Books in the Atlantis Studies In Mathematics For Engineering And Science series

This book provides an enduring response to modern economic problems and the consequent crises, dealing with the economic modelling of nations and the forecasting of economic growth.

This monograph, a sequel to the author's highly successfull "A Mathematical Treatment of Economic Cooperation and Competition Among Nations: With Nigeria, USA, UK, China and Middle East Examples" (Academic Press, 2005), extends the study to all member states of the United Nations. It derives the equations of the key economic variables of gross domestic product, interest rate, employment value of capital stock prices (inflation) and cumulative balance of payment. The derivation is based on the differential market principle of supply and demand and on the rational expectation principle. The models are validated using economic time series of each country and MATLAB programs. The emerging dynamics is a differential game of pursuit which is converted to a hereditary control system for a single nation. Following the same method we derive the full hereditary economic model of all members of the United Nation joined together by external trade, investment capital flow consumption employment and governments' economic intervention all mirrored by interacting gross domestic products. The system is validated with IMF and World Bank data. Studies are made on how to arrest economic recession and depression and promote economic growth and prosperity. Diffusion of wealth is also touched upon. Policies regarding economic stimulus, how to dam the decay of capital flow, as well as conditions to promote full employment are discussed. Examination is made to test for the global systems controllability the possibility of steering any current bad economic state to a state of growth of its GDP, low interest rate, full employment, good value of capital stock, low inflation and a positive value of the cumulative balance of payment. The book prescribes verifiable broad policies for all nations together to promote prosperity, diffusion of wealth and longevity. The book comes with full programs, output and identified equations. These can be downloaded from the publishers' website. The book

This book contains many important new results on the theory of wavelet transform, such as its relations with Hilbert transform and other fractional integral operators, convolution for wavelet transform. Wavelet transforms on certain distribution spaces, on spaces of type S and type W, and on generalized Sobolev space have been studied. Asymptotic expansions of the wavelet transform when translation or dilation parameter is large/small have been obtained. So far, these results are not published in book form. The results well-illustrated by means of specific examples and relevant figures will find applications in approximation theory, signal processing and in the study of partial differential equations. An overview of the various topics covered in the book facilitates easy reference. Research workers, interested in these topics, will find many open problems being treated in this book.

Dyadic (Walsh) analysis emerged as a new research area in applied mathematics and engineering in early seventies within attempts to provide answers to demands from practice related to application of spectral analysis of different classes of signals, including audio, video, sonar, and radar signals.

The second volume of the two volumes book is dedicated to various extensions and generalizations of Dyadic (Walsh) analysis and related applications.