A multiple window scan statistic for time series models

In this article we extend the results derived for scan statistics in Wang and Glaz (2014) for independent normal observations. We investigate the performance of two approximations for the distribution of fixed window scan statistics for time series models. An R algorithm for computing multivariate normal probabilities established in Genz and Bretz (2009) can be used along with proposed approximations to implement fixed window scan statistics for ARMA models. The accuracy of these approximations is investigated via simulation. Moreover, a multiple window scan statistic is defined for detecting a local change in the mean of a Gaussian white noise component in ARMA models, when the appropriate length of the scanning window is unknown. Based on the numerical results, for power comparisons of the scan statistics, we can conclude that when the window size of a local change is unknown, the multiple window scan statistic outperforms the fixed window scan statistics.     

ON THE INVERTIBILITY OF HILBERT SPACE IDEMPOTENTS

This note is to present some results on the group invertibility of linear combina- tions of idempotents when the difference of two idempotents is group invertible.     

An iterative approach to solve multiobjective linear fractional programming problems

This paper suggests an iterative parametric approach for solving multiobjective linear fractional programming (MOLFP) problems which only uses linear programming to obtain efficient solutions and always converges to an efficient solution. A numerical example shows that this approach performs better than some existing algorithms. Randomly generated MOLFP problems are also solved to demonstrate the performance of new introduced algorithm.     

Solving a bi-objective Transportation Location Routing Problem by metaheuristic algorithms

In this work we consider a Transportation Location Routing Problem (TLRP) that can be seen as an extension of the two stage Location Routing Problem, in which the first stage corresponds to a transportation problem with truck capacity. Two objectives are considered in this research, reduction of distribution cost and balance of workloads for drivers in the routing stage. Here, we present a mathematical formulation for the bi-objective TLRP and propose a new representation for the TLRP based on priorities. This representation lets us manage the problem easily and reduces the computational effort, plus, it is suitable to be used with both local search based and evolutionary approaches. In order to demonstrate its efficiency, it was implemented in two metaheuristic solution algorithms based on the Scatter Tabu Search Procedure for Non-Linear Multiobjective Optimization (SSPMO) and on the Non-dominated Sorting Genetic Algorithm II (NSGA-II) strategies. Computational experiments showed efficient results in solution quality and computing time.     

Flexible capacity strategy with multiple market periods under demand uncertainty and investment constraint

We establish a flexible capacity strategy model with multiple market periods under demand uncertainty and investment constraints. In the model, a firm makes its capacity decision under a financial budget constraint at the beginning of the planning horizon which embraces n market periods. In each market period, the firm goes through three decision-making stages: the safety production stage, the additional production stage and the optimal sales stage. We formulate the problem and obtain the optimal capacity, the optimal safety production, the optimal additional production and the optimal sales of each market period under different situations. We find that there are two thresholds for the unit capacity cost. When the capacity cost is very low, the optimal capacity is determined by its financial budget; when the capacity cost is very high, the firm keeps its optimal capacity at its safety production level; and when the cost is in between of the two thresholds, the optimal capacity is determined by the capacity cost, the number of market periods and the unit cost of additional production. Further, we explore the endogenous safety production level. We verify the conditions under which the firm has different optimal safety production levels. Finally, we prove that the firm can benefit from the investment only when the designed planning horizon is longer than a threshold. Moreover, we also derive the formulae for the above three thresholds.     

A synergy of multicriteria techniques to assess additive value models

The assessment of additive value functions in Multicriteria Decision Aid (MCDA) has to face issues of legitimacy and technical difficulties when real decision makers are involved. This paper presents a synergy of three complementary techniques to assess additive models on the whole criteria space. The synergy includes a revised MACBETH technique, the standard MAUT trade-off analysis and UTA-based methods for the assessment of both the marginal value functions and the weighting factors. The paper uses a set of original robustness measures and rules associated with revised MACBETH and UTA in order to manage multiple linear programming solutions and to extract robust conclusions from them. Finally, to illustrate the methods’ synergy, an application example is presented, dealing with the planning of metro extension lines.     

Convergence of densities of some functionals of Gaussian processes

The aim of this paper is to establish the uniform convergence of the densities of a sequence of random variables, which are functionals of an underlying Gaussian process, to a normal density. Precise estimates for the uniform distance are derived by using the techniques of Malliavin calculus, combined with Stein?s method for normal approximation. We need to assume some non-degeneracy conditions. First, the study is focused on random variables in a fixed Wiener chaos, and later, the results are extended to the uniform convergence of the derivatives of the densities and to the case of random vectors in some fixed chaos, which are uniformly non-degenerate in the sense of Malliavin calculus. Explicit upper bounds for the uniform norm are obtained for random variables in the second Wiener chaos, and an application to the convergence of densities of the least square estimator for the drift parameter in Ornstein–Uhlenbeck processes is discussed.     

电介质椭球内极化场强方向的研究

导出了椭球体内极化场强方向与外电场方向之间夹角大小的表达式,并对其进行了数值计算,分析认为对于椭球体而言,其体内的极化场强方向并不一定严格和外电场方向相反。     

Rb87基态超精细塞曼能级跃迁的偏振激发特性

本论述了Rb^87基态超精细塞曼能级光泵磁共振的偏振激发特性,给出了塞曼能级跃迁谱线随抽运光偏振特性的变化。