In this paper, we generalise the criterion of J. Moser. A sequence of invariants related to a linear differential system is defined. An algorithm is given which reduces a differential system to a super-irreducible form. The computation of these invariants follows directly from this form. A more general classification of the singularity is thus obtained, cf. [11] where the link between this form and the Newton polygon of the differential system is studied. The algorithm given is implemented in computer algebra system (REDUCE). R6sum6. Dans cet article, nous donnons une g6n6ralisation du crit+re de J. Moser. Une suite d'invariants associ6s b. un syst6me diff6rentiel est d6finie ainsi qu'un algorithme permettant de r6duire le syst6me diff6rentiel sous une forme super-irr~ductible. Le calcul de ces invariants est alors imm6diat. Nous obtenons ainsi une classification plus g6n6rale de la singularit6, cf. Ell] off on 6tudie le lien entre cette forme et le polygone de Newton d'un syst6me diff6rentiel lin6aire. L'algorithme donn6 est programm6 dans un langage de calcul formel (REDUCE). Subject Classifications: AMS(MOS): 65L07; G: 1.7.

Casablanca, Morocco's economic capital continues today to fight against the proliferation of informal settle- ments affecting its urban fabric illustrated especially by the slums. Actually Casablanca represents 25% of the total slums of Morocco [1]. These are the habitats of all deprived of healthy sanitary conditions and judged precarious from the perspective humanitarian and below the acceptable. The majority of the inhabi- tants of these slums are from the rural exodus with insufficient income to meet the basic needs of daily life. Faced with this situation and to eradicate these habitats, the Moroccan government has launched since 2004 an entire program to create cities without slums (C.W.S.) to resettle or relocate families. Indeed the process control and monitoring of this program requires first identifying and detecting spatial habitats. To achieve these tasks, conventional methods such as information gathering, mapping, use of databases and statistics often have shown their limits and are sometimes outdated. It is within this framework and that of the great German Morocco project “Urban agriculture as an integrative factor of development that fits our project de- tection of slums in Casablanca. The use of satellite imagery, particulary the HSR, has the advantage of providing the physical coverage of urban land but it raises the difficulty of choosing the appropriate method to apply.This paper is actually to develop new approaches based mainly on object-oriented classification of high spatial resolution satellite images for the detection of slums.This approach has been developed for mapping the urban land through by integration of several types of information (spectral, spatial, contextual ...) (Hofmann, P ., 2001, Herold et al. 2002b; Van Der Sande et al., 2003, Benz et al., 2004, Nobrega et al., 2006). In order to refine the result of classification, we applied mathematical morphology and in particular the closing filter. The data from this classification (binary image), which then will be used in a spatial data- base (ArcGIS)

Oued El Maleh watershed is considered the largest ocean basin of the Chaouia-Ouardigha region in Morocco. Severe flooding occurred in 1996, 2001 and 2002 in the watershed. Thus, significant economic and human damage has been caused. The floods of Mohammedia city, located in the outlet of the watershed, were due to the silting of the Oued El Maleh dam which has lost its ability to retain water. This work, therefore, aims to assess soil losses by water erosion in the Oued El Maleh watershed through modeling main factors involved in water erosion. The methodology used is based on the use of the universal soil loss equation (USLE). The model includes the following factors: soil erodibility, the inclination of slopes, the rainfall erosivity, vegetation cover and erosion control practices. The aggressiveness of rainfall was calculated for a number of stations bordering the study area and interpolated across the watershed using geostatistical model. Soil erodibility was extracted from soil map and soil survey. The effect of topography was approached by combining the degree of slope and slope length using a digital elevation model (ASTER) and ArcHydrology extension (ArcGIS). The vegetation cover was derived from Landsat image ETM through the supervised classification method. The index of erosion control practices was approached by field visits. All factors have been measured and integrated into a geographic information system which enabled us to spatialize the degree of sediment production at the watershed scale in a synthetic map. The annual soil loss is 8.21 t/ha/yr and the soil loss classification shows that surfaces affected by high erosion are equivalent to 10% of the watershed. Furthermore, this map is available to support land managers policy makers in the process of decision making related to soil conservation, infrastructure and citizens' property protection.

Along with being a dynamic process that affects large areas, desertification is also one of the most serious problems in many countries. The effects of this phenomenon threaten the sustainability of natural resources, namely water resources, agricultural production and major basic infrastructure, specifically roads and habitations. Several factors exacerbate this phenomenon such as the climate dryness, the geological and morphological characteristics of the terrain, the irrational use of space, population growth and the over-exploitation of vegetation and water resources. This work aims to evaluate the desertification index in the Oued-El-Maleh watershed, through the integration of key factors involved in the MEDALUS model (Mediterranean Desertification and Land Use) within a GIS. The model includes among its indexes: climate, vegetation, soil and management. Each index was obtained by the combination of sub-indexes. All the factors, measured and integrated into a geographic information system, enabled us to spatialize, on a synthetic map, the degree of the desertification effect throughout the watershed. This map is a managing tool available for decision-making regarding the selection of priority areas in the fight against desertification. High sensitivity to desertification class represents only 35% of the watershed. This class is concentrated in the north of the study area that corresponds to plains and low altitude. This could be explained by the dominance of agro-pastoral activity and the presence of a big population pressure.

Casablanca, main metropolis of Morocco concentrates more than 46% of the working population. She is considered as the most affected city by the increase of the temperature. We have therefore chosen to base our study on the city of Ca- sablanca. The main objective of this study is to estimate the ground temperature in order to evaluate the impact of the vegetation on cooling the ground temperature. In order to move to the achievement and to identify the formation of is- lands of warmth or coolness which occur in the urban municipalities of Casablanca, we have used the satellites images Landsat 5 TM. Graphical analysis based on studying the correlation was performed to quantify the strength of the link between the coolest urban surfaces and the green spaces. To achieve this, we used “mono-window” algorithm which re- quires knowledge of the atmospheric transmittance, the emissivity of soil and the effective temperature of the air. This study revealed a strong correlation between vegetation cover and cold areas (R² = 0.911) and allowed us to determine graphically that there is a strong link between the urban ground temperature and the density of buildings