Manoj Kumar

Finsler geometry generalizes Riemannian geometry in the same sense that Banach spaces generalize Hilbert spaces. This book presents some transformations in Riemann-Finsler geometry, which have recently undergone significant development but have not had a pedagogical treatment elsewhere. Each article will open the door to an active area of research and is suitable for a special topics course in graduate-level differential geometry.

This book introduces a variety of neural network methods for solving differential equations arising in science and engineering. The emphasis is placed on a deep understanding of the neural network techniques, which has been presented in a mostly heuristic and intuitive manner. This approach will enable the reader to understand the working, efficiency and shortcomings of each neural network technique for solving differential equations. The objective of this book is to provide the reader with a sound understanding of the foundations of neural networks and a comprehensive introduction to neural network methods for solving differential equations together with recent developments in the techniques and their applications.The book comprises four major sections. Section I consists of a brief overview of differential equations and the relevant physical problems arising in science and engineering. Section II illustrates the history of neural networks starting from their beginnings in the 1940s through to the renewed interest of the 1980s. A general introduction to neural networks and learning technologies is presented in Section III. This section also includes the description of the multilayer perceptron and its learning methods. In Section IV, the different neural network methods for solving differential equations are introduced, including discussion of the most recent developments in the field.Advanced students and researchers in mathematics, computer science and various disciplines in science and engineering will find this book a valuable reference source.

Disaster is the activity that occurs anytime, anywhere without prior information. It is very harmful and dangerous even a small one can affect the people's life, prosperity and their wealth. Disaster occurrence affects the whole mankind, human beings, animals and their prosperity. So we need alert system that we can acknowledge their occurrence before its happening. Disaster Management using WSN (wireless sensor network) that helps to the sense the environment factors and on the behalf of the factors use Leach (Low Energy Adaptive Clustering Hierarchy) algorithm that is hierarchical in nature and provide connection and communication between the nodes to prevent from snow avalanche and forest fire. To prevent the pilgrims or local people before falling of landslides we create an alert system for it by using modified particle filtering algorithm.in this we detect the change in position and velocity in the video image of rocks of mountain using modified particle filtering algorithm by tracking the movement of particles by using its likelihoods. To communicate between the nodes or sending the information form one node to another, we use Leach (Low Energy Adaptive Clustering Hierarchy)