A Note on the Linearity of Real-valued Functions with Respect to Suitable Metrics

In this paper we prove that for every real-valued Morse function φ on a smooth closed manifold ℳ and every neighborhood U of its critical points a suitable Riemannian metric μ _U exists such that φ is linear outside U     

Global Solution of Optimization Problems with Parameter-Embedded Linear Dynamic Systems

This paper develops a theory for the global solution of nonconvex optimization problems with parameter-embedded linear dynamic systems. A quite general problem formulation is introduced and a solution is shown to exists. A convexity theory for integrals is then developed to construct convex relaxations for utilization in a branch-and-bound framework to calculate a global minimum. Interval analysis is employed to generate bounds on the state variables implied by the bounds on the embedded parameters. These bounds, along with basic integration theory, are used to prove convergence of the branch-and-bound algorithm to the global minimum of the optimization problem. The implementation of the algorithm is then considered and several numerical case studies are examined thoroughly     

Lot-sizing with fixed charges on stocks: the convex hull

In this paper, we examine a variant of the uncapacitated lot-sizing model of Wagner–Whitin that includes fixed charges on the stocks. Such a model is natural in a production environment where stocking is a complex operation, and appears as a subproblem in more general network design problems.

Linear-programming formulations, a dynamic program, the convex hull of integer solutions and a separation algorithm are presented. All these turn out to be very natural extensions of the corresponding results of Barany et al. (Math. Programming Stud. 22 (1984) 32) for the uncapacitated lot-sizing problem. The convex hull proof is based on showing that an extended facility location formulation is tight and by projecting it onto the original space of variables.     

束流线性耦合效应的初步研究

在储存环的束流传输系统中,斜四极场和纵向螺线管场是引起束流线性耦合的主要原因.由于这种耦合,使得束流的幅度和发射度发生交换,引起束流横向包络的增大,严重的将造成束流损失.从Betatron运动方程出发研究了斜四极场和螺线管场存在时束流的幅度耦合效应,分析了斜四极场存在时束流发射度的变化.     

A technique to construct symmetric variable-stepsize linear multistep methods for second-order systems

Some previous works show that symmetric fixed- and variable-stepsize linear multistep methods for second-order systems which do not have any parasitic root in their first characteristic polynomial give rise to a slow error growth with time when integrating reversible systems. In this paper, we give a technique to construct variable-stepsize symmetric methods from their fixed-stepsize counterparts, in such a way that the former have the same order as the latter. The order and symmetry of the integrators obtained is proved independently of the order of the underlying fixed-stepsize integrators. As this technique looks for efficiency, we concentrate on explicit linear multistep methods, which just make one function evaluation per step, and we offer some numerical comparisons with other one-step adaptive methods which also show a good long-term behaviour.

     

On quasi-solution to infeasible linear complementarity problem obtained by Lemke’s method

For a linear complementarity problem with inconsistent system of constraints a notion of quasi-solution of Tschebyshev type is introduced. It’s shown that this solution can be obtained automatically by Lemke’s method if the constraint matrix of the original problem is copositive plus or belongs to the intersection of matrix classes P ₀ and Q ₀.     

On the advantage over a random assignment

We initiate the study of a new measure of approximation. This measure compares the performance of an approximation algorithm to the random assignment algorithm. This is a useful measure for optimization problems where the random assignment algorithm is known to give essentially the best possible polynomial time approximation. In this paper, we focus on this measure for the optimization problems Max‐Lin‐2 in which we need to maximize the number of satisfied linear equations in a system of linear equations modulo 2, and Max‐k‐Lin‐2, a special case of the above problem in which each equation has at most k variables. The main techniques we use, in our approximation algorithms and inapproximability results for this measure, are from Fourier analysis and derandomization. © 2004 Wiley Periodicals, Inc. Random Struct. Alg., 2004     

一般线性模型下方差最小范数二次无偏估计的稳健性

本文给出了一般线性模型下,由最小二乘得到的方差估计与最小范数二次无偏估计相等的充分必要条件,并且当Gauss-Markov估计与最小二乘估计相等时,可以得到一个简单的等价条件。     

On the role of the interface charge in non-ideal metal–semiconductor contacts

The bias dependent interface charge is considered as the origin of the observed non-ideality in current–voltage and capacitance–voltage characteristics. Using the simplified model for the interface electronic structure based on defects interacting with the continuum of interface states, the microscopic origin of empirical parameters describing the bias dependent interface charge function is investigated. The results show that in non-ideal metal–semiconductor contacts the interface charge function depends on the interface disorder parameter, density of defects, barrier pinning parameter and the effective gap center. The theoretical predictions are tested against several sets of published experimental data on bias dependent ideality factor and excess capacitance in various metal–semicoductor systems.     

广义线性模型(六)

本讲座是广义线性模型这个题目的一个比较系统的介绍。主要分 3部分 :建模、统计分析与模型选择和诊断。写作时依据的主要参考资料是L .Fahrmeir等人的 :《MultivariateStatisticalModel ingBasedonGeneralizedLinearModles》。