This book is composed of several sections which follow one another for flow. The focus is on the Whitehead theorem which implies that a space W is contractible if and only if W is both acyclic and has trivial fundamental group. So one would expect the fundamental group of an acyclic space to contain a lot of information. Moreover, acyclic spaces can be characterized in this way. This book contains super results for modern global analysis.

This book is a nice expository text to the study of elementary operators and tensor products.Technically speaking, tensor product is a technical approach used in analysis in solving problems and it is one of the nice approaches used in solving problems involving properties of elementary operators. good and simple examples are used for easy understanding of the book. There are also several examples that can help the learner to relate the ideas in this book with applications in other areas like physics.

This book examines the time vibration of the displacement of a structure due to the internal forces, with no damping or external forcing. Practically, vibrations decay with time but in theory these vibrations do not actually decay. For vibrations due to purely internal forces, the dynamic systems are referred to as conservative systems. The methods of solution adopted for solving non-linear single-degree-of-freedom problems may be extended to multi-degree-of-freedom problems. There are many studies in literature on the application of these methods of solution to linear problems and yet so few...

This book is about modeling of infectious diseases which are normally recurrent. The human immunodeficiency virus (HIV) pandemic presents a massive challenge to the control of recurrent diseases like tuberculosis (TB) at all levels. Tuberculosis is also one of the most common causes of morbidity and one of the leading causes of mortality in people living with HIV/AIDS (PLWHA). In this book, various mathematical models that capture the role played by HIV/AIDS in accelerating the infection and hence spread of Tuberculosis. We looked at TB progression among people with HIV and those without. The...

This book is about the estimation of market volatility (or variance of returns of an asset) is a crucial issue in modern applied finance. The measure of volatility and good forecasts of future volatility are crucial for implementation, evaluation of asset and derivative pricing of asset. In particular, volatility has been used in financial markets in assessments of risk associated with short-term fluctuations in financial time-series. Volatility has a key role to play in the determination of a risk and in the valuation of options and other derivative securities. Exercises and examples are...