激光诱导击穿光谱的自组织特征映射结合相关判别对天然地质样品分类方法研究

激光诱导击穿光谱技术具有微损、原位、快速分析的特点,在样品分类识别、成分分析等领域有广阔的应用前景。为探索该技术在天然地质样品识别应用的可行性,提出了一种自组织特征映射神经网络结合相关判别对天然地质样品LIBS光谱分类识别的方法。为减小全谱中背景噪声等不相关数据干扰、降低计算量,在元素谱线归属的基础上进行了特征谱线提取,实现了高维光谱数据的降维。以特征谱数据为输入建立网络训练模型,得到具有输入样本特征的权向量,通过权向量与待测样本进行相关分析可以实现样品分类。对16种天然地质样品的分类算法实验证明,在全谱、主成分降维和特征谱段三种数据处理方法中,特征谱的降维和提取LIBS数据主特征效果最优。改进的SOM网络结合相关判别算法比支持向量机方法和直接应用SOM网络方法的分类准确度更高,初步证实了该方法的有效性。     

The many limits of mixed means

The sequences introduced by Carlson (1971) are variants of the Gauss arithmetic geometric sequences (which have been elegantly discussed by D. A. Cox (1984, 1985)). Given (complex)a ₀,b ₀ we define

Covering and radius-covering arrays: Constructions and classification

The minimum number of rows in covering arrays (equivalently, surjective codes) and radius-covering arrays (equivalently, surjective codes with a radius) has been determined precisely only in special cases. In this paper, explicit constructions for numerous best known covering arrays (upper bounds) are found by a combination of combinatorial and computational methods. For radius-covering arrays, explicit constructions from covering codes are developed. Lower bounds are improved upon using connections to orthogonal arrays, partition matrices, and covering codes, and in specific cases by computation. Consequently for some parameter sets the minimum size of a covering array is determined precisely. For some of these, a complete classification of all inequivalent covering arrays is determined, again using computational techniques. Existence tables for up to 10 columns, up to 8 symbols, and all possible strengths are presented to report the best current lower and upper bounds, and classifications of inequivalent arrays.     

Exponential decay rate of survival probability in a disastrous random environment

Summary. We study the exponential decay rate of the survival probability up to time t>0 of a random walker moving in Zopf; ^d in a temporally and spatially fluctuating random environment. When the random walker has a speed parameter κ>0, we investigate the influence of κ on the exponential decay rate λ(d,κ). In particular we prove that for any fixed d≥1, λ(d,κ) behaves like as logκ as κ↘0. Received: 21 May 1996 / In revised form: 2 February 1997     

Quadrature for hp-Galerkin BEM in {\hbox{\sf l\kern-.13em R}}^3

Summary. The Galerkin discretization of a Fredholm integral equation of the second kind on a closed, piecewise analytic surface is analyzed. High order, -boundary elements on grids which are geometrically graded toward the edges and vertices of the surface give exponential convergence, similar to what is known in the -Finite Element Method. A quadrature strategy is developed which gives rise to a fully discrete scheme preserving the exponential convergence of the -Boundary Element Method. The total work necessary for the consistent quadratures is shown to grow algebraically with the number of degrees of freedom. Numerical results on a curved polyhedron show exponential convergence with respect to the number of degrees of freedom as well as with respect to the CPU-time. Received April 22, 1996     

A new class of particle methods

Summary. Particle methods are numerical methods designed to solve problems in fluid mechanics and related problems in continuum mechanics. A general approach to the construction of such particle methods is presented in this article. The particles are no mass points but possess a finite extension. They can rotate in space and have a spin. The conservation of mass is automatically guaranteed by the ansatz. The forces of interaction between the particles are derived in a canonical way from the force laws of continuum mechanics and are directly based on a regularized stress tensor. In the absence of external forces and of heat sources and sinks, momentum, angular momentum, and energy are conserved as in the continuum case. Received February 17, 1995 / Revised version received December 28, 1995     

Natural extensions of holomorphic motions

We consider an arbitrary real analytic family X_z, , over the closed unit disc , of real analytic plane Jordan curves X_z. Ifj _e ^iθ ,e ^iθ ∋ ∂D, is an arbitrary real-analytic family of orientation-reversing homeomorphisms of fixingX _e ^iθ pointwise, we show that there is a unique holomorphic motion of extending the given motion of Jordan curves and consistent with the given family of involutions. If these generalized reflections are defined using the barycentric extension construction of Douady-Earle-Nag, then the resulting extension method for holomorphic motions of X is natural, that is Moebius-invariant and continuous with respect to variation of the given motion of X₀.     

Harmonic maps with fixed singular sets

Suppose Ω is a smooth domain in R^m,N is a compact smooth Riemannian manifold, andZ is a fixed compact subset of Ω having finite (m − 3)-dimensional Minkowski content (e.g.,Z ism − 3 rectifiable). We consider various spaces of harmonic mapsu: Ω →N that have a singular setZ and controlled behavior nearZ. We study the structure of such spacesH and questions of existence, uniqueness, stability, and minimality under perturbation. In caseZ = 0,H is a Banach manifold locally diffeomorphic to a submanifold of the product of the boundary data space with a finite-dimensional space of Jacobi fields with controlled singular behavior. In this smooth case, the projection ofu εH tou |ϖΩ is Fredholm of index 0. R. H.’s research partially supported by the National Science Foundation.     

Some new domains with complete Kähler metrics of negative curvature

We add to the known examples of complete Kähler manifolds with negative sectional curvature by showing that the following three classes of domains in euclidean spaces also belong: perturbations of ellipsoidal domains in ?ⁿ, intersections of complex-ellipsoidal domains in ?², and intersections of fractional linear transforms of the unit ball in ?². In the process, we prove the following theorem in differential geometry: in the intersection of two complex-ellipsoidal domains in ?², the sum of the Bergman metrics is a Kähler metric with negative curvature operator.