Curve selection Lemma for semianalytic sets and conjugacy classes of finite order in Lie groups

Using a strong version of the Curve Selection Lemma for real semianalytic sets, we prove that for an arbitrary connected Lie group G, each connected component of the set E_n(G)of all elements of order n in G is a conjugacy class in G. In particular, all conjugacy classes of finite order in G are closed. Some properties of connected components of E_n(G) are also given.     

On maximizing the profit of a satellite launcher: Selecting and scheduling tasks with time windows and setups

At regular times, a satellite launcher company has to plan the use of its launcher to get the maximum profit. In a more formal way, the problem consists of selecting and scheduling a subset of unit-length jobs constrained by capacitated time slots so that the overall cost is a minimum. The data associated with each job are its weight, its time-window and its expected gain when it is performed. With each time slot are associated a setup cost and a capacity. The setup cost of a time slot is due when this time-slot is used to perform at least one job. Moreover the total weight of all jobs scheduled within a time slot is at most the time slot capacity. We first show that the general problem is hard and provide some easy special cases. We then propose a first dynamic-programming polynomial-time algorithm for the special case with unit weights. A second and more efficient dynamic programming algorithm is also provided for the special case of unit weights and agreeable time windows. This last algorithm is finally improved for the special case of equal gains.     

Unified Noncrossing Multiple Quantile Regressions Tree

In this article, we consider the estimation problem of a tree model for multiple conditional quantile functions of the response. Using the generalized, unbiased interaction detection and estimation algorithm, the quantile regression tree (QRT) method has been developed to construct a tree model for an individual quantile function. However, QRT produces different tree models across quantile levels because it estimates several QRT models separately. Furthermore, the estimated quantile functions from QRT often cross each other and consequently violate the basic properties of quantiles. This undesirable phenomenon reduces prediction accuracy and makes it difficult to interpret the resulting tree models. To overcome such limitations, we propose the unified noncrossing multiple quantile regressions tree (UNQRT) method, which constructs a common tree structure across all interesting quantile levels for better data visualization and model interpretation. Furthermore, the UNQRT estimates noncrossing multiple quantile functions simultaneously by enforcing noncrossing constraints, resulting in the improvement of prediction accuracy. The numerical results are presented to demonstrate the competitive performance of the proposed UNQRT over QRT. Supplementary materials for this article are available online.     

Functionally graded materials for impedance matching in elastic media

When functionally graded material layers are inserted between two impedance mismatching media, passbands with extremely large bandwidths can appear in these layered systems. An accurate and effective iterative method is developed to deal with these layered systems with extremely large layer number.     

分式规划模糊投资组合模型的遗传算法求解

将预期收益率表示为模糊数,以E-SV风险测度为基础给出了组合证券投资决策的效用函数,并建立了基于分式规划的模糊投资组合选择模型,考虑到模型求解的复杂性,我们利用遗传算法构造罚函数对模型进行了求解,并通过实例,验证了该模型解法的可行性和有效性.     

Exploring greedy criteria for the dynamic traveling purchaser problem

Given a set of products and a set of markets, the traveling purchaser problem looks for a tour visiting a subset of the markets to satisfy products demand at the minimum purchasing and traveling costs. In this paper, we analyze the dynamic variant of the problem (D-TPP) where the quantity made available in each market for each product may decrease over time. We introduce and compare several greedy strategies and test their impact on the solution in terms of feasibility and costs. In particular, we study an incremental approach where an initial naive strategy is improved and refined by a number of variants. Some of the proposed heuristics take into account either one of the two objective costs, while others are based on both traveling and purchasing costs. Extensive computational results are also provided on randomly generated instances.     

Maps of several variables of finite total variation. II. E. Helly-type pointwise selection principles

Given a=(a₁,…,an), b=(b₁,…,bn)∈Rn with a<b componentwise and a map f from the rectangle into a metric semigroup M=(M,d,+), denote by the Hildebrandt-Leonov total variation of f on , which has been recently studied in [V.V. Chistyakov, Yu.V. Tretyachenko, Maps of several variables of finite total variation. I, J. Math. Anal. Appl. (2010), submitted for publication]. The following Helly-type pointwise selection principle is proved: If a sequence{fj}_j∈Nof maps frominto M is such that the closure in M of the set{fj(x)}_j∈Nis compact for eachandis finite, then there exists a subsequence of{fj}_j∈N, which converges pointwise onto a map f such that. A variant of this result is established concerning the weak pointwise convergence when values of maps lie in a reflexive Banach space (M,‖⋅‖) with separable dual M^∗.     

Addendum to “Variations of selective separability” [Topology Appl. 156 (7) (2009) 1241-1252]

Two proofs omitted in the paper mentioned in the title are presented.     

An evolutionary approach for bandwidth multicoloring problems

In this paper we consider some generalizations of the vertex coloring problem, where distance constraints are imposed between adjacent vertices (bandwidth coloring problem) and each vertex has to be colored with more than one color (bandwidth multicoloring problem). We propose an evolutionary metaheuristic approach for the first problem, combining an effective tabu search algorithm with population management procedures. The approach can be applied to the second problem as well, after a simple transformation. Computational results on instances from the literature show that the overall algorithm is able to produce high quality solutions in a reasonable amount of time, outperforming the most effective algorithms proposed for the bandwidth coloring problem, and improving the best known solution of many instances of the bandwidth multicoloring problem.     

An improved simulated annealing algorithm for bandwidth minimization

In this paper, a simulated annealing algorithm is presented for the bandwidth minimization problem for graphs. This algorithm is based on three distinguished features including an original internal representation of solutions, a highly discriminating evaluation function and an effective neighborhood. The algorithm is evaluated on a set of 113 well-known benchmark instances of the literature and compared with several state-of-the-art algorithms, showing improvements of some previous best results.