On Asymptotic Behavior of Multilinear Eigenvalue Statistics of Random Matrices

We prove the Law of Large Numbers and the Central Limit Theorem for analogs of U- and V- (von Mises) statistics of eigenvalues of random matrices as their size tends to infinity. We show first that for a certain class of test functions (kernels), determining the statistics, the validity of these limiting laws reduces to the validity of analogous facts for certain linear eigenvalue statistics. We then check the conditions of the reduction statements for several most known ensembles of random matrices. The reduction phenomenon is well known in statistics, dealing with i.i.d. random variables. It is of interest that an analogous phenomenon is also the case for random matrices, whose eigenvalues are strongly dependent even if the entries of matrices are independent.     

Algebraic Reduction of the Ising Model

We consider the Ising model on a cylindrical lattice of L columns, with fixed-spin boundary conditions on the top and bottom rows. The spontaneous magnetization can be written in terms of partition functions on this lattice. We show how we can use the Clifford algebra of Kaufman to write these partition functions in terms of L by L determinants, and then further reduce them to m by m determinants, where m is approximately L/2. In this form the results can be compared with those of the Ising case of the superintegrable chiral Potts model. They point to a way of calculating the spontaneous magnetization of that more general model algebraically.     

Wigner Surmise for Domain Systems

In random matrix theory the spacing distribution functions p ⁽ⁿ⁾(s) are well fitted by the Wigner surmise and its generalizations. In this approximation the spacing functions are completely described by the behavior of the exact functions in the limits s→0 and s→∞. Most non equilibrium systems do not have analytical solutions for the spacing distribution and correlation functions. Because of that, we explore the possibility to use the Wigner surmise approximation in these systems. We found that this approximation provides a first approach to the statistical behavior of complex systems, in particular we use it to find an analytical approximation to the nearest neighbor distribution of the annihilation random walk.     

A Conjecture for the Superintegrable Chiral Potts Model

We adapt our previous results for the “partition function” of the superintegrable chiral Potts model with open boundaries to obtain the corresponding matrix elements of e^{−α H} , where H is the associated Hamiltonian. The spontaneous magnetization ℳ _r can be expressed in terms of particular matrix elements of e^{−α H} S ₁ ^r e^{−β H} , where S ₁ is a diagonal matrix. We present a conjecture for these matrix elements as an m by m determinant, where m is proportional to the width of the lattice. The author has previously derived the spontaneous magnetization of the chiral Potts model by analytic means, but hopes that this work will facilitate a more algebraic derivation, similar to that of Yang for the Ising model.     

On-line coupling of liquid chromatography and capillary gas chromatography for the determination of a trace pyrethroid insecticide in fruit extracts

The following paper presents a fast, selective, sensitive, and automated procedure for the residue analysis of the pyrethroid insecticide acrinathrin in various fruit samples by on-line combination of Liquid Chromatography (LC) with capillary Gas Chromatography (GC) and an Electron-Capture Detector (ECD). The loop-type interface and Fully Concurrent Solvent Evaporation (FCSE) were chosen due to their ease of use and low volatility of acrinathrin. Commercially available LC diol columns with small internal diameters (2.1 mm) provided the selectivity required for the separation of the solute from matrix components and permitted the transfer of fraction volumes up to 500 μl into the retention gap, located inside the gas chromatograph. Optimization of the operating conditions with standard solutions showed the influence of the GC initial transfer temperature on the response of acrinathrin and the quantitative nature of the transfer was established by liquid scintillation counting. The linearity and precision were studied with the aid of calibration plots, whereas quantitative recoveries of the analyte (at least 95 %) were determined in spiked fruits. Compared to the corresponding off-line technique, the on-line approach allows us to reach lower detection limits (ppb level when 20 μl LC injections are performed) with excellent repeatability between 0.6 and 6.6 %. Moreover, the integrated analytical set-up is robust, less time-consuming and subsequently brings a marked improvement in the sample preparation step of complex biological matrices. Finally, the versatility of the system renders it highly suitable for the determination of other similar pyrethroids in order to develop a multiresidue method.     

混浊介质中后向单次漫散射米勒矩阵特征

采用斯托克斯(Stokes)矢量形式,推导出当无限窄的连续光束垂直入射到混浊介质表面时,后向单次漫散射米勒(Mueller)矩阵的解析表达式。基于米氏(Mie)散射模式,详细分析了单次散射米勒矩阵元素的分布模式,以及与介质粒子数密度,粒子尺寸参量之间的关系。研究表明:单次散射米勒矩阵的方位变化随粒子数密度的增加,逐渐消失,而矩阵元素m22,m33,m23,m32随粒子数密度的变化,具有更显著的方位变化特征。矩阵元素m22,m33在方位角=45°时的值随尺寸参量的变化有一定的规律性,当尺寸参量小于某一特征参量时,其值呈下降趋势,反之则呈波动上升趋势。当介质粒子数密度以及粒子尺寸参量改变时,米勒矩阵元素强度的径向分布模式不变,即在任何方位,强度随径向距离都近似成指数规律衰减,方位变化呈周期性。     

Parameter estimation in systems of differential equations,based on three-way data arrays and random time changes

Consider a system of n₁ × n₂ differential equations depending on a vector θ of unknown parameters. We suggest an iterative estimation procedure for θ, based on a three-way array of observations. The method involves random time changes driven by multidimensional integrated Ornstein-Uhlenbeck processes.     

弹性矩形薄板受迫振动的功的互等定理法(Ⅲ)—悬臂矩形板

本文应用功的互等定理法给出了在均布谐载和在任意点受集中谐载作用下悬臂矩形板受迫振动的稳态解,并给出了有关弯矩和挠度幅值的图表.     

在—集中载荷作用下斜边自由的三角形板弯曲

本文应用功的互等定理研究了在—集中载荷作用下斜边自由两边固定的三角形板弯曲问题.该法简单、通用.     

Reciprocal theorem method for the forced vibration of elastic thick rectangular plates

I.IntroductionTheproblelllsofthefol.cedvibrationofelasticthickrectallgularplatestobesolvedareofgreattheoreticalsignificanceandpractical\7altle.Asthevibratinggoverningequationofthethickplateismorecomplicatedthallthatofthinplate.itisdil'ficulttoso]\'einmathematics.Manyscholarshat,eresearchedintotheseproblemsalldadvancedvariousspecialapproximations.Suchassuperpositionmethod.initialfLinctiollnletllod.thecombinedseriesot'theeigenftlnctionsofdeepbeamabouttilecorrespondillgboulldarycollditions.eller…