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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 wellknown 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 realword models; Lie and conditional symmetry classification problems of nonlinear PDEs; the application of symmetrybased methods for finding new exact solutions of nonlinear PDEs (especially reactiondiffusion equations) arising in applications; the application of the Lie method for solving nonlinear initial and boundaryvalue problems (especially those for modelling processes with diffusion, heat transfer, and chemotaxis).
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The problem of evil has vexed for centuries:
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  antitheodicy  theodicy  suffering  epistemic injustice  problem of evil  theodicy  antitheodicy  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
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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 PeterWeyl Theorem, the Pontryaginvan 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 ProLie Groups” by Karl Hofmann and Sidney A. Morris, demonstrates how powerful Lie Theory is in exposing the structure of infinitedimensional 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.
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The development of mathematical techniques, combined with new possibilities of computational simulation, have greatly broadened the study of nonlinear lattices, a theme among the most refined and interdisciplinaryoriented in the field of mathematical physics. This Special Issue mainly focuses on stateoftheart advancements concerning the many facets of nonlinear lattices, from the theoretical ones to more applied ones. The nonlinear 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 spacetime.
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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.
intermetallics  crystal structure  groupsubgroup  magnetic properties  XPS  coloring problem  band structure  structure optimizations  polar intermetallics  ternary Laves phases  electronic structure  Xray diffraction  total energy  stannides  plumbides  alkalineearth  polar intermetallics  symmetry reduction  chemical bond  Zintl  Ca14AlSb11  polar intermetallic  thermoelectric  COHP method  bonding analyses  intermetallic compounds  nitridometalate  crystal structure  powder diffraction  magnetism  Zintl compounds  liquid ammonia  crystal structure  n/a
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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, nonresidential 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 nonresidential 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.
obesity  built environment  activity space  regression analysis  UGCoP  foodscape exposure  activity space  commuting route  spacetime kernel density estimation  timeweighted 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  realtime traffic  crowdedness  wellbeing experience  longdistance 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  lifecourse perspectives  environmental exposures
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Emergent quantum mechanics explores the possibility of an ontology for quantum mechanics. The resurgence of interest in ""deeperlevel"" 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 BroglieBohm 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 deeperlevel 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 nonclassical ontology, which can be fully consistent with the known record of quantum observations in the laboratory.
quantum foundations  nonlocality  retrocausality  Bell’s theorem  Bohmian mechanics  quantum theory  surrealistic trajectories  Bell inequality  quantum mechanics  generalized Lagrangian paths  covariant quantum gravity  emergent spacetime  Gaussianlike solutions  entropy and time evolution  resonances in quantum systems  the Friedrichs model  complex entropy.  Bell’s theorem  the causal arrow of time  retrocausality  superdeterminism  toymodels  quantum ontology  subquantum dynamics  microconstituents  emergent spacetime  emergent quantum gravity  entropic gravity  black hole thermodynamics  SternGerlach  trajectories  spin  Bell theorem  fractal geometry  padic metric  singular limit  gravity  conspiracy  free will  number theory  quantum potential  Feynman paths  weak values  Bohm theory  nohiddenvariables theorems  observables  measurement problem  Bohmian mechanics  primitive ontology  Retrocausation  weak values  Stochastic Electrodynamics  quantum mechanics  decoherence  interpretations  pilotwave theory  Bohmian mechanics  Born rule statistics  measurement problem  quantum thermodynamics  strong coupling  operator thermodynamic functions  quantum theory  de Broglie–Bohm theory  contextuality  atomsurface scattering  bohmian mechanics  matterwave optics  diffraction  vortical dynamics  Schrödinger equation  de Broglie–Bohm theory  nonequilibrium thermodynamics  zeropoint field  de Broglie–Bohm interpretation of quantum mechanics  pilot wave  interiorboundary 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  nonlocality  discrete calculus  iterant  commutator  diffusion constant  LeviCivita 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  spacetime fluctuations  spontaneous state reduction  Poincaré recurrence  symplectic camel  quantum mechanics  Hamiltonian  molecule interference  matterwaves  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 nonequilibrium  Htheorem  ergodicity  ontological quantum mechanics  objective nonsignaling constraint  quantum inaccessibility  epistemic agent  emergent quantum state  selfreferential dynamics  dynamical chaos  computational irreducibility  undecidable dynamics  Turing incomputability  quantum ontology  nonlocality  timesymmetry  retrocausality  quantum causality  conscious agent  emergent quantum mechanics  Bohmian mechanics  de BroglieBohm theory
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This book includes papers in crossdisciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cuttingedge 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 mustread for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.
