Space Filling Curves

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Space-Filling Curves

Author : Hans Sagan
Publisher : Springer Science & Business Media
ISBN 13 : 1461208718
Total Pages : 200 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Space-Filling Curves by : Hans Sagan

Download or read book Space-Filling Curves written by Hans Sagan and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of space-filling curves has fascinated mathematicians for over a century and has intrigued many generations of students of mathematics. Working in this area is like skating on the edge of reason. Unfortunately, no comprehensive treatment has ever been attempted other than the gallant effort by W. Sierpiriski in 1912. At that time, the subject was still in its infancy and the most interesting and perplexing results were still to come. Besides, Sierpiriski's paper was written in Polish and published in a journal that is not readily accessible (Sierpiriski [2]). Most of the early literature on the subject is in French, German, and Polish, providing an additional raison d'etre for a comprehensive treatment in English. While there was, understandably, some intensive research activity on this subject around the turn of the century, contributions have, nevertheless, continued up to the present and there is no end in sight, indicating that the subject is still very much alive. The recent interest in fractals has refocused interest on space filling curves, and the study of fractals has thrown some new light on this small but venerable part of mathematics. This monograph is neither a textbook nor an encyclopedic treatment of the subject nor a historical account, but it is a little of each. While it may lend structure to a seminar or pro-seminar, or be useful as a supplement in a course on topology or mathematical analysis, it is primarily intended for self-study by the aficionados of classical analysis.

Space-Filling Curves

Author : Michael Bader
Publisher : Springer Science & Business Media
ISBN 13 : 3642310451
Total Pages : 286 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Space-Filling Curves by : Michael Bader

Download or read book Space-Filling Curves written by Michael Bader and published by Springer Science & Business Media. This book was released on 2012-10-14 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linking the differing techniques deployed in describing space-filling curves to their corresponding algorithms, this book introduces SFCs as tools in scientific computing, focusing in particular on the representation of SFCs and on the resulting algorithms.

Introduction to Global Optimization Exploiting Space-Filling Curves

Author : Yaroslav D. Sergeyev
Publisher : Springer Science & Business Media
ISBN 13 : 1461480426
Total Pages : 125 pages
Book Rating : 4.4/5 (614 download)

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Book Synopsis Introduction to Global Optimization Exploiting Space-Filling Curves by : Yaroslav D. Sergeyev

Download or read book Introduction to Global Optimization Exploiting Space-Filling Curves written by Yaroslav D. Sergeyev and published by Springer Science & Business Media. This book was released on 2013-08-13 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Global Optimization Exploiting Space-Filling Curves provides an overview of classical and new results pertaining to the usage of space-filling curves in global optimization. The authors look at a family of derivative-free numerical algorithms applying space-filling curves to reduce the dimensionality of the global optimization problem; along with a number of unconventional ideas, such as adaptive strategies for estimating Lipschitz constant, balancing global and local information to accelerate the search. Convergence conditions of the described algorithms are studied in depth and theoretical considerations are illustrated through numerical examples. This work also contains a code for implementing space-filling curves that can be used for constructing new global optimization algorithms. Basic ideas from this text can be applied to a number of problems including problems with multiextremal and partially defined constraints and non-redundant parallel computations can be organized. Professors, students, researchers, engineers, and other professionals in the fields of pure mathematics, nonlinear sciences studying fractals, operations research, management science, industrial and applied mathematics, computer science, engineering, economics, and the environmental sciences will find this title useful .

