Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

Partial Time-Varying Coefficient Regression and Autoregressive Mixed Model

Regression and autoregressive mixed models are classical models used to analyze the relationship between time series response variable and other covariates. The coefficients in traditional regression and autoregressive mixed models are constants. However, for complicated data, the coefficients of covariates may change with time. In this article, we propose a kind of partial time-varying coefficient regression and autoregressive mixed model and obtain the local weighted least-square estimators of coefficient functions by the local polynomial technique. The asymptotic normality properties of estimators are derived under regularity conditions, and simulation studies are conducted to empirically examine the finite-sample performances of the proposed estimators. Finally, we use real data about Lake Shasta inflow to illustrate the application of the proposed model.

GENERAL DECAY FOR A VISCOELASTIC EQUATION OF VARIABLE COEFFICIENTS WITH A TIME-VARYING DELAY IN THE BOUNDARY FEEDBACK AND ACOUSTIC BOUNDARY CONDITIONS

A variable coefficient viscoelastic equation with a time-varying delay in the boundary feedback and acoustic boundary conditions and nonlinear source term is considered.Under suitable assumptions, general decay results of the energy are established via suitable Lyapunov functionals and some properties of the convex functions. Our result is obtained without imposing any restrictive growth assumption on the damping term and the elements of the matrix A and the kernel function g.

Forced Axial and Torsional Vibrations of a Shaft Line Using the Transfer Matrix Method Related to Solution Coefficients

This present paper deals with a mathematical description of linear axial and torsional vibrations. The normal and tangential stress tensor components produced by axial-torsional deformations and vibrations in the propeller and intermediate shafts, under the influence of propeller-induced static and variable hydrodynamic excitations are also studied. The transfer matrix method related to the constant coefficients of differential equation solutions is used. The advantage of the latter as compared with a well-known method of transfer matrix associated with state vector is the possibility of reducing the number of multiplied matrices when adjacent shaft segments have the same material properties and diameters. The results show that there is no risk of buckling and confirm that the strength of the shaft line depends on the value of the static tangential stresses which is the most important component of the stress tensor.

Effect of matrix thermal properties on laser-induced plasma

The matrix thermal properties have an important impact on laser-induced plasma,as the thermal effect dominates the interaction between ns-pulsed laser and matter,especially in metals.We used a series of pure metals and aluminum alloys to measure plasma temperature and electron density through laser-induced breakdown spectroscopy,in order to investigate the effect of matrix thermal properties on laser-induced plasma.In pure metals,a significant negative linear correlation was observed between the matrix thermal storage coefficient and plasma temperature,while a weak correlation was observed with electron density.The results indicate that metals with low thermal conductivity or specific heat capacity require less laser energy for thermal diffusion or melting and evaporation,resulting in higher ablation rates and higher plasma temperatures.However,considering ionization energy,thermal effects may be a secondary factor affecting electron density.The experiment of aluminum alloy further confirms the influence of thermal conductivity on plasma temperature and its mechanism explanation.

ADDITIVE HAZARDS MODEL WITH TIME-VARYING REGRESSION COEFFICIENTS

This article discusses regression analysis of failure time under the additive hazards model, when the regression coefficients are time-varying. The regression coefficients are estimated locally based on the pseudo-score function [12] in a window around each time point. The proposed method can be easily implemented, and the resulting estimators are shown to be consistent and asymptotically normal with easily estimated variances. The simulation studies show that our estimation procedure is reliable and useful.

A Simulation Study on Comparing General Class of Semiparametric Transformation Models for Survival Outcome with Time-Varying Coefficients and Covariates

The consideration of the time-varying covariate and time-varying coefficient effect in survival models are plausible and robust techniques. Such kind of analysis can be carried out with a general class of semiparametric transformation models. The aim of this article is to develop modified estimating equations under semiparametric transformation models of survival time with time-varying coefficient effect and time-varying continuous covariates. For this, it is important to organize the data in a counting process style and transform the time with standard transformation classes which shall be applied in this article. In the situation when the effect of coefficient and covariates change over time, the widely used maximum likelihood estimation method becomes more complex and burdensome in estimating consistent estimates. To overcome this problem, alternatively, the modified estimating equations were applied to estimate the unknown parameters and unspecified monotone transformation functions. The estimating equations were modified to incorporate the time-varying effect in both coefficient and covariates. The performance of the proposed methods is tested through a simulation study. To sum up the study, the effect of possibly time-varying covariates and time-varying coefficients was evaluated in some special cases of semiparametric transformation models. Finally, the results have shown that the role of the time-varying covariate in the semiparametric transformation models was plausible and credible.

