A simple characterization of weighted Sobolev spaces with bounded multiplication operator

In this paper we give a simple characterization of weighted Sobolev spaces (with piecewise monotone weights) such that the multiplication operator is bounded: it is bounded if and only if the support of μ₀ is large enough. We also prove some basic properties of the appropriate weighted Sobolev spaces. To have bounded multiplication operator has important consequences in Approximation Theory: it implies the uniform bound of the zeros of the corresponding Sobolev orthogonal polynomials, and this fact allows to obtain the asymptotic behavior of Sobolev orthogonal polynomials.     

Efficient shift scheduling in the retail sector through two-stage optimization

Efficient workforce scheduling has an important impact on store profit and customer service. Standard scheduling problems do not recognize the effect of staff availability on customer sales, however, even though the latter is an important factor in the retail sector. In this paper a two-stage model is proposed for this purpose. In the first stage a sales response model is used to specify hourly staff requirements. The output of the sales response model is then used as the input of a mixed integer optimization model, which finds an optimum assignment of the staff to daily shifts. Simulations are used to validate the sales response function, and to revise the model for more accurate results. In the simulations, customer arrivals and sales response error values are generated using appropriate distribution functions. As a case study the proposed model is applied to a Turkish retailer in the apparel sector.     

Invariant manifolds and the stability of traveling waves in scalar viscous conservation laws

The stability of traveling wave solutions of scalar viscous conservation laws is investigated by decomposing perturbations into three components: two far-field components and one near-field component. The linear operators associated to the far-field components are the constant coefficient operators determined by the asymptotic spatial limits of the original operator. Scaling variables can be applied to study the evolution of these components, allowing for the construction of invariant manifolds and the determination of their temporal decay rate. The large time evolution of the near-field component is shown to be governed by that of the far-field components, thus giving it the same temporal decay rate. We also give a discussion of the relationship between this geometric approach and previous results, which demonstrate that the decay rate of perturbations can be increased by requiring that initial data lie in appropriate algebraically weighted spaces.     

Inversion of the Bessel potential operator in weighted variable Lebesgue spaces

We study the inversion problem of the Bessel potential operator within the frameworks of the weighted Lebesgue spaces with variable exponent. The inverse operator is constructed by using approximative inverse operators. This generalizes some classical results to the variable exponent setting.     

The scheduling of deliveries in a production-distribution system with multiple buyers

In a real production and distribution business environment with one supplier and multiple heterogeneous buyers, the differences in buyers’ ordering cycles have influence on production arrangements. Consequently, the average inventory level (AIL) at the supplier’s end is affected by both the production policy and the ordering policy, typically by the scheduling of deliveries. Consequently, the average inventory holding cost is most deeply affected. In this paper, it is proposed that the scheduling of deliveries be formulated as a decision problem to determine the time point at which deliveries are made to buyers in order to minimize the supplier’s average inventory. A formulation of the average inventory level (AIL) in a production cycle at the supplier’s end using a lot-for-lot policy is developed. Under the lot-for-lot policy, the scheduling of deliveries (SP) is formulated as a nonlinear programming model used to determine the first delivery point for each buyer with an objective to minimize the sum of the product of the individual demand quantity and the first delivery time for each buyer. Thus, the SP model determines not only the sequence of the first deliveries to individual buyers, but also the time when the deliveries are made. An iterative heuristic procedure (IHP) is developed to solve the SP model assuming a given sequence of buyers. Six sequence rules are considered and evaluated via simulation.     

计算机辅助管理在铁路供、配电调度中的运用

讨论了计算机辅助管理技术在铁路供、配电调度中的运用，并简述了在凯里供电段的铁路段供、配电调度管理系统，以及系统的建设目标、主要功能及其实现。     

不同权Bloch型空间之间的加权Cesàro 算子

该文讨论了$\a$-Bloch空间$\ba$和对数Bloch空间$\bl$之间的加权Ces\'aro算子$\tg$的有界性和紧性,给出$\tg$是$\ba$到$\bl$的有界算子或紧算子的充要条件和$\tg$是$\bl$到$\ba$的有界算子或紧算子的充要条件.     

On-line scheduling with non-crossing constraints

We consider the problem of on-line scheduling with non-crossing constraints. The objective is to minimize the latest completion time. We provide optimal competitive ratio heuristics for the on-line list and on-line time problems with unit processing times, and a 3-competitive heuristic for the general on-line time problem.     

Improved analysis of an algorithm for the coupled task problem with UET jobs

The coupled task problem is to schedule n jobs, each one consisting of two subtasks with exact delay times between them, on a single machine. We derive a new lower bound for the problem variant with unit execution times and correct a previously published analysis.     

Boundary value problems on weighted networks

We present here a systematic study of general boundary value problems on weighted networks that includes the variational formulation of such problems. In particular, we obtain the discrete version of the Dirichlet Principle and we apply it to the analysis of the inverse problem of identifying the conductivities of the network in a very general framework. Our approach is based on the development of an efficient vector calculus on weighted networks which mimetizes the calculus in the smooth case. The key tool is an adequate construction of the tangent space at each vertex. This allows us to consider discrete vector fields, inner products and general metrics. Then, we obtain discrete versions of derivative, gradient, divergence and Laplace-Beltrami operators, satisfying analogous properties to those verified by their continuous counterparts. On the other hand we develop the corresponding integral calculus that includes the discrete versions of the Integration by Parts technique and Green’s Identities. Finally, we apply our discrete vector calculus to analyze the consistency of difference schemes used to solve numerically a Robin boundary value problem in a square.