基于主成分分析法的综合评价方法的改进

针对用主成分分析法做综合评价存在的问题,提出了改进的方法即当第一主成分的综合评价值和熵值法得到的综合评价值具有一致性时,将两种评价结果进行集成综合评价,若两种评价结果不具有一致性时则采用主成分聚类法进行综合评价.     

二维正态分布的假设检验

将二维随机向量分解成互不相关的主成分,通过对两主成分的正态独立性检验达到二维随机向量正态性检验的目的.     

Hypersurfaces of the hyperbolic space with constant scalar curvature

We classify hypersurfaces of the hyperbolic space ?ⁿ⁺¹(c) with constant scalar curvature and with two distinct principal curvatures. Moreover, we prove that if Mⁿ is a complete hypersurfaces with constant scalar curvature n(n ? 1) R and with two distinct principal curvatures such that the multiplicity of one of the principal curvatures is n? 1, then R ≥ c. Additionally, we prove two rigidity theorems for such hypersurfaces.     

主转动角与主转动轴的显式表示

本文利用Cayley-Hamilton定理,给出了两种直接获得转动张量显式表示的方法。一种为只含变形梯度较低次幂的表达形式,利用此表示,获得了主转动角的计算公式和主转动轴的显式表示。而另一种则是不含复杂系数且含变量个数较少的高效获得转动张量的方法。进一步,给出了主转动角和主转动轴的一些性质。     

Principal Nested Spheres for Time-Warped Functional Data Analysis

There are often two important types of variation in functional data: the horizontal (or phase) variation and the vertical (or amplitude) variation. These two types of variation have been appropriately separated and modeled through a domain warping method (or curve registration) based on the Fisher–Rao metric. This article focuses on the analysis of the horizontal variation, captured by the domain warping functions. The square-root velocity function representation transforms the manifold of the warping functions to a Hilbert sphere. Motivated by recent results on manifold analogs of principal component analysis, we propose to analyze the horizontal variation via a principal nested spheres approach. Compared with earlier approaches, such as approximating tangent plane principal component analysis, this is seen to be an efficient and interpretable approach to decompose the horizontal variation in both simulated and real data examples.     

Spinor genera of binary quadratic forms

Spinor genera are defined for binary quadratic forms with integer coefficients in such a way that the theory fits in with the Gaussian theory of genera. It is shown that spinor generic characters exist which distinguish the various spinor genera in the principal genus, and how they can be determined. It is known that each ambiguous class contains exactly two forms of the type [a, 0, c] or [a, a, c], each with its associate [c, 0, a], [4c ? a, 4c ? a, c]. Since the principal class contains such a form with a = 1, it is an interesting question whether one can predict the second form (not counting associates). This question includes that of Dirichlet about the representability of ?1 by the principal class. Methods are given for evaluating the spinor-generic characters of ambiguous forms in the principal genus for variable discriminants d, and are carried through in the eleven cases where d is fundamental, there are two or four genera, and two spinor genera in the principal genus. The problem of determining the “second form” is thus completely solved except when there is more than one ambiguous class in the principal spinor genus.     

Multivariable Lagrange Inversion, Gessel-Viennot Cancellation, and the Matrix Tree Theorem

A new form of multivariable Lagrange inversion is given, with determinants occurring on both sides of the equality. These determinants are principal minors, for complementary subsets of row and column indices, of two determinants that arise singly in the best known forms of multivariable Lagrange inversion. A combinatorial proof is given by considering functional digraphs, in which one of the principal minors is interpreted as a Matrix Tree determinant, and the other by a form of Gessel-Viennot cancellation.     

Interpolation lattices in several variables

Principal lattices are classical simplicial configurations of nodes suitable for multivariate polynomial interpolation in n dimensions. A principal lattice can be described as the set of intersection points of n + 1 pencils of parallel hyperplanes. Using a projective point of view, Lee and Phillips extended this situation to n + 1 linear pencils of hyperplanes. In two recent papers, two of us have introduced generalized principal lattices in the plane using cubic pencils. In this paper we analyze the problem in n dimensions, considering polynomial, exponential and trigonometric pencils, which can be combined in different ways to obtain generalized principal lattices.We also consider the case of coincident pencils. An error formula for generalized principal lattices is discussed. Partially supported by the Spanish Research Grant BFM2003-03510, by Gobierno de Aragón and Fondo Social Europeo.     

