Fractional Calculus View of Complexity

Author: Bruce J. West
Publisher: CRC Press
ISBN: 149873801X
Format: PDF, Mobi
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This book is not a text devoted to a pedagogical presentation of a specialized topic nor is it a monograph focused on the author's area of research. It accomplishes both these things while providing a rationale for why the reader ought to be interested in learning about fractional calculus. This book is for researchers who has heard about many of these scientifically exotic activities, but could not see how they fit into their own scientific interests, or how they could be made compatible with the way they understand science. It is also for beginners who have not yet decided where their scientific talents could be most productively applied. The book provides insight into the long-term direction of science and show how to develop the skills necessary to successfully do research in the twenty-first century.

Nature s Patterns and the Fractional Calculus

Author: Bruce J. West
Publisher: Walter de Gruyter GmbH & Co KG
ISBN: 3110535130
Format: PDF, ePub, Mobi
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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. Contents Complexity Empirical allometry Statistics, scaling and simulation Allometry theories Strange kinetics Fractional probability calculus

Regional Analysis of Time Fractional Diffusion Processes

Author: Fudong Ge
Publisher: Springer
ISBN: 3319728962
Format: PDF, Kindle
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This monograph provides an accessible introduction to the regional analysis of fractional diffusion processes. It begins with background coverage of fractional calculus, functional analysis, distributed parameter systems and relevant basic control theory. New research problems are then defined in terms of their actuation and sensing policies within the regional analysis framework. The results presented provide insight into the control-theoretic analysis of fractional-order systems for use in real-life applications such as hard-disk drives, sleep stage identification and classification, and unmanned aerial vehicle control. The results can also be extended to complex fractional-order distributed-parameter systems and various open questions with potential for further investigation are discussed. For instance, the problem of fractional order distributed-parameter systems with mobile actuators/sensors, optimal parameter identification, optimal locations/trajectory of actuators/sensors and regional actuation/sensing configurations are of great interest. The book’s use of illustrations and consistent examples throughout helps readers to understand the significance of the proposed fractional models and methodologies and to enhance their comprehension. The applications treated in the book run the gamut from environmental science to national security. Academics and graduate students working with cyber-physical and distributed systems or interested in the applications of fractional calculus will find this book to be an instructive source of state-of-the-art results and inspiration for further research.

Simplifying Complexity Life is Uncertain Unfair and Unequal

Author: Bruce J. West
Publisher: Bentham Science Publishers
ISBN: 1681082179
Format: PDF, Kindle
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In life, we often face unavoidable complexities in terms of our ability to understand or influence outcomes. Some questions which arise due to these complexities are: Why can’t the future be made certain? Why do the some people or events always end up at the center of controversy? Why do only a select few get ahead of their peers? Each question pertains to three central elements of complexities and these elements are: uncertainty, inequality and unfairness. Simplifying Complexity explains the scientific study of complex cognitive networks, as well as the methods scientists use to parse difficult problems into manageable pieces. Readers are introduced to scientific methodology and thought processes, followed by a discourse on perspectives on the three elements of complexity through concepts such as normal and non-normal statistics, scaling and complexity management. Simplifying Complexity combines basic cognitive science and scientific philosophy for both advanced students (in the fields of sociology, cognitive science, complex networks and change management) and for general readers looking for a more scientific guide to understanding and managing the nature of change in a complex world.

Contemporary Computational Mathematics A Celebration of the 80th Birthday of Ian Sloan

Author: Josef Dick
Publisher: Springer
ISBN: 3319724568
Format: PDF, ePub, Mobi
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This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.

Eine kurze Geschichte der Menschheit

Author: Yuval Noah Harari
Publisher: DVA
ISBN: 364110498X
Format: PDF, ePub, Docs
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Krone der Schöpfung? Vor 100 000 Jahren war der Homo sapiens noch ein unbedeutendes Tier, das unauffällig in einem abgelegenen Winkel des afrikanischen Kontinents lebte. Unsere Vorfahren teilten sich den Planeten mit mindestens fünf weiteren menschlichen Spezies, und die Rolle, die sie im Ökosystem spielten, war nicht größer als die von Gorillas, Libellen oder Quallen. Vor 70 000 Jahren dann vollzog sich ein mysteriöser und rascher Wandel mit dem Homo sapiens, und es war vor allem die Beschaffenheit seines Gehirns, die ihn zum Herren des Planeten und zum Schrecken des Ökosystems werden ließ. Bis heute hat sich diese Vorherrschaft stetig zugespitzt: Der Mensch hat die Fähigkeit zu schöpferischem und zu zerstörerischem Handeln wie kein anderes Lebewesen. Anschaulich, unterhaltsam und stellenweise hochkomisch zeichnet Yuval Harari die Geschichte des Menschen nach und zeigt alle großen, aber auch alle ambivalenten Momente unserer Menschwerdung.

Eine kurze Geschichte der Zeit

Author: Stephen Hawking
Publisher: Rowohlt Verlag GmbH
ISBN: 3644008612
Format: PDF, ePub
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Ist das Universum unendlich oder begrenzt? Hat die Raumzeit einen Anfang, den Urknall? Dehnt sie sich aus? Wird sie wieder in sich zusammenstürzen? Liefe die Zeit dann rückwärts? Welchen Platz im Universum nehmen wir ein? Und ist in den atemberaubenden Modellen der Kosmologen noch Platz für einen Gott? – Es sind existenzielle Fragen, mit denen sich Stephen Hawking befasst, Fragen, die Forschung und Lehre in den Zentren der modernen Physik ebenso bestimmen wie die Diskussion von Geisteswissenschaftlern. Dieses Meisterwerk eines Jahrhundert-Genies hat unsere Weltsicht verändert. Zugleich hat Stephen Hawking damit neue Maßstäbe für die Erklärung komplexer physikalischer Zusammenhänge gesetzt. In diesem Buch, weltweit inzwischen über zehn Millionen Mal verkauft, ist das Credo des großen Physikers enthalten und lebendig. «Der Physiker Stephen Hawking ist im Begriff, die Formel zu finden, die das Universum erklärt.» ZEIT-Magazin

Laudato si

Author: Franziskus (Papst),
Publisher: Verlag Herder GmbH
ISBN: 345180736X
Format: PDF, ePub, Mobi
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Mit großer Spannung wurde sie erwartet, auch von Nicht-Katholiken: Die Umwelt-Enzyklika von Papst Franziskus nimmt die heute entscheidenden Themen in den Blick; es geht um die geht um soziale, ökologische und politische Zusammenhänge. Wohl selten war ein päpstliches Schreiben so aktuell und brisant und vor allem relevant für alle Gesellschaftsschichten und Menschen weltweit. Mit "Laudato si" beweist Franziskus, dass die Kirche nach wie vor eine unverzichtbare Stimme im Diskurs zur Gestaltung der modernen Welt ist. Wer verstehen will, wie Papst und Kirche die großen Herausforderungen unserer Zeit bestehen wollen, kommt an diesem Werk nicht vorbei. Ein Muss für jeden, der an den drängenden Fragen unserer Zeit interessiert ist.