The counter-propagating Rossby-wave perspective on baroclinic instability. II: Application to the Charney model

The constant-density Charney model describes the simplest unstable basic state with a planetary-vorticity gradient, which is uniform and positive, and baroclinicity that is manifest as a negative contribution to the potential-vorticity (PV) gradient at the ground and positive vertical wind shear. Together, these ingredients satisfy the necessary conditions for baroclinic instability. In Part I it was shown how baroclinic growth on a general zonal basic state can be viewed as the interaction of pairs of ‘counter-propagating Rossby waves’ (CRWs) that can be constructed from a growing normal mode and its decaying complex conjugate. In this paper the normal-mode solutions for the Charney model are studied from the CRW perspective. Clear parallels can be drawn between the most unstable modes of the Charney model and the Eady model, in which the CRWs can be derived independently of the normal modes. However, the dispersion curves for the two models are very different; the Eady model has a short-wave cut-off, while the Charney model is unstable at short wavelengths. Beyond its maximum growth rate the Charney model has a neutral point at finite wavelength (r=1). Thereafter follows a succession of unstable branches, each with weaker growth than the last, separated by neutral points at integer r—the so-called ‘Green branches’. A separate branch of westward-propagating neutral modes also originates from each neutral point. By approximating the lower CRW as a Rossby edge wave and the upper CRW structure as a single PV peak with a spread proportional to the Rossby scale height, the main features of the ‘Charney branch’ (0

Innovative approach to building systems integration problems: Using systems theory, technological forecasting and scenario planning

Building services are worth about 2% GDP and are essential for the effective and efficient operations of the building. It is increasingly recognised that the value of a building is related to the way it supports the client organisation’s ongoing business operations. Building services are central to the functional performance of buildings and provide the necessary conditions for health, well-being, safety and security of the occupants. They frequently comprise several technologically distinct sub-systems and their design and construction requires the involvement of numerous disciplines and trades. Designers and contractors working on the same project are frequently employed by different companies. Materials and equipment is supplied by a diverse range of manufacturers. Facilities managers are responsible for operation of the building service in use. The coordination between these participants is crucially important to achieve optimum performance, but too often is neglected. This leaves room for serious faults. The need for effective integration is important. Modern technology offers increasing opportunities for integrated personal-control systems for lighting, ventilation and security as well as interoperability between systems. Opportunities for a new mode of systems integration are provided by the emergence of PFI/PPP procurements frameworks. This paper attempts to establish how systems integration can be achieved in the process of designing, constructing and operating building services. The essence of the paper therefore is to envisage the emergent organisational responses to the realisation of building services as an interactive systems network.

Planning rigid body motions using elastic curves

This paper tackles the problem of computing smooth, optimal trajectories on the Euclidean group of motions SE(3). The problem is formulated as an optimal control problem where the cost function to be minimized is equal to the integral of the classical curvature squared. This problem is analogous to the elastic problem from differential geometry and thus the resulting rigid body motions will trace elastic curves. An application of the Maximum Principle to this optimal control problem shifts the emphasis to the language of symplectic geometry and to the associated Hamiltonian formalism. This results in a system of first order differential equations that yield coordinate free necessary conditions for optimality for these curves. From these necessary conditions we identify an integrable case and these particular set of curves are solved analytically. These analytic solutions provide interpolating curves between an initial given position and orientation and a desired position and orientation that would be useful in motion planning for systems such as robotic manipulators and autonomous-oriented vehicles.

