We study properties of a C2-cofinite vertex operator algebra V = ⊕ ∞ i=0Vi of CFT type. If it is also rational (i.e. all modules are completely reducible) and V ′ ∼= V , then the rigidity of the tensor category of modules has been proved by Huang [11], where V ′ denotes the restricted dual of V . However, when we treat irrational C2cofinite VOAs, the rigidity is too strong, because it is almost...

Let K be a discrete valuation field with ring of integers OK . Let f :X → Y be a finite morphism of curves overK . In this article, we study some possible relationships between the models over OK of X and of Y . Three such relationships are listed below. Consider a Galois cover f :X→ Y of degree prime to the characteristic of the residue field, with branch locus B. We show that if Y has semi-st...

AIM This study provides regional estimates of forest cover in dry African ecoregions and the changes in forest cover that occurred there between 1990 and 2000, using a systematic sample of medium-resolution satellite imagery which was processed consistently across the continent. LOCATION The study area corresponds to the dry forests and woodlands of Africa between the humid forests and the se...

An understanding of land use/land cover change at local, regional, and global scales is important in an increasingly human-dominated biosphere. Here, we report on an under-appreciated complexity in the analysis of land cover change important in arid and semi-arid environments. In these environments, some land cover types show a high degree of inter-annual variability in productivity. In this st...

Accurately mapping the spatial distribution of forests in sub-humid to semi-arid regions over time is important for forest management but a challenging task. Relatively large uncertainties still exist in the spatial distribution of forests and forest changes in the sub-humid and semi-arid regions. Numerous publications have used either optical or synthetic aperture radar (SAR) remote sensing im...

1 The relative roles of climate and management for driving changes in woody cover in savannas over the past century are the subject of active debate. Perspectives arising from short-term, small-scale, local experiments are rarely tested over larger scales and longer time frames. 2 Regression analysis and aerial photography were used to assess the relative importance of land-use history (fire an...

A new method of land cover mapping from satellite images using granulometric analysis is presented here. Discontinuous landscapes such as steppian bushes of semi arid regions and recently growing urban settlements are especially concerned by this study. Spatial organisations of the land cover are quantified by means of the size distribution analysis of the land cover units extracted from high r...

Water scarcity is one of the factors limiting plant growth and development. More than onethird of the global terrestrial ecosystems is located in arid and semi-arid regions. The mostimportant limiting factor for plant growth is water shortage. Drought could significantlychange the natural vegetation cover. Rainfall reduction in Iraq, Turkey and Syria hasreduced vegetation cover so that dust sto...