This book contains a collection of challenging problems in mathematical analysis which promote creative, nonstandard techniques for solving problems. It brings a host of new mathematical tools and strategies which develop a connection between analysis and other disciplines, such as physics and engineering. It is intended for graduate students in mathematics, as well as for researchers engaged in applied analysis, mathematical physics, and numerical analysis.
F.17 Transfer of existing technologies, know-how, methods and procedures into practice
COBISS.SI-ID: 15240281The doctoral dissertation contains a definition of descending and ascending regions of critical cells of a discrete Morse function. A consistency result for the obtained objects is given: as in the case of smooth Morse functions, a decomposition of the domain into nonintersection regions which are, after possibly finitely many subdivisions and extensions of the underlying discrete vector field, topological discs. A construction based on the discrete vector field is also described. This leads to an algorithm which is applied to qualitative analysis of natural and artificial data sets.
D.09 Tutoring for postgraduate students
COBISS.SI-ID: 15185241