Optimal convergence estimates for the trace of the polynomial L2-projection operator on a simplex

In this paper we study convergence of the L2-projection onto the space of polynomials up to degree p on a simplex in Rd, d >= 2. Optimal error estimates are established in the case of Sobolev regularity and illustrated on several numerical examples. The proof is based on the collapsed coordinate transform and the expansion into various polynomial bases involving Jacobi polynomials and their antiderivatives. The results of the present paper generalize corresponding estimates for cubes in Rd from [P. Houston, C. Schwab, E. Süli, Discontinuous hp-finite element methods for advection-diffusion-reaction problems. SIAM J. Numer. Anal. 39 (2002), no. 6, 2133-2163].

Occupying the margins: Labour integration and social exclusion in artisanal mining in Tanzania

This article examines the marginal position of artisanal miners in sub-Saharan Africa, and considers how they are incorporated into mineral sector change in the context of institutional and legal integration. Taking the case of diamond and gold mining in Tanzania, the concept of social exclusion is used to explore the consequences of marginalization on people's access to mineral resources and ability to make a living from artisanal mining. Because existing inequalities and forms of discrimination are ignored by the Tanzanian state, the institutionalization of mineral titles conceals social and power relations that perpetuate highly unequal access to resources. The article highlights the complexity of these processes, and shows that while legal integration can benefit certain wealthier categories of people, who fit into the model of an 'entrepreneurial small-scale miner', for others adverse incorporation contributes to socio-economic dependence, exploitation and insecurity. For the issue of marginality to be addressed within integration processes, the existence of local forms of organization, institutions and relationships, which underpin inequalities and discrimination, need to be recognized.

Spectral asymmetry of the massless Dirac operator on a 3-torus

Consider the massless Dirac operator on a 3-torus equipped with Euclidean metric and standard spin structure. It is known that the eigenvalues can be calculated explicitly: the spectrum is symmetric about zero and zero itself is a double eigenvalue. The aim of the paper is to develop a perturbation theory for the eigenvalue with smallest modulus with respect to perturbations of the metric. Here the application of perturbation techniques is hindered by the fact that eigenvalues of the massless Dirac operator have even multiplicity, which is a consequence of this operator commuting with the antilinear operator of charge conjugation (a peculiar feature of dimension 3). We derive an asymptotic formula for the eigenvalue with smallest modulus for arbitrary perturbations of the metric and present two particular families of Riemannian metrics for which the eigenvalue with smallest modulus can be evaluated explicitly. We also establish a relation between our asymptotic formula and the eta invariant.

Eigenvalues of a one-dimensional Dirac operator pencil

We study the spectrum of a one-dimensional Dirac operator pencil, with a coupling constant in front of the potential considered as the spectral parameter. Motivated by recent investigations of graphene waveguides, we focus on the values of the coupling constant for which the kernel of the Dirac operator contains a square integrable function. In physics literature such a function is called a confined zero mode. Several results on the asymptotic distribution of coupling constants giving rise to zero modes are obtained. In particular, we show that this distribution depends in a subtle way on the sign variation and the presence of gaps in the potential. Surprisingly, it also depends on the arithmetic properties of certain quantities determined by the potential. We further observe that variable sign potentials may produce complex eigenvalues of the operator pencil. Some examples and numerical calculations illustrating these phenomena are presented.

Toxin-allelopathy among phytoplankton species prevents competitive exclusion

Toxic or allelopathic compounds liberated by toxin-producing phytoplankton (TPP) acts as a strong mediator in plankton dynamics. On an analysis of a set of phytoplankton biomass data that have been collected by our group in the northwest part of the Bay of Bengal, and by analysis of a three-component mathematical model under a constant as well as a stochastic environment, we explore the role of toxin-allelopathy in determining the dynamic behavior of the competing phytoplankton species. The overall results, based on analytical and numerical wings, demonstrate that toxin-allelopathy due to the TPP promotes a stable co-existence of those competitive phytoplankton that would otherwise exhibit competitive exclusion of the weak species. Our study suggests that TPP might be a potential candidate for maintaining the co-existence and diversity of competing phytoplankton species.