Optimal kinematic control of an autonomous underwater vehicle

This note investigates the motion control of an autonomous underwater vehicle (AUV). The AUV is modeled as a nonholonomic system as any lateral motion of a conventional, slender AUV is quickly damped out. The problem is formulated as an optimal kinematic control problem on the Euclidean Group of Motions SE(3), where the cost function to be minimized is equal to the integral of a quadratic function of the velocity components. An application of the Maximum Principle to this optimal control problem yields the appropriate Hamiltonian and the corresponding vector fields give the necessary conditions for optimality. For a special case of the cost function, the necessary conditions for optimality can be characterized more easily and we proceed to investigate its solutions. Finally, it is shown that a particular set of optimal motions trace helical paths. Throughout this note we highlight a particular case where the quadratic cost function is weighted in such a way that it equates to the Lagrangian (kinetic energy) of the AUV. For this case, the regular extremal curves are constrained to equate to the AUV's components of momentum and the resulting vector fields are the d'Alembert-Lagrange equations in Hamiltonian form.

Stakeholder-defined corporate responsibility for a pre-credit-crunch financial service company: lessons for how good reputations are won and lost

This paper presents a study that identifies a stakeholder-defined concept of Corporate Responsibility (CR) in the context of a UK financial service organisation in the immediate pre-credit crunch era. From qualitative analysis of interviews and focus groups with employees and customers, we identify, in a wide-ranging stakeholder-defined concept of CR, six themes that together imply two necessary conditions for a firm to be regarded as responsible— both corporate actions and character must be consonant with CR. This provides both empirical support for a notable, recent theoretical contribution by Godfrey (in Acad Manag Rev 30:777–798, 2005) and novel lessons for reputation management practice.

Real options and game theoretical approaches to real estate development projects: multiple equilibria and the implications of different tie-breaking rules

This paper contributes to a fast growing literature which introduces game theory in the analysis of real option investments in a competitive setting. Specifically, in this paper we focus on the issue of multiple equilibria and on the implications that different equilibrium selections may have for the pricing of real options and for subsequent strategic decisions. We present some theoretical results of the necessary conditions to have multiple equilibria and we show under which conditions different tie-breaking rules result in different economic decisions. We then present a numerical exercise using the in formation set obtained on a real estate development in South London. We find that risk aversion reduces option value and this reduction decreases marginally as negative externalities decrease.

Toeplitz operators on Bergman spaces with locally integrable symbols

We study the boundedness of Toeplitz operators $T_a$ with locally integrable symbols on Bergman spaces $A^p(\mathbb{D})$, $1 < p < \infty$. Our main result gives a sufficient condition for the boundedness of $T_a$ in terms of some ``averages'' (related to hyperbolic rectangles) of its symbol. If the averages satisfy an ${o}$-type condition on the boundary of $\mathbb{D}$, we show that the corresponding Toeplitz operator is compact on $A^p$. Both conditions coincide with the known necessary conditions in the case of nonnegative symbols and $p=2$. We also show that Toeplitz operators with symbols of vanishing mean oscillation are Fredholm on $A^p$ provided that the averages are bounded away from zero, and derive an index formula for these operators.

Admissible conjectures and consistent conjectures

Firms' conjectures are consistent if their ex post behavior rationalizes their ex ante beliefs. Admissible conjectures are those that satisfy the necessary conditions for consistency. Competition is inadmissible unless aggregate output is stationary. Relaxing this restriction, admissibility eliminates Cournot behavior and constrains conduct to be collusive

Application of the direct Liapunov method to the problem of symmetric stability in the atmosphere

The problem of symmetric stability is examined within the context of the direct Liapunov method. The sufficient conditions for stability derived by Fjørtoft are shown to imply finite-amplitude, normed stability. This finite-amplitude stability theorem is then used to obtain rigorous upper bounds on the saturation amplitude of disturbances to symmetrically unstable flows.By employing a virial functional, the necessary conditions for instability implied by the stability theorem are shown to be in fact sufficient for instability. The results of Ooyama are improved upon insofar as a tight two-sided (upper and lower) estimate is obtained of the growth rate of (modal or nonmodal) symmetric instabilities.The case of moist adiabatic systems is also considered.

