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This book consists of the articles published in the special issues of this Symmetry journal based on twobytwo matrices and harmonic oscillators. The book also contains additional articles published by the guest editor in this Symmetry journal. They are of course based on harmonic oscillators and/or twobytwo matrices. The subject of symmetry is based on exactly soluble problems in physics, and the physical theory is not soluble unless it is based on oscillators and/or twobytwo matrices. The authors of those two special issues were aware of this environment when they submitted their articles. This book could therefore serve as an example to illustrate this important aspect of symmetry problems in physics.
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Historically, the notion of entropy emerged in conceptually very distinct contexts. This book deals with the connection between entropy, probability, and fractional dynamics as they appeared, for example, in solar neutrino astrophysics since the 1970's (Mathai and Rathie 1975, Mathai and Pederzoli 1977, Mathai and Saxena 1978, Mathai, Saxena, and Haubold 2010).The original solar neutrino problem, experimentally and theoretically, was resolved through the discovery of neutrino oscillations and was recently enriched by neutrino entanglement entropy. To reconsider possible new physics of solar neutrinos, diffusion entropy analysis, utilizing Boltzmann entropy, and standard deviation analysis was undertaken with SuperKamiokande solar neutrino data. This analysis revealed a nonGaussian signal with harmonic content. The Hurst exponent is different from the scaling exponent of the probability density function and both Hurst exponent and scaling exponent of the SuperKamiokande data deviate considerably from the value of ½, which indicates that the statistics of the underlying phenomenon is anomalous. Here experiment may provide guidance about the generalization of theory of Boltzmann statistical mechanics. Arguments in the socalled BoltzmannPlanckEinstein discussion related to Planck's discovery of the blackbody radiation law are recapitulated mathematically and statistically and emphasize from this discussion is pursued that a meaningful implementation of the complex ‘entropyprobabilitydynamics’ may offer two ways for explaining the results of diffusion entropy analysis and standard deviation analysis. One way is to consider an anomalous diffusion process that needs to use the fractional spacetime diffusion equation (Gorenflo and Mainardi) and the other way is to consider a generalized Boltzmann entropy by assuming a power law probability density function. Here new mathematical framework, invented by sheer thought, may provide guidance for the generalization of Boltzmann statistical mechanics. In this book Boltzmann entropy, generalized by Tsallis and Mathai, is considered. The second one contains a varying parameter that is used to construct an entropic pathway covering generalized type1 beta, type2 beta, and gamma families of densities. Similarly, pathways for respective distributions and differential equations can be developed. Mathai's entropy is optimized under various conditions reproducing the wellknown Boltzmann distribution, Raleigh distribution, and other distributions used in physics. Properties of the entropy measure for the generalized entropy are examined. In this process the role of special functions of mathematical physics, particularly the Hfunction, is highlighted.
special functions  fractional calculus  entropic functional  mathematical physics  applied analysis  statistical distributions  geometrical probabilities  multivariate analysis
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During the past 10 years, twodimensional materials have found incredible attention in the scientific community. The first twodimensional material studied in detail was graphene, and many groups explored its potential for electronic applications. Meanwhile, researchers have extended their work to twodimensional materials beyond graphene. At present, several hundred of these materials are known and part of them is considered to be useful for electronic applications. Rapid progress has been made in research concerning twodimensional electronics, and a variety of transistors of different twodimensional materials, including graphene, transition metal dichalcogenides, e.g., MoS2 and WS2, and phosphorene, have been reported. Other areas where twodimensional materials are considered promising are sensors, transparent electrodes, or displays, to name just a few. This Special Issue of Electronics is devoted to all aspects of twodimensional materials for electronic applications, including material preparation and analysis, device fabrication and characterization, device physics, modeling and simulation, and circuits. The devices of interest include, but are not limited to transistors (both fieldeffect transistors and alternative transistor concepts), sensors, optoelectronics devices, MEMS and NEMS, and displays.
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This Special Issue "Differential Geometrical Theory of Statistics" collates selected invited and contributed talks presented during the conference GSI'15 on "Geometric Science of Information" which was held at the Ecole Polytechnique, ParisSaclay Campus, France, in October 2015 (Conference web site: http://www.see.asso.fr/gsi2015).
Entropy  Coding Theory  Maximum entropy  Information geometry  Computational Information Geometry  Hessian Geometry  Divergence Geometry  Information topology  Cohomology  Shape Space  Statistical physics  Thermodynamics
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Metasurfaces, the twodimensional analog of metamaterials, have attracted progressively increasing attention in recent years due to their planar configurations and, thus, ease of fabrication, while enabling an unprecedented control over optical fields. The phase, amplitude, polarization, helicity, and even angular momentum of the reflected or transmitted optical fields can be controlled at will by tailoring optically thin planar arrays of resonant subwavelength elements arranged in a periodic or aperiodic manner. As a result, numerous applications and fascinating devices have been realized by designed planar metasurfaces, including beam deflectors, wave plates, flat lenses, holograms, surface wave couplers, and freeform metasurfaces.This Special Issue is launched to provide a possibility for researchers in the area of metasurfaces to highlight the most recent exciting developments and discuss different metasurface configurations in depth, so as to further promote practical applications of metasurfaces. There are 12 papers selected for this Special Issue, representing fascinating progress and potential applications in the area of metasurfaces, which is highly recommended and believed to benefit readers in various aspects.
