近红外光谱技术结合递归偏最小二乘算法对土壤速效磷与速效钾含量测定研究

土壤速效磷与速效钾在近红外区没有直接与它们相关的吸收峰,只能借助与其他拥有直接吸收峰物质(有机质,碳酸盐,粘土矿物,水分等)之间的相关关系而被近红外光谱技术所预测。这种相关关系会随着土壤样品构成的不同而不断变化,因此采用固定结构的近红外光谱模型很难对速效磷与速效钾取得较好的预测效果。提出采用递归偏最小二乘法(RPLS)在预测过程中递归更新土壤速效磷与速效钾的回归系数,以提高模型的预测能力;比较了偏最小二乘法(PLS),局部加权PLS(LW-PLS),滑动窗口LW-PLS(LW-PLS2)和RPLS对于土壤速效磷与速效钾含量的预测结果。194份土壤样品根据土壤类型分为建模集与预测集：建模集包含120份人为土样品;预测集则包含29份铁铝土样品,23份人为土样品和22份初育土样品。结果表明：RPLS模型取得了最优的预测结果,获得的决定系数(R2)分别为0.61与0.76,预测相对分析误差 (RPD)分别为1.60与2.05。说明RPLS通过不断更新模型的回归系数,能够适应新加入建模集样品的信息。相比于其他方法,预测精度更高,适用范围更广。     

DECIMAL SET WITH ZERO MEASURE AND FULL HAUSDORFF DIMENSION

Let Fκ = {χ ε (0,1)｜{2^nχ} ≥ 1/2^κ,n ε Z }, Z = {0,1,2,3}, κ ε N;F = Uκ^∞=1Fκ be a decimal set in (0, 1), where {2^nχ} is the fractional part of a number 2^nχ. In this note, we prove that dimHF = 1 and H^1(F) =0, where dimH is Hausdr off dimension, and H^1(F) is the Hausdorff measure of F.     

The residual based interactive stochastic gradient algorithms for controlled moving average models

This paper derives a residual based interactive stochastic gradient (ISG) parameter estimation algorithm for controlled moving average (CMA) models and studied the performance of the residual based ISG algorithm under weaker conditions on statistical properties of the noise. Compared with the residual based extended stochastic gradient algorithm for identifying CMA models, the proposed ISG algorithm can give highly accurate parameter estimates by the simulation example.     

Survival probability for a two-dimensional risk model

In this paper, we consider the survival probability for a two-dimensional risk model. We derive a partial integro-differential equation satisfied by the survival probability and prove its differentiability. We obtain explicit expressions for recursively calculating the survival probability by applying the partial integro-differential equation when claims are exponentially distributed.     

The semi-analytical method for time-dependent wave problems with uncertainties

This paper provides a constructive procedure for the computation of approximate solutions of random time-dependent hyperbolic mean square partial differential problems. Based on the theoretical representation of the solution as an infinite random improper integral, obtained via the random Fourier transform method, a double approximation process is implemented. Firstly, a random Gauss-Hermite quadrature is applied, and then, the evaluations at the nodes of the integrand are approximated by using a random Störmer numerical method. Numerical results are illustrated with examples.     

ERROR ESTIMATES FOR THE RECURSIVE LINEARIZATION OF INVERSE MEDIUM PROBLEMS

This paper is devoted to the mathematical analysis of a general recursive linearization algorithm for solving inverse medium problems with multi-frequency measurements. Under some reasonable assumptions, it is shown that the algorithm is convergent with error estimates. The work is motivated by our effort to analyze recent significant numerical results for solving inverse medium problems. Based on the uncertainty principle, the recursive linearization allows the nonlinear inverse problems to be reduced to a set of linear problems and be solved recursively in a proper order according to the measurements. As an application, the convergence of the recursive linearization algorithm [Chen, Inverse Problems 13（1997）, pp.253-282] is established for solving the acoustic inverse scattering problem.     

Design of RLS fixed-lag smoother using covariance information in linear discrete stochastic systems

This paper newly designs the recursive least-squares fixed-lag smoother using the covariance information in linear discrete-time stochastic systems. It is assumed that the signal is observed with additive white observation noise and the signal is uncorrelated with the observation noise. The fixed-lag smoother uses the covariance function of the signal in the semi-degenerate kernel form and the variance of the observation noise. The proposed fixed-lag smoother is suitable for the estimations of stationary or non-stationary stochastic signals generally.     

基于最大熵方法的水下航行体结构动力响应概率建模

水下航行体结构承受的水动力外载荷具有显著的时空分布不确定性,其引发的结构动力响应,诸如结构最大内力、最大内力发生时刻、最大内力发生位置等也由此产生了不确定性;同时,水下航行体的动力响应还会因其连接或分离结构的拉压刚度不同而出现非线性特征. 为了在水动力外载荷样本有限的基础上,分析水下航行体结构连接非线性对动力响应统计特性的影响, 利用水下航行体结构的简化动力学模型,计算了水动力横向载荷作用下响应的样本统计矩,采用最大熵方法实现了动力响应的概率建模. 在分别求出结构最大内力、最大内力发生时刻、最大内力发生位置的概率密度函数后,通过与蒙特卡洛模拟结果对比验证了最大熵方法拟合的响应概率密度函数精度;而后,基于这些结构响应概率密度曲线讨论了系统连接非线性参数变化对结构动力响应的影响. 最终得出如下结论:连接非线性会导致结构在只有横向力的作用时产生的轴力响应,并且最大轴力概率密度函数峰值会因连接结构非线性程度增大而逐渐增大;连接非线性对不确定性传播有显著影响,当连接非线性比较强时,输入正态分布的载荷所得到的内力响应不是正态分布的;最大内力响应的发生位置也会受到连接非线性程度的影响. 上述结果可以为结构优化提供技术支持.      

Criticality in the randomness-induced second-order phase transition of the triangular Ising antiferromagnet with nearest- and next-nearest-neighbor interactions

Using a Wang-Landau entropic sampling scheme, we investigate the effects of quenched bond randomness on a particular case of a triangular Ising model with nearest- (J_nn) and next-nearest-neighbor (J_nnn) antiferromagnetic interactions. We consider the case R=J_nnn/J_nn=1, for which the pure model is known to have a columnar ground state where rows of nearest-neighbor spins up and down alternate and undergo a weak first-order phase transition from the ordered to the paramagnetic state. With the introduction of quenched bond randomness we observe the effects signaling the expected conversion of the first-order phase transition to a second-order phase transition and using the Lee-Kosterlitz method, we quantitatively verify this conversion. The emerging, under random bonds, continuous transition shows a strongly saturating specific heat behavior, corresponding to a negative exponent α, and belongs to a new distinctive universality class with ν=1.135(11), γ/ν=1.744(9), and β/ν=0.124(8). Thus, our results for the critical exponents support an extensive but weak universality and the emerged continuous transition has the same magnetic critical exponent (but a different thermal critical exponent) as a wide variety of two-dimensional (2d) systems without and with quenched disorder.     

逐步聚合反应统计理论进展—递归计算法

本文介绍和评述了 Maeosko 等提出的聚合反应的新统计理论——递归计算法。该理论是基于逐步聚合过程的一级 Markov 统计特性以及这种链的递归性质。运用这种方法可以直接计算复杂的线性共聚体系的分子量、链长和序列分布等平均值,与其它统计方法相比,具有简单、通用性的优点。