human behaviour  organisational risk  multicriteria decisionmaking  DEMATEL  bottling process  cellular automata  game of life  brain dynamics  random nonautonomous second order linear differential equation  mean square analytic solution  random power series  uncertainty quantification  systems of nonlinear equations  iterative methods  Newton’s method  order of convergence  computational efficiency  basin of attraction  F110 frigate  decisionmaking  ASW  antitorpedo decoy  AHP  uncertainty modelling  Chikungunya disease  mathematical modeling  nonlinear dynamical systems  numerical simulations  parameter estimation  Markov chain Monte Carlo  block preconditioner  generalized eigenvalue problem  neutron diffusion equation  modified block Newton method  bone repair  macrophages  immune system  cytokines  stem cells  exponential polynomial  discrete dynamical systems  convergence  Hidden Markov models  mathematical linguistics  Voynich Manuscript  IPV  violence index  independence index  model  ode
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Carbon fiber is an oftreferenced 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.
interfacial adhesion  recycled carbon fiber  microwave heating  epoxy curing  thermoforming  prepreg  carbon fiber  fastcure epoxy resin  thermocouple  Seebeck coefficient  conductive yarn  nickelcoated carbon fiber  carbon fibre  surface treatment  polycarbonate  composites  interfacial adhesion  single fibre pull out  CFRP  fatigue  prestressed nearsurface mounted reinforcement (NSMR)  strengthening  tendon  AWJM  stack  CFRP  aluminum UNS A97050  SOM/SEM  kerf taper  surface quality  macrogeometric deviations  Carbon fiber  epoxy composite  cellulose derivative  lignin  surface modification  interfacial adhesion  computed tomography  sandwich composite  Xray transmission  CT cradle  carbon fiber  ethylene tar  isotropic pitch  air blowing  carbon fiber  structural analysis  monocoque structure  lightweight design  low consumption vehicle  threewheeler vehicle  composite  CFRP  thinwall  finite element model  contact problem  block copolymers  dual curing  electron beam  epoxy resins  toughness
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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 nonperturbative theory, such as statistical description. Furthermore, multiscale interactions are responsible for inevitably complex dynamics in strongly nonequilibrium systems, a proper understanding of which remains a main challenge in classical physics. As a remarkable consequence of multiscale interaction, a quasiequilibrium state (the socalled selforganisation) 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, selforganisation, 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 highspeed train, solar wind and industrial application.
pipe flow boundary layer  turbulent transition  large eddy simulation  channel flow  kinetic theory  fluid dynamics  turbulence  selforganisation  shear flows  coherent structures  turbulence  stochastic processes  Langevin equation  FokkerPlanck equation  information length  trailingedge flap  control strategy  floating wind turbine  turbulence  free vortex wake  nonlocal theory  Lévy noise  Tsallis entropy  fractional Fokker–Plank equation  anomalous diffusion  hybrid (U)RANSLES  IDDES methodology  attached and separated flows  complex dynamics  microcavity laser  spatiotemporal chaos  turbulent boundary layer  low speed streaks  magnetic confinement fusion  turbulence  heat transport  Tjunction  denoise  coherent structure  continuous wavelet transform  solar wind  scaling properties  fractals  chaos  turbulence  intermittency  multifractal  thermodynamics  drop breakage  drop coalescence  local intermittency  turbulent flow  population balance equation  high efficiency impeller  Rushton turbine  energy cascade  bifurcations  Lyapunov theory  turbulence  statistical mechanics  intermittency  coherent structure  multiscale problem  selforganisation  bifurcation  nonlocality  scaling  multifractal
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