基于偏最小二乘法判别分析与随机森林算法的牛肝菌种类鉴别

牛肝菌作为一种著名的野生食用菌,具有较高的食用价值和经济价值.牛肝菌种类繁多,不易区分,建立一种有效、快速、可信的种类鉴别技术,可为牛肝菌提高品质提供一种方法.本研究采集云南不同地区7种野生牛肝菌共计683株,获取样品中红外光谱和紫外光谱,分析不同种类牛肝菌平均光谱图特征.基于多种预处理组合(SNV+SG,2D+MSC...     

土壤水分去除算法的田间原位光谱反演棉田有机质

田间原位可见-近红外光谱(VIS-NIR)能够有效的提高土壤属性的检测效率,但由于原位土壤中水分因素的影响,土壤属性的预测精度很难达到预期。如何有效去除土壤中的水分对土壤其他属性光谱预测的影响,是利用田间原位光谱高精度预测土壤属性所面临的难题,也是土壤光谱技术由室内转向田间的突破口。该问题的有效解决,可减除土壤样品的采集与室内预处理等过程,实现土壤属性的田间原位光谱测定。以新疆南部地区阿拉尔垦区十二团棉田为研究区,采用网格采样法共采集了116个0～20 cm深度的表层土壤样品,剔除1个异常值样品,得到115个有用样品,利用SR-3500型便携式地物光谱仪采集了231个样点的田间原位光谱数据,土样经风干、研磨和过筛等处理后测定其室内光谱和有机质含量。利用Kennard-Stone算法将115个土样分为69个转换子集及46个预测集,采用外部参数正交化法(EPO)、光谱直接转换法(DS)及光谱间接转换法(PDS)三种去除水分算法结合原位光谱反射率(R)、反射率一阶微分(R′)、反射率对数(LOG(R))以及反射率倒数(1/R)四种数学变换方式,运用随机森林(RF)模型进行不同组合模型的构建及精度评价。结果表明：(1)土壤有机质含量越高,土壤光谱反射率越低。土壤田间原位光谱反射率低于土壤室内光谱反射率;(2)室内光谱反射率与土壤有机质含量之间的相关性大于田间原位光谱,室内光谱经一阶微分变换后与土壤有机质含量之间的相关性显著提升。(3)土壤室内光谱反射率模型预测精度(R2=0.86, RPD=2.08, RMSE=1.55 g·kg-1, MAPE= 0.14)高于田间原位光谱反射率模型(R2=0.71, RPD=1.49, RMSE=2.17 g·kg-1, MAPE=0.20)。在去除水分算法模型中,以EPO一阶微分模型去除水分效果最好,决定系数R2由0.71提高到0.83,RPD由1.49提高到2.04,RMSE由2.17 g·kg-1降低至1.58 g·kg-1,MAPE由0.20降低至0.14。本研究实现了去除土壤水分因素的影响,提高了田间原位光谱预测土壤有机质的精度,为南疆棉田大尺度土壤有机质的预测及土壤肥力的评价提供了重要的参考。     

基于高斯回归分析的水稻氮素敏感波段筛选及含量估算

水稻氮素含量的准确监测是稻田精准施肥的重要环节,水稻叶片氮素含量发生变化会引起叶片、冠层的光谱发射率发生变化,高光谱遥感是目前作物氮素无损监测的关键技术之一.以2018年—2019年湖北监利两年水稻氮肥试验为基础,分别获取水稻分蘖期、拔节期、孕穗期、扬花期、灌浆期五个生育期水稻叶片和冠层两个尺度的高光谱反射率数据及对应...     

On the division of polynomial matrices

The main purpose of this paper is to determine two new algorithmsfor the division of the polynomial matrix B(s) R[s]^pxq by A(s) R[s]^pxp (a) based on the Laurent matrix expansion at s = =of the inverse of A(s), i.e. A(s)^–1, and (b) in a waysimilar to the one presented by Gantmacher (1959).     

Absolutely continuous spectrum for random Schrödinger operators on the Bethe strip

The Bethe strip of width m is the cartesian product $\mathbb {B}\times \lbrace 1,\ldots ,m\rbrace$, where $\mathbb {B}$ is the Bethe lattice (Cayley tree). We prove that Anderson models on the Bethe strip have “extended states” for small disorder. More precisely, we consider Anderson‐like Hamiltonians $H_\lambda =\frac{1}{2} \Delta \otimes 1 + 1 \otimes A\,+\,\lambda \mathcal {V}$ on a Bethe strip with connectivity K ≥ 2, where A is an m × m symmetric matrix, $\mathcal {V}$ is a random matrix potential, and λ is the disorder parameter. Given any closed interval $I\subset \big (\!-\!\sqrt{K}+a_{{\rm max}},\sqrt{K}+a_{\rm {min}}\big )$, where a_min and a_max are the smallest and largest eigenvalues of the matrix A, we prove that for λ small the random Schrödinger operator H_λ has purely absolutely continuous spectrum in I with probability one and its integrated density of states is continuously differentiable on the interval I.     

正则条件全竞赛空间与混合策略竞赛空间上的两个极值定理

在正则的全竞赛空间与混合策略竞赛空间推广并证明了两个新的最优决策存在定理．     

A Taylor expansion approach for solving partial differential equations with random Neumann boundary conditions

Nonlinear partial differential equation with random Neumann boundary conditions are considered. A stochastic Taylor expansion method is derived to simulate these stochastic systems numerically. As examples, a nonlinear parabolic equation (the real Ginzburg-Landau equation) and a nonlinear hyperbolic equation (the sine-Gordon equation) with random Neumann boundary conditions are solved numerically using a stochastic Taylor expansion method. The impact of boundary noise on the system evolution is also discussed.     

The new identity for the scattering matrix of exactly solvable models

We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one-dimensional Bose gas and XXZ Heisenberg quantum spin chain. Received: 4 December 1997 / Accepted: 17 March 1998     

Immanant positivity for Catalan-Stieltjes matrices

We give some sufficient conditions for the nonnegativity of immanants of square submatrices of Catalan-Stieltjes matrices and their corresponding Hankel matrices. To obtain these sufficient conditions, we construct new planar networks with a recursive nature for Catalan-Stieltjes matrices. As applications, we provide a unified way to produce inequalities for many combinatorial polynomials, such as the Eulerian polynomials, Schröder polynomials, and Narayana polynomials.