Addressing rural social exclusion through African social purpose ventures

Objectives. The overarching aim of this paper is to consider the relationship between social entrepreneurship and rural development, and as a mechanism to address social exclusion in the Global South, with specific reference to Sub-Saharan Africa. Drawing upon a number of case examples of social purpose ventures in Kenya, Mozambique and Zambia the objectives of this paper are: - To provide a synthesis of existing literature on the interaction between social purpose ventures and rural BoP communities in the developing world; - To explore extant social exclusion literature including economic, political and international development dimensions; and - To analyse the case study examples to consider the channels through which social purpose ventures contribute to tackling social exclusion amongst the rural BoP. Prior Work. There is growing interest in the role that social enterprises and wider social purpose ventures can play in sustainable development in the Global South. In many developing countries the majority of the population still reside in rural areas with these areas often particularly marginalised and underdeveloped. Previous studies have provided anecdotal examples where social purpose ventures have the potential to provide innovative solutions to the development challenges faced by rural households and communities. Yet research in this area remains relatively nascent and fragmented. In depth empirical studies examining social purpose ventures and rural development in the Global South are furthermore limited. Approach. Data was collected during in-depth case study research with social purpose ventures in Zambia, Kenya and Mozambique. Cases were selected through a purposive sample with access negotiated to rural BoP communities through gatekeeper partners. Qualitative research methods were primarily employed including interviews, stakeholder focus groups and observational research. Results Six channels through which social purpose ventures contribute to tackling social exclusion amongst rural BoP communities are identified. These include ventures with the BoP as employees, producers, consumers, entrepreneurs, service users and shareholders. A number of shared characteristics for successful social purpose ventures are also outlined. Finally implications for policy, practice and research are discussed. Implications. Despite the increasing attention being given to social purpose ventures as a mechanism for global sustainable development many questions remain unanswered. Limited empirical work has been undertaken on such ventures operating in rural settings in the developing world, particularly Africa. The paper will add to academic and practitioner knowledge in this area especially in relation to up-scaling impact, the long term sustainability and viability of social purpose enterprise ventures, and effective supporting interventions. This paper adds to knowledge in the field of social purpose venturing in the developing world. It identifies various channels through which such ventures help tackle rural social exclusion and also factors influencing their success. The paper provides insights for practitioners and policy makers, particularly in relation to facilitating successful social purpose venturing. Value This paper will provide insights relevant to both academic and practitioner audiences. It addresses a subject area and geographical region that has received limited research attention to date. The paper adds to knowledge on social purpose ventures and social entrepreneurship in Africa and wider developing world environments, and contributes to debates on its potential and present limitations as a vehicle for development and societal transformation

Superinfection exclusion and the long-term survival of honey bees in Varroa-infested colonies

Over the past 50 years, many millions of European honey bee (Apis mellifera) colonies have died as the ectoparasitic mite, Varroa destructor, has spread around the world. Subsequent studies have indicated that the mite's association with a group of RNA viral pathogens (Deformed Wing Virus, DWV) correlates with colony death. Here, we propose a phenomenon known as superinfection exclusion that provides an explanation of how certain A. mellifera populations have survived, despite Varroa infestation and high DWV loads. Next-generation sequencing has shown that a non-lethal DWV variant 'type B' has become established in these colonies and that the lethal 'type A' DWV variant fails to persist in the bee population. We propose that this novel stable host-pathogen relationship prevents the accumulation of lethal variants, suggesting that this interaction could be exploited for the development of an effective treatment that minimises colony losses in the future.The ISME Journal advance online publication, 27 October 2015; doi:10.1038/ismej.2015.186.

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials V, we prove that the eigenvalues of the indefinite Sturm–Liouville operator A = sign(x)(−Δ+V(x)) accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.