Women’s empowerment and the commercialisation of African agriculture.

This brief presents a summary of key issues in research on women’s empowerment, drawn from an APRA working paper commissioned to support the design of APRA’s research on pathways to agricultural commercialisation in Africa. In the context of African agriculture, as women move along different pathways of commercialisation, the source of their disempowerment may shift from local to more global actors and factors, and the means of empowerment towards more collective and political processes. Researching the effectiveness of different pathways of agricultural commercialisation to empowering women and girls, therefore, requires an approach which explores the relationships between global and local, shifting dynamics as women move into and up global value chains, and changing gender relations in a specific local context

Lax Operator for the Quantised Orthosymplectic Superalgebra U_q[osp(2|n)]

Each quantum superalgebra is a quasi-triangular Hopf superalgebra, so contains a \textit{universal $R$-matrix} in the tensor product algebra which satisfies the Yang-Baxter equation. Applying the vector representation $\pi$, which acts on the vector module $V$, to one side of a universal $R$-matrix gives a Lax operator. In this paper a Lax operator is constructed for the $C$-type quantum superalgebras $U_q[osp(2|n)]$. This can in turn be used to find a solution to the Yang-Baxter equation acting on $V \otimes V \otimes W$ where $W$ is an arbitrary $U_q[osp(2|n)]$ module. The case $W=V$ is included here as an example.Comment: 15 page

Exploring Attitudes towards Genetically Modified Foods: Is there a Connection between People who are Concerned About the Environment and their Attitudes towards GM Foods

Genetically modified (GM) foods provide many advantages to modern agriculture, such as increased yields due to insect and pathogen resistance, productivity improvements, and offer a potential solution to address world hunger. However, GM foods have the potential to cause serious environmental harm, triggering public attitudes towards them to be divided. People are often suspicious of genetic modification, which may inhibit future development and adoption. This study considers GM foods, and aims to explore attitudes towards them, testing the hypotheses that people who are concerned about the environment are less likely to favour GM foods. Data collected through an online questionnaire, yielding 214 responses, is used to correlate environmental concern with attitudes towards GM foods, represented by a GM score. The data shows that total green score correlated against GM score showed a significant, but weak correlation. However, there were clear signs of heteroscedasticity in the data, showing that more environmentally concerned individuals show a greater variation in their attitude towards GM foods. Age also affected attitudes towards GM foods, with individuals between 46 and 60 being more likely to be against GM foods. The data shows that respondents’ main hesitations towards GM foods resulted from insufficient knowledge on the subject, concern over corporations using them for personal gain, and the uncertainty of the long-term effects on human and environmental health. If GM is to be used as part of the solution to sustainable food production, more emphasis is required on educating individuals on GM foods, their uses and future impacts

Generalised Perk--Schultz models: solutions of the Yang-Baxter equation associated with quantised orthosymplectic superalgebras

The Perk--Schultz model may be expressed in terms of the solution of the Yang--Baxter equation associated with the fundamental representation of the untwisted affine extension of the general linear quantum superalgebra $U_q[sl(m|n)]$, with a multiparametric co-product action as given by Reshetikhin. Here we present analogous explicit expressions for solutions of the Yang-Baxter equation associated with the fundamental representations of the twisted and untwisted affine extensions of the orthosymplectic quantum superalgebras $U_q[osp(m|n)]$. In this manner we obtain generalisations of the Perk--Schultz model.Comment: 10 pages, 2 figure

Stability of spikes in the shadow Gierer-Meinhardt system with Robin boundary conditions

We consider the shadow system of the Gierer-Meinhardt system in a smooth bounded domain RN,At=2A−A+,x, t>0, ||t=−||+Ardx, t>0 with the Robin boundary condition +aAA=0, x, where aA>0, the reaction rates (p,q,r,s) satisfy 1<p<()+, q>0, r>0, s0, 1<<+, the diffusion constant is chosen such that 1, and the time relaxation constant is such that 0. We rigorously prove the following results on the stability of one-spike solutions: (i) If r=2 and 1<p<1+4/N or if r=p+1 and 1<p<, then for aA>1 and sufficiently small the interior spike is stable. (ii) For N=1 if r=2 and 1<p3 or if r=p+1 and 1<p<, then for 0<aA<1 the near-boundary spike is stable. (iii) For N=1 if 3<p<5 and r=2, then there exist a0(0,1) and µ0>1 such that for a(a0,1) and µ=2q/(s+1)(p−1)(1,µ0) the near-boundary spike solution is unstable. This instability is not present for the Neumann boundary condition but only arises for the Robin boundary condition. Furthermore, we show that the corresponding eigenvalue is of order O(1) as 0. ©2007 American Institute of Physic

On the structure of the set of bifurcation points of periodic solutions for multiparameter Hamiltonian systems

This paper deals with periodic solutions of the Hamilton equation with many parameters. Theorems on global bifurcation of solutions with periods $2\pi/j,$ $j\in\mathbb{N},$ from a stationary point are proved. The Hessian matrix of the Hamiltonian at the stationary point can be singular. However, it is assumed that the local topological degree of the gradient of the Hamiltonian at the stationary point is nonzero. It is shown that (global) bifurcation points of solutions with given periods can be identified with zeros of appropriate continuous functions on the space of parameters. Explicit formulae for such functions are given in the case when the Hessian matrix of the Hamiltonian at the stationary point is block-diagonal. Symmetry breaking results concerning bifurcation of solutions with different minimal periods are obtained. A geometric description of the set of bifurcation points is given. Examples of constructive application of the theorems proved to analytical and numerical investigation and visualization of the set of all bifurcation points in given domain are provided. This paper is based on a part of the author's thesis [W. Radzki, ``Branching points of periodic solutions of autonomous Hamiltonian systems'' (Polish), PhD thesis, Nicolaus Copernicus University, Faculty of Mathematics and Computer Science, Toru\'{n}, 2005].Comment: 35 pages, 4 figures, PDFLaTe

Einstein-Weyl structures corresponding to diagonal K\"ahler Bianchi IX metrics

We analyse in a systematic way the four dimensionnal Einstein-Weyl spaces equipped with a diagonal K\"ahler Bianchi IX metric. In particular, we show that the subclass of Einstein-Weyl structures with a constant conformal scalar curvature is the one with a conformally scalar flat - but not necessarily scalar flat - metric ; we exhibit its 3-parameter distance and Weyl one-form. This extends previous analysis of Pedersen, Swann and Madsen , limited to the scalar flat, antiself-dual case. We also check that, in agreement with a theorem of Derdzinski, the most general conformally Einstein metric in the family of biaxial K\"ahler Bianchi IX metrics is an extremal metric of Calabi, conformal to Carter's metric, thanks to Chave and Valent's results.Comment: 15 pages, Latex file, minor modifications, to be published in Class. Quant. Gra

A nonlocal eigenvalue problem and the stability of spikes for reaction-diffusion systems with fractional reaction rates

We consider a nonlocal eigenvalue problem which arises in the study of stability of spike solutions for reaction-diffusion systems with fractional reaction rates such as the Sel'kov model, the Gray-Scott system, the hypercycle Eigen and Schuster, angiogenesis, and the generalized Gierer-Meinhardt system. We give some sufficient and explicit conditions for stability by studying the corresponding nonlocal eigenvalue problem in a new range of parameters