Solvability and spectral properties of integral equations on the real line: I. Weighted spaces of continuous functions

We consider in this paper the solvability of linear integral equations on the real line, in operator form (λ−K)φ=ψ, where and K is an integral operator. We impose conditions on the kernel, k, of K which ensure that K is bounded as an operator on . Let Xa denote the weighted space as |s|→∞}. Our first result is that if, additionally, |k(s,t)|⩽κ(s−t), with and κ(s)=O(|s|−b) as |s|→∞, for some b>1, then the spectrum of K is the same on Xa as on X, for 01. As an example where kernels of this latter form occur we discuss a boundary integral equation formulation of an impedance boundary value problem for the Helmholtz equation in a half-plane.

On Hamiltonian balanced dynamics and the slowest invariant manifold

The concept of a slowest invariant manifold is investigated for the five-component model of Lorenz under conservative dynamics. It is shown that Lorenz's model is a two-degree-of-freedom canonical Hamiltonian system, consisting of a nonlinear vorticity-triad oscillator coupled to a linear gravity wave oscillator, whose solutions consist of regular and chaotic orbits. When either the Rossby number or the rotational Froude number is small, there is a formal separation of timescales, and one can speak of fast and slow motion. In the same regime, the coupling is weak, and the Kolmogorov–Arnold-Moser theorem is shown to apply. The chaotic orbits are inherently unbalanced and are confined to regions sandwiched between invariant tori consisting of quasi-periodic regular orbits. The regular orbits generally contain free fast motion, but a slowest invariant manifold may be geometrically defined as the set of all slow cores of invariant tori (defined by zero fast action) that are smoothly related to such cores in the uncoupled system. This slowest invariant manifold is not global; in fact, its structure is fractal; but it is of nearly full measure in the limit of weak coupling. It is also nonlinearly stable. As the coupling increases, the slowest invariant manifold shrinks until it disappears altogether. The results clarify previous definitions of a slowest invariant manifold and highlight the ambiguity in the definition of “slowness.” An asymptotic procedure, analogous to standard initialization techniques, is found to yield nonzero free fast motion even when the core solutions contain none. A hierarchy of Hamiltonian balanced models preserving the symmetries in the original low-order model is formulated; these models are compared with classic balanced models, asymptotically initialized solutions of the full system and the slowest invariant manifold defined by the core solutions. The analysis suggests that for sufficiently small Rossby or rotational Froude numbers, a stable slowest invariant manifold can be defined for this system, which has zero free gravity wave activity, but it cannot be defined everywhere. The implications of the results for more complex systems are discussed.

An evolutionary innovation perspective on the selection of low and zero carbon technologies in new housing

The Code for Sustainable Homes (the Code) will require new homes in the United Kingdom to be ‘zero carbon’ from 2016. Drawing upon an evolutionary innovation perspective, this paper contributes to a gap in the literature by investigating which low and zero carbon technologies are actually being used by house builders, rather than the prevailing emphasis on the potentiality of these technologies. Using the results from a questionnaire three empirical contributions are made. First, house builders are selecting a narrow range of technologies. Second, these choices are made to minimise the disruption to their standard design and production templates (SDPTs). Finally, the coalescence around a small group of technologies is expected to intensify with solar-based technologies predicted to become more important. This paper challenges the dominant technical rationality in the literature that technical efficiency and cost benefits are the primary drivers for technology selection. These drivers play an important role but one which is mediated by the logic of maintaining the SDPTs of the house builders. This emphasises the need for construction diffusion of innovation theory to be problematized and developed within the context of business and market regimes constrained and reproduced by resilient technological trajectories.

Spin equilibrium and outflows in young stellar objects

We present N-body simulations of accretion discs about young stellar objects (YSOs). The simulation includes the presence of a magnetic loop structure on the central star which interacts with the particles by means of a magnetic drag force. We find that an equilibrium spin rate is achieved when the corotation radius coincides with the edge of the loop. This spin rate is consistent with observed values for TTauri stars, being an order of magnitude less than the breakup value. The material ejected from the system by the rotating loop has properties consistent with the observed molecular outflows, given the presence of a suitable containing cavity.

