Kategoria BISAC: Mathematics >> Geometry - General

This monograph deals with mathematical constructions that are foundational in such an important area of data mining as pattern recognition. By using combinatorial and graph theoretic techniques, a closer look is taken at infeasible systems of linear inequalities, whose generalized solutions act as building blocks of geometric decision rules for pattern recognition.
Infeasible systems of linear inequalities prove to be a key object in pattern recognition problems described in geometric terms thanks to the committee method. Such infeasible systems of inequalities represent an important...

This collection of high-quality articles in the field of combinatorics, geometry, algebraic topology and theoretical computer science is a tribute to Jiři Matousek, who passed away prematurely in March 2015. It is a collaborative effort by his colleagues and friends, who have paid particular attention to clarity of exposition - something Jirka would have approved of.

The original research articles, surveys and expository articles, written by leading experts in their respective fields, map Jiři Matousek's numerous areas of mathematical interest.

In this volume, the authors present a collection of surveys on various aspects of the theory of bifurcations of differentiable dynamical systems and related topics. By selecting these subjects, they focus on those developments from which research will be active in the coming years. The surveys are intended to educate the reader on the recent literature on the following subjects: transversality and generic properties like the various forms of the so-called Kupka-Smale theorem, the Closing Lemma and generic local bifurcations of functions (so-called catastrophe theory) and generic local...

Aufbauend auf Grundkenntnissen der Analysis und der linearen Algebra behandelt dieses Lehrbuch die Geometrie der Kegel in geordneten normierten Raumen. Einerseits werden grundlegende Konzepte wie geordnete Vektorraume erlautert, andererseits werden - Grundkenntnisse in der Funktionalanalysis vorausgesetzt - Eigenschaften von Kegeln und deren dualen Kegeln in normierten Raumen systematisch untersucht sowie Kegel im Raum der linearen stetigen Operatoren behandelt.

Diese Ubersetzung vereint die beiden kleinen (in Russisch erschienenen) Broschuren "Einfuhrung in die Theorie der Kegel...

This book explores fundamental aspects of geometric network optimisation with applications to a variety of real world problems. It presents, for the first time in the literature, a cohesive mathematical framework within which the properties of such optimal interconnection networks can be understood across a wide range of metrics and cost functions. The book makes use of this mathematical theory to develop efficient algorithms for constructing such networks, with an emphasis on exact solutions.

Marcus Brazil and Martin Zachariasen focus principally on the geometric structure of...

This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems - those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas. It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad.

Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions. The author uses a...

This book presents a topological approach to combinatorial configurations, in particular graphs, by introducing a new pair of homology and cohomology via polyhedra. On this basis, a number of problems are solved using a new approach, such as the embeddability of a graph on a surface (orientable and nonorientable) with given genus, the Gauss crossing conjecture, the graphicness and cographicness of a matroid, and so forth. Notably, the specific case of embeddability on a surface of genus zero leads to a number of corollaries, including the theorems of Lefschetz (on double coverings), of...