Random matrices with complex Gaussian entries

In this paper we give new and purely analytical proofs of a number of classical results on the asymptotic behavior of large random matrices of complex Wigner type (the GUE-case) or of complex Wishart type: Wigner's semi-circle law, the Harer-Zagier recursion formula, the Marchenko-Pastur law, the Geman-Silverstein results on the largest and smallest eigenvalues and other related results. Our approach is based on the derivation of explicit formulae for the moment generating functions for random matrices of the two considered types.     

含有各阶导数的高阶微分方程边值问题三个单调正解的存在性

利用五个泛函的不动点定理,研究一类含有各阶导数的2m阶微分方程边值问题的三个单调正解的存在性.     

On the pth moment exponential stability criteria of neutral stochastic functional differential equations

The paper discusses the pth moment exponential stability for a general class of neutral stochastic functional differential equations of the Ito type. This investigation can be very complicated, even in many special cases, by using usual methods based on Lyapunov functionals. In this paper we present criteria which are relatively easy to verify the pth moment exponential stability of the solutions of such equations.     

Identifiability of mixtures of power-series distributions and related characterizations

The concept of the identifiability of mixtures of distributions is discussed and a sufficient condition for the identifiability of the mixture of a large class of discrete distributions, namely that of the power-series distributions, is given. Specifically, by using probabilistic arguments, an elementary and shorter proof of the Lüxmann-Ellinghaus's (1987,Statist. Probab. Lett.,5, 375–378) result is obtained. Moreover, it is shown that this result is a special case of a stronger result connected with the Stieltjes moment problem. Some recent observations due to Singh and Vasudeva (1984,J. Indian Statist. Assoc.,22, 93–96) and Johnson and Kotz (1989,Ann. Inst. Statist. Math.,41, 13–17) concerning characterizations based on conditional distributions are also revealed as special cases of this latter result. Exploiting the notion of the identifiability of power-series mixtures, characterizations based on regression functions (posterior expectations) are obtained. Finally, multivariate generalizations of the preceding results have also been addressed.     

Competing polarization mechanisms in the heavy-fermion paramagnet CeCu<Subscript><Emphasis Type="Bold">6</Emphasis></Subscript>

Nuclear magnetic resonance (NMR) and relaxation of ⁶³Cu and ⁶⁵Cu in a powder sample of the heavy-fermion paramagnet CeCu₆ is measured and analysed quantitatively. Five different Cu sites are accessible to a detailed analysis. We derive quadrupolar splitting frequencies, Ce to Cu transferred hyperfine field coupling constants, and transversal as well as longitudinal relaxation behaviour. Only small relaxation anomalies are observed at the orthorhombic to monoclinic structural phase transition of CeCu₆. We point to the different importance of transferred hyperfine interaction and local conduction electron density for static or dynamic part, respectively, of Cu hyperfine interaction. The different sign of the transferred hyperfine interaction from Ce³⁺ to different Cu neighbours reveals the different competing interaction mechanisms, giving rise to the heavy-fermion paramagnetic behavior of CeCu₆. Received 20 November 2001     

Modified Moment Problem in Complex Domains

We study the moment problem in a complex domain. The results obtained generalize and sharpen the well-known Kaz'min result. We also consider applications of these results to the Abel--Goncharov problem (the uniqueness and construction problem) and to the completeness problem for systems of analytic functions.     

凸数列的一个等价条件及其应用,Ⅱ

将涉及控制向量的凸数列的一个等价条件扩展到弱控制的情形，并给出此等价条件在代数、分析、凸体几何、概率论等诸多方面的应用。     

居民家庭耐用消费品的消费时机选择:实物期权的方法

针对当前居民家庭消费的特点，为了合理地选择耐用消费品的最佳购买时机，本分析耐用品的价格和性能具有实物期权的属性，建立了一个关于“性价比”变量的随机微分方程，并且求出了购买时机临界值的解析公式。最后对日常生活中发生的购买时间现象给予了解释。     

Multispectrum fitting of line parameters for C2H2 in the 3.8-μm spectral region

Using FT spectra (Bruker IFS 120, unapodized FWHM resolution ≈ 0.001 cm⁻¹) of acetylene ¹²C₂H₂, absolute positions and intensities have been measured for about 250 lines between 2600 and 2800 cm⁻¹ in the and cold bands, and in the and hot bands. These measurements improve the accuracy of wavenumbers previously available and lead to individual line intensities for the first time in this spectral region. A multispectrum fitting procedure has been used to retrieve line parameters from five experimental spectra recorded at different pressures. The frequencies of the ν₃ band of ¹²C¹⁶O₂ allowed to perform an absolute wavenumber calibration. The accuracy of the amount of ¹²C₂H₂ in the sample has been checked using the cold band around 2100 cm⁻¹, and has been estimated to be around ±2%. The average absolute accuracy of the line parameters obtained in this work has then been estimated to be ±0.0002 cm⁻¹ for line positions, and ±5% for line intensities. For each studied band, the vibrational transition dipole moment squared value has been determined, as also empirical Herman-Wallis coefficients. A complete line list containing positions and intensities for the five strongest bands around 3.8 μm has been set up for atmospheric applications.