The location of median paths on grid graphs

In this paper we consider the location of a path shaped facility on a grid graph. In the literature this problem was extensively studied on particular classes of graphs as trees or series-parallel graphs. We consider here the problem of finding a path which minimizes the sum of the (shortest) distances from it to the other vertices of the grid, where the path is also subject to an additional constraint that takes the form either of the length of the path or of the cardinality. We study the complexity of these problems and we find two polynomial time algorithms for two special cases, with time complexity of O(n) and O(nℓ) respectively, where n is the number of vertices of the grid and ℓ is the cardinality of the path to be located. The literature about locating dimensional facilities distinguishes between the location of extensive facilities in continuous spaces and network facility location. We will show that the problems presented here have a close connection with continuous dimensional facility problems, so that the procedures provided can also be useful for solving some open problems of dimensional facilities location in the continuous case.     

The Asymptotic Behaviour of the Fourier Transforms of Orthogonal Polynomials I: Mellin Transform Techniques

The Fourier transform of orthogonal polynomials with respect to their own orthogonality measure defines the family of Fourier–Bessel functions. We study the asymptotic behaviour of these functions and of their products, for large real values of the argument. By employing a Mellin analysis we construct a general framework to exhibit the relation of the asymptotic decay laws to certain dimensions of the orthogonality measure, that are defined via the divergence abscissas of suitable integrals. The unifying r?le of Mellin transform techniques in deriving classical and new results is underlined. Submitted: November 5, 2004. Accepted: January 6, 2006.     

Learning and transfer in dynamic decision environments

An important aspect of learning is the ability to transfer knowledge to new contexts. However, in dynamic decision tasks, such as bargaining, firefighting, and process control, where decision makers must make repeated decisions under time pressure and outcome feedback may relate to any of a number of decisions, such transfer has proven elusive. This paper proposes a two-stage connectionist model which hypothesizes that decision makers learn to identify categories of evidence requiring similar decisions as they perform in dynamic environments. The model suggests conditions under which decision makers will be able to use this ability to help them in novel situations. These predictions are compared against those of a one-stage decision model that does not learn evidence categories, as is common in many current theories of repeated decision making. Both models' predictions are then tested against the performance of decision makers in an Internet bargaining task. Both models correctly predict aspects of decision makers' learning under different interventions. The two-stage model provides closer fits to decision maker performance in a new, related bargaining task and accounts for important features of higher-performing decision makers' learning. Although frequently omitted in recent accounts of repeated decision making, the processes of evidence category formation described by the two-stage model appear critical in understanding the extent to which decision makers learn from feedback in dynamic tasks. Faison (Bud) Gibson is an Assistant Professor at College of Business, Eastern Michigan University. He has extensive experience developing and empirically testing models of decision behavior in dynamic decision environments.     

Necessary conditions and duality for inexact nonlinear semi-infinite programming problems

First order necessary conditions and duality results for general inexact nonlinear programming problems formulated in nonreflexive spaces are obtained. The Dubovitskii–Milyutin approach is the main tool used. Particular cases of linear and convex programs are also analyzed and some comments about a comparison of the obtained results with those existing in the literature are given.     

Timetabling County Cricket Fixtures Using a Form of Tabu Search

This paper concerns a computer system which has been devised to timetable the county cricket matches in England. The context of the work is discussed and the many constraints and objectives described. Details of the solution method are given; it involves tabu search with a form of diversification dependent on the solution subcosts as well as the overall cost. Experiments are described which suggest that this type of diversification may have wide applicability to large, complex, multi-objective combinatorial problems.     

The Nature of Community OR

This paper outlines the results of a study undertaken to investigate the nature of Community Operational Research (COR). The objective was to contact the people involved in COR through a series of personal interviews and a questionnaire survey, in order to clarify many of the issues that have emerged within the profession relating to the practice of OR within the community and voluntary sector. A total of 20 individuals were successfully contacted, and they have been responsible for at least two-thirds of the projects in the COR area.     

Analysis of nitrite and nitrate as 1-nitro-2,4,6-trimethoxybenzene derivatives by reversed-phase HPLC with UV-detection

Summary A reversed-phase HPLC method for the determination of nitrite and nitrate in aqueous solutions, biological buffers and human urine is described. The method is based on the conversion of nitrite and nitrate into their 1-nitro-2,4,6-trimethoxybenzene (NTBM) derivatives by using 1,3,5-trimethoxybenzene and concentrated sulphuric acid. NTMB is extracted by benzene, the solvent evaporated, the residue reconstructed in methanol/water (3/4, v/v) and subsequently analyzed by reversed-phase HPLC and UV detection (360 nm). The specificity of the nitration reaction, good reproducibility (C.V. 6.2%) and high sensitivity (8.4 ng nitrite) show the applicability of this method to the quantitative analysis of nitrite and nitrate in several matrices including human urine.     

Positivity of Lyapunov Exponents for a Continuous Matrix-Valued Anderson Model

We study a continuous matrix-valued Anderson-type model. Both leading Lyapunov exponents of this model are proved to be positive and distinct for all energies in (2, +∞) except those in a discrete set, which leads to absence of absolutely continuous spectrum in (2, +∞). This result is an improvement of a previous result with Stolz. The methods, based upon a result by Breuillard and Gelander on dense subgroups in semisimple Lie groups, and a criterion by Goldsheid and Margulis, allow for singular Bernoulli distributions.      

Composition of the Canadian Total Force: Issues and Findings for the Air Components

In 1987 the Canadian Department of National Defence enunciated the Total Force concept. The Total Force is comprised of Regular and Reserve components. The intention is to make maximum use of the Reserve to reduce defence expenditures and at the same time to ensure that military capability remains adequate to support national policy objectives. This paper discusses some of the governing parameters that affect the modelling of the composition of the Total Force and analyses the mix of regular and reserve forces. The interplay between the key factors and their marginal costs will be stressed. The models are employed to study two units in the Canadian Forces, a maintenance support unit and a tactical unit with high operational activity cost. The lessons drawn from these studies are highlighted.