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Branching Solutions To One-dimensional Variational Problems

2001-01-17 Mathematics
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Release : 2001-01-17
Genre : Mathematics
Kind : eBook
Book Rating : 33X/5 ( reviews)

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Book Synopsis Branching Solutions To One-dimensional Variational Problems by : Alexandr Ivanov

Download or read book Branching Solutions To One-dimensional Variational Problems written by Alexandr Ivanov. This book was released on 2001-01-17. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the new class of one-dimensional variational problems — the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane.

Branching Solutions to One-dimensional Variational Problems

2001 Mathematics
Download Branching Solutions to One-dimensional Variational Problems PDF Online Free

Author :
Release : 2001
Genre : Mathematics
Kind : eBook
Book Rating : 714/5 ( reviews)

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Book Synopsis Branching Solutions to One-dimensional Variational Problems by : Alexander O. Ivanov

Download or read book Branching Solutions to One-dimensional Variational Problems written by Alexander O. Ivanov. This book was released on 2001. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the new class of one-dimensional variational problems OCo the problems with branching solutions. Instead of extreme curves (mappings of a segment to a manifold) we investigate extreme networks, which are mappings of graphs (one-dimensional cell complexes) to a manifold. Various applications of the approach are presented, such as several generalizations of the famous Steiner problem of finding the shortest network spanning given points of the plane. Contents: Preliminary Results; Networks Extremality Criteria; Linear Networks in R N; Extremals of Length Type Functionals: The Case of Parametric Networks; Extremals of Functionals Generated by Norms. Readership: Researchers in differential geometry and topology."

Optimization and Approximation

2017-09-07 Mathematics
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Release : 2017-09-07
Genre : Mathematics
Kind : eBook
Book Rating : 438/5 ( reviews)

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Book Synopsis Optimization and Approximation by : Pablo Pedregal

Download or read book Optimization and Approximation written by Pablo Pedregal. This book was released on 2017-09-07. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a basic, initial resource, introducing science and engineering students to the field of optimization. It covers three main areas: mathematical programming, calculus of variations and optimal control, highlighting the ideas and concepts and offering insights into the importance of optimality conditions in each area. It also systematically presents affordable approximation methods. Exercises at various levels have been included to support the learning process.

Differential Geometric Structures and Applications

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Kind : eBook
Book Rating : 867/5 ( reviews)

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Book Synopsis Differential Geometric Structures and Applications by : Vladimir Rovenski

Download or read book Differential Geometric Structures and Applications written by Vladimir Rovenski. This book was released on . Available in PDF, EPUB and Kindle. Book excerpt:

The Steiner Ratio

2013-03-14 Computers
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Release : 2013-03-14
Genre : Computers
Kind : eBook
Book Rating : 986/5 ( reviews)

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Book Synopsis The Steiner Ratio by : Dietmar Cieslik

Download or read book The Steiner Ratio written by Dietmar Cieslik. This book was released on 2013-03-14. Available in PDF, EPUB and Kindle. Book excerpt: Steiner's Problem concerns finding a shortest interconnecting network for a finite set of points in a metric space. A solution must be a tree, which is called a Steiner Minimal Tree (SMT), and may contain vertices different from the points which are to be connected. Steiner's Problem is one of the most famous combinatorial-geometrical problems, but unfortunately it is very difficult in terms of combinatorial structure as well as computational complexity. However, if only a Minimum Spanning Tree (MST) without additional vertices in the interconnecting network is sought, then it is simple to solve. So it is of interest to know what the error is if an MST is constructed instead of an SMT. The worst case for this ratio running over all finite sets is called the Steiner ratio of the space. The book concentrates on investigating the Steiner ratio. The goal is to determine, or at least estimate, the Steiner ratio for many different metric spaces. The author shows that the description of the Steiner ratio contains many questions from geometry, optimization, and graph theory. Audience: Researchers in network design, applied optimization, and design of algorithms.

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