A high order energy preserving scheme for the strongly coupled nonlinear Schrōdinger system

A high order energy preserving scheme for a strongly coupled nonlinear Schrōdinger system is roposed by using the average vector field method. The high order energy preserving scheme is applied to simulate the soliton evolution of the strongly coupled Schrōdinger system. Numerical results show that the high order energy preserving scheme can well simulate the soliton evolution, moreover, it preserves the discrete energy of the strongly coupled nonlinear Schrōdinger system exactly.     

A Frisch-Newton Algorithm for Sparse Quantile Regression

Recent experience has shown that interior-point methods using a log barrier approach are far superior to classical simplex methods for computing solutions to large parametric quantile regression problems. In many large empirical applications, the design matrix has a very sparse structure. A typical example is the classical fixed-effect model for panel data where the parametric dimension of the model can be quite large, but the number of non-zero elements is quite small. Adopting recent developments in sparse linear algebra we introduce a modified version of the Prisch-Newton algorithm for quantile regression described in Portnoy and Koenker~([28]). The new algorithm substantially reduces the storage (memory) requirements and increases computational speed. The modified algorithm also facilitates the development of nonparametric quantile regression methods. The pseudo design matrices employed in nonparametric quantile regression smoothing are inherently sparse in both the fidelity and roughness penalty components. Exploiting the sparse structure of these problems opens up a whole range of new possibilities for multivariate smoothing on large data sets via ANOVA-type decomposition and partial linear models.     

基于IABC-SVR算法的拉曼光谱定量分析山羊血清蛋白含量

提出了一种基于拉曼光谱和改进人工蜂群算法优化支持向量机回归(IABC-SVR)算法快速定量检测山羊血清蛋白含量的方法.传统人工蜂群算法在数据区域规模较大时,收敛速度逐渐减慢,出现效率低、精准度下降、局部最优解概率高等问题.所提出的算法解决了这些问题,使算法在进化前期避免陷入局部最优解,在进化中后期能够保持解的全局搜索能...     

有机磷酸酯类化合物气相色谱定量结构保留关系研究

采用分子电性距离矢量(MEDV)表征有机磷酸酯类化合物的分子结构,运用多元线性回归建立定量结构-色谱保留关系(QSRR)模型,同时采用逐步回归结合统计检测对模型进行变量筛选,建立了35个有机磷酸酯类化合物在3种不同固定相(OV-101,DB-1701和DB-WX)上气相色谱保留指数(RI)与MEDV的定量相关模型.在3种固定相上的QSRR模型的建模计算值复相关系数(R)、留一法(leave-one-out)交互校验复相关系数(QCV)分别为0.998 0和0.995 1(OV-101);0.996 3和0.989 6(DB-1701);0.993 7和0.984 1(DB-WX),表明模型具有良好估计能力与稳定性.     

三维荧光光谱结合稀疏主成分分析和支持向量机的油类识别方法研究

石油污染的出现,导致生态环境遭到破坏。因此,油类识别方法的研究对于环境的保护具有重要意义。采用荧光光谱法获得石油光谱数据,并对其进行预处理,再通过降维方法来提取特征信息,最后利用模式识别算法进行分类,从而可以实现对油类的定性分析,因此研究一种更高效的数据降维方法以及识别分类算法极其重要。基于三维荧光光谱技术,利用稀疏主成分分析（SPCA）对FS920光谱仪测得的荧光光谱数据进行特征提取,再利用支持向量机（SVM）算法对提取的特征数据进行分类识别,获得了一种更加高效的油类识别方法。首先,利用海水和十二烷基硫酸钠（SDS）配制成浓度为0.1 mol·L-1的胶束溶液,将其作为溶剂配制柴油、航空煤油、汽油以及润滑油各20种不同浓度的溶液;然后,利用FS920光谱仪测得样本溶液的三维荧光光谱数据,对得到的光谱数据进行预处理;最后,对预处理后的数据分别利用SPCA和主成分分析（PCA）进行特征提取,再利用SVM和K最近邻（KNN）两种模式识别算法对特征向量进行分类,最终得到四种模型PCA-KNN,SPCA-KNN,PCA-SVM以及SPCA-SVM的分类结果。研究结果表明,由四种模型得到的分类准确率分别为85%,90%,90%和95%,其中,在同种分类算法中,利用SPCA进行特征提取得到的分类准确率均比PCA的准确率高5%,因此可知,SPCA的稀疏性具有突出主要成分的作用,在提取光谱特征时能够减小非必要成分的影响,并且载荷矩阵的稀疏化可以去除变量之间的冗余信息,优化降维特征信息,为后续分类提供更有效的数据特征信息;在同种特征提取算法下,利用SVM算法进行分类得到的分类准确率均比KNN算法得到的准确率高5%,表明SVM算法在分类中更具有优势。因此,本文利用三维荧光光谱技术结合SPCA和SVM算法,实现了对石油的准确识别与分类,为今后对石油污染物的高效检测提供了新思路。     