Globalization and technology-mediated distance education: developing countries’ perspective

The contemporary global economy places great value on highly educated workers but devalues workers in repetitive or low skill jobs. In order to thrive in this new economy, countries must ensure sufficient higher education opportunities for their population. However, a lack of resources is a major barrier faced by many developing countries in expanding their higher education systems. Technology-mediated distance education has the potential to be an invaluable tool in offering educational opportunities to people, if the other necessary conditions for participation are met. Although technology-mediated education was first considered to be a medium to bridge the learning divide across space, today it is feared that it could well become an inequality intensifier. Drawing on examples from developing countries, this paper considers factors regarding implementing technology-mediated distance education, including failure to address contextual issues and possible consequences. Challenges and policy implications are also discussed.

An aggregate resource efficiency perspective on sustainability: a Sustainable Value application to the EU-15 countries

The Sustainable Value approach integrates the efficiency with regard to environmental, social and economic resources into a monetary indicator. It gained significant popularity as evidenced by diverse applications at the corporate level. However, its introduction as a measure adhering to the strong sustainability paradigm sparked an ardent debate. This study explores its validity as a macroeconomic strong sustainability measure by applying the Sustainable Value approach to the EU-15 countries. Concretely, we assessed environmental, social and economic resources in combination with the GDP for all EU-15 countries from 1995 to 2006 for three benchmark alternatives. The results show that several countries manage to adequately delink resource use from GDP growth. Furthermore, the remarkable difference in outcome between the national and EU-15 benchmark indicates a possible inefficiency of the current allocation of national resource ceilings imposed by the European institutions. Additionally, by using an effects model we argue that the service degree of the economy and governmental expenditures on social protection and research and development are important determinants of overall resource efficiency. Finally, we sketch out three necessary conditions to link the Sustainable Value approach to the strong sustainability paradigm.

Necessary and sufficient conditions for realizability of point processes

We give necessary and sufficient conditions for a pair of (generali- zed) functions 1(r1) and 2(r1, r2), ri 2X, to be the density and pair correlations of some point process in a topological space X, for ex- ample, Rd, Zd or a subset of these. This is an infinite-dimensional version of the classical “truncated moment” problem. Standard tech- niques apply in the case in which there can be only a bounded num- ber of points in any compact subset of X. Without this restriction we obtain, for compact X, strengthened conditions which are necessary and sufficient for the existence of a process satisfying a further re- quirement—the existence of a finite third order moment. We general- ize the latter conditions in two distinct ways when X is not compact.

Some necessary and sufficient conditions for eigenstructure assignment

Some necessary and sufficient conditions for closed-loop eigenstructure assignment by output feedback in time-invariant linear multivariable control systems are presented. A simple condition on a square matrix necessary and sufficient for it to be the closed-loop plant matrix of a given system with some output feedback is the basis of the paper. Some known results on entire eigenstructure assignment are deduced from this. The concept of an inner inverse of a matrix is employed to obtain a condition concerning the assignment of an eigenstructure consisting of the eigenvalues and a mixture of left and right eigenvectors.

Interaction of heat-moisture conditions and physical properties in oat processing: II. Flake quality

Product quality is an important determinant of consumer acceptance. Consistent oat flake properties are thus necessary in the mill as well as in the marketplace. The effects of kilning and tempering conditions (30, 60 or 90 min at 80, 95 or 110 degrees C) on flake peroxidase activity, size, thickness, strength and water absorption were therefore determined. After kilning, some peroxidase activity remained but steaming and tempering effectively destroyed the activity of these enzymes. Thus the supposed protective effect of kilning or groat durability was not confirmed. Kilning resulted in an increase in flake specific weight, but no other significant effect on flake quality was observed. Tempering time and temperature interacted significantly to produce complex effects on flake specific weight, thickness and water absorption. Flake thickness and specific weight were significantly correlated (r = 0.808, n = 54). Longer tempering times resulted in an increased fines' fraction, from 1.45% at 30 min to 1.75% at 90 min. It is concluded that whilst kilning has little effect on flake quality, the heat treatment immediately prior to flaking, can be used to adjust flake quality independently of flake thickness.