LATIN '95: Theoretical Informatics

Author : Ricardo Baeza-Yates
Publisher : Springer Science & Business Media
ISBN 13 : 9783540591757
Total Pages : 550 pages
Book Rating : 4.5/5 (917 download)

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Book Synopsis LATIN '95: Theoretical Informatics by : Ricardo Baeza-Yates

Download or read book LATIN '95: Theoretical Informatics written by Ricardo Baeza-Yates and published by Springer Science & Business Media. This book was released on 1995-03-20 with total page 550 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume constitutes the proceedings of the Second International Symposium, Latin American Theoretical Informatics, LATIN '95, held in Valparaiso, Chile in April 1995. The LATIN symposia are intended to be comprehensive events on the theory of computing; they provide a high-level forum for theoretical computer science research in Latin America and facilitate a strong and healthy interaction with the international community. The 38 papers presented in this volume were carefully selected from 68 submissions. Despite the intended broad coverage there are quite a number of papers devoted to computational graph theory; other topics strongly represented are complexity, automata theory, networks, symbolic computation, formal languages, data structures, and pattern matching.

Brainfilling Curves - A Fractal Bestiary

Author : Jeffrey Ventrella
Publisher : Lulu.com
ISBN 13 : 0983054622
Total Pages : 206 pages
Book Rating : 4.9/5 (83 download)

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Book Synopsis Brainfilling Curves - A Fractal Bestiary by : Jeffrey Ventrella

Download or read book Brainfilling Curves - A Fractal Bestiary written by Jeffrey Ventrella and published by Lulu.com. This book was released on 2012-03-01 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: * A lovingly-crafted visual expedition, lead by a lifelong fractal wizard with an obsession for categorizing fractal species * Hundreds of beautiful color images * An in-depth taxonomy of Koch-constructed Fractal Curves * An intuitive introduction to Koch construction * A must-read for anyone interested in fractal geometry

Encyclopedia of GIS

Author : Shashi Shekhar
Publisher : Springer Science & Business Media
ISBN 13 : 038730858X
Total Pages : 1392 pages
Book Rating : 4.3/5 (873 download)

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Book Synopsis Encyclopedia of GIS by : Shashi Shekhar

Download or read book Encyclopedia of GIS written by Shashi Shekhar and published by Springer Science & Business Media. This book was released on 2007-12-12 with total page 1392 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of GIS provides a comprehensive and authoritative guide, contributed by experts and peer-reviewed for accuracy, and alphabetically arranged for convenient access. The entries explain key software and processes used by geographers and computational scientists. Major overviews are provided for nearly 200 topics: Geoinformatics, Spatial Cognition, and Location-Based Services and more. Shorter entries define specific terms and concepts. The reference will be published as a print volume with abundant black and white art, and simultaneously as an XML online reference with hyperlinked citations, cross-references, four-color art, links to web-based maps, and other interactive features.

ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics

Author : Luigi Cocchiarella
Publisher : Springer
ISBN 13 : 3319955888
Total Pages : 2334 pages
Book Rating : 4.3/5 (199 download)

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Book Synopsis ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics by : Luigi Cocchiarella

Download or read book ICGG 2018 - Proceedings of the 18th International Conference on Geometry and Graphics written by Luigi Cocchiarella and published by Springer. This book was released on 2018-07-06 with total page 2334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gathers peer-reviewed papers presented at the 18th International Conference on Geometry and Graphics (ICGG), held in Milan, Italy, on August 3-7, 2018. The spectrum of papers ranges from theoretical research to applications, including education, in several fields of science, technology and the arts. The ICGG 2018 mainly focused on the following topics and subtopics: Theoretical Graphics and Geometry (Geometry of Curves and Surfaces, Kinematic and Descriptive Geometry, Computer Aided Geometric Design), Applied Geometry and Graphics (Modeling of Objects, Phenomena and Processes, Applications of Geometry in Engineering, Art and Architecture, Computer Animation and Games, Graphic Simulation in Urban and Territorial Studies), Engineering Computer Graphics (Computer Aided Design and Drafting, Computational Geometry, Geometric and Solid Modeling, Image Synthesis, Pattern Recognition, Digital Image Processing) and Graphics Education (Education Technology Research, Multimedia Educational Software Development, E-learning, Virtual Reality, Educational Systems, Educational Software Development Tools, MOOCs). Given its breadth of coverage, the book introduces engineers, architects and designers interested in computer applications, graphics and geometry to the latest advances in the field, with a particular focus on science, the arts and mathematics education.

