Nature’s Patterns and the Fractional Calculus / / Bruce J. West.
Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexit...
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Place / Publishing House: | Berlin ;, Boston : : De Gruyter, , [2017] ©2017 |
Year of Publication: | 2017 |
Language: | English |
Series: | Fractional Calculus in Applied Sciences and Engineering ,
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Physical Description: | 1 online resource (XIV, 199 p.) |
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West, Bruce J., author. aut http://id.loc.gov/vocabulary/relators/aut Nature’s Patterns and the Fractional Calculus / Bruce J. West. Berlin ; Boston : De Gruyter, [2017] ©2017 1 online resource (XIV, 199 p.) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Fractional Calculus in Applied Sciences and Engineering , 2509-7210 ; 2 Frontmatter -- Foreword -- Acknowledgement -- Contents -- 1. Complexity -- 2. Empirical allometry -- 3. Statistics, scaling and simulation -- 4. Allometry theories -- 5. Strange kinetics -- 6. Fractional probability calculus -- Epilogue -- Bibliography -- Index restricted access http://purl.org/coar/access_right/c_16ec online access with authorization star Complexity increases with increasing system size in everything from organisms to organizations. The nonlinear dependence of a system’s functionality on its size, by means of an allometry relation, is argued to be a consequence of their joint dependency on complexity (information). In turn, complexity is proven to be the source of allometry and to provide a new kind of force entailed by a system‘s information gradient. Based on first principles, the scaling behavior of the probability density function is determined by the exact solution to a set of fractional differential equations. The resulting lowest order moments in system size and functionality gives rise to the empirical allometry relations. Taking examples from various topics in nature, the book is of interest to researchers in applied mathematics, as well as, investigators in the natural, social, physical and life sciences. ContentsComplexityEmpirical allometryStatistics, scaling and simulationAllometry theoriesStrange kineticsFractional probability calculus Issued also in print. Mode of access: Internet via World Wide Web. In English. Description based on online resource; title from PDF title page (publisher's Web site, viewed 28. Feb 2023) Allometry. Fractional calculus. Pattern formation (Biology). pattern formation. MATHEMATICS / Complex Analysis. bisacsh Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 9783110762495 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017 9783110719543 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 9783110540550 ZDB-23-DGG Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE ENGLISH 2017 9783110625264 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 9783110548204 ZDB-23-DMA EPUB 9783110534276 print 9783110534115 https://doi.org/10.1515/9783110535136 https://www.degruyter.com/isbn/9783110535136 Cover https://www.degruyter.com/document/cover/isbn/9783110535136/original |
language |
English |
format |
eBook |
author |
West, Bruce J., West, Bruce J., |
spellingShingle |
West, Bruce J., West, Bruce J., Nature’s Patterns and the Fractional Calculus / Fractional Calculus in Applied Sciences and Engineering , Frontmatter -- Foreword -- Acknowledgement -- Contents -- 1. Complexity -- 2. Empirical allometry -- 3. Statistics, scaling and simulation -- 4. Allometry theories -- 5. Strange kinetics -- 6. Fractional probability calculus -- Epilogue -- Bibliography -- Index |
author_facet |
West, Bruce J., West, Bruce J., |
author_variant |
b j w bj bjw b j w bj bjw |
author_role |
VerfasserIn VerfasserIn |
author_sort |
West, Bruce J., |
title |
Nature’s Patterns and the Fractional Calculus / |
title_full |
Nature’s Patterns and the Fractional Calculus / Bruce J. West. |
title_fullStr |
Nature’s Patterns and the Fractional Calculus / Bruce J. West. |
title_full_unstemmed |
Nature’s Patterns and the Fractional Calculus / Bruce J. West. |
title_auth |
Nature’s Patterns and the Fractional Calculus / |
title_alt |
Frontmatter -- Foreword -- Acknowledgement -- Contents -- 1. Complexity -- 2. Empirical allometry -- 3. Statistics, scaling and simulation -- 4. Allometry theories -- 5. Strange kinetics -- 6. Fractional probability calculus -- Epilogue -- Bibliography -- Index |
title_new |
Nature’s Patterns and the Fractional Calculus / |
title_sort |
nature’s patterns and the fractional calculus / |
series |
Fractional Calculus in Applied Sciences and Engineering , |
series2 |
Fractional Calculus in Applied Sciences and Engineering , |
publisher |
De Gruyter, |
publishDate |
2017 |
physical |
1 online resource (XIV, 199 p.) Issued also in print. |
contents |
Frontmatter -- Foreword -- Acknowledgement -- Contents -- 1. Complexity -- 2. Empirical allometry -- 3. Statistics, scaling and simulation -- 4. Allometry theories -- 5. Strange kinetics -- 6. Fractional probability calculus -- Epilogue -- Bibliography -- Index |
isbn |
9783110535136 9783110762495 9783110719543 9783110540550 9783110625264 9783110548204 9783110534276 9783110534115 |
issn |
2509-7210 ; |
url |
https://doi.org/10.1515/9783110535136 https://www.degruyter.com/isbn/9783110535136 https://www.degruyter.com/document/cover/isbn/9783110535136/original |
illustrated |
Not Illustrated |
dewey-hundreds |
500 - Science |
dewey-tens |
510 - Mathematics |
dewey-ones |
515 - Analysis |
dewey-full |
515.83 |
dewey-sort |
3515.83 |
dewey-raw |
515.83 |
dewey-search |
515.83 |
doi_str_mv |
10.1515/9783110535136 |
oclc_num |
1004563253 |
work_keys_str_mv |
AT westbrucej naturespatternsandthefractionalcalculus |
status_str |
n |
ids_txt_mv |
(DE-B1597)477871 (OCoLC)1004563253 |
carrierType_str_mv |
cr |
hierarchy_parent_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 Title is part of eBook package: De Gruyter DG Plus eBook-Package 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE ENGLISH 2017 Title is part of eBook package: De Gruyter EBOOK PACKAGE Mathematics 2017 |
is_hierarchy_title |
Nature’s Patterns and the Fractional Calculus / |
container_title |
Title is part of eBook package: De Gruyter DG Plus DeG Package 2017 Part 1 |
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1770177683096862720 |
fullrecord |
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