This volume deals with first and second order complex equations of hyperbolic and mixed types. Various general boundary value problems for linear and quasilinear complex equations are investigated in detail. To obtain results for complex equations of mixed types, some discontinuous boundary value problems for elliptic complex equations are discussed. Mixed complex equations are included in the quasilinear case, and the text considers both boundary value conditions in the general oblique derivative case and multiply connected domains. Complex analytical methods are used to investigate various...

Although the basic statistical theory behind modern genetics is not very difficult, most statistical genetics papers are not easy to read for beginners in the field, and formulae quickly become very tedious to fit a particular area of application. Introduction to Statistical Methods in Modern Genetics distinguishes between the necessary and unnecessary complexity in a presentation designed for graduate-level statistics students. The author keeps derivations simple, but does so without losing the mathematical details. He also provides the required background in modern genetics for those...

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(x, y)=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(x, y) for given parameters (x, y). This text explores a concept, Gamma-lines, which generalizes the...