Curves for the Mathematically Curious

Author : Julian Havil
Publisher : Princeton University Press
ISBN 13 : 0691206139
Total Pages : 280 pages
Book Rating : 4.6/5 (912 download)

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Book Synopsis Curves for the Mathematically Curious by : Julian Havil

Download or read book Curves for the Mathematically Curious written by Julian Havil and published by Princeton University Press. This book was released on 2021-11-02 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ten amazing curves personally selected by one of today's most important math writers Curves for the Mathematically Curious is a thoughtfully curated collection of ten mathematical curves, selected by Julian Havil for their significance, mathematical interest, and beauty. Each chapter gives an account of the history and definition of one curve, providing a glimpse into the elegant and often surprising mathematics involved in its creation and evolution. In telling the ten stories, Havil introduces many mathematicians and other innovators, some whose fame has withstood the passing of years and others who have slipped into comparative obscurity. You will meet Pierre Bézier, who is known for his ubiquitous and eponymous curves, and Adolphe Quetelet, who trumpeted the ubiquity of the normal curve but whose name now hides behind the modern body mass index. These and other ingenious thinkers engaged with the challenges, incongruities, and insights to be found in these remarkable curves—and now you can share in this adventure. Curves for the Mathematically Curious is a rigorous and enriching mathematical experience for anyone interested in curves, and the book is designed so that readers who choose can follow the details with pencil and paper. Every curve has a story worth telling.

Illustrating Mathematics

Author : Diana Davis
Publisher : American Mathematical Soc.
ISBN 13 : 1470461226
Total Pages : 171 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Illustrating Mathematics by : Diana Davis

Download or read book Illustrating Mathematics written by Diana Davis and published by American Mathematical Soc.. This book was released on 2020-10-16 with total page 171 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is for anyone who wishes to illustrate their mathematical ideas, which in our experience means everyone. It is organized by material, rather than by subject area, and purposefully emphasizes the process of creating things, including discussions of failures that occurred along the way. As a result, the reader can learn from the experiences of those who came before, and will be inspired to create their own illustrations. Topics illustrated within include prime numbers, fractals, the Klein bottle, Borromean rings, tilings, space-filling curves, knot theory, billiards, complex dynamics, algebraic surfaces, groups and prime ideals, the Riemann zeta function, quadratic fields, hyperbolic space, and hyperbolic 3-manifolds. Everyone who opens this book should find a type of mathematics with which they identify. Each contributor explains the mathematics behind their illustration at an accessible level, so that all readers can appreciate the beauty of both the object itself and the mathematics behind it.

Algorithms and Computation

Author : Toshihide Ibaraki
Publisher : Springer Science & Business Media
ISBN 13 : 3540206957
Total Pages : 764 pages
Book Rating : 4.5/5 (42 download)

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Book Synopsis Algorithms and Computation by : Toshihide Ibaraki

Download or read book Algorithms and Computation written by Toshihide Ibaraki and published by Springer Science & Business Media. This book was released on 2003-12-03 with total page 764 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 14th International Symposium on Algorithms and Computation, ISAAC 2003, held in Kyoto, Japan, in December 2003. The 73 revised full papers presented were carefully reviewed and selected from 207 submissions. The papers are organized in topical sections on computational geometry, graph and combinatorial algorithms, computational complexity, quantum computing, combinatorial optimization, scheduling, computational biology, distributed and parallel algorithms, data structures, combinatorial and network optimization, computational complexity and cryptography, game theory and randomized algorithms, and algebraic and arithmetic computation.

