Spectral theory of some non-selfadjoint linear differential operators

We give a characterisation of the spectral properties of linear differential operators with constant coefficients, acting on functions defined on a bounded interval, and determined by general linear boundary conditions. The boundary conditions may be such that the resulting operator is not selfadjoint. We associate the spectral properties of such an operator $S$ with the properties of the solution of a corresponding boundary value problem for the partial differential equation $\partial_t q \pm iSq=0$. Namely, we are able to establish an explicit correspondence between the properties of the family of eigenfunctions of the operator, and in particular whether this family is a basis, and the existence and properties of the unique solution of the associated boundary value problem. When such a unique solution exists, we consider its representation as a complex contour integral that is obtained using a transform method recently proposed by Fokas and one of the authors. The analyticity properties of the integrand in this representation are crucial for studying the spectral theory of the associated operator.

The economic theory of international business: a supply chain perspective

This paper proposes a way of addressing unresolved issues in international business theory by modelling the multinational enterprise as a coordinator of supply chains. It identifies a new market seeking strategy that is an alternative to conventional strategies such as exporting, licensing and FDI, and analyses the conditions under which it will be adopted by firms. The new strategy involves the off-shoring of production and the out-sourcing of R&D, and is implemented through co-operation between a source country firm and a host country firm.

The economic theory of international supply chains: a systems view

This paper offers an integrated analysis of out-sourcing, off-shoring and foreign direct investment within a systems view of international business. This view takes the supply chain rather than the firm as the basic unit of analysis. It argues that competition in the global economy selects supply chains that maximise the joint profit of all the firms in the chain. The systems view is compared with the firm-centred view commonly used in strategy literature. The paper shows that a firm’s strategy must be embedded within an efficient supply chain strategy, and that this strategy must be negotiated with, rather than imposed upon, other firms. The paper analyses the conditions under which various supply chain strategies - and by implication various firm-level strategies - are efficient. Only by adopting a systems view of supply chains is it possible to determine which firm-level strategies will succeed in a volatile global economy.

Application of the Lighthill-Ford theory of spontaneous imbalance to clear-air turbulence forecasting

A new method of clear-air turbulence (CAT) forecasting based on the Lighthill–Ford theory of spontaneous imbalance and emission of inertia–gravity waves has been derived and applied on episodic and seasonal time scales. A scale analysis of this shallow-water theory for midlatitude synoptic-scale flows identifies advection of relative vorticity as the leading-order source term. Examination of leading- and second-order terms elucidates previous, more empirically inspired CAT forecast diagnostics. Application of the Lighthill–Ford theory to the Upper Mississippi and Ohio Valleys CAT outbreak of 9 March 2006 results in good agreement with pilot reports of turbulence. Application of Lighthill–Ford theory to CAT forecasting for the 3 November 2005–26 March 2006 period using 1-h forecasts of the Rapid Update Cycle (RUC) 2 1500 UTC model run leads to superior forecasts compared to the current operational version of the Graphical Turbulence Guidance (GTG1) algorithm, the most skillful operational CAT forecasting method in existence. The results suggest that major improvements in CAT forecasting could result if the methods presented herein become operational.

Electronic structure of point defects in controlled self-doping of the TiO2 (110) surface: Combined photoemission spectroscopy and density functional theory study

Point defects in metal oxides such as TiO2 are key to their applications in numerous technologies. The investigation of thermally induced nonstoichiometry in TiO2 is complicated by the difficulties in preparing and determining a desired degree of nonstoichiometry. We study controlled self-doping of TiO2 by adsorption of 1/8 and 1/16 monolayer Ti at the (110) surface using a combination of experimental and computational approaches to unravel the details of the adsorption process and the oxidation state of Ti. Upon adsorption of Ti, x-ray and ultraviolet photoemission spectroscopy (XPS and UPS) show formation of reduced Ti. Comparison of pure density functional theory (DFT) with experiment shows that pure DFT provides an inconsistent description of the electronic structure. To surmount this difficulty, we apply DFT corrected for on-site Coulomb interaction (DFT+U) to describe reduced Ti ions. The optimal value of U is 3 eV, determined from comparison of the computed Ti 3d electronic density of states with the UPS data. DFT+U and UPS show the appearance of a Ti 3d adsorbate-induced state at 1.3 eV above the valence band and 1.0 eV below the conduction band. The computations show that the adsorbed Ti atom is oxidized to Ti2+ and a fivefold coordinated surface Ti atom is reduced to Ti3+, while the remaining electron is distributed among other surface Ti atoms. The UPS data are best fitted with reduced Ti2+ and Ti3+ ions. These results demonstrate that the complexity of doped metal oxides is best understood with a combination of experiment and appropriate computations.

A groove-ploughing theory for the production of mega-scale glacial lineations, and implications for ice-stream mechanics

Mega-scale glacial lineations (MSGLs) are longitudinally aligned corrugations (ridge-groove structures 6-100 km long) in sediment produced subglacially. They are indicators of fast flow and a common signature of ice-stream beds. We develop a qualitative theory that accounts for their formation, and use numerical modelling, and observations of ice-stream beds to provide supporting evidence. Ice in contact with a rough (scale of 10-10(3) m) bedrock surface will mimic the form of the bed. Because of flow acceleration and convergence in ice-stream onset zones, the ice-base roughness elements experience transverse strain, transforming them from irregular bumps into longitudinally aligned keels of ice protruding downwards. Where such keels slide across a soft sedimentary bed, they plough through the sediments, carving elongate grooves, and deforming material up into intervening ridges. This explains MSGLs and has important implications for ice-stream mechanics. Groove ploughing provides the means to acquire new lubricating sediment and to transport large volumes of it downstream. Keels may provide basal drag in the force budget of ice streams, thereby playing a role in flow regulation and stability We speculate that groove ploughing permits significant ice-stream widening, thus facilitating high-magnitude ice discharge.

Contemporary organizational theory in the management of construction projects

The level of insolvencies in the construction industry is high, when compared to other industry sectors. Given the management expertise and experience that is available to the construction industry, it seems strange that, according to the literature, the major causes of failure are lack of financial control and poor management. This indicates that with a good cash flow management, companies could be kept operating and financially healthy. It is possible to prevent failure. Although there are financial models that can be used to predict failure, they are based on company accounts, which have been shown to be an unreliable source of data. There are models available for cash flow management and forecasting and these could be used as a starting point for managers in rethinking their cash flow management practices. The research reported here has reached the stage of formulating researchable questions for an in-depth study including issues such as how contractors manage their cash flow, how payment practices can be managed without damaging others in the supply chain and the relationships between companies" financial structures and the payment regimes to which they are subjected.

Reconciling internalization theory and the eclectic paradigm

The eclectic paradigm of Dunning (1980) (with its OLI and four motives for FDI framework) can be reconciled with the firm and country matrix of Rugman (1981). However, the fit is not perfect. The main reason for misalignment is that Dunning is focused upon outward FDI into host economies, whereas Rugman’s matrix is for firm-level strategy covering MNE activity in both home and host countries.