一类M-矩阵阿达玛积最小特征根的下界

讨论一个 M- 矩阵与另一个 M- 矩阵的逆的阿达玛积的最小特征根,证明了对任一矩阵B,如果 B- 1 的主对角线元素的值相等,则q( A‘B- 1) > 1n ·q( A)q( B) .     

The consistency of model selection for dynamic Semi-varying coefficient models with autocorrelated errors

The consistency of model selection criterion BIC has been well and widely studied for many nonlinear regression models. However, few of them had considered models with lag variables as regressors and auto-correlated errors in time series settings, which is common in both linear and nonlinear time series modeling. This paper studies a dynamic semi-varying coefficient model with ARMA errors, using an approach based on spectrum analysis of time series. The consistency property of the proposed model selection criteria is established and an implementation procedure of model selection is proposed for practitioners. Simulation studies have also been conducted to numerically show the consistency property.     

Smoothing spline ANOPOW

This paper is motivated by the pioneering work of Emanuel Parzen wherein he advanced the estimation of (spectral) densities via kernel smoothing and established the role of reproducing kernel Hilbert spaces (RKHS) in field of time series analysis. Here, we consider analysis of power (ANOPOW) for replicated time series collected in an experimental design where the main goals are to estimate, and to detect differences among, group spectra. To accomplish these goals, we obtain smooth estimators of the group spectra by assuming that each spectral density is in some RKHS; we then apply penalized least squares in a smoothing spline ANOPOW. For inference, we obtain simultaneous confidence intervals for the estimated group spectra via bootstrapping.     

Multitaper testing of spectral lines and the detection of the solar rotation frequency and its harmonics

We develop statistical testing methodology for closely spaced spectral lines based on multitaper spectrum estimates and apply it to a time series of solar magnetic field magnitude data recorded by the Ulysses spacecraft. The test is formulated through complex-valued weighted least squares. Using this test in combination with the test for well-separated lines, we can accurately detect the solar equatorial rotation frequency of the sun, and its harmonics, from data recorded by Ulysses's magnetometer at solar mid-latitudes; this is a potentially important result for solar physicists, since it has implications for the structure and dynamics of magnetic fields in the solar corona.     

线性方程组的单调收敛

本文讨论了线性方程组Au=b的单调收敛性,给出了某些线性方程组Au=b占之单调收敛性的判定条件.     

附着滴在粗糙多孔介质表面铺展渗透的数值研究

为了探究附着滴在粗糙多孔介质表面的动力学行为,课题组通过ANSYS FLUENT对液滴在多孔介质上的铺展渗透进行了研究。首先用凹凸槽来代替表面粗糙度的方法,然后使用VOF模型追踪液滴形态变化,最后利用PISO 算法进行数值模拟计算。定量分析了邦德数、平衡接触角、达西数和多孔介质表面粗糙度对液滴铺展半径和渗透深度的影响。结果表明：随着液滴邦德数的增大,液滴更易变形,铺展和渗透深度增加;随着平衡接触角的增大,液滴越难铺展和渗透,但液滴后期阶段渗透深度增加;随着达西数增大,多孔介质的渗透率增大,所以渗透深度增加,而铺展半径相对减小;随着多孔介质表面粗糙度的增大,铺展半径减小,渗透深度增大。该研究的成果有利于提高生产质量和减少环境污染。     

Lévy Processes,Phase-Type Distributions,and Martingales

Lévy processes are defined as processes with stationary independent increments and have become increasingly popular as models in queueing, finance, etc.; apart from Brownian motion and compound Poisson processes, some popular examples are stable processes, variance gamma processes, CGMY Lévy processes (tempered stable processes), NIG (normal inverse Gaussian) Lévy processes, and hyperbolic Lévy processes. We consider here a dense class of Lévy processes, compound Poisson processes with phase-type jumps in both directions and an added Brownian component. Within this class, we survey how to explicitly compute a number of quantities that are traditionally studied in the area of Lévy processes, in particular two-sided exit probabilities and associated Laplace transforms, the closely related scale function, one-sided exit probabilities and associated Laplace transforms coming up in queueing problems, and similar quantities for a Lévy process with reflection in 0. The solutions are in terms of roots to polynomials, and the basic equations are derived by purely probabilistic arguments using martingale optional stopping; a particularly useful martingale is the so-called Kella-Whitt martingale. Also, the relation to fluid models with a Brownian component is discussed.     

一类两端奇异带有转移条件的S-L问题的Weyl矩阵与谱矩阵

研究了一类带有转移条件二阶S-L问题两端奇异的情形,在定义的新的内积空间下进行,首先在有限区间I上进行讨论,然后将有限区间I的结论进一步推广到无限区间,最终给出了Weyl矩阵与谱矩阵的关系.     

BLLac天体谱的性质

本以喷流加速模型为基础，从有效谱指数出发讨论两种选择BLLac天体（RBLs，XBLs）的统一性。     

迭代矩阵特征值模的界

在用迭代法解线性方程组时,迭代矩阵的谱半径估计在迭代法的收敛性分析中起着重要的作用。该文对一类Baily-Crabtree型对角占优矩阵M,给出了迭代矩阵M?1N的特征值模的上下界估计。并以此为基础,在一定条件下给出了当M是α?严格对角占优矩阵时的M?1N的特征值模的上下界估计。并以具体例子说明了所得结果的有效性。