High Dimensional Spatial Indexing Using Space-Filling Curves

Author : Ankush Chauhan
Publisher : Grin Publishing
ISBN 13 : 9783668260122
Total Pages : 16 pages
Book Rating : 4.2/5 (61 download)

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Book Synopsis High Dimensional Spatial Indexing Using Space-Filling Curves by : Ankush Chauhan

Download or read book High Dimensional Spatial Indexing Using Space-Filling Curves written by Ankush Chauhan and published by Grin Publishing. This book was released on 2016-07-21 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: Scientific Essay from the year 2015 in the subject Mathematics - Miscellaneous, language: English, abstract: Representation of two dimensional objects into one dimensional space is simple and efficient when using a two coordinate system imposed upon a grid. However, when the two dimensions are expanded far beyond visual and sometimes mental understanding, techniques are used to quantify and simplify the representation of such objects. These techniques center around spatial interpretations by means of a space-filling curve. Since the late 1800's, mathematicians and computer scientists have succeeded with algorithms that express high dimensional geometries. However, very few implementations of the algorithms beyond three dimensions for computing these geometries exist. We propose using the basic spatial computations developed by pioneers in the field like G. Peano, D. Hilbert, E. H. Moore, and others in a working model. The algorithms in this paper are fully implemented in high-level programming languages utilizing a relation database management system. We show the execution speeds of the algorithms using a space-filling curve index for searching compared to brute force searching. Finally, we contrast three space-filling curve algorithms: Moore, Hilbert, and Morton, in execution time of searching for high dimensional data in point queries and range queries.

The Family Tree of Fractal Curves

Author : Jeffrey Ventrella
Publisher : Eyebrain Books
ISBN 13 : 9780983054634
Total Pages : 154 pages
Book Rating : 4.0/5 (546 download)

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Book Synopsis The Family Tree of Fractal Curves by : Jeffrey Ventrella

Download or read book The Family Tree of Fractal Curves written by Jeffrey Ventrella and published by Eyebrain Books. This book was released on 2019-07 with total page 154 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explains a taxonomy of plane-filling curves (fractal curves with a fractal dimension of 2). it includes the classic fractal curves described in Mandelbrot's original book. Many new fractal curves are introduced. The taxonomy is based upon the Gaussian integers and the Eisenstein integers - each forming a lattice (square and triangular). These lattices have algebraic properties, which allows number theory to be used in describing and classifying these curves. This work has been under development for over 30 years. An earlier version of this taxonomy is described in the book ""Brain-filling Curves"", also by Jeffrey Ventrella. More on plane-filling curves can be found at fractalcurves.com

Mathematica in Action

Author : Stan Wagon
Publisher : Springer Science & Business Media
ISBN 13 : 9780387986845
Total Pages : 624 pages
Book Rating : 4.9/5 (868 download)

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Book Synopsis Mathematica in Action by : Stan Wagon

Download or read book Mathematica in Action written by Stan Wagon and published by Springer Science & Business Media. This book was released on 1999 with total page 624 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Mathematica in Action, 2nd Edition," is designed both as a guide to the extraordinary capabilities of Mathematica as well as a detailed tour of modern mathematics by one of its leading expositors, Stan Wagon. Ideal for teachers, researchers, mathematica enthusiasts. This second edition of the highly sucessful W.H. Freeman version includes an 8 page full color insert and 50% new material all organized around Elementary Topics, Intermediate Applications, and Advanced Projects. In addition, the book uses Mathematica 3.0 throughtout. Mathematica 3.0 notebooks with all the programs and examples discussed in the book are available on the TELOS web site (www.telospub.com). These notebooks contain materials suitable for DOS, Windows, Macintosh and Unix computers. Stan Wagon is well-known in the mathematics (and Mathematica) community as Associate Editor of the "American Mathematical Monthly," a columnist for the "Mathematical Intelligencer" and "Mathematica in Education and Research," author of "The Banach-Tarski Paradox" and "Unsolved Problems in Elementary Geometry and Number Theory (with Victor Klee), as well as winner of the 1987 Lester R. Ford Award for Expository Writing.

