Books in the SpringerBriefs in Mathematical Methods series

This book puts forward a new mathematical theory to study chaotic phenomenon. The uniform theory is established on the basis of two elementary concept of circle and externally tangent square in mathematics. The author studies the uniformity of a finite set of points distributed in space by uniform theory. This book also illustrates that uniform theory performs better than other indices such as entropy and Lyapunov exponent in chaos measurement by numerous examples. This book develops a new mathematical tool for studying chaos so it will be appealing to students and researchers interested in theory of chaos. It also has potential applications in various fields such as Engineering, Forestry and Ecology.

The contents of the book consist of three parts: (i) basic theory of stochastic control and formulation of various option pricing models, (ii) design of finite volume, finite difference and penalty-based algorithms for solving the models and (iii) stability and convergence analysis of the algorithms.

This book presents a concise introduction to piecewise deterministic Markov processes (PDMPs), with particular emphasis on their applications to biological models.

This book develops continuum modeling skills and approaches the topic from three sides: (1) derivation of global integral laws together with the associated local differential equations, (2) design of constitutive laws and (3) modeling boundary processes.

The book also demonstrates the methods on the WikiLeaks Afghan War Diary, the results showing that this approach allows deeper insights into conflict dynamics and allows a strikingly statistically accurate forward prediction of armed opposition group activity in 2010, based solely on data from preceding years.

This is the first book to focus on the topological index, the Harary index, of a graph, including its mathematical properties, chemical applications and some related and attractive open problems.

This book covers the application to two mutation models: single step mutation for microsatellite loci and single-base substitutions.