For Honours, Post Graduate and M.Phil Students of All Indian Universities, Engineering Students and Various Competitive Examinations

Questions of existence, multiplicity, and regularity of free boundaries for prescribed data need to be addressed and their solutions lead to nonlinear problems. In this paper an equivalence is established between Bernoulli free-boundary problems and a class of equations for real-valued functions of one real variable.

This first part of this book deals with the boundary value problem with equivalued surfaces, while the second part is concerned with the mathematical model and method, including the numerical method, of the resistivity well-logging for the three-lateral well-logging.

This is a research report about my work on sequential statistic~ during 1980 - 1984. Two themes are treated which are closely related to each other and to the law of the iterated logarithm:· I) curved boundary first passage distributions of Brownian motion, 11) optimal properties of sequential tests with parabolic and nearly parabolic boundaries. In the first chapter I discuss the tangent approximation for Brownianmotion as a global approximation device. This is an extension of Strassen' s approach to t'he law of the iterated logarithm which connects results of fluctuation theory of Brownian motion with classical methods of sequential statistics. In the second chapter I make use of these connections and derive optimal properties of tests of power one and repeated significance tests for the simpiest model of sequential statistics, the Brownian motion with unknown drift. To both topics:there under1ies an asymptotic approach which is closely linked to large deviation theory: the stopping boundaries recede to infinity. This is a well-known approach in sequential stötistics which is extensively discussed in Siegmund's recent book ·Sequential Analysis". This approach also leads to some new insights about the law of the iterated logarithm (LIL). Although the LIL has been studied for nearly seventy years the belief is still common that it applies only for large sampIe sizes which can never be obser ved in practice.

This book studies fundamental properties of the logarithmic potential and their connections to the theory of Fourier series, to potential theory, and to function theory. The material centers around a study of Poisson's integral in two dimensions and of the corresponding Stieltjes integral. The results are then extended to the integrals in terms of Green's functions for general regions. There are some thirty exercises scattered throughout the text. These are designed in part to familiarize the reader with the concepts introduced, and in part to complement the theory. The reader should know something of potential theory, functions of a complex variable, and Lebesgue integrals. The book is based on lectures given by the author in 1924-1925 at the Rice Institute and at the University of Chicago.

This Fourth Edition of Cartography: Visualization of Geospatial Data serves as an excellent introduction to general cartographic principles. It is an examination of the best ways to optimize the visualization and use of spatiotemporal data. Fully revised, it incorporates all the changes and new developments in the world of maps, such as OpenStreetMap and GPS (Global Positioning System) based crowdsourcing, and the use of new web mapping technology and adds new case studies and examples. Now printed in colour throughout, this edition provides students with the knowledge and skills needed to read and understand maps and mapping changes and offers professional cartographers an updated reference with the latest developments in cartography. Written by the leading scholars in cartography, this work is a comprehensive resource, perfect for senior undergraduate and graduate students taking courses in GIS (geographic information system) and cartography. New in This Edition: Provides an excellent introduction to general cartographic visualization principles through full-colour figures and images Addresses significant changes in data sources, technologies and methodologies, including the movement towards more open data sources and systems for mapping Includes new case studies and new examples for illustrating current trends in mapping Provides a societal and institutional framework in which future mapmakers are likely to operate, based on UN global development sustainability goals