Thermodynamic approach of spin-state excitations in LaCoO3

Magnetic susceptibility and heat capacity due to spin-state excitations in LaCoO₃ were analyzed with an irregular solution model composed of Co³⁺ ions in the low-spin ground state and in the high-spin excited state. An energy-levels diagram proposed by Ropka and Radvanskii [1] was used for the high-spin excited state. This analysis showed that the entropy of mixing is less than that of ideal solutions and the enthalpy of mixing is negative, indicating that the high-spin Co ions are arranged as far apart as possible.     

Preparing of coherent superposition state in serial multi-A-type system by stimulated Raman adiabatic passage

A scheme for creating an arbitrary coherent superposition of two atomic states in serial multi-A-type system is proposed.This technique with the application of a control field is based on the existence of two degenerate dark states and their interaction.The mixing of the dark states can be controlled by changing the relative delay time of the control pulse.One can get any desired superposition by changing the delay time of the control pulse.     

单相超导体CaLaBaCu_(3-x)BxO_(7-δ)正常态热电势率研究

从 77K到 30 0 K之间对 Ca L a Ba Cu3 -x Bx O7-δ单相体系的正常态热电势率进行了微分法测量 ,发现随着硼含量 x从 0向 0 .4的逐步增加 ,样品体系正常态特性从金属性向类半导体性质转变 ,其主要载流子由空穴型为主转变为电子型为主 .根据以上的性质转变 ,我们采用双带模型及半导体模型对 x的不同值进行曲线模拟 ,拟合的热电势率—温度曲线与实验曲线相当吻合 ,同时根据模型对样品的费米能及有效能隙进行了计算     

A new polynomial sequence as a guide to numerical solutions for applied‐physics‐related partial differential equations under Dirichlet‐Newman‐type exogenous boundary conditions

In this article, a new set of polynomials is proposed as a new tool for solving bivaried partial differential equation related with some appropriated applied physics problems. A concrete formulation of canonical expressions, with respect to more common boundary conditions, is yielded out of the recently established Boubaker polynomials. © 2008 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2009     

Direct amplitude detection of Zernike modes by computer-generated holographic wavefront sensor: Modeling and simulation

A fast holographic wavefront sensor is proposed using a computer-generated hologram (CGH). This CGH is a multiplexed hologram of different Zernike mode–amplitude combinations, and is designed in such a manner as to get the corresponding spots on the detector according to the presence and strength of a particular aberration. Interference between the aberrated wavefront (with a single mode–amplitude combination) and the Fourier transform of an image with single bright pixel (defined as dot image) is numerically calculated for one hologram. Different mode–amplitude combination and corresponding different positions of bright pixels (dots) are taken to compute various holograms and then all the holograms are multiplexed to get the final hologram. When the aberrated wavefront with a particular mode–amplitude combination is incident onto the multiplexed hologram, the corresponding dot is generated in the Fourier plane. A lens performs the Fourier transform in optical domain and provides the instant detection of amplitude of the respective Zernike mode. The main advantage of the scheme is to avoid the need of any computations, which makes it really fast. The simulation results are presented with the cross-talk analysis for few Zernike terms.     

HeNa及HeNa~+光谱的理论研究

利用从头算Molecule-UHF程序计算得到HeNa分子的基态~2∑3s及激发态~2∏3p和HeNa~+的~1∑2p、~3∑3s及~t∑3s态的势能曲线,并在此基础上利用自编的程序计算了态-态间光谱跃迁的Franck-Condon因子.结果说明HeNa分子的基态是不稳定的,激发态2∏3p有一个较浅的势阱,HeNa~+的1∑2p有一个较浅的势阱,而~3∑3s态及~t∑3s态分别存在一个很深的势阱.     

Cross-validation and the smoothing of orthogonal series density estimators

We describe a class of smoothed orthogonal series density estimates, including the classical sequential-series introduced by [6], Soviet Math. Dokl. 3 1559–1562) and [16], Ann. Math. Statist. 38 1261–1265), and [23], Ann. Statist 9 146–156) two-parameter smoothing. The Bowman-Rudemo method of least-squares cross-validation (1982, Manchester-Sheffield School of Probability and Statistics Research Report 84/AWB/1; 1984, Biometrika 71 353–360; [14], Scand. J. Statist. 9 65–78), is suggested as a practical way of choosing smoothing parameters automatically. Using techniques of [18], Ann. Statist. 12 1285–1297), that method is shown to perform asymptotically optimally in the case of cosine and Hermite series estimators. The same argument may be used for other types of series.     

Algebras Generated by Linearly Dependent Elements with Prescribed Spectra

We consider associative algebras presented by a finite set of generators and relations of special form: each generator is annihilated by some polynomial, and the sum of generators is zero. The growth of this algebra in dependence on the degrees of the polynomials annihilating the generators is studied. The tuples of degrees for which the algebras are finite-dimensional, have polynomial growth, or have exponential growth are indicated. To the tuple of degrees, we assign a graph, and the above-mentioned cases correspond to Dynkin diagrams, extended Dynkin diagrams, and the other graphs, respectively. For extended Dynkin diagrams, we indicate the hyperplane in the space of parameters (roots of the polynomials) on which the corresponding algebras satisfy polynomial identities.     

The best quadrature formula based on Hermite information for the class KW~2[a,b]

The best quadrature formula has been found in the following sense:for afunction whose norm of the second derivative is bounded by a given constant and thebest quadrature formula for the approximate evaluation of integration of that function canminimize the worst possible error if the values of the function and its derivative at certainnodes are known.The best interpolation formula used to get the quadrature formula aboveis also found.Moreover,we compare the best quadrature formula with the open compoundcorrected trapezoidal formula by theoretical analysis and stochastic experiments.