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Lie and non-Lie Symmetries: Theory and Applications for Solving Nonlinear Models

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ISBN: 9783038425267 9783038425274 Year: Pages: XII, 414 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics
Added to DOAB on : 2017-10-25 13:19:05
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Since the end of the 19th century when the prominent Norwegian mathematician Sophus Lie created the theory of Lie algebras and Lie groups and developed the method of their applications for solving differential equations, his theory and method have continuously been the research focus of many well-known mathematicians and physicists. This book is devoted to recent development in Lie theory and its applications for solving physically and biologically motivated equations and models. The book contains the articles published in two Special Issue of the journal Symmetry, which are devoted to analysis and classification of Lie algebras, which are invariance algebras of real-word models; Lie and conditional symmetry classification problems of nonlinear PDEs; the application of symmetry-based methods for finding new exact solutions of nonlinear PDEs (especially reaction-diffusion equations) arising in applications; the application of the Lie method for solving nonlinear initial and boundary-value problems (especially those for modelling processes with diffusion, heat transfer, and chemotaxis).

Theodicy

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ISBN: 9783038972280 / 9783038972297 Year: Pages: 190 DOI: 10.3390/books978-3-03897-229-7 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Religion
Added to DOAB on : 2019-06-26 08:44:06
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The problem of evil has vexed for centuries:

Keywords

theodicy --- queer reading --- gay studies --- liberation theology --- sadomasochism --- suffering --- theodicy --- theodicism --- antitheodicy --- antitheodicism --- realism --- metaphysical realism --- recognition --- acknowledgment --- literature --- the Book of Job --- Roth, Joseph --- creation --- philosophy of religion --- multiverses --- suffering --- black lives matter --- theodicy --- race --- racial disregard --- Marilynne Robinson --- Home --- Gilead trilogy --- problem of evil --- theodicy --- suffering love --- hope --- the problem of evil --- type and token values --- indeterminism --- Paul Celan --- Nelly Sachs --- Martin Heidegger --- Todtnauberg --- Zurichat the Stork --- enestological theodicy --- god --- evil --- infinite value --- the problem of evil --- Anselmianism --- God --- evil --- universe --- world --- multiverse --- Almeida --- problem of evil --- theodicy --- Marilyn Adams --- Richard Swinburne --- mystical body --- god --- evil --- goodness --- religion --- problem of evil --- theodicy --- Qur’an --- Job --- good --- evil --- al Ghaz?l? --- mysticism --- Islam --- theodicy --- problem of evil --- horrendous evil --- disability --- rational moral wish satisfaction --- Marilyn McCord Adams --- anti-theodicy --- theodicy --- suffering --- epistemic injustice --- problem of evil --- theodicy --- anti-theodicy --- Emmanuel Levinas --- Primo Levi --- suffering --- Margaret Cavendish --- theodicy --- problem of evil --- free will --- feminist ethics --- atrocity paradigm --- redemptive goods --- divine justice --- Flannery O’Connor --- Teilhard de Chardin --- good and evil --- theodicy --- Christian vision --- n/a

Topological Groups: Yesterday, Today, Tomorrow

ISBN: 9783038422686 9783038422693 Year: Pages: VIII, 220 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Mathematics
Added to DOAB on : 2016-12-05 09:30:44
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In 1900, David Hilbert asked whether each locally euclidean topological group admits a Lie group structure. This was the fifth of his famous 23 questions which foreshadowed much of the mathematical creativity of the twentieth century. It required half a century of effort by several generations of eminent mathematicians until it was settled in the affirmative. These efforts resulted over time in the Peter-Weyl Theorem, the Pontryagin-van Kampen Duality Theorem for locally compact abelian groups, and finally the solution of Hilbert 5 and the structure theory of locally compact groups, through the combined work of Andrew Gleason, Kenkichi Iwasawa, Deane Montgomery, and Leon Zippin. For a presentation of Hilbert 5 see the 2014 book “Hilbert’s Fifth Problem and Related Topics” by the winner of a 2006 Fields Medal and 2014 Breakthrough Prize in Mathematics, Terence Tao.It is not possible to describe briefly the richness of the topological group theory and the many directions taken since Hilbert 5. The 900 page reference book in 2013 “The Structure of Compact Groups” by Karl H. Hofmann and Sidney A. Morris, deals with one aspect of compact group theory. There are several books on profinite groups including those written by John S. Wilson (1998) and by Luis Ribes and ‎Pavel Zalesskii (2012). The 2007 book “The Lie Theory of Connected Pro-Lie Groups” by Karl Hofmann and Sidney A. Morris, demonstrates how powerful Lie Theory is in exposing the structure of infinite-dimensional Lie groups.The study of free topological groups initiated by A.A. Markov, M.I. Graev and S. Kakutani, has resulted in a wealth of interesting results, in particular those of A.V. Arkhangelʹskiĭ and many of his former students who developed this topic and its relations with topology. The book “Topological Groups and Related Structures” by Alexander Arkhangelʹskii and Mikhail Tkachenko has a diverse content including much material on free topological groups. Compactness conditions in topological groups, especially pseudocompactness as exemplified in the many papers of W.W. Comfort, has been another direction which has proved very fruitful to the present day.

