IMPROVED ESTIMATES OF THE COVARIANCE MATRIX IN GENERAL LINEAR MIXED MODELS

In this article, the problem of estimating the covariance matrix in general linear mixed models is considered. Two new classes of estimators obtained by shrinking the eigenvalues towards the origin and the arithmetic mean, respectively, are proposed. It is shown that these new estimators dominate the unbiased estimator under the squared error loss function. Finally, some simulation results to compare the performance of the proposed estimators with that of the unbiased estimator are reported. The simulation results indicate that these new shrinkage estimators provide a substantial improvement in risk under most situations.

The Additive-multiplicative Hazards Model for Multiple Type of Recurrent Gap Times

Recurrent event gap times data frequently arise in biomedical studies and often more than one type of event is of interest. To evaluate the effects of covariates on the marginal recurrent event hazards functions, there exist two types of hazards models： the multiplicative hazards model and the additive hazards model. In the paper, we propose a more flexible additive-multiplicative hazards model for multiple type of recurrent gap times data, wherein some covariates are assumed to be additive while others are multiplicative. An estimating equation approach is presented to estimate the regression parameters. We establish asymptotic properties of the proposed estimators.

LOWER BOUNDS OF DIRICHLET EIGENVALUES FOR A CLASS OF FINITELY DEGENERATE GRUSHIN TYPE ELLIPTIC OPERATORS

Let Ω be a bounded open domain in Rn with smooth boundary Ω, X =（X1,X2,... ,Xm） be a system of real smooth vector fields defined on Ω and the bound-ary Ω is non-characteristic for X. If X satisfies the HSrmander＇s condition, then the vectorfield is finitely degenerate and the sum of square operator △X =m∑j=1 X2 j is a finitely de-generate elliptic operator. In this paper, we shall study the sharp estimate of the Dirichlet eigenvalue for a class of general Grushin type degenerate elliptic operators △x on Ω.

Global population estimate and conservation gap analysis for the Nordmann's Greenshank(Tringa guttifer)

Nordmann's Greenshank(Tringa guttifer)is a globally endangered species that has received little research attention.It is threatened by rapid habitat loss,an incomplete network of protected sites,and lack of long-term data on population dynamics.Citizen science data can be combined with survey data to support population estimation and conservation gap analysis.From 2020 to 2021,Nordmann's Greenshank was surveyed in Tiaozini,Xiaoyangkou,and Dongling on the southern coast of Jiangsu Province,China,and the global population of the species was re-evaluated using the data obtained.We integrated citizen science data from eBird and the China Bird Report from 2000 to 2020 with the survey results to identify important habitats harboring over 1%of its total population,and compared this data with existing protected areas to identify gaps in its global conservation.Our survey found that Tiaozini supported at least 1194 individuals.Consequently,its global population was reestimated to be 1500-2000.Moreover,45 important habitats were identified based on citizen data and survey results.Although 44.4%and 50.0%of the priority sites in the world and China,respectively,are located outside protected areas,the Conservation Effectiveness Index(C)is 68.4%and 71.1%,respectively,showing that the current coverage of protected areas for this part of its range is reasonable.This study presents the most complete and recent population data to date.Tiaozini is the most important migration stopover site for Nordmann's Greenshanks.The species is under threat in terms of breeding,wintering,and stopover sites.Therefore,we suggest improving monitoring,establishing new protected sites to complete the habitat protection network,and improving the effectiveness of existing habitat protection strategies,including further developing high tide roosting sites.

Some Trace Formulas of a Eigenvalue Problem

In present paper, using some methods of approximation theory, the trace formulas for eigenvalues of a eigenvalue problem are calculated under the periodic condition and the decaying condition at x∞.

基于EVD分解的OFDM系统时变信道估计

OFDM系统中,需要获得信道状态信息实现相干解调。信道的时变性会带来子载波间干扰(ICI),降低信道估计算法的精度。针对信道的快时变性,提出一种基于特征值分解的时变信道估计方法,同时设计一种新的导频结构。该方法利用信道矩阵时域及频域相关性,将信道频域矩阵表示为其特征向量的线性加权,并用贝叶斯模型估计加权系数。仿真结果表明,所提方法能有效降低ICI对系统性能的影响,可较好地满足快时变信道环境的要求。

基于求根MUSIC算法的低复杂度OFDMA频偏盲估计

为了解决OFDMA系统频率同步困难的问题,针对子载波交织分配的OFDMA上行链路提出了一种基于多项式求根的多用户载波频偏盲估计算法.首先对接收信号的协方差矩阵进行特征值分解,并利用噪声子空间的特征向量构造一个多项式,然后求解最接近于单位圆的K个根来获得各个载波频偏.此算法的优点是能够在一个OFDMA符号块内同时估计出所有用户的载波频偏而无需信道状态、训练序列和导频等先验信息,同时在低信噪比下也具有良好的准确性.通过仿真表明,相对于一般的谱峰搜索方法,算法不仅减少了噪声对频偏估计的影响,而且有着更低的计算复杂度和更高的分辨率.

