Exploring Non Orientable Topology Deriving The Poincar Conjecture And Possibility Of Experimental Vindication With Liquid Crystal
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Exploring Non Orientable Topology Deriving The Poincar Conjecture And Possibility Of Experimental Vindication With Liquid Crystal
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Author : Victor Christianto
language : en
Publisher: Infinite Study
Release Date : 2023-11-11
Exploring Non Orientable Topology Deriving The Poincar Conjecture And Possibility Of Experimental Vindication With Liquid Crystal written by Victor Christianto and has been published by Infinite Study this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-11-11 with Mathematics categories.
This review investigates the potential of non-orientable topology as a fundamental framework for understanding the Poincaré conjecture and its implications across various scientific disciplines. Integrating insights from Dokuchaev (2020), Rapoport, Christianto, Chandra, Smarandache (under review), and other pioneering works, this article explores the theoretical foundations linking non-orientable spaces to resolving the Poincaré conjecture and its broader implications in theoretical physics, geology, cosmology, and biology.
Ricci Flow And The Poincare Conjecture
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Author : John W. Morgan
language : en
Publisher: American Mathematical Soc.
Release Date : 2007
Ricci Flow And The Poincare Conjecture written by John W. Morgan and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
For over 100 years the Poincare Conjecture, which proposes a topological characterization of the 3-sphere, has been the central question in topology. Since its formulation, it has been repeatedly attacked, without success, using various topological methods. Its importance and difficulty were highlighted when it was chosen as one of the Clay Mathematics Institute's seven Millennium Prize Problems. in 2002 and 2003 Grigory Perelman posted three preprints showing how to use geometric arguments, in particular the Ricci flow as introduced and studied by Hamilton, to establish the Poincare Conjecture in the affirmative. This book provides full details of a complete proof of the Poincare Conjecture following Perelman's three preprints. After a lengthy introduction that outlines the entire argument, the book is divided into four parts. The first part reviews necessary results from Riemannian geometry and Ricci flow, including much of Hamilton's work. The second part starts with Perelman's length function, which is used to establish crucial non-collapsing theorems. Then it discusses the classification of non-collapsed, ancient solutions to the Ricci flow equation. The third part concerns the existence of Ricci flow with surgery for all positive time and an analysis of the topological and geometric changes introduced by surgery. The last part follows Perelman's third preprint to prove that when the initial Riemannian 3-manifold has finite fundamental group, Ricci flow with surgery becomes extinct after finite time. The proofs of the Poincare Conjecture and the closely related 3-dimensional spherical space-form conjectu The existence of Ricci flow with surgery has application to 3-manifolds far beyond the Poincare Conjecture. It forms the heart of the proof via Ricci flow of Thurston's Geometrization Conjecture. Thurston's Geometrization Conjecture, which classifies all compact 3-manifolds, will be the subject of a follow-up article. The organization of the material in this book differs from that given by Perelman. From the beginning the authors present all analytic and geometric arguments in the context of Ricci flow with surgery. in addition, the fourth part is a much-expanded version of Perelman's third preprint; it gives the first complete and detailed proof of the finite-time extinction theorem. With the large amount of background material that is presented and the detailed versions of the central arguments, this book is suitable for all mathematicians from advanced graduate students to specialists in geometry and topology. Clay Mathematics Institute Monograph Series The Clay Mathematics Institute Monograph Series publishes selected expositions of recent developments, both in emerging areas and in older subjects transformed by new insights or unifying ideas. Information for our distributors: Titles in this series are co-published with the Clay Mathematics Institute (Cambridge, MA).
Tales Of Physicists And Mathematicians
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Author : Simon Gindikin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Tales Of Physicists And Mathematicians written by Simon Gindikin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
This revised and greatly expanded edition of the Russian classic contains a wealth of new information about the lives of many great mathematicians and scientists, past and present. Written by a distinguished mathematician and featuring a unique mix of mathematics, physics, and history, this text combines original source material and provides careful explanations for some of the most significant discoveries in mathematics and physics. What emerges are intriguing, multifaceted biographies that will interest readers at all levels.
Biological Autonomy
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Author : Alvaro Moreno
language : en
Publisher: Springer
Release Date : 2015-05-04
Biological Autonomy written by Alvaro Moreno and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-05-04 with Philosophy categories.
Since Darwin, Biology has been framed on the idea of evolution by natural selection, which has profoundly influenced the scientific and philosophical comprehension of biological phenomena and of our place in Nature. This book argues that contemporary biology should progress towards and revolve around an even more fundamental idea, that of autonomy. Biological autonomy describes living organisms as organised systems, which are able to self-produce and self-maintain as integrated entities, to establish their own goals and norms, and to promote the conditions of their existence through their interactions with the environment. Topics covered in this book include organisation and biological emergence, organisms, agency, levels of autonomy, cognition, and a look at the historical dimension of autonomy. The current development of scientific investigations on autonomous organisation calls for a theoretical and philosophical analysis. This can contribute to the elaboration of an original understanding of life - including human life - on Earth, opening new perspectives and enabling fecund interactions with other existing theories and approaches. This book takes up the challenge.
On Art And Science
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Author : Shyam Wuppuluri
language : en
Publisher: Springer Nature
Release Date : 2019-11-02
On Art And Science written by Shyam Wuppuluri and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-02 with Science categories.
