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In this paper we explore the relation between the A-numerical range and the A-spectrum of A-bounded operators in the setting of semi-Hilbertian structure. We introduce a new definition of A-normal operator and prove that closure of the A-numerical range of an A-normal operator is the convex hull of the A-spectrum. We further prove Anderson's theorem for the sum of A-normal and A-compact operators which improves and generalizes the existing result on Anderson's theorem for A-compact operators. Finally we introduce strongly A-numerically closed class of operators and along with other results prove that the class of A-normal operators is strongly A-numerically closed.

Natural disasters are responsible for disturbing the foundation of a stable system which affects man to a large extent. Man usually has no control on natural disasters. However, if precautionary measures are taken in advance, then the colossal loss of human lives and property caused by a disaster can be averted. In the world of rapidly developing technology, several machine learning algorithms along with GIS and Remote Sensing has been used by researchers to prepare disaster susceptibility map which in turn aided in adoption of appropriate mitigation measures. The present research work aimed for the preparation of landslide susceptibility map of West Sikkim district of Sikkim state in India by using three machine learning techniques namely Frequency Ratio (FR), Analytical Hierarchy Process (AHP) and Critic method. The study revealed that all these three techniques are ideal for landslide susceptibility mapping with AUC values of 0.824 for FR, 0.739 for AHP and 0.757 for Critic and hence concluded that FR is the best machine learning algorithm that can be used for preparing landslide susceptibility maps.

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