Multiple stationary solutions of an irradiated slab

A mathematical model describing the heat budget of an irradiated medium is introduced. The one-dimensional form of the equations and boundary conditions are presented and analysed. Heat transport at one face of the slab occurs by absorption (and reflection) of an incoming beam of short-wave radiation with a fraction of this radiation penetrating into the body of the slab, a diffusive heat flux in the slab and a prescribed incoming heat flux term. The other face of the slab is immersed in its own melt and is considered to be a free surface. Here, temperature continuity is prescribed and evolution of the surface is determined by a Stefan condition. These boundary conditions are flexible enough to describe a range of situations such as a laser shining on an opaque medium, or the natural environment of polar sea ice or lake ice. A two-stream radiation model is used which replaces the simple Beer’s law of radiation attenuation frequently used for semi-infinite domains. The stationary solutions of the governing equations are sought and it is found that there exists two possible stationary solutions for a given set of boundary conditions and a range of parameter choices. It is found that the existence of two stationary solutions is a direct result of the model of radiation absorption, due to its effect on the albedo of the medium. A linear stability analysis and numerical calculations indicate that where two stationary solutions exist, the solution corresponding to a larger thickness is always stable and the solution corresponding to a smaller thickness is unstable. Numerical simulations reveal that when there are two solutions, if the slab is thinner than the smaller stationary thickness it will melt completely, whereas if the slab is thicker than the smaller stationary thickness it will evolve toward the larger stationary thickness. These results indicate that other mechanisms (e.g. wave-induced agglomeration of crystals) are necessary to grow a slab from zero initial thickness in the parameter regime that yields two stationary solutions.

Success and failure of grassroots innovations for addressing climate change: the case of the Transition Movement

Grassroots innovations emerge as networks generating innovative solutions for climate change adaptation and mitigation. However, it is unclear if grassroots innovations can be successful in responding to climate change. Little evidence exists on replication, international comparisons are rare, and research tends to overlook discontinued responses in favour of successful ones. We take the Transition Movement as a case study of a rapidly spreading transnational grassroots network, and include both active and non-active local transition initiatives. We investigate the replication of grassroots innovations in different contexts with the aim to uncover general patterns of success and failure, and identify questions for future research. An online survey was carried out in 23 countries (N=276). The data analysis entailed testing the effect of internal and contextual factors of success as drawn from the existing literature, and the identification of clusters of transition initiatives with similar internal and contextual factor configurations. Most transition initiatives consider themselves successful. Success is defined along the lines of social connectivity and empowerment, and external environmental impact. We find that less successful transition initiatives might underestimate the importance of contextual factors and material resources in influencing success. We also find that their diffusion is linked to the combination of local-global learning processes, and that there is an incubation period during which a transition initiative is consolidated. Transition initiatives seem capable of generalising organisational principles derived from unique local experiences that seem to be effective in other local contexts. However, the geographical locations matter with regard to where transition initiatives take root and the extent of their success, and ‘place attachment’ may have a role in the diffusion of successful initatives. We suggest that longitudinal comparative studies can advance our understanding in this regard, as well as inform the changing nature of the definition of success at different stages of grassroots innovation development, and the dynamic nature of local and global linkages.

Conceptualising public-private partnerships: a critical appraisal of approaches to meanings and forms

Purpose – The purpose of this article is to survey various meanings attached to a public-private partnership (PPP) and related aspects in Western literature, and identify commonalities and differences between them. Additionally, the article intends to critically assess conflicting and overlapping views on contractual and institutional PPPs, their forms and models, and draw insights for transitional economies. Design/methodology/approach – The article contrasts and compares views on PPP meanings, forms and models within Western PPP literature, and also draws comparisons with understanding of partnership aspects in the Russian language sources. The article examines theories underpinning PPPs, builds connections to PPP advantages and drawbacks, and provides critical assessment of net benefits that PPPs may bring along to the society. Findings – The article concludes that future PPP research in transitional countries such as Kazakhstan and Russia, particularly in the area of organisational and power arrangements in partnerships, may delineate new concepts such as government as a guarantor of a PPP project, social significance of a PPP project, and risk management in a country's contextual environment. Practical implications – In transitional countries, in which PPPs are in their infancy, clarification of theoretical positions, and identification of commonalities and differences between meanings attached to the PPP terminology may enable better decisions by researchers and practitioners in their selection and further development of partnerships and related concepts. Originality/value – Research in the field of PPPs in transitional countries such as Russia and Kazakhstan is in its infancy. The paper intends to contribute to the body of knowledge about PPPs by providing detailed account and categorisation of their principal meanings, forms, models, underpinning theories, and drawing insights for future research in transitional countries.