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Understanding the origins of the Universe and how it works and evolves is the present mission of a large community of physicists. It calls for a large scale vision, involving general relativity, astrophysics, and cosmology. Theoretical physics is presently at an important moment in its history. As predicted by Einstein, gravitational waves have been experimentally proven to exist. With the discovery of the Higgs boson, the set of interactions and elementary particles that is called the ""standard model"" (SM), is complete. Yet the Higgs boson itself, and how it breaks the electroweak symmetry, remains a fascinating subject requiring further studies and verification. Furthermore, several experimental facts are not accounted for by the SM: (i) the baryon asymmetry of the Universe, (ii) the nature and origin of dark matter, and (iii) the origin of neutrino masses; these have no unique, if any, explanation in the SM and yet will require answers from particle physics. We need to explore further both SM and its extensions. This is a subject of papers included in this book, which gives representation to the topics discussed during the Matter to the Deepest conference in 2019 in Poland (http://indico.if.us.edu.pl/event/5).
QED  exponentiation  Wboson  neutrinos  seesaw mechanism  radiative masses  spectrum calculator  axion stars  Bose stars  oscillons  exotic R4 and cosmology  space topology changes  exotic K3  spacetime  gauge symmetry  extension of the standard model of particle interactions  neutrino masses  theoretical physics  particle physics  beyond Standard Model  scalar sector  lepton masses and mixing  family symmetry
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Investigations involving the theory and applications of mathematical analytic tools and techniques are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences. In this Special Issue, we invite and welcome review, expository and original research articles dealing with the recent advances in mathematical analysis and its multidisciplinary applications.
Mathematical (or Higher Transcendental) Functions and Their Applications  Fractional Calculus and Its Applications  qSeries and qPolynomials  Analytic Number Theory  Special Functions of Mathematical Physics and Applied Mathematics  Geometric Function Theory of Complex Analysis
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During the past four decades or so, various operators of fractional calculus, such as those named after Riemann–Liouville, Weyl, Hadamard, Grunwald–Letnikov, Riesz, Erdelyi–Kober, Liouville–Caputo, and so on, have been found to be remarkably popular and important due mainly to their demonstrated applications in numerous diverse and widespread fields of the mathematical, physical, chemical, engineering, and statistical sciences. Many of these fractional calculus operators provide several potentially useful tools for solving differential, integral, differintegral, and integrodifferential equations, together with the fractionalcalculus analogues and extensions of each of these equations, and various other problems involving special functions of mathematical physics, as well as their extensions and generalizations in one and more variables. In this Special Issue, we invite and welcome review, expository, and original research articles dealing with the recent advances in the theory of fractional calculus and its multidisciplinary applications.
operators of fractional calculus  chaos and fractional dynamics  fractional differential  fractional differintegral equations  fractional integrodifferential equations  fractional integrals  fractional derivatives associated with special functions of mathematical physics  applied mathematics  identities and inequalities involving fractional integrals  fractional derivatives
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The book starts with a review of the established facts on the numerical simulations of binary neutron star mergers and simulations of short GRB jets that highlights the issues that need to be revised and further clarified, as the need to understand how the relativistic outflow was launched, what the initial structure of the outflow is, and how it evolved through its interaction with the binary ejecta. Constraints on a local population of faint short duration GRBs are then provided in light of the GW170817/GRB 170817A event at d~40
gammaray bursts  gammaray burst  prompt emission  spectrum  binary neutron stars  short gammaray bursts  GW170817  short gammaray bursts  physics  progenitors  host galaxies  short GRBs  galaxies  compact object mergers
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Various cosmological observations support not only cosmological inflation in the early universe, which is also known as exponential cosmic expansion, but also that the expansion of the latetime universe is accelerating. To explain this phenomenon, the existence of dark energy is proposed. In addition, according to the rotation curve of galaxies, the existence of dark matter, which does not shine, is also suggested. If primordial gravitational waves are detected in the future, the mechanism for realizing inflation can be revealed. Moreover, there exist two main candidates for dark matter. The first is a new particle, the existence of which is predicted in particle physics. The second is an astrophysical object which is not found by electromagnetic waves. Furthermore, there are two representative approaches to account for the accelerated expansion of the current universe. One is to assume the unknown dark energy in general relativity. The other is to extend the gravity theory to large scales. Investigation of the origins of inflation, dark matter, and dark energy is one of the most fundamental problems in modern physics and cosmology. The purpose of this book is to explore the physics and cosmology of inflation, dark matter, and dark energy.
bransdicke theory  dark energy model  cosmological parameters  Dark Energy  statistical analysis  Baryon Acoustic Oscillation (BAO)  Supernovae  cosmological model  Hubble constant  Cosmic Microwave Background (CMB) temperature  n/a  Dark Energy  Dark Matter  memory  dark matter  galactic rotation curve  cosmoligical parameters  dark energy models  loop quantum cosmology  dark energy  spacetime symmetry  de Sitter vacuum  quantum optical systems  astronomical and spaceresearch instrumentation  instruments, apparatus, and components common to several branches of physics and astronomy  normal galaxies, extragalactic objects and systems  field theory  comparative planetology  properties of specific particles  quantum optics  fundamental astronomy  EinsteinAether theory of gravity  dosmological parameters  dark energy models  cosmology  particle physics  cosmo–particle physics  QCD  hypercolor  dark atoms  composite dark matter  scalar–tensor gravity  junction conditions  null hypersurfaces  higher dimension gauged supergravity black hole  quantum gravity  quantum tunneling phenomenon  Hawking radiation  dynamical Chern–Simons modified gravity  parametrizations  cosmological parameters
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