Non-commutative oscillator with Kepler-type dynamical symmetry

A 3-dimensional non-commutative oscillator with no mass term but with a certain momentum-dependent potential admits a conserved Runge-Lenz vector, derived from the dual description in momentum space. The latter corresponds to a Dirac monopole with a fine-tuned inverse-square plus Newtonian potential, introduced by McIntosh, Cisneros, and by Zwanziger some time ago. The trajectories are (arcs of) ellipses, which, in the commutative limit, reduce to the circular hodographs of the Kepler problem. The dynamical symmetry allows for an algebraic determination of the bound-state spectrum and actually extends to the conformal algebra o(4,2).Comment: 10 pages, 3 figures. Published versio

Dynamical supersymmetry of spin particle-magnetic field interaction

We study the super and dynamical symmetries of a fermion in a monopole background. The Hamiltonian also involves an additional spin-orbit coupling term, which is parameterized by the gyromagnetic ratio. We construct the superinvariants associated with the system using a SUSY extension of a previously proposed algorithm, based on Grassmann-valued Killing tensors. Conserved quantities arise for certain definite values of the gyromagnetic factor: $\N=1$ SUSY requires $g=2$; a Kepler-type dynamical symmetry only arises, however, for the anomalous values $g=0$ and $g=4$. The two anomalous systems can be unified into an $\N=2$ SUSY system built by doubling the number of Grassmann variables. The planar system also exhibits an $\N=2$ supersymmetry without Grassmann variable doubling.Comment: 23 page

Conserved quantities in non-abelian monopole fields

Van Holten's covariant Hamiltonian framework is used to find conserved quantities for an isospin-carrying particle in a non-Abelian monopole-like field. For a Wu-Yang monopole we find the most general scalar potential such that the combined system admits a conserved Runge-Lenz vector. It generalizes the fine-tuned inverse-square plus Coulomb potential, found before by McIntosh and Cisneros, and by Zwanziger, for a charged particle in the field of a Dirac monopole. Following Feh\'er, the result is interpreted as describing motion in the asymptotic field of a self-dual Prasad-Sommerfield monopole. In the effective non-Abelian field for nuclear motion in a diatomic molecule due to Moody, Shapere and Wilczek, a conserved angular momentum is constructed, despite the non-conservation of the electric charge. No Runge-Lenz vector has been found.Comment: 8 pages, RevTex no figures. An error corrected and a new Section adde

Particle dynamics near extreme Kerr throat and supersymmetry

The extreme Kerr throat solution is believed to be non-supersymmetric. However, its isometry group SO(2,1) x U(1) matches precisely the bosonic subgroup of N=2 superconformal group in one dimension. In this paper we construct N=2 supersymmetric extension of a massive particle moving near the horizon of the extreme Kerr black hole. Bosonic conserved charges are related to Killing vectors in a conventional way. Geometric interpretation of supersymmetry charges remains a challenge.Comment: V2: 10 pages; discussion in sect. 4 and 5 extended, acknowledgements and references adde

Social Perceptions of Forest Ecosystem Services in the Democratic Republic of Congo

The forests of the Albertine Rift are known for their high biodiversity and the important ecosystem services they provide to millions of inhabitants. However, their conservation and the maintenance of ecosystem service delivery is a challenge, particularly in the Democratic Republic of the Congo. Our research investigates how livelihood strategy and ethnicity affects local perceptions of forest ecosystem services. We collected data through 25 focus-group discussions in villages from distinct ethnic groups, including farmers (Tembo, Shi, and Nyindu) and hunter-gatherers (Twa). Twa identify more food-provisioning services and rank bush meat and honey as the most important. They also show stronger place attachment to the forest than the farmers, who value other ecosystem services, but all rank microclimate regulation as the most important. Our findings help assess ecosystem services trade-offs, highlight the important impacts of restricted access to forests resources for Twa, and point to the need for developing alternative livelihood strategies for these communities

AMMI analysis of cassava response to contrasting environments: case study of genotype by environment effect on pests and diseases, root yield, and carotenoids content in Cameroon

Published online: 11 Aug 2018Genotype by environment interaction remains a substantial issue in all breeding programs. Crop genotypes are generally developed in a central breeding location, but always require the evaluation of breeding products in different environments. This is particularly relevant in countries that have a wide range of climates. Eighteen cassava genotypes were evaluated in Cameroon in eight environments—varying in seasonal rainfall and temperature patterns and soil characteristics—over two cropping seasons. Soil nutrient content was analyzed and trials were established in a randomized complete block design in three replications. Response of genotypes to major cassava pests and diseases, yield and carotenoids content was evaluated. It was observed that four genotypes did not show cassava mosaic disease (CMD) symptoms irrespective of the environments. The local check had highest CMD incidence and severity across all environments. Average number of whitefly per plant across all environments was highest on TMS 96/0023. Average cassava green mite (CGM) infestation was low on all the genotypes. Fresh root yield of five genotypes ranged between 25 and 30 tons per ha for both years. Significant and positive correlation was found across locations between fresh root yield and soil K, P and Mg. AMMI analysis revealed highly significant differences among genotypes and environments and significant genotype × environment interaction for most of the estimated traits, indicating variability in genotypes performance with environment