Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
Author: Wolfgang Reichel
Publsiher: Springer
Total Pages: 158
Release: 2004-05-13
Genre: Mathematics
ISBN: 3540218394

Download Uniqueness Theorems for Variational Problems by the Method of Transformation Groups Book in PDF, Epub and Kindle

A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space V does {\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups

Uniqueness Theorems for Variational Problems by the Method of Transformation Groups
Author: Wolfgang Reichel
Publsiher: Springer
Total Pages: 158
Release: 2004-04-30
Genre: Mathematics
ISBN: 9783540409151

Download Uniqueness Theorems for Variational Problems by the Method of Transformation Groups Book in PDF, Epub and Kindle

A classical problem in the calculus of variations is the investigation of critical points of functionals {\cal L} on normed spaces V. The present work addresses the question: Under what conditions on the functional {\cal L} and the underlying space V does {\cal L} have at most one critical point? A sufficient condition for uniqueness is given: the presence of a "variational sub-symmetry", i.e., a one-parameter group G of transformations of V, which strictly reduces the values of {\cal L}. The "method of transformation groups" is applied to second-order elliptic boundary value problems on Riemannian manifolds. Further applications include problems of geometric analysis and elasticity.

Punctured Torus Groups and 2 Bridge Knot Groups I

Punctured Torus Groups and 2 Bridge Knot Groups  I
Author: Hirotaka Akiyoshi,Makoto Sakuma,Masaaki Wada,Yasushi Yamashita
Publsiher: Springer
Total Pages: 256
Release: 2007-05-26
Genre: Mathematics
ISBN: 9783540718079

Download Punctured Torus Groups and 2 Bridge Knot Groups I Book in PDF, Epub and Kindle

Here is the first part of a work that provides a full account of Jorgensen's theory of punctured torus Kleinian groups and its generalization. It offers an elementary and self-contained description of Jorgensen's theory with a complete proof. Through various informative illustrations, readers are naturally led to an intuitive, synthetic grasp of the theory, which clarifies how a very simple fuchsian group evolves into complicated Kleinian groups.

Lower Central and Dimension Series of Groups

Lower Central and Dimension Series of Groups
Author: Roman Mikhailov,Inder Bir Singh Passi
Publsiher: Springer
Total Pages: 352
Release: 2008-10-20
Genre: Mathematics
ISBN: 9783540858188

Download Lower Central and Dimension Series of Groups Book in PDF, Epub and Kindle

A fundamental object of study in group theory is the lower central series of groups. Understanding its relationship with the dimension series, which consists of the subgroups determined by the augmentation powers, is a challenging task. This monograph presents an exposition of different methods for investigating this relationship. In addition to group theorists, the results are also of interest to topologists and number theorists. The approach is mainly combinatorial and homological. A novel feature is an exposition of simplicial methods for the study of problems in group theory.

Inequalities and Applications 2010

Inequalities and Applications 2010
Author: Catherine Bandle,Attila Gilányi,László Losonczi,Michael Plum
Publsiher: Springer Science & Business Media
Total Pages: 274
Release: 2012-05-26
Genre: Mathematics
ISBN: 9783034802499

Download Inequalities and Applications 2010 Book in PDF, Epub and Kindle

Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, they constitute a challenging research field of their own. Inequalities also appear directly in mathematical models for applications in science, engineering, and economics. This edited volume covers divers aspects of this fascinating field. It addresses classical inequalities related to means or to convexity as well as inequalities arising in the field of ordinary and partial differential equations, like Sobolev or Hardy-type inequalities, and inequalities occurring in geometrical contexts. Within the last five decades, the late Wolfgang Walter has made great contributions to the field of inequalities. His book on differential and integral inequalities was a real breakthrough in the 1970’s and has generated a vast variety of further research in this field. He also organized six of the seven “General Inequalities” Conferences held at Oberwolfach between 1976 and 1995, and co-edited their proceedings. He participated as an honorary member of the Scientific Committee in the “General Inequalities 8” conference in Hungary. As a recognition of his great achievements, this volume is dedicated to Wolfgang Walter’s memory. The “General Inequalities” meetings found their continuation in the “Conferences on Inequalities and Applications” which, so far, have been held twice in Hungary. This volume contains selected contributions of participants of the second conference which took place in Hajdúszoboszló in September 2010, as well as additional articles written upon invitation. These contributions reflect many theoretical and practical aspects in the field of inequalities, and will be useful for researchers and lecturers, as well as for students who want to familiarize themselves with the area.

Optimal Transportation Networks

Optimal Transportation Networks
Author: Marc Bernot,Vicent Caselles,Jean-Michel Morel
Publsiher: Springer Science & Business Media
Total Pages: 204
Release: 2009
Genre: Business & Economics
ISBN: 9783540693147

Download Optimal Transportation Networks Book in PDF, Epub and Kindle

The transportation problem can be formalized as the problem of finding the optimal way to transport a given measure into another with the same mass. In contrast to the Monge-Kantorovitch problem, recent approaches model the branched structure of such supply networks as minima of an energy functional whose essential feature is to favour wide roads. Such a branched structure is observable in ground transportation networks, in draining and irrigation systems, in electrical power supply systems and in natural counterparts such as blood vessels or the branches of trees. These lectures provide mathematical proof of several existence, structure and regularity properties empirically observed in transportation networks. The link with previous discrete physical models of irrigation and erosion models in geomorphology and with discrete telecommunication and transportation models is discussed. It will be mathematically proven that the majority fit in the simple model sketched in this volume.

Compactifying Moduli Spaces for Abelian Varieties

Compactifying Moduli Spaces for Abelian Varieties
Author: Martin C. Olsson
Publsiher: Springer
Total Pages: 286
Release: 2008-07-25
Genre: Mathematics
ISBN: 9783540705192

Download Compactifying Moduli Spaces for Abelian Varieties Book in PDF, Epub and Kindle

This volume presents the construction of canonical modular compactifications of moduli spaces for polarized Abelian varieties (possibly with level structure), building on the earlier work of Alexeev, Nakamura, and Namikawa.

Iterative Approximation of Fixed Points

Iterative Approximation of Fixed Points
Author: Vasile Berinde
Publsiher: Springer
Total Pages: 326
Release: 2007-04-20
Genre: Mathematics
ISBN: 9783540722342

Download Iterative Approximation of Fixed Points Book in PDF, Epub and Kindle

This monograph gives an introductory treatment of the most important iterative methods for constructing fixed points of nonlinear contractive type mappings. For each iterative method considered, it summarizes the most significant contributions in the area by presenting some of the most relevant convergence theorems. It also presents applications to the solution of nonlinear operator equations as well as the appropriate error analysis of the main iterative methods.