Non-Linear Lattice

ISBN: 9783038423065 9783038423072 Year: Pages: XVI, 274 Language: English
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General)
Added to DOAB on : 2016-12-28 09:52:41
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The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of non-linear lattices, a theme among the most refined and interdisciplinary-oriented in the field of mathematical physics. This Special Issue mainly focuses on state-of-the-art advancements concerning the many facets of non-linear lattices, from the theoretical ones to more applied ones. The non-linear and discrete systems play a key role in all ranges of physical experience, from macrophenomena to condensed matter, up to some models of space discrete space-time.

Compounds with Polar Metallic Bonding

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ISBN: 9783039210701 / 9783039210718 Year: Pages: 154 DOI: 10.3390/books978-3-03921-071-8 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Chemistry (General) --- Inorganic Chemistry
Added to DOAB on : 2019-08-28 11:21:27
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The Special Edition 'Compounds with Polar Metallic Bonding' is a collection of eight original research reports presenting a broad variety of chemical systems, analytical methods, preparative pathways and theoretical descriptions of bonding situations, with the common aim of understanding the complex interplay of conduction electrons in intermetallic compounds that possess different types of dipoles. Coulombic dipoles introduced by electronegativity differences, electric or magnetic dipoles, polarity induced by symmetry reduction—all the possible facets of the term 'polarity'—can be observed in polar intermetallic phases and have their own and, in most cases, unique consequences on the physical and chemical behaviour. Elucidation of the structure–property relationships in compounds with polar metallic bonding is a modern and growing scientific field which combines solid state physics, preparative chemistry, metallurgy, modern analytic methods, crystallography, theoretical calculations of the electronic state and many more disciplines.

Human Mobility, Spatiotemporal Context, and Environmental Health: Recent Advances in Approaches and Methods

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ISBN: 9783039211838 / 9783039211845 Year: Pages: 382 DOI: 10.3390/books978-3-03921-184-5 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Medicine (General)
Added to DOAB on : 2019-08-28 11:21:27
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Environmental health researchers have long used concepts like the neighborhood effect to assessing people’s exposure to environmental influences and the associated health impact. However, these are static notions that ignore people’s daily mobility at various spatial and temporal scales (e.g., daily travel, migratory movements, and movements over the life course) and the influence of neighborhood contexts outside their residential neighborhoods. Recent studies have started to incorporate human mobility, non-residential neighborhoods, and the temporality of exposures through collecting and using data from GPS, accelerometers, mobile phones, various types of sensors, and social media. Innovative approaches and methods have been developed. This Special Issue aims to showcase studies that use new approaches, methods, and data to examine the role of human mobility and non-residential contexts on human health behaviors and outcomes. It includes 21 articles that cover a wide range of topics, including individual exposure to air pollution, exposure and access to green spaces, spatial access to healthcare services, environmental influences on physical activity, food environmental and diet behavior, exposure to noise and its impact on mental health, and broader methodological issues such as the uncertain geographic context problem (UGCoP) and the neighborhood effect averaging problem (NEAP). This collection will be a valuable reference for scholars and students interested in recent advances in the concepts and methods in environmental health and health geography.