Preoperative predictors for postoperative problems in heart transplantation: psychiatric and psychosocial considerations

The psychiatric and psychosocial evaluation of the heart transplant candidate can identify particular predictors for postoperative problems. These factors, as identified during the comprehensive evaluation phase, provide an assessment of the candidate in context of the proposed transplantation protocol. Previous issues with compliance, substance abuse, and psychosis are clear indictors of postoperative problems. The prolonged waiting list time provides an additional period to evaluate and provide support to patients having a terminal disease who need a heart transplant, and are undergoing prolonged hospitalization. Following transplantation, the patient is faced with additional challenges of a new self-image, multiple concerns, anxiety, and depression. Ultimately, the success of the heart transplantation remains dependent upon the recipient's ability to cope psychologically and comply with the medication regimen. The limited resource of donor hearts and the high emotional and financial cost of heart transplantation lead to an exhaustive effort to select those patients who will benefit from the improved physical health the heart transplant confers.

The statistical downscaling model-decision centric (SDSM-DC): conceptual basis and applications

Regional climate downscaling has arrived at an important juncture. Some in the research community favour continued refinement and evaluation of downscaling techniques within a broader framework of uncertainty characterisation and reduction. Others are calling for smarter use of downscaling tools, accepting that conventional, scenario-led strategies for adaptation planning have limited utility in practice. This paper sets out the rationale and new functionality of the Decision Centric (DC) version of the Statistical DownScaling Model (SDSM-DC). This tool enables synthesis of plausible daily weather series, exotic variables (such as tidal surge), and climate change scenarios guided, not determined, by climate model output. Two worked examples are presented. The first shows how SDSM-DC can be used to reconstruct and in-fill missing records based on calibrated predictor-predictand relationships. Daily temperature and precipitation series from sites in Africa, Asia and North America are deliberately degraded to show that SDSM-DC can reconstitute lost data. The second demonstrates the application of the new scenario generator for stress testing a specific adaptation decision. SDSM-DC is used to generate daily precipitation scenarios to simulate winter flooding in the Boyne catchment, Ireland. This sensitivity analysis reveals the conditions under which existing precautionary allowances for climate change might be insufficient. We conclude by discussing the wider implications of the proposed approach and research opportunities presented by the new tool.

Observations on the flight paths of the day-flying moth Virbia lamae during periods of mate location: do males have a strategy for contacting the pheromone plume?

1. To maximize the probability of rapid contact with a female’s pheromone plume, the trajectories of male foraging flights might be expected to be directed with respect to wind flow and also to be energetically efficient. 2. Flights directed either upwind, downwind, or crosswind have been proposed as optimal strategies for rapid and/or energetically efficient plume contact. Other possible strategies are random and Lévy walks, which have trajectories and turn frequencies that are not dictated by the direction of wind flow. 3. The planar flight paths of males of the day-active moth Virbia lamae were recorded during the customary time of its sexual activity. 4. We found no directional preference in these foraging flights with respect to the direction of contemporaneous wind flow, but, because crosswind encompasses twice the possible orientations of either upwind or downwind, a random orientation is in effect a de facto crosswind strategy. 5. A crosswind preference should be favoured when the plume extends farther downwind than crosswind, and this strategy is realized by V. lamae males by a random orientation of their trajectories with respect to current wind direction

Real estate and social inequality in Latin America: approaches in Argentina, Brazil, Chile and Colombia

Latin America is known as the most unequal region in the world, where extreme displays of wealth and exposure to scarcity lay bare in the urban landscape. Inequality is not just a social issue; it has considerable impact on economic development. This is because social inequality generates instability and conflict, which can create unsettling conditions for investment. At the macro level, social inequality can also present barriers to economic development, as most government policies and resources tend to be directed in solving social conflict rather than to promote and generate growth. This is one of the reasons usually cited in explaining the development gap between Latin America and other emerging economies, take East Asia for example - they have similar policies to those applied recently in Latin America, but are achieving better growth. The other reason cited is institutional; this includes governance as well as property rights and enforcement of contracts. The latter is the focus of this chapter.

Anna In-Between: Caribbean and not Caribbean: attachment, loss and strange Longing: a conversation with Elizabeth Nunez

Presents an interview with Elizabeth Nunez, author and professor. Nunez discusses the issues on migration, family, and intimacy which are the topics of her novel "Anna In-Between." She explains the demands of the publishing industry that cast a shadow in the world of the novel and the real world of Caribbean writers. This interview was translated by Maria Lusia Ruiz.