Fast reconstruction of harmonic functions from Cauchy data using the Dirichlet-to-Neumann map and integral equations

We propose and investigate a method for the stable determination of a harmonic function from knowledge of its value and its normal derivative on a part of the boundary of the (bounded) solution domain (Cauchy problem). We reformulate the Cauchy problem as an operator equation on the boundary using the Dirichlet-to-Neumann map. To discretize the obtained operator, we modify and employ a method denoted as Classic II given in [J. Helsing, Faster convergence and higher accuracy for the Dirichlet–Neumann map, J. Comput. Phys. 228 (2009), pp. 2578–2576, Section 3], which is based on Fredholm integral equations and Nyström discretization schemes. Then, for stability reasons, to solve the discretized integral equation we use the method of smoothing projection introduced in [J. Helsing and B.T. Johansson, Fast reconstruction of harmonic functions from Cauchy data using integral equation techniques, Inverse Probl. Sci. Eng. 18 (2010), pp. 381–399, Section 7], which makes it possible to solve the discretized operator equation in a stable way with minor computational cost and high accuracy. With this approach, for sufficiently smooth Cauchy data, the normal derivative can also be accurately computed on the part of the boundary where no data is initially given.

Understanding high-value manufacturing in Scottish SMEs

Purpose: The purpose of this paper is to investigate the use of high-value manufacturing (HVM) concepts in Scottish SMEs and define how they are being used to gain competitive advantage. Design/methodology/approach: Cross-sectional research carried out using a large-scale survey of 435 SMEs and semi-structured interviews of a subset of 50 SMEs. Findings: Findings indicate that HVM is not a homogeneous state but an umbrella term for a number of operational models adopted by manufacturers that are progressively moving from simple price-based production; companies must, as a foundation, be operationally excellent in all lifecycle phases before extending their capability by offering a more comprehensive service; HVM is not a static state but a journey that differs in nature for each manufacturer depending on the nature of its market and customer. Research limitations/implications: The approach to theory must be more integrated combining aspects of marketing, strategic and operational theory. Research must be carried out using the supply chain, rather than the firm, as the unit of analysis. Practical implications: Manufacturing efficiency has now become an order qualifier and competitive advantage should now be sought through the integration of design, production and service activities from strategic levels down to operational levels across all the functions of a business which link seamlessly to customer and supplier activities. Originality/value: This paper contains insights into Scottish SMEs and their practice of HVM; defines the activity that makes up HVM at an operational as opposed to an economic or strategic level; proposes a model that characterises the stages of HVM that SMEs transition through. © Emerald Group Publishing Limited.

To what extent and in what manner do Chinese and Indian contract research organisation learn and upgrade with the unbundling the global pharmaceutical R&D value chain?

The paper applies the GVC framework to analyse the organisational and geographical reconfiguration of the global R&D function of leading US and European pharmaceutical MNCs. Though pharmaceutical MNCs have been outsourcing clinical trial activities since the mid-1990s, the outsourcing of discovery research tasks is a phenomenon of the 2000s (Ramirez 2013). Moreover, in the context of a crisis of R&D productivity and increasing pressure from shareholders, a number of US and European pharmaceutical MNCs are breaking up their R&D function in an attempt to increase flexibility and reduce risk as well as costs and are thereby restructuring the global architecture of their R&D function. This break-up, or unbundling (Sako 2006), of the R&D function is particularly interesting given the prevalence of market failure in innovation (Howells et al 2008), the non-modular nature of the R&D process in this industry (Pisano 2006) and the strategic important of this activity to the core competence and long-term competitive advantage of firms in this sector. The focus of this paper is on the outsourcing of R&D activities to Chinese and Indian independently-owned contract research organisations (CROs) and the way these firms are becoming integrated as service providers into the global R&D function (or R&D value chain) of pharmaceutical MNCs. Above all the paper is concerned with the development of capabilities of CROs from these two countries and the dynamics of upgrading in GVCs in knowledge-intensive functions. The paper therefore discusses the role of both knowledge flows within global pharmaceutical R&D value chains as well as national innovation systems on the development of capabilities of Chinese and Indian CROs. Our analysis is based on data from semi-structured interviews collected from senior R&D managers from a sample of ten US and European pharmaceutical MNCs and owners and senior R&D managers from five Chinese and five Indian CROs who are providing research services to MNCs in this industry. We discuss the emergence of R&D outsourcing in this industry and the nature and mechanisms of knowledge flows within R&D value chains. The embeddedness of CROS in the national innovation systems of their home countries is also discussed.

Numerical solution of the Dirichlet initial boundary value problem for the heat equation in exterior 3-dimensional domains using integral equations

A numerical method for the Dirichlet initial boundary value problem for the heat equation in the exterior and unbounded region of a smooth closed simply connected 3-dimensional domain is proposed and investigated. This method is based on a combination of a Laguerre transformation with respect to the time variable and an integral equation approach in the spatial variables. Using the Laguerre transformation in time reduces the parabolic problem to a sequence of stationary elliptic problems which are solved by a boundary layer approach giving a sequence of boundary integral equations of the first kind to solve. Under the assumption that the boundary surface of the solution domain has a one-to-one mapping onto the unit sphere, these integral equations are transformed and rewritten over this sphere. The numerical discretisation and solution are obtained by a discrete projection method involving spherical harmonic functions. Numerical results are included.