A High-Order Conservative Numerical Method for Gross-Pitaevskii Equation with Time-Varying Coefficients in Modeling BEC

We propose a high-order conservative method for the nonlinear Sehodinger/Gross-Pitaevskii equation with time- varying coefficients in modeling Bose Einstein condensation （BEC）. This scheme combined with the sixth-order compact finite difference method and the fourth-order average vector field method, finely describes the condensate wave function and physical characteristics in some small potential wells. Numerical experiments are presented to demonstrate that our numerical scheme is efficient by the comparison with the Fourier pseudo-spectral method. Moreover, it preserves several conservation laws well and even exactly under some specific conditions.

ASYMPTOTIC HOMOGENIZATION IN A PARABOLIC SEMILINEAR PROBLEM WITH PERIODIC COEFFICIENTS AND INTEGRABLE INITIAL DATA

In this paper, we study the large time behavior of solutions of the parabolic semilinear equation δtu-div（a（x）△↓u） = -｜u｜^αu in （0,∞） × R^N, where α 〉 0 is constant and a∈ Cb^1（R^N） is a symmetric periodic matrix satisfying some ellipticity assumptions.Considering an integrable initial data u0 and α ∈ （2/N, 3/N）, we prove that the large time behavior of solutions is given by the solution U（t, x） of the homogenized linear problem δtU-div（a^h△↓U）=0,U（0） = C, where a^h is the homogenized matrix of a（x）, C is a positive constant and δ is the Dirac measure at 0.

ESTIMATE FOR DISTANCE-COEFFICIENT OF MATRICES

Motivation of this paper is an open problem exposed by B. Beauzamy .Let M be a 3×3 matrix and d(M) is the distance to the diagonal algebra. Let α(M)= sup {‖P ⊥MP‖∶P is a projection in the diagonal algebra} and then call K(M)=d(Μ)α(M) the distance coefficient of M. The following results are obtained: (1) If M has two zero entries apart from its diagonal, then K(M)322; (2) If M has one zero entry apart from its diagonal, then K(M)4132; (3) If M is arbitrary, then K(M)32.

On the Covariance of Regression Coefficients

In many applications, such as in multivariate meta-analysis or in the construction of multivariate models from summary statistics, the covariance of regression coefficients needs to be calculated without having access to individual patients’ data. In this work, we derive an alternative analytic expression for the covariance matrix of the regression coefficients in a multiple linear regression model. In contrast to the well-known expressions which make use of the cross-product matrix and hence require access to individual data, we express the covariance matrix of the regression coefficients directly in terms of covariance matrix of the explanatory variables. In particular, we show that the covariance matrix of the regression coefficients can be calculated using the matrix of the partial correlation coefficients of the explanatory variables, which in turn can be calculated easily from the correlation matrix of the explanatory variables. This is very important since the covariance matrix of the explanatory variables can be easily obtained or imputed using data from the literature, without requiring access to individual data. Two important applications of the method are discussed, namely the multivariate meta-analysis of regression coefficients and the so-called synthesis analysis, and the aim of which is to combine in a single predictive model, information from different variables. The estimator proposed in this work can increase the usefulness of these methods providing better results, as seen by application in a publicly available dataset. Source code is provided in the Appendix and in http://www.compgen.org/tools/regression.

