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This volume has been divided into two parts: Geometry and
Applications. The geometry portion of the book relates primarily
to geometric flows, laminations, integral formulae, geometry of
vector fields on Lie groups and osculation; the articles in the
applications portion concern some particular problems of the
theory of dynamical systems, including mathematical problems of
liquid flows and a study of cycles for non-dynamical systems.... more...

In questo libro si raccolgono in modo sistematico i risultati di
oltre vent’anni di ricerche didattiche sul tema delle macchine
matematiche, realizzate in Italia e all’estero, in tutti gli
ordini scolastici. L’esplorazione guidata delle macchine consente
di ricostruire il significato geometrico-spaziale di concetti o
procedure di solito affrontati solo nel quadro algebrico e di
esplorare dinamicamente le configurazioni assunte allo... more...

Provides a thorough introduction to the theory of topological rings
and modules--focusing on problems of topologization and extensions
of ring topologies.

Following on from the success of Fractal Geometry: Mathematical
Foundations and Applications, this new sequel presents a variety of
techniques in current use for studying the mathematics of
fractals.
Much of the material presented in this book has come to the fore in
recent years. This includes methods for studying dimensions and
other parameters of fractal sets and measures, as well as more
sophisticated techniques such as thermodynamic formalism... more...

This book covers the necessary topics for learning the basic
properties of complex manifolds, offering an easy, friendly, and
accessible introduction into the subject while aptly guiding the
reader to topics of current research and to more advanced
publications.
The first half of the book provides an introduction to complex
differential geometry and the properties of complex manifolds.
The second half describes the properties of... more...

The familiar plane geometry of high school figures composed of
lines and circles takes on a new life when viewed as the study of
properties that are preserved by special groups of
transformations. No longer is there a single, universal geometry:
different sets of transformations of the plane correspond to
intriguing, disparate geometries.
This book is the concluding Part IV of Geometric
Transformations, but it can be studied... more...

This book serves as a reference on links and on the invariants
derived via algebraic topology from covering spaces of link
exteriors. It emphasizes the features of the multicomponent case
not normally considered by knot-theorists, such as longitudes, the
homological complexity of many-variable Laurent polynomial rings,
the fact that links are not usually boundary links, free coverings
of homology boundary links, the lower central series as a source of... more...

This comprehensive modern account of the theory of Lie groupoids
and Lie algebroids reveals their importance in differential
geometry, in particular, their relations with Poisson geometry and
general connection theory. It covers much research since the mid
1980s, including the first analysis in book form of Poisson
groupoids, Lie bialgebroids and double vector bundles. The volume
will be of great interest to all learning the modern theory of Lie... more...

This book brings together papers that cover a wide spectrum of
areas and give an unsurpassed overview of research into
differential geometry.

This introductory textbook for a graduate course in pure
mathematics provides a gateway into the two difficult fields of
algebraic geometry and commutative algebra. Algebraic geometry,
supported fundamentally by commutative algebra, is a cornerstone of
pure mathematics.
Along the lines developed by Grothendieck, this book delves into
the rich interplay between algebraic geometry and commutative
algebra. A selection is made from the wealth of... more...