Boundary integral equations for acoustical inverse sound-soft scattering

The shape of a plane acoustical sound-soft obstacle is detected from knowledge of the far field pattern for one time-harmonic incident field. Two methods based on solving a system of integral equations for the incoming wave and the far field pattern are investigated. Properties of the integral operators required in order to apply regularization, i.e. injectivity and denseness of the range, are proved.

On Finite Element Methods for 2nd order (semi–) periodic Eigenvalue Problems

We deal with a class of elliptic eigenvalue problems (EVPs) on a rectangle Ω ⊂ R^2 , with periodic or semi–periodic boundary conditions (BCs) on ∂Ω. First, for both types of EVPs, we pass to a proper variational formulation which is shown to fit into the general framework of abstract EVPs for symmetric, bounded, strongly coercive bilinear forms in Hilbert spaces, see, e.g., [13, §6.2]. Next, we consider finite element methods (FEMs) without and with numerical quadrature. The aim of the paper is to show that well–known error estimates, established for the finite element approximation of elliptic EVPs with classical BCs, hold for the present types of EVPs too. Some attention is also paid to the computational aspects of the resulting algebraic EVP. Finally, the analysis is illustrated by two non-trivial numerical examples, the exact eigenpairs of which can be determined.

Numerical solution of parabolic Cauchy problems in planar corner domains

An iterative method for the parabolic Cauchy problem in planar domains having a finite number of corners is implemented based on boundary integral equations. At each iteration, mixed well-posed problems are solved for the same parabolic operator. The presence of corner points renders singularities of the solutions to these mixed problems, and this is handled with the use of weight functions together with, in the numerical implementation, mesh grading near the corners. The mixed problems are reformulated in terms of boundary integrals obtained via discretization of the time-derivative to obtain an elliptic system of partial differential equations. To numerically solve these integral equations a Nyström method with super-algebraic convergence order is employed. Numerical results are presented showing the feasibility of the proposed approach. © 2014 IMACS.

On a Singular Value Problem for the Fractional Laplacian on the Exterior of the Unit Ball

2000 Mathematics Subject Classification: Primary 26A33; Secondary 47G20, 31B05

Recent research trend of economic-lot scheduling problems

Purpose - This research note aims to present a summary of research concerning economic-lot scheduling problem (ELSP). Design/methodology/approach - The paper's approach is to review over 100 selected studies published in the last 15 years (1997-2012), which are then grouped under different research themes. Findings - Five research themes are identified and insights for future studies are reported at the end of this paper. Research limitations/implications - The motivation of preparing this research note is to summarize key research studies in this field since 1997, when the ELSP problems have been verified as NP-hard. Originality/value - ELSP is an important scheduling problem that has been studied since the 1950s. Because of its complexity in delivering a feasible analytical closed form solution, many studies in the last two decades employed heuristic algorithms in order to come up with good and acceptable solutions. As a consequence, the solution approaches are quite diversified. The major contribution of this paper is to provide researchers who are interested in this area with a quick reference guide on the reviewed studies. © Emerald Group Publishing Limited.

A fuzzy expected value approach under generalized data envelopment analysis

Fuzzy data envelopment analysis (DEA) models emerge as another class of DEA models to account for imprecise inputs and outputs for decision making units (DMUs). Although several approaches for solving fuzzy DEA models have been developed, there are some drawbacks, ranging from the inability to provide satisfactory discrimination power to simplistic numerical examples that handles only triangular fuzzy numbers or symmetrical fuzzy numbers. To address these drawbacks, this paper proposes using the concept of expected value in generalized DEA (GDEA) model. This allows the unification of three models - fuzzy expected CCR, fuzzy expected BCC, and fuzzy expected FDH models - and the ability of these models to handle both symmetrical and asymmetrical fuzzy numbers. We also explored the role of fuzzy GDEA model as a ranking method and compared it to existing super-efficiency evaluation models. Our proposed model is always feasible, while infeasibility problems remain in certain cases under existing super-efficiency models. In order to illustrate the performance of the proposed method, it is first tested using two established numerical examples and compared with the results obtained from alternative methods. A third example on energy dependency among 23 European Union (EU) member countries is further used to validate and describe the efficacy of our approach under asymmetric fuzzy numbers.

