Due 2018-09-18
1st ed. 2018, VII, 138 p.
Softcover
ISBN 978-981-13-1597-8
Series
SpringerBriefs in Mathematics
Provides broader examples of Finsler metrics with nice curvature properties
Establishes a lot of beautiful classification theorems
Presents PDE method to study Riemann-Finsler geometry
This book presents properties, examples, rigidity theorems and classification results of such
Finsler metrics. In particular, this book introduces how to investigate spherically symmetric
Finsler geometry using ODE or PDE methods.Spherically symmetric Finsler geometry is a
subject that concerns domains in R^n with spherically symmetric metrics. Recently, a significant
progress has been made in studying Riemannian-Finsler geometry. However, constructing nice
examples of Finsler metrics turn out to be very difficult. In spherically symmetric Finsler
geometry, we find many nice examples with special curvature properties using PDE technique.
The studying of spherically symmetric geometry shows closed relation among geometry, group
and equation.
Due 2018-09-23
1st ed. 2018, XVIII, 315 p.
Hardcover
ISBN 978-3-319-96516-1
Series
Springer Monographs in Mathematics
Interactions Between Them
Provides a comprehensive study of the adic completion and its left-derived
(the local homology functors) for modules and complexes over commutative rings
Studies the relation between ech and local homology, respectively
cohomology, mainly in the setting of an ideal generated by a weakly proregular
sequence and unbounded complexes
Provides the duality between ech (respectively local) homology and
cohomology and further dualities in various new aspects including dualizing complexes
Contains various criteria about completions and an analysis of the role of the
assumptions illustrated by several examples
The aim of the present monograph is a thorough study of the adic-completion, its left derived
functors and their relations to the local cohomology functors, as well as several completeness
criteria, related questions and various dualities formulas. A basic construction is theech
complex with respect to a system of elements and its free resolution. The study of its
homology and cohomology will play a crucial role in order to understand left derived functors
of completion and right derived functors of torsion. This is useful for the extension and
refinement of results known for modules to unbounded complexes in the more general setting
of not necessarily Noetherian rings. The book is divided into three parts. The first one is
devoted to modules, where the adic-completion functor is presented in full details with
generalizations of some previous completeness criteria for modules. Part II is devoted to the
study of complexes. Part III is mainly concerned with duality, starting with those between
completion and torsion and leading to new aspects of various dualizing complexes. The
Appendix covers various additional and complementary aspects of the previous investigations
and also provides examples showing the necessity of the assumptions.
Due 2018-09-21
1st ed. 2018, VIII, 358 p. 42 illus.
Hardcover
ISBN 978-3-319-95224-6
Series
Birkhauser Advanced Texts Basler
Presents a precise definition and examples of the symmetries of a
Hamiltonian, including transformations that depend explicitly on the time
Contains the definition and examples of R-separable solutions of the
Hamilton-?Jacobi equation
Illustrates a complete and simplified proof for the Liouville Theorem and
examples of its application
Includes a complete list of detailed solutions for self-study students
This textbook examines the Hamiltonian formulation in classical mechanics with the basic
mathematical tools of multivariate calculus. It explores topics like variational symmetries,
canonoid transformations, and geometrical optics that are usually omitted from an introductory
classical mechanics course. For students with only a basic knowledge of mathematics and
physics, this book makes those results accessible through worked-out examples and wellchosen
exercises. For readers not familiar with Lagrange equations, the first chapters are
devoted to the Lagrangian formalism and its applications. Later sections discuss canonical
transformations, the Hamilton?Jacobi equation, and the Liouville Theorem on solutions of the
Hamilton?Jacobi equation. Graduate and advanced undergraduate students in physics or
mathematics who are interested in mechanics and applied math will benefit from this
treatment of analytical mechanics. The text assumes the basics of classical mechanics, as well
as linear algebra, differential calculus, elementary differential equations and analytic geometry.
Designed for self-study, this book includes detailed examples and exercises with complete
solutions, although it can also serve as a class text.
ISBN 978-3-319-95224-6 / BIC: PBWR / SPRINGER NATURE: SCM1204X Part of
Prices and other details are subject to change without notice. All errors and omissions excepted. Americas: Tax will
be added where applicable. Canadian residents please add PST, QST or GST. Please add $5.00 for shipping one
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additional book. If an order cannot be fulfilled within 90 days, payment will be refunded upon request. Prices are
payable in US currency or its equivalent.
Due 2018-09-15
1st ed. 2018, Approx. 270 p.
Hardcover
ISBN 978-3-319-94880-5
Series :Abel Symposia
First publication of surveys on recent developments on moduli spaces in
algebraic geometry
Comprehensive collection
Will serve both as a reference and a guide to important directions in the
geometric study of moduli spaces
The proceedings from the Abel Symposium on Geometry of Moduli, held at Svinoya Rorbuer,
Svolvar in Lofoten, in August 2017, present both survey and research articles on the recent
surge of developmentsin understanding moduli problems in algebraic geometry. Written
bymany of the main contributors to this evolving subject, the book provides a
comprehensivecollection of new methods and the various directions in which moduli theory
isadvancing. These include the geometry of moduli spaces, non-reductive geometric
invarianttheory, birational geometry, enumerative geometry, hyper-kahler geometry, syzygies
ofcurves and Brill-Noether theory and stability conditions. Moduli theory is ubiquitous
inalgebraic geometry, and this is reflected in the list of moduli spaces addressed in this
volume: sheaveson varieties, symmetric tensors, abelian differentials, (log) Calabi-Yau varieties,
points onschemes, rational varieties, curves, abelian varieties and hyper-Kahler manifolds.
Due 2018-09-18
1st ed. 2018, VIII, 292 p. 4
illus., 2 illus. in color.
Hardcover
ISBN 978-3-319-95362-5
Unifies recent results in time-optimal control into a new framework for
minimal and maximal time-optimal control problems
Introduces three different types of Pontryagin’s maximum principles from
geometric points of view
Provides examples of control problems for a variety of dynamical systems to
demonstrate applications of time-optimal control
Discusses different ways of using the bang-bang property in finite and infinite
dimensional cases
This monograph develops a framework for time-optimal control problems, focusing on minimal
and maximal time-optimal controls for linear-controlled evolution equations. Its use in optimal
control provides a welcome update to Fattorini’s work on time-optimal and norm-optimal
control problems. By discussing the best way of representing various control problems and
equivalence among them, this systematic study gives readers the tools they need to solve
practical problems in control.After introducing preliminaries in functional analysis, evolution
equations, and controllability and observability estimates, the authors present their time-optimal
control framework, which consists of four elements: a controlled system, a control constraint
set, a starting set, and an ending set. From there, they use their framework to address areas of
recent development in time-optimal control, including the existence of admissible controls and
optimal controls, Pontryagin’s maximum principle for optimal controls, the equivalence of
different optimal control problems, and bang-bang properties. This monograph will appeal to
researchers and graduate students in time-optimal control theory, as well as related areas of
controllability and dynamic programming. For ease of reference, the text itself is self-contained
on the topic of time-optimal control. Frequent examples throughout clarify the applications of
theorems and definitions, although experience with functional analysis and differential
equations will be useful.
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