PARAMETER IDENTIFICATION OF DYNAMIC MODELS USING A BAYES APPROACH

The Bayesian method of statistical analysis has been applied to the parameter identification problem. A method is presented to identify parameters of dynamic models with the Bayes estimators of measurement frequencies. This is based on the solution of an inverse generalized evaluate problem. The stochastic nature of test data is considered and a normal distribution is used for the measurement frequencies. An additional feature is that the engineer's confidence in the measurement frequencies is quantified and incorporated into the identification procedure. A numerical example demonstrates the efficiency of the method.

Rapid report of June 1,2022 M_(W) 5.9 Lushan earthquake,China with geodetic and teleseismic data

Timely response to earthquake characterization can facilitate earthquake emergency rescue and further scientific investigations.On June 1,2022,M_(W) 5.9 earthquake occurred in the southern area of the Longmenshan fault zone.This event also happened at the south end of the Dayi seismic gap and is the largest earthquake that has occurred in this seismic gap since the 1970 M 6.2 event.The slip-distribution model constrained by the seismic waveforms suggests a thrust-dominated faulting mechanism.The main slip occurs at a depth of~14 km,and the cumulative energy is released in the first 6 s.The variations of Coulomb stress caused by the mainshock show a positive change in the southwest area of the Dayi seismic gap,indicating possible activation of future earthquakes.In addition,we emphasize the importance of rapid estimation of deformation for near-field hazard delineation,especially when interferometric radar fails to image coseismic deformation in a high relief terrain.

基于JADE的MIMO-OFDM信号信噪比盲估计算法

针对非协作通信背景中MIMO-OFDM信号信噪比盲估计问题,提出了一种新的MIMO-OFDM信号SNR盲估计算法。首先,计算接收信号的自相关矩阵并进行特征值分解,再用最小描述长度(The Minimum Description Length,MDL)估计发射天线数;然后,把接收信号进行子空间分解估计噪声功率;最后,利用JADE(Joint Approximate Diagonalization of Eigenvalue Matrix)估计出信号功率,从而有效估计出MIMO-OFDM的信噪比。实验结果表明,该方法不需要任何先验信息,当SNR>3 dB时,估计的均方误差小于0.1,同现有的算法相对比,该文的估计方法性能更优越。

三七GAP栽培的环境质量评价

目的 对三七 GAP种植基地的环境质量进行评价 ,为制定三七 SOP和建立三七 GAP种植基地建设提供科学依据。方法 采用文献方法对三七 GAP种植基地规划区进行水资源、土壤环境和大气环境进行分析评价。结果 三七 GAP种植基地规划区大气环境质量达 GB30 95 - 82 (大气环境质量标准 )一级标准 ,水资源达 GB5 0 84-85 (农田灌溉水质标准 )的一类标准 ,土壤环境达 GB15 6 18- 1995 (土壤环境质量标准 )二级标准。结论 三七GAP种植区环境质量良好 ,符合绿色药材栽培的环境质量要求。

甘肃当归GAP栽培的环境质量评价

目的 对甘肃当归栽培基地的环境质量进行评价 ,为制定当归SOP和建立当归GAP栽培基地建设提供科学依据。方法 采用文献法对当归栽培基地进行土壤环境、大气环境和水资源进行分析评价。结果 当归栽培基地大气环境质量达GB30 95 - 82 (大气环境质量标准 )一级标准 ,土壤环境达GB1 5 6 1 8- 1 995 (土壤环境质量标准 )二级标准 ;水资源达GB5 0 84 - 85(农田灌溉水质标准 )的一类标准。结论 当归栽培基地环境优良 。

The Eigenvalue Properties of a Kind of Singular Differential Equations in 3-Dimensional Space

In this paper,we consider the eigenvalue problem of the singular differential equation-Δu_(i)-h/|x|^(2) u_(i)+V(x)u_(i)=λ_(i)(V,h)u_(i) in a bounded open ball with Dirichlet boundary condition in 3-dimensional space,where,V∈V={a∈L^(∞)(Ω)|0≤a≤M a.e.,M is a given constant}.And we have made a detailed characterization of the weak solution space.Furthermore,the existence of the minimum eigenvalue and the fundamental gap are provided.

