The Minimum Rank of a 3 × 3 Partial Block Matrix

After recalling the definition and some basic properties of finite hypergroups—a notion introduced in a recent paper by one of the authors—several non-trivial examples of such hypergroups are constructed. The examples typically consist of n n×n matrices, each of which is an appropriate polynomial in a certain tri-diagonal matrix. The crucial result required in the construction is the following: ‘let A be the matrix with ones on the super-and sub-diagonals, and with main diagonal given by a ₁…a _n which are non-negative integers that form either a non-decreasing or a symmetric unimodal sequence; then A_k =P_k (A) is a non-negative matrix, where p_k denotes the characteristic polynomial of the top k× k principal submatrix of A, for k=1,…,n. The matrices A_k as well as the eigenvalues of A, are explicitly described in some special cases, such as (i) a_i =0 for all ior (ii) a_i =0 for i<n and a_n =1. Characters ot finite abelian hypergroups are defined, and that naturally leads to harmonic analysis on such hypergroups.     

高光谱成像的土壤剖面水分含量反演及制图

传统土壤水分的获取方法仅可获得离散的土壤水分点位数据,难以获得剖面上精细且连续的水分含量分布图。研究了野外条件下利用近红外高光谱（882～1 709 nm）成像反演剖面土壤水分含量（SMC）,并实现精细制图的可行性。研究剖面位于江苏省东台市,我们利用近红外高光谱成像仪对剖面进行了5天原位连续观测,共采集了280个土样用于烘干法测定SMC。原始高光谱图像经数字量化值（DN）校正、黑白校正、拼接、几何校正、剪切和掩膜等一系列预处理后,提取各采样点的平均光谱反射率。提取光谱（Raw）经吸光度[LOG₁₀(1/R)],Savitzky-Golay平滑（SG）、一阶微分（FD）、二阶微分（SD）、多元散射校正（MSC）和标准正态变量（SNV）转换后,采用偏最小二乘回归（PLSR）和最小二乘支持向量机（LS-SVM）方法建立SMC预测模型,并对比分析不同光谱预处理方法与建模方法组合条件下SMC的预测精度。结果表明,光谱反射率随SMC增加逐渐降低,不同光谱预处理方法的预测精度有所差异,除MSC方法外,同一光谱预处理方法的LS-SVM模型预测精度均高于PLSR模型,并且基于LOG₁₀(1/R)光谱的LS-SVM模型对SMC预测精度最高,其建模集的决定系数（R2_c）和均方根误差（RMSE_c）分别为0.96和0.65%,预测集的决定系数（R2_p）、均方根误差（RMSE_p）和相对分析误差（RPD_p）分别为0.88,1.05%和2.88。利用最优模型进行剖面SMC的高空间分辨率精细制图,通过比较SMC反演图中提取的预测值与实测值关系发现预测精度较高（R2: 0.85～0.95, RMSE: 0.94%～1.02%）,且两者在剖面中的变化趋势基本一致,说明SMC反演图不仅能很好地反映出土壤水分在整个剖面中毫米级的含量分布信息,也可反映出同一位置处不同天数间的含量差异。因此,利用近红外高光谱成像结合优化的预测模型,能够实现土壤剖面SMC的定量预测及精细制图,有助于快速、有效监测田间剖面土壤水分状况。     

The maximum multiplicity of the largest k-th eigenvalue in a matrix whose graph is acyclic or unicyclic

Given a graph $G$ we are interested in studying the symmetric matrices associated to $G$ with a fixed number of negative eigenvalues. For this class of matrices we focus on the maximum possible nullity. For trees this parameter has already been studied and plenty of applications are known. In this work we derive a formula for the maximum nullity and completely describe its behavior as a function of the number of negative eigenvalues. In addition, we also carefully describe the matrices associated with trees that attain this maximum nullity. The analysis is then extended to the more general class of unicyclic graphs. Further our work is applied to re-describing all possible partial inertias associated with trees, and is employed to study an instance of the inverse eigenvalue problem for certain trees.     

一类波动方程耦合系统具Dirichlet边界控制的部分精确边界同步性

作者对具有Dirichlet边界控制的一类波动方程耦合系统提出了部分精确边界同步性的概念,并对其进行了深入的讨论,得到了实现部分精确边界同步性的充要条件.同时对部分同步态进行了讨论,得到了部分同步态不依赖于边界控制的一个充分条件.     

常微分方程近似解的LS-SVM改进求法

提出一种基于最小二乘支持向量机(LS-SVMs)的求解常微分方程近似解的改进方法.该方法首先通过离散计算域,将常微分方程转换为有约束条件的目标优化问题,然后利用径向基(RBF)核函数可导的性质,用带有导数形式的LS-SVM模型将此优化问题转化为LS-SVM回归问题,进而进行求解.最终得到的闭式近似解具有精度高、连续可微、结构简单且形式固定的特点.该方法适用于任意阶非刚性和奇异的线性常微分方程初值问题和边值问题,以及一阶非线性常微分方程问题.仿真结果验证了该方法具有良好的有效性.     

