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Landslide susceptibility maps are very important tools in the planning and management of landslide prone areas. Qualitative and quantitative methods each have their own advantages and dis-advantages in landslide susceptibility mapping. The aim of this study is to compare three models, i.e., frequency ratio (FR), Shannon’s entropy and analytic hierarchy process (AHP) by implementing them for the preparation of landslide susceptibility maps. Shimla, a district in Himachal Pradesh (H.P.), India was chosen for the study. A landslide inventory containing more than 1500 landslide events was prepared using previous literature, available historical data and a field survey. Out of the total number of landslide events, 30% data was used for training and 70% data was used for testing purpose. The frequency ratio, Shannon’s entropy and AHP models were implemented and three landslide susceptibility maps were prepared for the study area. The final landslide susceptibility maps were validated using a receiver operating characteristic (ROC) curve. The frequency ratio (FR) model yielded the highest accuracy, with 0.925 fitted ROC area, while the accuracy achieved by Shannon’s entropy model was 0.883. Analytic hierarchy process (AHP) yielded the lowest accuracy, with 0.732 fitted ROC area. The results of this study can be used by engineers and planners for better management and mitigation of landslides in the study area.

This paper analyzes the existence of resonance stability of the triangular equilibrium points of the planar elliptical restricted three-body problem when both the primaries are oblate spheroid as well as the source of radiation under the particular case, whene=0. We have derived Hamiltonian function describing the motion of infinitesimal mass in the neighborhood of the triangular equilibrium solutions taken as a convergent series. Hamiltonian function for the system has been derived and also expanded in powers of the generalized components of momenta. We have used canonical transformation to make the Hamiltonian function independent of true anomaly. The most interesting and distinguishable results of this study are establishing the relation for determining the range of stability at and near the resonanceω2=1/2around the binary system.