curvature (velocity) vanishes. Beyond this point, which is distinct from the VBS point and the Lifshitz point, the minimum lies at an incommensurate value that goes smoothly to when approaches , the Lai-Sutherland point. The mode remains isolated from the other states: there is no evidence of spinon deconfinement before the point .These findings explain recent observation of the behavior of the magnetization curve for . Received 16 December 1998     

Polarization-Dependent Phase-Conjugate Reflectivity in Randomly Oriented Saturable Absorbers: Effects of Direction of Transition Dipole Moment Associated with Excited-State Absorption

The effects of the direction of transition dipole moment on polarization-dependent phase-conjugate (PC) reflectivity by degenerate four-wave mixing in a saturable-dye-doped film are theoretically investigated. On the basis of a four-energy-level model for the saturable dyes, the pump-intensity dependence of the PC reflectivity is calculated for the two cases of a probe wave being polarized either parallel or perpendicular to pump waves, when the transition dipole moment associated with excited-state absorption tilts from that associated with ground-state one. For the parallel polarization, in the case of two transition dipole moments having different directions, a dip appears in the PC reflectivity curve near a resonant frequency on account of the characteristics of nonlinear absorption, whereas it disappears when the frequency of light is off resonance due to the influence of nonlinear refractive index.