Keywords

obesity --- built environment --- activity space --- regression analysis --- UGCoP --- foodscape exposure --- activity space --- commuting route --- space-time kernel density estimation --- time-weighted exposure --- Beijing --- cycling for transportation --- bike paths --- train stations --- subway stations --- adults --- Brazil --- fuel consumption --- emissions estimation --- GPS trace --- big data --- air pollution exposure --- human mobility --- mobile phone data --- dynamic assessment --- GIS --- GPS --- activity space --- environmental exposure --- the uncertain geographic context problem --- noise pollution --- mental disorders --- built environment --- multilevel model --- China --- PM concentrations --- crop residue burning --- correlation analysis --- interannual and seasonal variations --- China --- the neighborhood effect averaging problem (NEAP) --- human mobility --- environmental exposure --- the uncertain geographic context problem --- UGCoP --- car ownership --- car use --- built environment --- spatial autocorrelation --- multilevel Bayesian model --- geographical accessibility --- Healthcare services --- GIS --- E2SFCA --- CHAS --- Singapore --- environmental health --- food environment --- environmental context cube --- environmental context exposure index --- the uncertain geographic context problem (UGCoP) --- GPS --- GIS --- healthcare accessibility --- catchment areas --- access probability --- taxi GPS trajectories --- E2SFCA --- greenspace exposure --- health --- human mobility --- physical activity --- structural equation modeling --- Guangzhou --- healthcare accessibility --- population demand --- geographic impedance --- the elderly --- urban planning --- 3SFCA --- real-time traffic --- crowdedness --- well-being experience --- long-distance walking --- collective leisure activity --- walking event --- urban leisure --- missing data --- spatial data --- imputation --- geographic imputation --- activity space --- ecological momentary assessment --- EMA --- walking --- active travel --- ageing --- physical environment --- personal projects --- activity space --- Public Participatory GIS (PPGIS) --- spatial accessibility --- multimodal network --- primary healthcare --- China --- 2009 influenza A(H1N1) pandemic --- transport modes --- rail travel --- spatial spread --- quantile regression --- green space --- road traffic accidents --- cognitive aging --- activity space --- life-course perspectives --- environmental exposures

Emergent Quantum Mechanics. David Bohm Centennial Perspectives

Authors: --- --- ---
ISBN: 9783038976165 Year: Pages: 544 DOI: 10.3390/books978-3-03897-617-2 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Physics (General) --- Science (General)
Added to DOAB on : 2019-04-05 10:34:31
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Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in ""deeper-level"" theories for quantum phenomena challenges the standard, textbook interpretation. The book presents expert views that critically evaluate the significance—for 21st century physics—of ontological quantum mechanics, an approach that David Bohm helped pioneer. The possibility of a deterministic quantum theory was first introduced with the original de Broglie-Bohm theory, which has also been developed as Bohmian mechanics. The wide range of perspectives that were contributed to this book on the occasion of David Bohm’s centennial celebration provide ample evidence for the physical consistency of ontological quantum mechanics. The book addresses deeper-level questions such as the following: Is reality intrinsically random or fundamentally interconnected? Is the universe local or nonlocal? Might a radically new conception of reality include a form of quantum causality or quantum ontology? What is the role of the experimenter agent? As the book demonstrates, the advancement of ‘quantum ontology’—as a scientific concept—marks a clear break with classical reality. The search for quantum reality entails unconventional causal structures and non-classical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.