Fixed-Time Adaptive Time-Varying Matrix Projective Synchronization of Time-Delayed Chaotic Systems with Different Dimensions

This paper deals with the fixed-time adaptive time-varying matrix projective synchronization(ATVMPS)of different dimensional chaotic systems(DDCSs)with time delays and unknown parameters.Firstly,to estimate the unknown parameters,adaptive parameter updated laws are designed.Secondly,to realize the fixed-time ATVMPS of the time-delayed DDCSs,an adaptive delay-unrelated controller is designed,where time delays of chaotic systems are known or unknown.Thirdly,some simple fixed-time ATVMPS criteria are deduced,and the rigorous proof is provided by employing the inequality technique and Lyapunov theory.Furthermore,the settling time of fixed-time synchronization(Fix-TS)is obtained,which depends only on controller parameters and system parameters and is independent of the system’s initial states.Finally,simulation examples are presented to validate the theoretical analysis.

Surface Reflection Coefficient of Impregnated RAM Honeycomb with Incident Normally Plan Wave to the Side Wall

The impregnated radar absorbing material(RAM) honeycomb is often used to fabricate parts of the war plane for reducing radar cross section. The incident wave vector may be divided into two components: one perpendicular to its hole and the other to its side wall. Until now, there has not been a program to calculate the input impedance or its equivalent electromagnetic parameters for the later case. In this paper, an approach for analyzing the reflection characteristics of the impregnated honeycomb when its side wall faces the incident plane wave is proposed. Experiments prove it an effective, accurate and fast solution to this subject.

基于表面阻抗测量的声学覆盖层吸声系数测试及修正

[目的]鉴于采用传统的水声管试验方法测量潜艇声学覆盖层的表面阻抗要求较高,提出一种可简化试验的基于阻抗测量的吸声系数测试方法,并解决阻抗测量中非平面波反射的修正问题。[方法]首先,将覆盖层简化为阻抗率矩阵边界和结合流体边界条件,推导出覆盖层表面不同半径处的速度;然后,通过汉克尔积分变换建立非平面反射波压力与轴向速度的关系,得到修正非平面波反射的吸声系数公式;最后,对模型样品进行数值计算和表面阻抗测量,分别与理论计算和传统的水声管测试方法所得结果相互比较,以验证所提方法的有效性。[结果]数值计算结果表明:实心覆盖层得到的结果与理论结果一致;圆柱空腔结果与理论结果有明显差异。阻抗测量的结果经平面波处理后与水声管试验结果有较大误差,经修正后与水声管试验结果较为吻合。[结论]覆盖层空腔易引起非平面波反射,在阻抗测量中需要予以修正;经修正后的阻抗测量方法得到的吸声系数与传统的水声管试验方法在所关注的频段内一致,且简化了试验,具有一定实践价值。

新的互正交互补序列集构造

针对互正交互补序列集(MOCSS)设计方法的局限性和构造参数的不足,提出了一种基于仿酉矩阵的MOCSS构造方法。该方法引入系数仿酉矩阵的新概念,并通过结合矩阵乘积、克罗内克积和矩阵迭代技术,构造了3类不同阶数的仿酉矩阵。利用仿酉矩阵与MOCSS之间的等价性,开发了一系列参数选择灵活的多相MOCSS,补充了现有文献设计结果。考虑到多载波码分多址系统峰均功率比(PAPR)抑制问题,进一步利用布尔函数设计了一种具有低列向量PAPR特性的系数仿酉矩阵。实验结果表明,采用这类系数仿酉矩阵构造的MOCSS,其列序列PAPR有效控制在2以内的范围,同时保持了码容量和长度的灵活性,为系统提供了多样化的信号选择。

压电复合材料梯度分布声学特性研究

目前,压电复合材料在吸声降噪领域应用广泛,但其低频吸声性能并不理想。为解决此问题,以0-3型压电复合材料为研究对象,提出使压电陶瓷体积含量呈梯度分布以提高其低频吸声系数的方法。首先,基于声电类比法和传递矩阵法,推导多梯度分布的理论公式,并通过文献构型对其进行验证;其次,将均匀分布与梯度分布的吸声系数进行比较,发现梯度分布会改变材料的声阻抗,从而改变吸声系数。最后,进行梯度分布压电复合材料数值分析,结果表明,同等条件下,当压电陶瓷体积含量呈梯度递减,且梯度差和第一梯度的厚度增加时,可明显提高低频吸声系数。