EFFICIENT SPECTRAL METHODS FOR EIGENVALUE PROBLEMS OF THE INTEGRAL FRACTIONAL LAPLACIAN ONABALLOFANYDIMENSION

An efficient spectral-Galerkin method for eigenvalue problems of the integral fractional Laplacian on a unit ball of any dimension is proposed in this paper.The symmetric positive definite linear system is retained explicitly which plays an important role in the numerical analysis.And a sharp estimate on the algebraic system's condition number is established which behaves as N4s with respect to the polynomial degree N,where 2s is the fractional derivative order.The regularity estimate of solutions to source problems of the fractional Laplacian in arbitrary dimensions is firstly investigated in weighted Sobolev spaces.Then the regularity of eigenfunctions of the fractional Laplacian eigenvalue problem is readily derived.Meanwhile,rigorous error estimates of the eigenvalues and eigenvectors are ob-tained.Numerical experiments are presented to demonstrate the accuracy and efficiency and to validate the theoretical results.

Estimates for eigenvalues of Laplacian operator with any order

Let D be a bounded domain in an n-dimensional Euclidean space ? n . Assume that $$0 < \lambda _1 \leqslant \lambda _2 \leqslant \cdots \leqslant \lambda _k \leqslant \cdots $$ are the eigenvalues of the Dirichlet Laplacian operator with any order l: $$\left\{ \begin{gathered} ( - \vartriangle )^l u = \lambda u, in D \hfill \\ u = \frac{{\partial u}}{{\partial \vec n}} = \cdots = \frac{{\partial ^{l - 1} u}}{{\partial \vec n^{l - 1} }} = 0, on \partial D \hfill \\ \end{gathered} \right.$$ . Then we obtain an upper bound of the (k+1)-th eigenvalue λ k+1 in terms of the first k eigenvalues. $$\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )} \leqslant \frac{1}{n}[4l(n + 2l - 2)]^{\tfrac{1}{2}} \left\{ {\sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{{l - 1}}{l}} \sum\limits_{i = 1}^k {(\lambda _{(k + 1)} - \lambda _i )^{\tfrac{1}{2}} \lambda _i^{\tfrac{1}{l}} } } } \right\}^{\tfrac{1}{2}} $$ . This ineguality is independent of the domain D. Furthermore, for any l ? 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.

THE EIGENVALUE PROBLEM FOR THE LAPLACIAN EQUATIONS

This article studies the Dirichlet eigenvalue problem for the Laplacian equations △u = -λu, x ∈Ω , u = 0, x ∈δΩ, where Ω belong to R^n is a smooth bounded convex domain. By using the method of appropriate barrier function combined with the maximum principle, authors obtain a sharp lower bound of the difference of the first two eigenvalues for the Dirichlet eigenvalue problem. This study improves the result of S.T. Yau et al.

A new source number estimation method based on the beam eigenvalue

Most source number estimation methods based on the eigenvalues are decomposed by covariance matrix in MUSIC algorithm. To develop the source number estimation method which has lower signal to noise ratio and is suitable to both correlated and uncorrelated impinging signals, a new source number estimation method called beam eigenvalue method (BEM) is proposed in this paper. Through analyzing the space power spectrum and the correlation of the line array, the covariance matrix is constructed in a new way, which is decided by the line array shape when the signal frequency is given. Both of the theory analysis and the simulation results show that the BEM method can estimate the source number for correlated signals and can be more effective at lower signal to noise ratios than the normal source number estimation methods.

铁皮石斛GAP种植基地的环境质量评价

目的对铁皮石斛GAP种植基地的环境质量进行评价,为种植基地的建设提供科学依据。方法采用国家标准的方法对铁皮石斛种植基地进行大气环境、水资源及土壤环境进行分析评价。结果铁皮石斛GAP种植基地大气符合GB3095-95标准,土壤符合GB15618-1995土壤二级标准,灌溉水符合《农田灌溉水质标准》(GB5084-1992)标准。结论铁皮石斛GAP种植区环境良好,符合绿色中药材栽培的环境质量要求。

ESTIMATES OF EIGENVALUES FOR UNIFORMLY ELLIPTIC OPERATOR OF SECOND ORDER

This paper derives the bounds of the eigenvalues for the uniformly eiliptic operator of second order with variable coefficients. The bounds of the(n+1)th eigenvalue are shown by the first n eigenvalues. These estimates do not depend on the domain in which the problem is cozisidered.

Geometric Estimates of the First Eigenvalue of(p,q)-elliptic Quasilinear System Under Integral Curvature Condition

Consider(M,g)as a complete,simply connected Riemannian manifold.The aim of this paper is to provide various geometric estimates in different cases for the first eigenvalue of(p,q)-elliptic quasilinear system in both Dirichlet and Neumann conditions on Riemannian manifold.In some cases we add integral curvature condition and maybe we prove some theorems under other conditions.