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Author: Jun Kigami
Publisher: Springer Nature
ISBN: 3030541541
Category : Mathematics
Languages : en
Pages : 164
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Book Description
The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.
Author: Jun Kigami
Publisher: Springer Nature
ISBN: 3030541541
Category : Mathematics
Languages : en
Pages : 164
Get Book Here
Book Description
The aim of these lecture notes is to propose a systematic framework for geometry and analysis on metric spaces. The central notion is a partition (an iterated decomposition) of a compact metric space. Via a partition, a compact metric space is associated with an infinite graph whose boundary is the original space. Metrics and measures on the space are then studied from an integrated point of view as weights of the partition. In the course of the text: It is shown that a weight corresponds to a metric if and only if the associated weighted graph is Gromov hyperbolic. Various relations between metrics and measures such as bilipschitz equivalence, quasisymmetry, Ahlfors regularity, and the volume doubling property are translated to relations between weights. In particular, it is shown that the volume doubling property between a metric and a measure corresponds to a quasisymmetry between two metrics in the language of weights. The Ahlfors regular conformal dimension of a compact metric space is characterized as the critical index of p-energies associated with the partition and the weight function corresponding to the metric. These notes should interest researchers and PhD students working in conformal geometry, analysis on metric spaces, and related areas.
Author: Alexander Grigor'yan
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 311070076X
Category : Mathematics
Languages : en
Pages : 526
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Book Description
The book covers the latest research in the areas of mathematics that deal the properties of partial differential equations and stochastic processes on spaces in connection with the geometry of the underlying space. Written by experts in the field, this book is a valuable tool for the advanced mathematician.
Author: Suzanne Lenhart
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110792788
Category : Mathematics
Languages : en
Pages : 365
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Book Description
This volume is dedicated to the legacy of David R. Adams (1941-2021) and discusses calculus of variations, functional - harmonic - potential analysis, partial differential equations, and their applications in modeling, mathematical physics, and differential - integral geometry.
Author: Juha Heinonen
Publisher: Cambridge University Press
ISBN: 1107092345
Category : Mathematics
Languages : en
Pages : 447
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Book Description
This coherent treatment from first principles is an ideal introduction for graduate students and a useful reference for experts.
Author: Tushar Das
Publisher: American Mathematical Soc.
ISBN: 1470434652
Category : Mathematics
Languages : en
Pages : 321
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Book Description
This book presents the foundations of the theory of groups and semigroups acting isometrically on Gromov hyperbolic metric spaces. Particular emphasis is paid to the geometry of their limit sets and on behavior not found in the proper setting. The authors provide a number of examples of groups which exhibit a wide range of phenomena not to be found in the finite-dimensional theory. The book contains both introductory material to help beginners as well as new research results, and closes with a list of attractive unsolved problems.
Author: Csaba D. Toth
Publisher: CRC Press
ISBN: 1351645919
Category : Computers
Languages : en
Pages : 2354
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Book Description
The Handbook of Discrete and Computational Geometry is intended as a reference book fully accessible to nonspecialists as well as specialists, covering all major aspects of both fields. The book offers the most important results and methods in discrete and computational geometry to those who use them in their work, both in the academic world—as researchers in mathematics and computer science—and in the professional world—as practitioners in fields as diverse as operations research, molecular biology, and robotics. Discrete geometry has contributed significantly to the growth of discrete mathematics in recent years. This has been fueled partly by the advent of powerful computers and by the recent explosion of activity in the relatively young field of computational geometry. This synthesis between discrete and computational geometry lies at the heart of this Handbook. A growing list of application fields includes combinatorial optimization, computer-aided design, computer graphics, crystallography, data analysis, error-correcting codes, geographic information systems, motion planning, operations research, pattern recognition, robotics, solid modeling, and tomography.
Author: André Gagalowicz
Publisher: Springer Science & Business Media
ISBN: 3540289690
Category : Computers
Languages : en
Pages : 881
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Book Description
This volume presents the proceedings of the 11th International Conference on Computer Analysis of Images and Patterns (CAIP 2005). This conference - ries started about 20 years ago in Berlin. Initially, the conference served as a forum for meetings between scientists from Western and Eastern-block co- tries. Nowadays, the conference attracts participants from all over the world. The conference gives equal weight to posters and oral presentations, and the selected presentation mode is based on the most appropriate communication medium. The program follows a single-track format, rather than parallel s- sions. Non-overlapping oral and poster sessions ensure that all attendees have the opportunity to interact personally with presenters. As for the numbers, we received a total of 185 submissions. All papers were reviewed by two to four members of the Program Committee. The ?nal selection was carried out by the Conference Chairs. Out of the 185 papers, 65 were - lected for oral presentation and 43 as posters. CAIP is becoming well recognized internationally, and this year’s presentations came from 26 di?erent countries. South Korea proved to be the most active scienti?cally with a total of 16 - cepted papers. At this point, we wish to thank the Program Committee and additional referees for their timely and high-quality reviews. The paper s- mission and review procedure was carried out electronically. We also thank the invited speakers Reinhardt Koch and Thomas Vetter for kindly accepting to present invited papers.
Author: Tamal Krishna Dey
Publisher: Cambridge University Press
ISBN: 1009103199
Category : Mathematics
Languages : en
Pages : 456
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Book Description
Topological data analysis (TDA) has emerged recently as a viable tool for analyzing complex data, and the area has grown substantially both in its methodologies and applicability. Providing a computational and algorithmic foundation for techniques in TDA, this comprehensive, self-contained text introduces students and researchers in mathematics and computer science to the current state of the field. The book features a description of mathematical objects and constructs behind recent advances, the algorithms involved, computational considerations, as well as examples of topological structures or ideas that can be used in applications. It provides a thorough treatment of persistent homology together with various extensions – like zigzag persistence and multiparameter persistence – and their applications to different types of data, like point clouds, triangulations, or graph data. Other important topics covered include discrete Morse theory, the Mapper structure, optimal generating cycles, as well as recent advances in embedding TDA within machine learning frameworks.
Author: N. L. Carothers
Publisher: Cambridge University Press
ISBN: 9780521497565
Category : Mathematics
Languages : en
Pages : 420
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Book Description
A text for a first graduate course in real analysis for students in pure and applied mathematics, statistics, education, engineering, and economics.
Author: Pavel Zezula
Publisher: Springer Science & Business Media
ISBN: 0387291512
Category : Computers
Languages : en
Pages : 227
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Book Description
The area of similarity searching is a very hot topic for both research and c- mercial applications. Current data processing applications use data with c- siderably less structure and much less precise queries than traditional database systems. Examples are multimedia data like images or videos that offer query by example search, product catalogs that provide users with preference based search, scientific data records from observations or experimental analyses such as biochemical and medical data, or XML documents that come from hetero- neous data sources on the Web or in intranets and thus does not exhibit a global schema. Such data can neither be ordered in a canonical manner nor meani- fully searched by precise database queries that would return exact matches. This novel situation is what has given rise to similarity searching, also - ferred to as content based or similarity retrieval. The most general approach to similarity search, still allowing construction of index structures, is modeled in metric space. In this book. Prof. Zezula and his co authors provide the first monograph on this topic, describing its theoretical background as well as the practical search tools of this innovative technology.