Keywords

quantum foundations --- nonlocality --- retrocausality --- Bell’s theorem --- Bohmian mechanics --- quantum theory --- surrealistic trajectories --- Bell inequality --- quantum mechanics --- generalized Lagrangian paths --- covariant quantum gravity --- emergent space-time --- Gaussian-like solutions --- entropy and time evolution --- resonances in quantum systems --- the Friedrichs model --- complex entropy. --- Bell’s theorem --- the causal arrow of time --- retrocausality --- superdeterminism --- toy-models --- quantum ontology --- sub-quantum dynamics --- micro-constituents --- emergent space-time --- emergent quantum gravity --- entropic gravity --- black hole thermodynamics --- Stern-Gerlach --- trajectories --- spin --- Bell theorem --- fractal geometry --- p-adic metric --- singular limit --- gravity --- conspiracy --- free will --- number theory --- quantum potential --- Feynman paths --- weak values --- Bohm theory --- no-hidden-variables theorems --- observables --- measurement problem --- Bohmian mechanics --- primitive ontology --- Retrocausation --- weak values --- Stochastic Electrodynamics --- quantum mechanics --- decoherence --- interpretations --- pilot-wave theory --- Bohmian mechanics --- Born rule statistics --- measurement problem --- quantum thermodynamics --- strong coupling --- operator thermodynamic functions --- quantum theory --- de Broglie–Bohm theory --- contextuality --- atom-surface scattering --- bohmian mechanics --- matter-wave optics --- diffraction --- vortical dynamics --- Schrödinger equation --- de Broglie–Bohm theory --- nonequilibrium thermodynamics --- zero-point field --- de Broglie–Bohm interpretation of quantum mechanics --- pilot wave --- interior-boundary condition --- ultraviolet divergence --- quantum field theory --- Aharonov–Bohm effect --- physical ontology --- nomology --- interpretation --- gauge freedom --- Canonical Presentation --- relational space --- relational interpretation of quantum mechanics --- measurement problem --- non-locality --- discrete calculus --- iterant --- commutator --- diffusion constant --- Levi-Civita connection --- curvature tensor --- constraints --- Kilmister equation --- Bianchi identity --- stochastic differential equations --- Monte Carlo simulations --- Burgers equation --- Langevin equation --- fractional velocity --- interpretations of quantum mechanics --- David Bohm --- mind–body problem --- quantum holism --- fundamental irreversibility --- space-time fluctuations --- spontaneous state reduction --- Poincaré recurrence --- symplectic camel --- quantum mechanics --- Hamiltonian --- molecule interference --- matter-waves --- metrology --- magnetic deflectometry --- photochemistry --- past of the photon --- Mach–Zehnder interferometer --- Dove prism --- photon trajectory --- weak measurement --- transition probability amplitude --- atomic metastable states --- Bell’s theorem --- Bohmian mechanics --- nonlocality --- many interacting worlds --- wavefunction nodes --- bouncing oil droplets --- stochastic quantum dynamics --- de Broglie–Bohm theory --- quantum non-equilibrium --- H-theorem --- ergodicity --- ontological quantum mechanics --- objective non-signaling constraint --- quantum inaccessibility --- epistemic agent --- emergent quantum state --- self-referential dynamics --- dynamical chaos --- computational irreducibility --- undecidable dynamics --- Turing incomputability --- quantum ontology --- nonlocality --- time-symmetry --- retrocausality --- quantum causality --- conscious agent --- emergent quantum mechanics --- Bohmian mechanics --- de Broglie-Bohm theory

Mathematical Modelling in Engineering & Human Behaviour 2018

Authors: --- ---
ISBN: 9783038978046 / 9783038978053 Year: Pages: 196 DOI: 10.3390/books978-3-03897-805-3 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-06-26 10:09:00
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This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.

Carbon Fibers and Their Composite Materials

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ISBN: 9783039211029 / 9783039211036 Year: Pages: 186 DOI: 10.3390/books978-3-03921-103-6 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Chemistry (General)
Added to DOAB on : 2019-08-28 11:21:27
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Carbon fiber is an oft-referenced material that serves as a means to remove mass from large transport infrastructure. Carbon fiber composites, typically plastics reinforced with the carbon fibers, are key materials in the 21st century and have already had a significant impact on reducing CO2 emissions. Though, as with any composite material, the interface where each component meets, in this case the fiber and plastic, is critical to the overall performance.

Intermittency and Self-Organisation in Turbulence and Statistical Mechanics

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ISBN: 9783039211081 / 9783039211098 Year: Pages: 298 DOI: 10.3390/books978-3-03921-109-8 Language: eng
Publisher: MDPI - Multidisciplinary Digital Publishing Institute
Subject: Science (General) --- Mathematics
Added to DOAB on : 2019-08-28 11:21:27
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There is overwhelming evidence, from laboratory experiments, observations, and computational studies, that coherent structures can cause intermittent transport, dramatically enhancing transport. A proper description of this intermittent phenomenon, however, is extremely difficult, requiring a new non-perturbative theory, such as statistical description. Furthermore, multi-scale interactions are responsible for inevitably complex dynamics in strongly non-equilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multi-scale interaction, a quasi-equilibrium state (the so-called self-organisation) can however be maintained. This special issue aims to present different theories of statistical mechanics to understand this challenging multiscale problem in turbulence. The 14 contributions to this Special issue focus on the various aspects of intermittency, coherent structures, self-organisation, bifurcation and nonlocality. Given the ubiquity of turbulence, the contributions cover a broad range of systems covering laboratory fluids (channel flow, the Von Kármán flow), plasmas (magnetic fusion), laser cavity, wind turbine, air flow around a high-speed train, solar wind and industrial application.

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