Einstein once remarked "After a certain high level of technical skill is achieved, science and art tend to coalesce in aesthetics, plasticity, and form. The greatest scientists are always artists as well". In this volume, some of the world’s leading thinkers come together to expound on the interrelations between sciences and arts. While one can segregate art and place it outside the scientific realm, it is, nevertheless, inextricably linked to our essential cognitive/emotional/perceptual modalities and abilities, and therefore lies alongside and in close contact with the method of science and philosophy. What inspiration can scientists draw from art and how can scientific spirit foster our understanding and creation of aesthetic works? How are art and science grounded in our cognition? What role does perception play in science and art? Are criteria for beauty in art and science the same? How does evolution shape our understanding of art? How do science, art and scientifico-artistic frameworks shape society as a whole and help us address its pressing issues? The epistemological and ontological aspects haunt artists, philosophers and scientists alike. The essays in this volume address these manifold questions while also elucidating the pragmatic role they play in our daily life.
Waves And Particles In Light And Matter
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Author : Augusto Garuccio
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Waves And Particles In Light And Matter written by Augusto Garuccio and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
From September 24 through 30, 1992 the Workshop on "Waves and Parti cles in Light and Matter" was held in the Italian city of Trani in celebration of the centenary of Louis de Broglie's birth. As is well known, the relationship between quantum theory and ob jective reality was one of the main threads running through the researches of this French physicist. It was therefore in a fitting tribute to him on his 90th birthday that ten years ago an international conference on the same subject was convened in Perugia. On that occasion, physicists from all over the world interested in the problematics of wave-particle duality engaged in thoughtful debates (the proceedings of which were subsequently published) on recent theoretical and experimental developments in our understanding of the foundations of quantum mechanics. This time around, about 120 scientists, coming from 5 continents, in the warm and pleasant atmosphere of Trani's Colonna Conference Center focussed their discussions on recent results concerned with the EPR para dox, matter-interferometry, reality of de Broglie's waves, photon detection, macroscopic quantum coherence, alternative theories to usual quantum mechanics, special relativity, state reduction, and other related topics. The workshop was organized in plenary sessions, round tables, and poster sessions, and the present volume collects most-but not all-of the presented papers. A number of acknowledgements are due. We thank, first of all, the contributors, without whose constant dedication this volume could not have been published.
The Reality Of The Unobservable
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Author : E. Agazzi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
The Reality Of The Unobservable written by E. Agazzi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Science categories.
Observability and Scientific Realism It is commonly thought that the birth of modern natural science was made possible by an intellectual shift from a mainly abstract and specuJative conception of the world to a carefully elaborated image based on observations. There is some grain of truth in this claim, but this grain depends very much on what one takes observation to be. In the philosophy of science of our century, observation has been practically equated with sense perception. This is understandable if we think of the attitude of radical empiricism that inspired Ernst Mach and the philosophers of the Vienna Circle, who powerfully influenced our century's philosophy of science. However, this was not the atti tude of the f ounders of modern science: Galileo, f or example, expressed in a f amous passage of the Assayer the conviction that perceptual features of the world are merely subjective, and are produced in the 'anima!' by the motion and impacts of unobservable particles that are endowed uniquely with mathematically expressible properties, and which are therefore the real features of the world. Moreover, on other occasions, when defending the Copernican theory, he explicitly remarked that in admitting that the Sun is static and the Earth turns on its own axis, 'reason must do violence to the sense' , and that it is thanks to this violence that one can know the tme constitution of the universe.
Electrodynamics From Amp Re To Einstein
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Author : Olivier Darrigol
language : en
Publisher: Oxford University Press
Release Date : 2003-06-26
Electrodynamics From Amp Re To Einstein written by Olivier Darrigol and has been published by Oxford University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Medical categories.
This book recounts the developments of fundamental electrodynamics from Ampère's investigation of the forces between electric currents to Einstein's introduction of a new doctrine of space and time. The emphasis is on the diverse, evolving practices of electrodynamics and the interactions between the corresponding scientific traditions. A richly documented, clearly written, and abundantly illustrated history of the subject.
Computing Nature
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Author : Gordana Dodig-Crnkovic
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-21
Computing Nature written by Gordana Dodig-Crnkovic and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-21 with Technology & Engineering categories.
This book is about nature considered as the totality of physical existence, the universe, and our present day attempts to understand it. If we see the universe as a network of networks of computational processes at many different levels of organization, what can we learn about physics, biology, cognition, social systems, and ecology expressed through interacting networks of elementary particles, atoms, molecules, cells, (and especially neurons when it comes to understanding of cognition and intelligence), organs, organisms and their ecologies? Regarding our computational models of natural phenomena Feynman famously wondered: “Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do?” Phenomena themselves occur so quickly and automatically in nature. Can we learn how to harness nature’s computational power as we harness its energy and materials? This volume includes a selection of contributions from the Symposium on Natural Computing/Unconventional Computing and Its Philosophical Significance, organized during the AISB/IACAP World Congress 2012, held in Birmingham, UK, on July 2-6, on the occasion of the centenary of Alan Turing’s birth. In this book, leading researchers investigated questions of computing nature by exploring various facets of computation as we find it in nature: relationships between different levels of computation, cognition with learning and intelligence, mathematical background, relationships to classical Turing computation and Turing’s ideas about computing nature - unorganized machines and morphogenesis. It addresses questions of information, representation and computation, interaction as communication, concurrency and agent models; in short this book presents natural computing and unconventional computing as extension of the idea of computation as symbol manipulation.
Introduction To The Philosophy Of Science
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Author : Merrilee H. Salmon
language : en
Publisher: Hackett Publishing
Release Date : 1999-01-01
Introduction To The Philosophy Of Science written by Merrilee H. Salmon and has been published by Hackett Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Science categories.
Originally published: Englewood Cliffs, N.J.: Prentice Hall, c1992.