Kolmogorov Width of Classes of Smooth Functions on the Sphere

Let ^d−1{(x₁,…,x_d) ^d:x²₁+···+x²_d=1} be the unit sphere of the d-dimensional Euclidean space ^d. For r>0, we denote by B^r_p (1p∞) the class of functions f on ^d−1 representable in the formwhere dσ(y) denotes the usual Lebesgue measure on ^d−1, and P^λ_k(t) is the ultraspherical polynomial.For 1p,q∞, the Kolmogorov N-width of B^r_p in L^q( ^d−1) is given bythe left-most infimum being taken over all N-dimensional subspaces X_N of L^q( ^d−1).The main result in this paper is that for r2(d−1)²,where A_NB_N means that there exists a positive constant C, independent of N, such that C⁻¹A_NB_NCA_N.This extends the well-known Kashin theorem on the asymptotic order of the Kolmogorov widths of the Sobolev class of the periodic functions.     

Time-domain numerical computation of noise reduction by diffraction and finite impedance of barriers

A new time-domain numerical method is presented for the estimation of noise reduction by the diffraction and finite impedance of barriers. High order finite difference schemes conventionally used for computational aeroacoustics, and time-domain impedance boundary conditions are utilized for the development of the time-domain method. Compared with other methods, this method can be applied more easily to the problems related to nonlinear noise propagation such as impulsive noise and broadband noise. Linearized Euler equations in Cartesian co-ordinates are considered and solved numerically. Straight and T-shaped barriers with and without surface admittance are calculated. In order to assess the accuracy of this time-domain method, comparison with the results of SYSNOISE software (Ver. 5.3) are made. There are very good agreements between the results of the present time-domain numerical method and the boundary element method of the SYSNOISE software.     

Electron–hole complexes in self-assembled quantum dots in strong magnetic fields

We present results of calculations and experiments on electron–hole complexes in InGaAs/GaAs self-assembled quantum dots in high magnetic field (B). Due to hidden symmetries, the chemical potential of an N-exciton system at special B fields becomes insensitive to the exciton number as well as the magnetic field. This results in plateau regions of high intensity in measured magneto-PL spectrum. Theoretical calculations using exact diagonalization techniques successfully explain the measured magneto-photoluminescence spectrum with B fields up to 28 T.     

一种不等带宽光学梳状滤波器

提出了一种新型—Michelson—三面镜FabryPerot型50GHz不等带宽光学梳状滤波器设计方案,分析和模拟表明:该器件将一路信道间隔为50GHz的输入信号分离成信道间隔为100GHz的奇偶两路输出信号,其中在3dB处,奇数信道带宽大于30GHz用于10Gb/s传输,偶数信道带宽大于60GHz用于40Gb/s传输对于将来的40Gb/s系统,该器件具有优势.     

Effects of B′-site transition metal on the properties of double perovskites Sr2FeMO6 (M=Mo, W): B′ 4d-5d system

The crystal structure, magnetic and magnetotransport properties of the variation of B′-site transition metal in Sr₂FeMO₆ (M=Mo, W) with double perovskites structure have been investigated systematically. Measurements of magnetization vs. temperature at H=5 T show that Sr₂FeMoO₆ is a ferromagnet and Sr₂FeWO₆ is an antiferromagnet with T_N∼35 K. Additionally, the large magnetoresistance ratio (MR) of ∼22% (H=3 T) at room temperature (RT) was observed in the Sr₂FeWO₆ compound. However, the Sr₂FeMoO₆ compound did not show any significant MR even at high fields and RT (MR∼1%; H=3 T and 300 K). The implications of these findings are supported by band structure calculations to explain the interaction between the 4d(Mo) and 5d(W) orbitals of transition metal ions and oxygen ions.     

差分吸收光谱法测量大气痕量气体浓度误差分析及改善方法

差分吸收光谱技术(DOAS)中采用线性最小二乘拟合方法,用痕量气体标准差分吸收截面对测量得到的差分吸收光谱进行拟合,得出大气中痕量气体的浓度.计算结果的准确性不仅取决于光谱的测量精度,而且受标准差分吸收截面以及仪器函数和温度等诸多因素的影响.详细地分析了计算误差的产生原因,提出了用高浓度样品池得到标准吸收截面的方法,针对光谱固有结构,以及温度对标准吸收截面的影响,改进了浓度反演算法.大量的实验表明,综合运用上述方法,即便对低浓度的样气,相对测量误差也能降低到10%以下.     

Analytical Study of Nonlinear Dust Acoustic Waves in Two-Dimensional Dust Plasma with Dust Charge Variation

The nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation is analytically investigated by using the formally variable separation approach. New analytical solutions for the governing equation of this system have been obtained for dust acoustic waves in a dust plasma for the first time. We derive exact analytical expressions for the general case of the nonlinear dust acoustic waves in two-dimensional dust plasma with dust charge variation.     

Regular Balanced Cayley Maps for Cyclic, Dihedral and Generalized Quaternion Groups

A Cayley map is a Cayley graph embedded in an orientable surface such that. the local rotations at every vertex are identical. In this paper, balanced regular Cayley maps for cyclic groups, dihedral groups, and generalized quaternion groups are classified.     

On oriented 2-factorable graphs

Oriented 2-factorable graphs are reduced to bouquets by permutation voltage assignment in this paper. Introducing the concept ofk-class index of a permutation group, various oriented 2-factorable graphs are enumerated in this paper.     

A lithium ethyl­ene­diphos­phon­ate containing lithium chains and symmetric hydrogen bonds

In the title compound, catena‐poly[lithium‐μ₃‐ethyl­ene­diphos­phon­ato], [Li(C₂H₇O₆P₂)]_n, the supra­molecular monoclinic (C2/c) structure consists of one‐dimensional lithium chains [Li⋯Li = 2.7036 (8) Å] that are embedded within ethyl­ene­diphosphon­ate anions linked by strong symmetric hydrogen bonds [O⋯O = 2.473 (3) Å]. The Li atoms and the H atom in the symmetric hydrogen bond reside on twofold rotation axes and there is an inversion center at the mid‐point of the C—C bond of the ethylenediphosphonate ligand.