近红外光谱定量分析的新方法:半监督最小二乘支持向量回归机

在近红外光谱定量分析中,样品化学值测定的准确度是运用数学模型进行定量分析精确度的理论极限。但能够准确获取化学值的样品数量比较少,许多模型在建模时只考虑这部分样品数据,而不考虑大量的无化学值的样品数据。针对该问题,本文在LS-SVR的基础上,提出了可以同时利用有化学值(标签)和无化学值样品数据的半监督LS-SVR(S2LS-SVR)模型。类似于LS-SVR,该模型也只需求解一个线性方程组。最后,以烤烟样品数据集为实验材料,建立了四种样品成分(总糖、还原糖、总氮和烟碱)的定量分析模型。四种样品成分的预测值与实际值的平均误差分别为6.62%,7.56%,6.11%和8.20%,相关系数分别为0.974 1,0.973 3,0.923 0和0.948 6。经分析比较发现S2LS-SVR模型优于PLS和LS-SVR,从而验证了S2LS-SVR模型的可行性和有效性。     

近红外漫反射线性加和光谱在烟叶复烤配方中的应用

应用近红外光谱分析技术进行烟叶复烤配方的辅助分析以及设计过程中,需要大量的不同混合比例的样品光谱,而混合样品光谱在实际生产过程中是很难获得的;且不同分级的样品很难实现均匀混合,不可避免的引入误差.文章提出了应用近红外漫反射光谱的线性加和原理产生"理论混合均匀光谱"来代替实际的混合样品光谱,不仅能够消除混合不均匀造成的误...     

On the M‐essential spectra of two‐group transport equations

In this paper, we deal with the M‐essential spectra of unbounded linear operators in Banach spaces where some generalizations of earlier work are given. Furthermore, we give an application from transport theory. Copyright © 2013 John Wiley & Sons, Ltd.     

Multicolor Ramsey Numbers For Complete Bipartite Versus Complete Graphs

Let be graphs. The multicolor Ramsey number is the minimum integer r such that in every edge‐coloring of by k colors, there is a monochromatic copy of in color i for some . In this paper, we investigate the multicolor Ramsey number , determining the asymptotic behavior up to a polylogarithmic factor for almost all ranges of t and m. Several different constructions are used for the lower bounds, including the random graph and explicit graphs built from finite fields. A technique of Alon and Rödl using the probabilistic method and spectral arguments is employed to supply tight lower bounds. A sample result is for any t and m, where c₁ and c₂ are absolute constants.     

On the completeness of root vectors generated by systems of coupled hyperbolic equations

The paper is the second in a set of two papers, which are devoted to a unified approach to the problem of completeness of the generalized eigenvectors (the root vectors) for a specific class of linear non‐selfadjoint unbounded matrix differential operators. The list of the problems for which such operators are the dynamics generators includes the following: (a) initial boundary‐value problem (IBVP) for a non‐homogeneous string with both distributed and boundary damping; (b) IBVP for small vibrations of an ideal filament with a one‐parameter family of dissipative boundary conditions at one end and with a heavy load at the other end; this filament problem is treated for two cases of the boundary parameter: non‐singular and singular; (c) IBVP for a three‐dimensional damped wave equation with spherically symmetric coefficients and both distributed and boundary damping; (d) IBVP for a system of two coupled hyperbolic equations constituting a Timoshenko beam model with variable coefficients and boundary damping; (e) IBVP for a coupled Euler‐Bernoulli and Timoshenko beam model with boundary energy dissipation (the model known in engineering literature as bending‐torsion vibration model); (f) IBVP for two coupled Timoshenko beams model, which is currently accepted as an appropriate model describing vibrational behavior of a longer double‐walled carbon nanotube. Problems have been discussed in the first paper of the aforementioned set. Problems are discussed in the present paper.     

Spectrum created by line defects in periodic structures

We study a Helmholtz‐type spectral problem related to the propagation of electromagnetic waves in photonic crystal waveguides. The waveguide is created by introducing a linear defect into a three‐dimensional periodic medium; the defect is infinitely extended in one direction, but compactly supported in the remaining two. This perturbation introduces guided mode spectrum inside the band gaps of the fully periodic, unperturbed spectral problem. We will show that even small perturbations lead to additional spectrum in the spectral gaps of the unperturbed operator and investigate some properties of the spectrum that is created.     

拟绝对-*-κ-仿正规算子的谱性质

引入了拟绝对-*-k-仿正规算子,获得了拟绝对-*-k-仿正规算子的一个充要条件.并证明了拟绝对-*-k-仿正规算子在0≤k≤1上是有限上升的,作为此性质的应用,证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则Weyl谱和本质近似点谱的谱映射定理成立.最后证明了若T是拟绝对-*-k-仿正规算子,其中0≤k≤1,则σ_(ja)(T)\{0}=σ_a(T)\{0}.     

飞秒脉冲的远场反射谱特性

从平面波的角谱表示出发,得到了超短脉冲光束由分层介质表面反射的频谱特性,数值计算给出了飞秒高斯脉冲经自由空间中介质薄膜反射的远场谱分布.由于光与介质的相互作用,反射谱呈现谱线变窄、红移、蓝移以及出现旁瓣而分裂成多重谱线的现象.     

Linear Least Squares Estimation of Regression Models for Two-Dimensional Random Fields

We consider the problem of estimating regression models of two-dimensional random fields. Asymptotic properties of the least squares estimator of the linear regression coefficients are studied for the case where the disturbance is a homogeneous random field with an absolutely continuous spectral distribution and a positive and piecewise continuous spectral density. We obtain necessary and sufficient conditions on the regression sequences such that a linear estimator of the regression coefficients is asymptotically unbiased and mean square consistent. For such regression sequences the asymptotic covariance matrix of the linear least squares estimator of the regression coefficients is derived.     

路或圈的笛卡尔乘积图的支撑树数

设G是路或圈的笛卡尔乘积图，t(G)表示G的支撑树数.该文借助于第二类Chebyshev多项式给出t(G)的公式，并考虑了t(G)的线性递归关系及渐近性态.