Un modèle ES–BGK pour des mélanges de gaz

In this note, we derive an ES–BGK model for gas mixtures that is able to give the correct Prandtl number obtained from the true Boltzmann equation. The derivation principle is based on the resolution of an entropy minimisation problem under moments constraints. The set of constraints is constructed by introducing a relaxation of some non-conserved moments. The non-conserved moments are dissipated according to some relaxation rates. Finally the BGK model that is obtained satisfies the classical properties of the Boltzmann operator for inert gas mixtures.     

关于Morley元的误差估计

§1.引言 解薄板弯曲问题的三角形Morley元是六十年代出现的一种非协调元,它的形函数是完整的二次多项式,节点参数是单元顶点上的三个函数值及三边中点上的法向导数值.由于板弯曲问题的常应变是二次多项式,所以这是一个参数最少的非协调板元.由     

Local Sensitivity Analysis in Estimation Problems

This article deals with the problem of local sensitivity analysis, that is, how sensitive are the results of a statistical analysis to changes in the data? A general methodology of sensitivity analysis is applied to some statistical problems. The proposed methods are applicable to any statistical problem that can be expressed as an optimization problem or that involves solving a system of equations. As some particular examples, the methodology is applied to the maximum likelihood method, the standard and constrained methods of moments and the standard and constrained probability weighted moments methods. Unlike the standard method of moments, the constrained method of moments ensures that the obtained estimates are always consistent with the data. Closed analytical formulas for the calculation of these local sensitivities are derived. The obtained sensitivities include: (a) the objective function sensitivities to data points and (b) the sensitivities of the estimated parameters to data points. The derived formulas for the sensitivities are based on recent results in the area of mathematical programming. Several examples of parameter estimation problems are used to illustrate the methodology.     

Higher order moments of multivariate normal distribution using matrix derivatives

A general formula for the central moments of multivariate normal distribution is derived by differentiating its characteristic function using matrix derivatives. An explicit expression for the moments is obtained. Two applications of these results are given. The sixth order moments are arranged in a square matrix using the properties of commutation matrices and vec operators     

单纯形上Meyer-Knig and Zeller算子的二阶矩量

该文讨论了单纯形上Meyer- Konig and Zeller算子的矩量问题.首先得到了二阶矩量在广义积分下的显式表示,并由此导出了二阶矩量的二元Appell超几何函数表示,超几何级数表示和完全渐近公式.     

单纯形上Meyer Konig and Zeller算子的二阶矩量 [DM)]

该文讨论了单纯形上Meyer Konig and Zeller算子的矩量问题. 首先得到了二阶矩量在广义积分下的显式表示，并由此导出了二阶矩量的二元Appell超几何函数表示，超几何级数表示和完全渐近公式.      

二进小波的构造方法研究

提出两种二进小波的构造方法.首先,将Mallat构造的B-样条二进小波推广得到一种构造B-样条二进小波的新方法;其次,基于二进提升方案提出构造二进小波的另一种新方法—–构造定理,并通过调整定理中提升参数的形式、以新的B-样条二进小波作为初始二进小波,具体构造了具有有限长单位脉冲响应、高阶消失矩、线性相位的提升二进小波,这些提升二进小波不能由Sweldens提升方案得到.     

Lower Bounds on the Generalized Central Moments of the Optimal Alignments Score of Random Sequences

We present a general approach to the problem of determining tight asymptotic lower bounds for generalized central moments of the optimal alignment score of two independent sequences of i.i.d. random variables. At first, these are obtained under a main assumption for which sufficient conditions are provided. When the main assumption fails, we nevertheless develop a “uniform approximation” method leading to asymptotic lower bounds. Our general results are then applied to the length of the longest common subsequences of binary strings, in which case asymptotic lower bounds are obtained for the moments and the exponential moments of the optimal score. As a by-product, a local upper bound on the rate function associated with the length of the longest common subsequences of two binary strings is also obtained.     

Spectral analysis of the fourth moment matrix

The fourth moment of a random vector is a matrix whose elements are all moments of order four which can be obtained from the random vector itself. In this paper, we give a lower bound for its dominant eigenvalue and show that its eigenvectors corresponding to positive eigenvalues are vectorized symmetric matrices. Fourth moments of standardized and exchangeable random vectors are examined in more detail.     

Graph presentations for moments of noncentral Wishart distributions and their applications

We provide formulas for the moments of the real and complex noncentral Wishart distributions of general degrees. The obtained formulas for the real and complex cases are described in terms of the undirected and directed graphs, respectively. By considering degenerate cases, we give explicit formulas for the moments of bivariate chi-square distributions and 2 × 2 Wishart distributions by enumerating the graphs. Noting that the Laguerre polynomials can be considered to be moments of a noncentral chi-square distributions formally, we demonstrate a combinatorial interpretation of the coefficients of the Laguerre polynomials.     