Filtration, automorphisms, and classification of infinite-dimensional odd contact superalgebras

The principal filtration of the infinite-dimensional odd contact Lie superalgebra over a field of characteristic p>2 is proved to be invariant under the automorphism group by investigating ad-nilpotent elements and determining certain invariants such as subalgebras generated by some ad-nilpotent elements. Then, it is proved that two automorphisms coincide if and only if they coincide on the -1 component with respect to the principal grading. Finally, all the odd contact superalgebras are classified up to isomorphisms.     

Geometric structures encoded in the lie structure of an Atiyah algebroid

We investigate Atiyah algebroids, i.e. the infinitesimal objects of principal bundles, from the viewpoint of the Lie algebraic approach to space. First we show that if the Lie algebras of smooth sections of two Atiyah algebroids are isomorphic, then the corresponding base manifolds are necessarily diffeomorphic. Further, we give two characterizations of the isomorphisms of the Lie algebras of sections for Atiyah algebroids associated to principal bundles with semisimple structure groups. For instance we prove that in the semisimple case the Lie algebras of sections are isomorphic if and only if the corresponding Lie algebroids are, or, as well, if and only if the integrating principal bundles are locally isomorphic. Finally, we apply these results to describe the isomorphisms of sections in the case of reductive structure groups—surprisingly enough they are no longer determined by vector bundle isomorphisms and involve dive rgences on the base manifolds.     

Some results on the analysis of asymmetric stress

The structure of the principal directions of stress is characterized for the general case of asymmetric stress. It is shown that, for asymmetric stress, the principal directions can comprise either only one direction, or only two directions, or only three directions, or a plane of directions, or a plane of directions together with a direction external to this plane. The asymmetric stress obtained by combining a one-dimensional stress field with a skew-symmetric stress field is analyzed in detail.     

约束矩阵方程的中心对称解及其在振动理论反问题中的应用

研究了中心主子矩阵约束下矩阵方程的中心对称解. 利用矩阵向量化、Kronecker乘积及奇异值分解方法,得到了有解的充分必要条件及解的一般表达形式．同时,考虑了与之相关的对任意给定矩阵的最佳逼近问题．进而,给出在振动理论反问题中的应用, 利用截断的主质量矩阵（或主刚度矩阵）、截断模态矩阵以及质量矩阵（或刚度矩阵）的中心主子阵,求系统的质量矩阵（或刚度矩阵）．最后用两个例子说明文中方法的有效性.     

Multiple imputation in principal component analysis

The available methods to handle missing values in principal component analysis only provide point estimates of the parameters (axes and components) and estimates of the missing values. To take into account the variability due to missing values a multiple imputation method is proposed. First a method to generate multiple imputed data sets from a principal component analysis model is defined. Then, two ways to visualize the uncertainty due to missing values onto the principal component analysis results are described. The first one consists in projecting the imputed data sets onto a reference configuration as supplementary elements to assess the stability of the individuals (respectively of the variables). The second one consists in performing a principal component analysis on each imputed data set and fitting each obtained configuration onto the reference one with Procrustes rotation. The latter strategy allows to assess the variability of the principal component analysis parameters induced by the missing values. The methodology is then evaluated from a real data set.     

Real hypersurfaces with constant principal curvatures in complex space forms

We present the motivation and current state of the classification problem of real hypersurfaces with constant principal curvatures in complex space forms. In particular, we explain the classification result of real hypersurfaces with constant principal curvatures in nonflat complex space forms and whose Hopf vector field has nontrivial projection onto two eigenspaces of the shape operator. This constitutes the following natural step after Kimura and Berndt?s classifications of Hopf real hypersurfaces with constant principal curvatures in complex space forms.     