杭州老虎洞窑古陶瓷成分的化学计量学研究

用支持向量机算法研究了与杭州老虎洞古陶瓷有关的两个断源、断代问题。作为化学计量学的～种新型分类算法,支持向量机在小样本问题上表现出良好的泛化能力,与特征选择方法结合,可以有效处理样本少,特征多的问题。本研究综合利用支持向量机、特征选择算法和其它化学计量学算法研究了杭州凤凰山麓万松岭附近的古窑遗址和“传世哥窑”的断源、断代问题,证明老虎洞窑与郊坛下窑产品截然不同,万松岭附近地面收集瓷片样本是老虎洞窑宋代地层的瓷片滑落所致,而“传世哥窑”样品可能是老虎洞窑元代时的产品。实验表明：支持向量机算法与化学分析相结合可以成为研究古陶瓷断源和断代问题的一种新方法。     

多氯代二苯并呋喃在不同色谱柱上的气相色谱保留行为——定量结构-色谱保留关系(QSRR)的研究

 以一种拟原子的方式处理多氯代二苯并呋喃 (PCDFs)异构体中的苯环 ,将PCDFs异构体中的原子或基团分为 3类 ,即 :氯原子 (Cl) (记为“1”) ,氧原子 (O) (记为“2”)及拟原子 (B) (记为“3”)。在烷烃分子距边矢量的基础上 ,提出一种以基团为基准的分子距离边数矢量 (μ矢量 ) ,借助多元线性回归方法分别建立了多氯代二苯并呋喃在不同色谱柱上的色谱保留指数与表征其结构的 μ矢量间的定量结构 色谱保留关系 (QSRR)相关模型。各样本总体所建模型的相关系数均在 0 98以上。     

On Darboux helices in Euclidean 4‐space

The notion of Darboux helix in Euclidean 3‐space was introduced and studied by Yayl? et al. 2012. They show that the class of Darboux helices coincide with the class of slant helices. In a special case, if the curvature functions satisfy the equality κ² + τ² = constant, then these curves are curve of the constant precession. In this paper, we study Darboux helices in Euclidean 4‐space, and we give a characterization for a curve to be a Darboux helix. We also prove that Darboux helices coincide with the general helices. In a special case, if the first and third curvatures of the curve are equal, then Darboux helix, general helix, and V₄‐slant helix are the same concepts.     

On the dynamics of generic non-Abelian free actions

We investigate some global generic properties of the dynamics associated to non-Abelian free actions in certain special cases. The main properties considered in this paper are related to the existence of dense orbits, to ergodicity and to topological rigidity. We first deal with them in the case of conservative homeomorphisms of a manifold and C ¹-diffeomorphisms of a surface. Groups of analytic diffeomorphisms of a manifold which, in addition, contain a Morse-Smale element and possess a generating set close to the identity are considered as well. From our discussion we also derive the existence of a rigidity phenomenon for groups of skew-products which is opposed to the phenomenon present in Furstenbergs celebrated example of a minimal diffeomorphism that is not ergodic (cf. [Ma]).     

利用同步荧光光谱快速鉴别潲水油

为快速鉴别潲水油,采用三维同步荧光光谱结合平行因子法解析潲水油的特征波长差(Δλ),并利用支持向量机建立潲水油鉴别模型。结果表明,潲水油的特征Δλ为60 nm;特征Δλ下的样品原始同步荧光光谱经过主成分分析提取5个主成分,以径向基函数(RBF)为核函数,利用网格搜索和6-fold交叉验证优化建模参数,得到惩罚因子C=512、核参数g=0.5,该条件下建立的模型对训练集和预测集的判别率均达到100%。采用同步荧光光谱可以快速、准确地鉴别潲水油。