SPA-PLS的高含水原油近红外光谱含水率分析

准确及时的检测原油含水率对注水策略调整、原油开采能力评估、油井开发寿命预测等均具有重要意义。然而,当前我国大多数油田均已进入高含水的开发中晚期,含水率测量难度大且准确率不高。在此背景下,开展了高含水情况下利用近红外光谱进行原油含水率测量的研究。 首先介绍了目前原油含水率检测的常用方法,分析了它们的优劣。理论上,由于水的近红外光吸收带与原油中C-H键的吸收带有明显区别,根据Lambert-Beer吸收定律和吸光度线性叠加定律可知,不同含水率高含水原油近红外光谱会存在较强响应差异。为此,对高含水原油进行近红外光谱检测,建立原油含水率与近红外光谱响应间的非线性映射模型,可实现高含水原油含水率的精确测量。为了验证该方法的有效性,搭建了近红外光谱数据采集实验装置：采用白炽灯作为光源,经过光路调节成平行光后垂直射入样品池,用近红外光谱仪（海洋光学NIR512）采集光谱用于分析。其中,接收光谱仪带宽为900～1 700 nm,平均分成512个波段。光谱数据利用光谱仪配套软件储存在电脑中。样本采用相同厚度不同比例的油水混合物,样本含水率范围为70%～99%,共采集数据60组,每组重复3次取平均值。得到原始数据后,先进行原始数据预处理,以减少数据采集时来自高频随机噪音及温度不稳定、样本不均匀、基线漂移、光散射等不利因素的影响。分别选用了S-G滤波、一阶导数和S-G滤波+一阶导数作为数据预处理的方法,利用连续投影算法(SPA)对光谱数据进行降维,并利用偏最小二乘法（PLS）和多元线性回归（MLR）进行建模,模型精度通过计算均方根误差值（RMSE）和相关系数（r）来验证。对比发现,使用S-G滤波+一阶导数建立的模型RMSE值最小（RMSE=0.007 0,r=0.998 3）。使用SPA降维后的模型要优于全波段PLS模型（RMSE=0.083 3,r=0.920 6）与MLR模型（RMSE=0.099 9,r=0.967 1）。利用SPA提取出的31个特征波长建立的模型仅占全波段的6.05%,并获得了较好的精度。证明了利用光谱检测高含水原油含水率可行性,并且得到了满意的精度,为高含水原油的含水率检测提供了新的方法, 为进一步利用近红外光进行高含水原油的快速检测与在线监测提供参考。     

An optimal replenishment policy for an EOQ model with partial backlogging

We study an inventory system where demand on the stockout period is partially backlogged. The backlogged demand ratio is a mixture of two exponential functions. The shortage cost has two significant costs: the unit backorder cost (which includes a fixed cost and a cost proportional to the length of time for which the backorder exists) and the cost of lost sales. A general procedure to determine the optimal policy and the minimum inventory cost for all the parameter values is developed. This model generalizes several inventory systems analyzed by different authors. Numerical examples are used to illustrate the theoretical results.     

Comparison of two-dimensional integration methods for shape reconstruction from gradient data

As a requisite and key step in some gradient-based measurement techniques, the reconstruction of the shape, more generally the scalar potential, from the measured gradient data has been studied for many years. In this work, three types of two-dimensional integration methods are compared under various conditions. The merits and drawbacks of each integration method are consequently revealed to provide suggestions in selection of a proper integration method for a particular application.     

Adaptive RAKE receiver in chaos based pilot-added DS-CDMA system

This paper presents the theoretical analysis of adaptive multiuser RAKE receiver scheme in frequency selective fading channel for direct-sequence code division multiple access (DS-CDMA) system. Least mean square (LMS) algorithm is used to estimate the channel coefficients. Chaotic sequences are used as spreading sequence and corresponding bit error rate (BER) in closed form is derived for imperfect channel estimation conditions. Performances of chaotic sequences are compared with pseudorandom noise (PN) sequences. Under perfect synchronization assumption, various simulation results are shown to investigate the performance of the proposed system.     

用于光谱解混的正交向量投影算法

光谱解混是高光谱技术中的关键部分,对地物成分的定量分析至关重要。线性光谱解混方法在计算端元丰度时,大多需要涉及矩阵求逆或方阵行列式的计算,导致软件实现的计算复杂度高,且硬件实现困难。同时,当端元数量增加时,算法的计算量也会随之呈指数级快速增长。论文基于传统的正交子空间投影方法,利用正交原理,提出了一种新的光谱解混方法——正交向量投影。该方法首先利用Gram-Schmidt过程计算每个端元的最终正交向量分量,并将其作为代表端元的投影向量。然后对于任意的待解混光谱向量,直接将其投影到该正交向量上。最后,计算得到投影分量的长度与正交向量的长度比,即为该正交向量所代表端元的无约束丰度。该过程避免了正交子空间投影和最小方差方法中计算复杂、实现困难的矩阵求逆运算,更便于并行计算的设计和硬件实现。通过理论的推导分析,证明了该算法与正交子空间投影和最小方差方法是完全一致的。另外,由于算法避免了矩阵相乘和求逆运算,简化了解混过程,通过对不同算法复杂度的具体分析,也证明该算法相对其他算法可以对端元数量降低一个量级。最后,在模拟数据和实际图像上分别进行实验测试,结果的分析和比较,也说明了算法的有效性。