Multivariate analysis for the assessment of factors affecting industrial competitiveness: The case of Greek food and beverage industries

Principal component analysis is integrated with canonical analysis to examine aspects of the competitiveness of two different sectors of the Greek manufacturing, i.e. the food and the beverage industries. Different measures of labour productivity, vertical integration, technological innovation and size of the firms which are considered as critical factors of industrial competitiveness are used in the application of the principal component analysis. Canonical analysis is then applied to correlate the variables of labour productivity with the other variables. In the case of the food and beverage integrated sector, the results of the principal component analysis pinpoint that there are two main principal components: (a) labour productivity and vertical integration, and (b) technological innovation and size. The first factor depicts the internal organizational, structural and production processes changes realized so that the competitiveness of the sector firms improves, whereas the second factor reflects the response of the sector to technological and growth trends. The two variables of labour productivity are affected by the degree of vertical integration and, at a lesser degree, by a common factor of the size of the firm and the level of investment for technological innovation. Copyright © 2000 John Wiley & Sons, Ltd.     

Vanishing pseudo–Schur complements,reverse order laws,absorption laws and inheritance properties

The problem of vanishing of a (generalized) Schur complement of a block matrix (corresponding to the leading principal subblock) implying that the other (generalized) Schur complement (corresponding to the trailing principal subblock) is zero, is revisited. Absorption laws for two important classes of generalized inverses are considered next. Inheritance properties of the generalized Schur complements in relation to the absorption laws are derived. Inheritance by the generalized principal pivot transform is also studied.     

带上下界的双参与人双向委托代理模型及优化算法研究

考虑现实中双参与人同时具有委托人和代理人双重身份情形下,双参与人间的互为委托代理关系,设计虚拟委托人期望效用函数表达式,建立带上下界的双参与人双边约束双向委托代理模型,利用不动点定理确定参数的上下界,并运用不等式组的旋转算法并结合序列二次规划算法进行求解.通过算例分析表明,为达到联盟总效用最大化,需通过确定联盟成员各自合适的保留效用值,以平衡联盟成员的投资和回报,真正实现对联盟成员的激励.     

On Laguerre form and Laguerre isoparametric hypersurfaces

Let x : Mn-1→ Rnbe an umbilical free hypersurface with non-zero principal curvatures.M is called Laguerre isoparametric if it satisfies two conditions, namely, it has vanishing Laguerre form and has constant Lauerre principal curvatures. In this paper, under the condition of having constant Laguerre principal curvatures, we show that the hypersurface is of vanishing Laguerre form if and only if its Laguerre form is parallel with respect to the Levi–Civita connection of its Laguerre metric.     

Choice of the best time scale for preventive maintenance in heterogeneous environments

A principal feature of the model considered in this paper is the presence of several time scales for lifetime measurements when similar objects operate in heterogeneous conditions. A typical example are lifetimes of an aircraft module which can be measured in the total time in air and in the number of flights. A family of lifetimes can be generated by considering a linear combination of the above two principal time scales. We consider a problem of finding an optimal maintenance period for an equipment operating during a single maintenance/replacement cycle, in heterogeneous environmental conditions. Our main concern is finding the time scale which provides the maximal value of the return (cost) functional. We consider two “principal” time scales (the operation time and the total number of shocks) and show numerically that the optimal linear combination of these two scales has also the minimal coefficient of variation (c.v.) of system lifetime. We develop some general theory to connect the optimality in terms of the return functional with the optimality in terms of c.v.     

Computational approaches to estimation in the principal component analysis of a stochastic process

After performing a review of the classical procedures for estimation in the principal component analysis (PCA) of a second order stochastic process, two alternative procedures have been developed to approach such estimates. The first is based on the orthogonal projection method and uses cubic interpolating splines when the data are discrete. The second is based on the trapezoidal method. The accuracy of both procedures is tested by simulating approximated sample-functions of the Brownian motion and the Brownian bridge. The real principal factors of these stochastic processes, which can be evaluated directly, are compared with those estimated by means of the two mentioned algorithms. An application for estimation in the PCA of tourism evolution in Spain from real data is also included.