Gamma-Lines

The history of mathematics is to a considerable extent connected with the study of solutions of the equation f(x)=a=const for functions f(x) of one real or complex variable. Therefore it is surprising that we know very little about solutions of u(xy)=A=const for functions of two real variables. These two solutions called level of sets are very important with regard to applications in physics biology and economics as they make a map of appropriate processes described by the function u(xy) for given parameters (xy). This text explores a concept Gamma-lines which generalizes the concept of levels of sets and at the same time the concept of a-points. The authors provide a book on Gamma-lines for the broad specialist and show the large range of their field of applications. The general methods proposed in this volume are useful for both physicists and engineers.