On perturbations of Dirac operators with variable magnetic field of constant direction

We carry out the spectral analysis of matrix valued perturbations of 3-dimensional Dirac operators with variable magnetic field of constant direction. Under suitable assumptions on the magnetic field and on the pertubations, we obtain a limiting absorption principle, we prove the absence of singular continuous spectrum in certain intervals and state properties of the point spectrum. Various situations, for example when the magnetic field is constant, periodic or diverging at infinity, are covered. The importance of an internal-type operator (a 2-dimensional Dirac operator) is also revealed in our study. The proofs rely on commutator methods.Comment: 12 page

A sweet deal? Sugarcane, water and agricultural transformation in Sub-Saharan Africa

Globally, the area of sugarcane is rising rapidly in response to growing demands for bioethanol and increased sugar demand for human consumption. Despite considerable diversity in production systems and contexts, sugarcane is a particularly “high impact” crop with significant positive and negative environmental and socio-economic impacts. Our analysis is focused on Sub-Saharan Africa (SSA), which is a critical region for continued expansion, due to its high production potential, low cost of production and proximity, and access, to European markets. Drawing on a systematic review of scientific evidence, combined with information from key informants, stakeholders and a research-industry workshop, we critically assess the impacts of sugarcane development on water, soil and air quality, employment, food security and human health. Our analysis shows that sugarcane production is, in general, neither explicitly good nor bad, sustainable nor unsustainable. The impacts of expansion of sugarcane production on the environment and society depend on the global political economy of sugar, local context, quality of scheme, nature of the production system and farm management. Despite threats from climate change and forthcoming changes in the trade relationship with the European Union, agricultural development policies are driving national and international interest and investment in sugarcane in SSA, with expansion likely to play an important role in sustainable development in the region. Our findings will help guide researchers and policy makers with new insights in understanding the situated environmental and social impacts associated with alternative sugar economy models, production technologies and qualities of management

Cluster magnetic field observations in the magnetosheath: four-point measurements of mirror structures

International audienceThe Cluster spacecraft have returned the first simultaneous four-point measurements of the magnetosheath. We present an analysis of data recorded on 10 November 2000, when the four spacecrafts observed an interval of strong mirrorlike activity. Correlation analysis between spacecraft pairs is used to examine the scale size of the mirror structures in three dimensions. Two examples are presented which suggest that the scale size of mirror structures is ~ 1500?3000 km along the flow direction, and shortest along the magnetopause normal (< 600 km), which, in this case, is approximately perpendicular to both the mean magnetic field and the magnetosheath flow vector. Variations on scales of ~ 750?1000 km are found along the maximum variance direction. The level of correlation in this direction, however, and the time lag observed, are found to be variable. These first results suggest that variations occur on scales of the order of the spacecraft separation ( ~ 1000 km) in at least two directions, but analysis of further examples and a statistical survey of structures observed with different magnetic field orientations and tetrahedral configurations will enable us to describe more fully the size and orientation of mirror structures

Interval valued (\in,\ivq)-fuzzy filters of pseudo BLBL-algebras

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (\in,\ivq)-fuzzy filters of pseudo $BL$-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo $BL$-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo $BL$-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed

Quantum mechanical virial theorem in systems with translational and rotational symmetry

Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G, H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J^{2}, J_{z} and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.Comment: 24 pages, accepted for publication in International Journal of Theoretical Physic

Estimating Annual CO2 Flux for Lutjewad Station Using Three Different Gap-Filling Techniques

Long-term measurements of CO2 flux can be obtained using the eddy covariance technique, but these datasets are affected by gaps which hinder the estimation of robust long-term means and annual ecosystem exchanges. We compare results obtained using three gap-fill techniques: multiple regression (MR), multiple imputation (MI), and artificial neural networks (ANNs), applied to a one-year dataset of hourly CO2 flux measurements collected in Lutjewad, over a flat agriculture area near the Wadden Sea dike in the north of the Netherlands. The dataset was separated in two subsets: a learning and a validation set. The performances of gap-filling techniques were analysed by calculating statistical criteria: coefficient of determination (R2), root mean square error (RMSE), mean absolute error (MAE), maximum absolute error (MaxAE), and mean square bias (MSB). The gap-fill accuracy is seasonally dependent, with better results in cold seasons. The highest accuracy is obtained using ANN technique which is also less sensitive to environmental/seasonal conditions. We argue that filling gaps directly on measured CO2 fluxes is more advantageous than the common method of filling gaps on calculated net ecosystem change, because ANN is an empirical method and smaller scatter is expected when gap filling is applied directly to measurements

Substorm observations in the early morning sector with Equator-S and Geotail

International audienceData from Equator-S and Geotail are used to study the dynamics of the plasma sheet observed during a substorm with multiple intensifications on 25 April 1998, when both spacecraft were located in the early morning sector (03?04 MLT) at a radial distance of 10?11 RE. In association with the onset of a poleward expansion of the aurora and the westward electrojet in the premidnight and midnight sector, both satellites in the morning sector observed plasma sheet thinning and changes toward a more tail-like field configuration. During the subsequent poleward expansion in a wider local time sector (20?04 MLT), on the other hand, the magnetic field configuration at both satellites changed into a more dipolar configuration and both satellites encountered again the hot plasma sheet. High-speed plasma flows with velocities of up to 600 km/s and lasting 2?5 min were observed in the plasma sheet and near its boundary during this plasma sheet expansion. These high-speed flows included significant dawn-dusk flows and had a shear structure. They may have been produced by an induced electric field at the local dipolarization region and/or by an enhanced pressure gradient associated with the injection in the midnight plasma sheet