Maps of manifolds into the plane which lift to standard embeddings in codimension two

Let be a smooth map of a closed n-dimensional manifold (n2) into the plane and let be an orthogonal projection. We say that f has the standard lifting property, if every embedding with is standard in a certain sense. In this paper we give some sufficient conditions for a generic smooth map f to have the standard lifting property when M is a closed surface or an n-dimensional homotopy sphere.     

纤维加强金属基复合材料热机械疲劳模型的研究进展

纤维增强金属基复合材料的热机械疲劳(thermomechanical fatigue 简称TMF)特性的研究在近年受到高度重视.本文根据国内外近期进行的理论研究以及获得的主要成果作一概要介绍.对于热机械循环特性,主要介绍基于细观力学方法的轴向性质模型,以及基于断裂与损伤理论的横向性质模型.对于热机械疲劳性能研究,结合横向性质导出两种热机械疲劳模型,然后分析基体的细观结构对疲劳寿命的影响.      

应用特征波段和反射变形差的方法进行土壤属性估算

传统的土壤分析是昂贵的、费时的并且可能带来环境污染问题。应用近红外光谱分析技术测定土壤参数具有快速、花费少和非破坏性的特点。利用GPS野外定位,在江西省的红壤站、鄱阳湖站和千烟州站周边共取得41个耕层(0～20 cm)土壤样品。通过对土壤样品高光谱反射率的室内分析测定,研究了土壤在紫外/可见光/近红外波段光谱的反射特性。研究的目的是应用波谱反射建立一个新的研究方法来估算土壤属性含量值。随后应用多元线性逐步回归方法对反射光谱数据进行分析,“B22+H13”光谱数据作为自变量,土壤属性含量作为因变量,建立了土壤属性含量的高光谱预测模型, 并对模型的稳定性和预测能力进行了检验。结果是土壤的pH、有机碳、全氮、全磷、阳离子代换量和碱解氮的相关系数都达到了0.80,而TK、速效磷、速效钾的相关系数在0.68左右。结果表明,应用此方法估算一些土壤属性含量是可行的。     

Models for representing piecewise linear cost functions

We study formulations of linear programs with piecewise linear objective functions with and without additional binary variables. We show that the two formulations without additional binary variables have the same LP bounds as those of the corresponding formulations with binary variables and therefore are preferable for efficient computation.     

Testing primitivity on partial words

Primitive words, or strings over a finite alphabet that cannot be written as a power of another string, play an important role in numerous research areas including formal language theory, coding theory, and combinatorics on words. Testing whether or not a word is primitive can be done in linear time in the length of the word. Indeed, a word is primitive if and only if it is not an inside factor of its square. In this paper, we describe a linear time algorithm to test primitivity on partial words which are strings that may contain a number of “do not know” symbols. Our algorithm is based on the combinatorial result that under some condition, a partial word is primitive if and only if it is not compatible with an inside factor of its square. The concept of special, related to commutativity on partial words, is foundational in the design of our algorithm. A World Wide Web server interface at http://www.uncg.edu/mat/primitive/ has been established for automated use of the program.     

Formulae concerning the computation of the Clausen integral Cl2(Θ)

The main problem under study concerns the expression of the Clausen integral Cl₂(Θ) in closed form in terms of known constants and special functions when Θ is equal to a rational multiple of π belonging to [0, 2π]. A general formula giving $\text{Cl}{}_2\text{(}\text{pπ}\text{q}\text{)}$ in terms of the derivative of the di-gamma function and the sine function is deduced from an appropriate Fourier series expansion. Some variants of this formula are obtained. In further sections, the formulae expressing Cl₂(2Θ) and, more generally, Cl₂(mΘ)(m=2,3,4,…) as linear combinations of terms of the form Cl₂(Θ+α) (α: const.) are established. The various results are illustrated by means of typical examples of practical application. The last section contains two simple approximations enabling the computation of Cl(Θ) for any Θ in [0,π] with a relative error smaller than 0.63% and 0.003%, resp.. The paper ends with an appendix in which, among other things, a peculiar trigonometric identity is established as a by-product.     

A special ordered set approach for optimizing a discontinuous separable piecewise linear function

We give a special ordered set (SOS) approach that optimizes a discontinuous separable piecewise linear function, even when a mixed-integer programming (MIP) model is not available for it. When a MIP model is available, our SOS model gives a linear programming relaxation bound that is as good as the MIPs.     

Invariants of the Riemann tensor: A classical approach

This paper describes the start of an investigation into the application of classical invariant theory to scalar polynomial invariants of the Riemann tensor. In particular, the classical methods of enumerating invariants are discussed with the aim, not achieved in this paper, of verifying Sneddon's result, obtained by explicit calculation of the invariants that the dimension of a Hilbert basis is 38.