Giant Molecules

Author : A. I?U. Grosberg
Publisher : World Scientific
ISBN 13 : 9812839224
Total Pages : 347 pages
Book Rating : 4.8/5 (128 download)

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Book Synopsis Giant Molecules by : A. I?U. Grosberg

Download or read book Giant Molecules written by A. I?U. Grosberg and published by World Scientific. This book was released on 2011 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: ?? Giant molecules are important in our everyday life. But, as pointed out by the authors, they are also associated with a culture. What Bach did with the harpsichord, Kuhn and Flory did with polymers. We owe a lot of thanks to those who now make this music accessible ??Pierre-Gilles de GennesNobel Prize laureate in Physics(Foreword for the 1st Edition, March 1996)This book describes the basic facts, concepts and ideas of polymer physics in simple, yet scientifically accurate, terms. In both scientific and historic contexts, the book shows how the subject of polymers is fascinating, as it is behind most of the wonders of living cell machinery as well as most of the newly developed materials. No mathematics is used in the book beyond modest high school algebra and a bit of freshman calculus, yet very sophisticated concepts are introduced and explained, ranging from scaling and reptations to protein folding and evolution. The new edition includes an extended section on polymer preparation methods, discusses knots formed by molecular filaments, and presents new and updated materials on such contemporary topics as single molecule experiments with DNA or polymer properties of proteins and their roles in biological evolution.

Peano

Author : H. Kennedy
Publisher : Springer Science & Business Media
ISBN 13 : 9400989849
Total Pages : 238 pages
Book Rating : 4.4/5 (9 download)

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Book Synopsis Peano by : H. Kennedy

Download or read book Peano written by H. Kennedy and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: All students of mathematics know of Peano's postulates for the natural numbers and his famous space-filling curve, yet their knowledge often stops there. Part of the reason is that there has not until now been a full-scale study of his life and works. This must surely be surprising, when one realizes the length of his academic career (over 50 years) and the extent of his publica tions (over 200) in a wide variety of fields, many of which had immediate and long-term effects on the development of modern mathematics. A study of his life seems long overdue. It appeared to me that the most likely person to write a biography of Peano would be his devoted disciple Ugo Cassina, with whom I studied at the University of Milan in 1957-58. I wrote to Professor Cassina on 29 October, 1963, inquiring if he planned to write the biography, and I offered him my assistance, since I hoped to return to Italy for a year. He replied on 28 November, 1963, suggesting that we collaborate, meaning by this that I would write the biography, in English, using his material and advice. I gladly agreed to this suggestion, but work on the project had hardly begun when Professor Cassina died unexpectedly on 5 October, 1964. I then decided to continue the project on my own. I spent the academic year 1966-67 in Turin; completion of the book took ten years.

The Theory of Functions of a Real Variable and the Theory of Fourier's Series

Author : Ernest William Hobson
Publisher :
ISBN 13 :
Total Pages : 791 pages
Book Rating : 4.L/5 ( download)

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Book Synopsis The Theory of Functions of a Real Variable and the Theory of Fourier's Series by : Ernest William Hobson

Download or read book The Theory of Functions of a Real Variable and the Theory of Fourier's Series written by Ernest William Hobson and published by . This book was released on 1907 with total page 791 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Advanced Computing

Author : Michael Bader
Publisher : Springer Science & Business Media
ISBN 13 : 3642387624
Total Pages : 255 pages
Book Rating : 4.6/5 (423 download)

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Book Synopsis Advanced Computing by : Michael Bader

Download or read book Advanced Computing written by Michael Bader and published by Springer Science & Business Media. This book was released on 2013-09-26 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume collects review articles that summarize research conducted at the Munich Centre of Advanced Computing (MAC) from 2008 to 2012. The articles address the increasing gap between what should be possible in Computational Science and Engineering due to recent advances in algorithms, hardware, and networks, and what can actually be achieved in practice; they also examine novel computing architectures, where computation itself is a multifaceted process, with hardware awareness or ubiquitous parallelism due to many-core systems being just two of the challenges faced. Topics cover both the methodological aspects of advanced computing (algorithms, parallel computing, data exploration, software engineering) and cutting-edge applications from the fields of chemistry, the geosciences, civil and mechanical engineering, etc., reflecting the highly interdisciplinary nature of the Munich Centre of Advanced Computing.