A curvilinear method based on minimal-memory BFGS updates

We present a new matrix-free method for the computation of negative curvature directions based on the eigenstructure of minimal-memory BFGS matrices. We determine via simple formulas the eigenvalues of these matrices and we compute the desirable eigenvectors by explicit forms. Consequently, a negative curvature direction is computed in such a way that avoids the storage and the factorization of any matrix. We propose a modification of the L-BFGS method in which no information is kept from old iterations, so that memory requirements are minimal. The proposed algorithm incorporates a curvilinear path and a linesearch procedure, which combines two search directions; a memoryless quasi-Newton direction and a direction of negative curvature. Results of numerical experiments for large scale problems are also presented.     

中国对外直接投资的贸易效应研究:基于对北美自贸区、欧盟、东盟投资的比较分析

中国对外贸易发展成熟、国际地位显著,但从长期看,其边际收益呈现递减趋势.而对外直接投资虽规模较小,且尚在起步阶段,但其发展速度快、市场潜力巨大.在拓展Anderson和Wincoop模型基础上,理论分析了对外直接投资与贸易之间的关系.然后通过建立计量模型,利用1995-2011年面板数据进行固定模型分析.由于中国对外直接投资的贸易效应存在明显的区域性,以北美自贸区、欧盟和东盟作为研究对象,实证检验了中国对外直接投资与贸易的关系,旨在考察中国对三种不同类型区域一体化组织投资的贸易效应差异.研究结果表明,从长期看,中国对北美自由贸易区、欧盟和东盟投资均具有明显的贸易创造效应.这种贸易创造效应的大小依次是东盟欧盟北美自贸区.     

Topological sensitivity analysis of a multi‐scale constitutive model considering a cracked microstructure

This paper deals with the sensitivity analysis of the macroscopic elasticity tensor to topological microstructural changes of the underlying material. In particular, the microstucture is topologicaly perturbed by the nucleation of a small circular inclusion. The derivation of the proposed sensitivity relies on the concept of topological derivative, applied within a variational multi‐scale constitutive framework where the macroscopic strain and stress at each point of the macroscopic continuum are defined as volume averages of their microscopic counterparts over a representative volume element (RVE) of material associated with that point. We consider that the RVE can contain a number of voids, inclusions and/or cracks. It is assumed that non‐penetration conditions are imposed at the crack faces, which do not allow the opposite crack faces to penetrate each other. The derived sensitivity leads to a symmetric fourth‐order tensor field over the unperturbed RVE domain, which measures how the macroscopic elasticity parameters estimated within the multi‐scale framework changes when a small circular inclusion is introduced at the micro‐scale level. Copyright © 2009 John Wiley & Sons, Ltd.     

气候政策的经济环境效应分析与比较—基于碳税、许可交易和总量控制的动态微分博弈

基于产品差别化假设,建立双寡头动态微分博弈模型,比较碳税和许可交易以及总量控制3种气候政策的经济环境效应.研究发现,不同气候政策对两国的经济效应不同.进一步研究还发现,在企业产品差别化竞争时,从碳排放流量来看,碳税政策和许可交易政策与总量控制政策之间没有严格的优劣之分;碳排放存量对碳税政策最敏感.从碳存量对政策的边际影响来看,许可交易政策与总量控制政策是相同的,而碳税政策与之相反.当两国生产的产品完全同质时,从均衡碳排放流量和碳排放存量来看,许可交易政策最优,总量控制政策次之,碳税政策最差.若政府单纯以控制碳排放量为目的,许可交易政策是最佳选择.     

Análise da confiabilidade de estruturas de concreto armado com uma metodologia para inclusão de efeitos estocásticos de propriedades dos materiais

In this paper, special emphasis is given to the inclusion of uncertainties in the evaluation of structural behaviour aiming at a better representation of the system characteristics and the quantification of the importance of these uncertainties in the project. It deals with the structural reliability analysis problem accounting the effect of spatial variability of material properties. To this end it is proposed a finite element model to represent the behaviour of reinforced concrete for short and long-term loads, which includes the main features observed in this material. It was developed a model for the generation of multidimensional non-Gaussian stochastic fields for the material properties that is independent of the finite element mesh. First, an example of a two-dimensional non-Gaussian stochastic field generation in a square steel plate is presented. Latter, the reliability analysis is performed to a limit state function based on prescribed values of mid-span displacements on a simply-supported reinforced beam. Finally, the influence of long-term effects on the reliability of a reinforced concrete beam is studied considering the effect of steel reinforcement corrosion.     

Generalized elementary functions

We use the theory of generalized linear differential equations to introduce new definitions of the exponential, hyperbolic and trigonometric functions. We derive some basic properties of these generalized functions, and show that the time scale elementary functions with Lebesgue integrable arguments represent a special case of our definitions.     

Invariant scale matrix hypothesis tests under elliptical symmetry

The usual assumption in multivariate hypothesis testing is that the sample consists of n independent, identically distributed Gaussian m-vectors. In this paper this assumption is weakened by considering a class of distributions for which the vector observations are not necessarily either Gaussian or independent. This class contains the elliptically symmetric laws with densities of the form f(X(n × m)) = ψ[tr(X ? M)′ (X ? M)Σ^?1]. For testing the equality of k scale matrices and for the sphericity hypothesis it is shown, by using the structure of the underlying distribution rather than any specific form of the density, that the usual invariant normal-theory tests are exactly robust, for both the null and non-null cases, under this wider class.     

Shrinkage estimators of the location parameter for certain spherically symmetric distributions

We consider estimation of a location vector for particular subclasses of spherically symmetric distributions in the presence of a known or unknown scale parameter. Specifically, for these spherically symmetric distributions we obtain slightly more general conditions and larger classes of estimators than Brandwein and Strawderman (1991,Ann. Statist.,19, 1639–1650) under which estimators of the formX +ag(X) dominateX for quadratic loss, concave functions of quadratic loss and general quadratic loss.Research supported by NSF grant DMS-88-22622     

Scale Invariance Properties in the Simulated Annealing Algorithm

The Boltzmann distribution used in the steady-state analysis of the simulated annealing algorithm gives rise to several scale invariant properties. Scale invariance is first presented in the context of parallel independent processors and then extended to an abstract form based on lumping states together to form new aggregate states. These lumped or aggregate states possess all of the mathematical characteristics, forms and relationships of states (solutions) in the original problem in both first and second moments. These scale invariance properties therefore permit new ways of relating objective function values, conditional expectation values, stationary probabilities, rates of change of stationary probabilities and conditional variances. Such properties therefore provide potential applications in analysis, statistical inference and optimization. Directions for future research that take advantage of scale invariance are also discussed.