基于Relief算法的不平衡数据分类分级算法仿真

不平衡数据的分类分级是保证大数据技术高效使用过程中不可缺少的环节,但分类分级过程易受数据属性、冗余性、不均衡性等问题的干扰。为解决上述问题,提出不平衡数据朴素贝叶斯分类分级算法。采用合成少数类过采样技术降低数据的不平衡度,通过距离相关系数与最大信息系数完成不平衡数据的特征选择与筛选,采用Relief算法对筛选的特征做权重分配,并输入到朴素贝叶斯模型中实现分类,再结合动态阈值算法完成数据的分级。实验结果表明,所提算法的运行时间短、分类精度高,能够有效提升数据处理效果。

锆合金氧化膜及基体中氧的扩散

锆合金氧化膜及基体中氧的扩散系数是锆合金腐蚀动力学中的重要参数,目前文献报道的氧在锆及氧化膜中的扩散系数数值差异较大。本文通过真空退火试验,得到不同温度下氧化膜中氧浓度分布,计算了氧在锆合金基体中的扩散系数;通过氧化膜的等效扩散模型,由腐蚀转折前的腐蚀增重曲线,估算锆合金氧化膜中氧的扩散系数,得到Zr-Sn-Nb合金基体中氧的扩散系数随温度的变化规律为D_(Zr)(cm^(2)/s)=0.18exp(-180 000/RT);通过转折前的腐蚀增重曲线,估算得到氧化膜中氧的扩散系数随温度的变化规律为D_(ox)(cm^(2)/s)=3×10^(-7)exp(-101 550/RT)。

Hydromechanical characterization of gas transport amidst uncertainty for underground nuclear explosion detection

Given the challenge of definitively discriminating between chemical and nuclear explosions using seismic methods alone,surface detection of signature noble gas radioisotopes is considered a positive identification of underground nuclear explosions(UNEs).However,the migration of signature radionuclide gases between the nuclear cavity and surface is not well understood because complex processes are involved,including the generation of complex fracture networks,reactivation of natural fractures and faults,and thermo-hydro-mechanical-chemical(THMC)coupling of radionuclide gas transport in the subsurface.In this study,we provide an experimental investigation of hydro-mechanical(HM)coupling among gas flow,stress states,rock deformation,and rock damage using a unique multi-physics triaxial direct shear rock testing system.The testing system also features redundant gas pressure and flow rate measurements,well suited for parameter uncertainty quantification.Using porous tuff and tight granite samples that are relevant to historic UNE tests,we measured the Biot effective stress coefficient,rock matrix gas permeability,and fracture gas permeability at a range of pore pressure and stress conditions.The Biot effective stress coefficient varies from 0.69 to 1 for the tuff,whose porosity averages 35.3%±0.7%,while this coefficient varies from 0.51 to 0.78 for the tight granite(porosity<1%,perhaps an underestimate).Matrix gas permeability is strongly correlated to effective stress for the granite,but not for the porous tuff.Our experiments reveal the following key engineering implications on transport of radionuclide gases post a UNE event:(1)The porous tuff shows apparent fracture dilation or compression upon stress changes,which does not necessarily change the gas permeability;(2)The granite fracture permeability shows strong stress sensitivity and is positively related to shear displacement;and(3)Hydromechanical coupling among stress states,rock damage,and gas flow appears to be stronger in tight granite than in porous tuff.

New criterion for delay-dependent absolute stability of Lurie system with interval time-varying delay

The delay-dependent absolute stability for a class of Lurie systems with interval time-varying delay is studied. By employing an augmented Lyapunov functional and combining a free-weighting matrix approach and the reciprocal convex technique, an improved stability condition is derived in terms of linear matrix inequalities （LMIs）. By retaining some useful terms that are usually ignored in the derivative of the Lyapunov function, the proposed sufficient condition depends not only on the lower and upper bounds of both the delay and its derivative, but it also depends on their differences, which has wider application fields than those of present results. Moreover, a new type of equality expression is developed to handle the sector bounds of the nonlinear function, which achieves fewer LMIs in the derived condition, compared with those based on the convex representation. Therefore, the proposed method is less conservative than the existing ones. Simulation examples are given to demonstrate the validity of the approach.