A note on the moments of order statistics from doubly truncated exponential distribution

Summary In a recent paper [2], the author has obtained some recurrence relations between the moments of order statitics from the exponential and right truncated exponential distributions. In this paper, similar relations are derived for a doubly truncated exponential distribution. It is shown that one can obtain all the moments by using these recurrence relations.     

对M/T-SPH/1排队平稳指标的进一步研究—数值计算与渐近分析

讨论M/T-SPH/1排队平稳队长分布的数值计算,以及平稳队长和逗留时间分布各阶矩的数值计算及渐近分析.其中T-SPH表示可数状态吸收生灭链吸收时间的分布.在分布PGF和LST的基础上,首先给出了计算平稳队长分布,平稳队长以及逗留时间分布各阶矩的数值结果的递推公式.其次还讨论了平稳队长及平稳逗留时间分布各阶矩的尾部渐近...     

Second-order accurate inference on eigenvalues of covariance and correlation matrices

Edgeworth expansions and saddlepoint approximations for the distributions of estimators of certain eigenfunctions of covariance and correlation matrices are developed. These expansions depend on second-, third-, and fourth-order moments of the sample covariance matrix. Expressions for and estimators of these moments are obtained. The expansions and moment expressions are used to construct second-order accurate confidence intervals for the eigenfunctions. The expansions are illustrated and the results of a small simulation study that evaluates the finite-sample performance of the confidence intervals are reported.     

Diffusion approximation to a queueing system with time-dependent arrival and service rates

A time nonhomogeneous diffusion approximation to a single server-single queue service system is obtained. Under various assumptions on the time-dependent functions appearing in the infinitesimal moments, transient and steady-state behaviour are analyzed. In particular, a diffusion approximation characterized by space-linear and time-varying moments is studied. The density of the busy period and the probability for the busy period to terminate are obtained. Finally, estimates of the goodness of the diffusion approximation are given.     

Time-dependent moments of the counts on a BMAP

Consider a batch Markovian arrival process (BMAP) as a counting process over an underlying Markov process representing the state of environment. Such a process is useful as a model of correlated inputs, that is, burst traffics made of video and voice, for example. We consider Laplace transformation of the first and second factorial moments of the counts of the BMAP. From this, we get the eigenvalue expression for these moments without assuming distinct eigenvalues of the infinitesimal generator. In this formula, matrix exponential functions are replaced by ordinary exponentials, and the exact time-dependent form of the moments are also obtained. This seems to be profitable for model fitting.     

Some inequalities for differentiable convex mapping with application to weighted trapezoidal formula and higher moments of random variables

Several inequalities for differentiable convex, wright-convex and quasi-convex mapping are obtained respectively that are connected with the celebrated Hermite-Hadamard integral inequality. Also, some error estimates for weighted Trapezoid formula and higher moments of random variables are given.     

The moments of forward recurrence time

The moments of the forward recurrence time of an ordinary renewal process are derived in terms of the renewal function and the moments of the common lifetime distribution. The covariance between the forward recurrence time and the number of renewals is also obtained. Asymptotic formulae as the process is allowed to run on for a fixed long time are given.     

Behaviour of queueing approximations based on sample moments

We investigate moment–based queueing approximations in the presence of sampling error. Let L be the steady–state mean number in the system for a GI/M/1 queue. We focus on the estimation of L under the assumption that only sample moments of the interarrival–time distribution are known. A simulation experiment is carried out for several interarrival–time distributions. For each case, sample moments from the interarrival–time distribution are matched to an approximating phase–type distribution and the corresponding estimate L is obtained. We show that the sampling error in the moments induces bias as well as variability in L. Based on our simulation experiment, we suggest matching only two moments when the sample coefficient of variation is low or when sample size is low; otherwise, matching three moments is preferable.     

Hydrodynamic analogy for direct shear force and bending moment evaluation in a plate

A brand new interpretation of the plate bending equations is given using hydrodynamic analogy. It permits one to determine directly the shear forces and bending moments of a plate without the need of finding deflections. In engineering design of a plate it is more important to know shear forces and bending moments than the deflections. The existing numerical methods of solution of plate problems consist in determining deflections; then shear forces and bending moments are obtained by differentiating the deflection three and two times which produces great loss of accuracy. The hydrodynamic analogy method has the advantage over other numerical methods because the shear forces and bending moments are obtained directly, without the need of finding deflections and because they are obtained with better accuracy. The hydrodynamic analogy can be applied to a plate of arbitrary shape, with arbitrary boundary conditions under an arbitrary loading.     

Second Order Expansions for the Moments of Minimum Point of an Unbalanced Two-sided Normal Random Walk

In this paper, the second order expansions for the first two moments of the minimum point of an unbalanced two-sided normal random walk are obtained when the drift parameters approach zero. The basic technique is the uniform strong renewal theorem in the exponential family. The comparison with numerical values shows that the approximations are very accurate. It is shown, particularly, that the first moment is significantly different from its continuous Brownian motion analog while the second moments are the same in the first order. The results can be used to study properties of the maximum likelihood estimator for the change point.