The effects of material variations in high value manufacturing industries

It has never been easy for manufacturing companies to understand their confidence level in terms of how accurate and to what degree of flexibility parts can be made. This brings uncertainty in finding the most suitable manufacturing method as well as in controlling their product and process verification systems. The aim of this research is to develop a system for capturing the company’s knowledge and expertise and then reflect it into an MRP (Manufacturing Resource Planning) system. A key activity here is measuring manufacturing and machining capabilities to a reasonable confidence level. For this purpose an in-line control measurement system is introduced to the company. Using SPC (Statistical Process Control) not only helps to predict the trend in manufacturing of parts but also minimises the human error in measurement. Gauge R&R (Repeatability and Reproducibility) study identifies problems in measurement systems. Measurement is like any other process in terms of variability. Reducing this variation via an automated machine probing system helps to avoid defects in future products.Developments in aerospace, nuclear, oil and gas industries demand materials with high performance and high temperature resistance under corrosive and oxidising environments. Superalloys were developed in the latter half of the 20th century as high strength materials for such purposes. For the same characteristics superalloys are considered as difficult-to-cut alloys when it comes to formation and machining. Furthermore due to the sensitivity of superalloy applications, in many cases they should be manufactured with tight tolerances. In addition superalloys, specifically Nickel based, have unique features such as low thermal conductivity due to having a high amount of Nickel in their material composition. This causes a high surface temperature on the work-piece at the machining stage which leads to deformation in the final product.Like every process, the material variations have a significant impact on machining quality. The main cause of variations can originate from chemical composition and mechanical hardness. The non-uniform distribution of metal elements is a major source of variation in metallurgical structures. Different heat treatment standards are designed for processing the material to the desired hardness levels based on application. In order to take corrective actions, a study on the material aspects of superalloys has been conducted. In this study samples from different batches of material have been analysed. This involved material preparation for microscopy analysis, and the effect of chemical compositions on hardness (before and after heat treatment). Some of the results are discussed and presented in this paper.

Evaluating the Risk in Selection Problems

The procedure used should guarantee that the risk of decision asserted from the observations is at most some specified value P*.

Microlocal Approach to Tensor Tomography and Boundary and Lens Rigidity

2000 Mathematics Subject Classification: 53C24, 53C65, 53C21.

Exact Solutions of Nonlocal Pluriparabolic Problems

MSC 2010: 44A35, 44A40

A method of fundamental solutions for radially symmetric and axisymmetric backward heat conduction problems

We propose and investigate an application of the method of fundamental solutions (MFS) to the radially symmetric and axisymmetric backward heat conduction problem (BHCP) in a solid or hollow cylinder. In the BHCP, the initial temperature is to be determined from the temperature measurements at a later time. This is an inverse and ill-posed problem, and we employ and generalize the MFS regularization approach [B.T. Johansson and D. Lesnic, A method of fundamental solutions for transient heat conduction, Eng. Anal. Boundary Elements 32 (2008), pp. 697–703] for the time-dependent heat equation to obtain a stable and accurate numerical approximation with small computational cost.

Collaborating to achieve corporate social responsibility and sustainability? Possibilities and problems

Purpose: The purpose of this paper is to investigate the possibilities and problems for collaboration in the area of corporate social responsibility (CSR) and sustainability. The paper explores the nature and concept of collaboration and its forms, and critically evaluates the potential contribution a collaborative approach between agencies might offer to these agendas. Design/methodology/approach: The paper explores different forms of research on collaboration, together with a UK Government report on collaboration, to evaluate how the issue is addressed in theory and practice. Findings: Sustainable development creates extensive challenges for a wide range of agencies, including governments, non-governmental organizations, businesses and civil society. It is unlikely, however, that solutions will be found in any one quarter. Collaboration between agencies in some form would seem a logical step in supporting measures towards a more responsible and environmentally sustainable global economy. Originality/value: The paper offers new insights into developing a research and praxis agenda for collaborative possibilities towards the advancement of CSR and sustainability. © Emerald Group Publishing Limited.

The Shapley value for shortest path games

In this paper shortest path games are considered. The transportation of a good in a network has costs and benet too. The problem is to divide the prot of the transportation among the players. Fragnelli et al (2000) introduce the class of shortest path games, which coincides with the class of monotone games. They also give a characterization of the Shapley value on this class of games. In this paper we consider further four characterizations of the Shapley value (Shapley (1953)'s, Young (1985)'s, Chun (1989)'s, and van den Brink (2001)'s axiomatizations), and conclude that all the mentioned axiomatizations are valid for shortest path games. Fragnelli et al (2000)'s axioms are based on the graph behind the problem, in this paper we do not consider graph specic axioms, we take TU axioms only, that is, we consider all shortest path problems and we take the view of abstract decision maker who focuses rather on the abstract problem than on the concrete situations.

The Shapley value for airport and irrigation games

In this paper cost sharing problems are considered. We focus on problems given by rooted trees, we call these problems cost-tree problems, and on the induced transferable utility cooperative games, called irrigation games. A formal notion of irrigation games is introduced, and the characterization of the class of these games is provided. The well-known class of airport games Littlechild and Thompson (1977) is a subclass of irrigation games. The Shapley value Shapley (1953) is probably the most popular solution concept for transferable utility cooperative games. Dubey (1982) and Moulin and Shenker (1992) show respectively, that Shapley's Shapley (1953) and Young (1985)'s axiomatizations of the Shapley value are valid on the class of airport games. In this paper we show that Dubey (1982)'s and Moulin and Shenker (1992)'s results can be proved by applying Shapley (1953)'s and Young (1985)'s proofs, that is those results are direct consequences of Shapley (1953)'s and Young (1985)'s results. Furthermore, we extend Dubey (1982)'s and Moulin and Shenker (1992)'s results to the class of irrigation games, that is we provide two characterizations of the Shapley value for cost sharing problems given by rooted trees. We also note that for irrigation games the Shapley value is always stable, that is it is always in the core Gillies (1959).