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Prototypical quantum optics models, such as the Jaynes–Cummings, Rabi, Tavis–Cummings, and Dicke models, are commonly analyzed with diverse techniques, including analytical exact solutions, meanfield theory, exact diagonalization, and so on. Analysis of these systems strongly depends on their symmetries, ranging, e.g., from a U(1) group in the Jaynes–Cummings model to a Z2 symmetry in the fullfledged quantum Rabi model. In recent years, novel regimes of light–matter interactions, namely, the ultrastrong and deepstrong coupling regimes, have been attracting an increasing amount of interest. The quantum Rabi and Dicke models in these exotic regimes present new features, such as collapses and revivals of the population, bounces of photonnumber wave packets, as well as the breakdown of the rotatingwave approximation. Symmetries also play an important role in these regimes and will additionally change depending on whether the few or manyqubit systems considered have associated inhomogeneous or equal couplings to the bosonic mode. Moreover, there is a growing interest in proposing and carrying out quantum simulations of these models in quantum platforms such as trapped ions, superconducting circuits, and quantum photonics. In this Special Issue Reprint, we have gathered a series of articles related to symmetry in quantum optics models, including the quantum Rabi model and its symmetries, Floquet topological quantum states in optically driven semiconductors, the spin–boson model as a simulator of nonMarkovian multiphoton Jaynes–Cummings models, parityassisted generation of nonclassical states of light in circuit quantum electrodynamics, and quasiprobability distribution functions from fractional Fourier transforms.
quasiprobability distribution functions  fractional Fourier transform  reconstruction of the wave function  microwave photons  quantum entanglement  superconducting circuits  circuit quantum electrodynamics  quantum Rabi model  spinboson model  JaynesCummings model  multiphoton processes  quantum simulation  topological excitations  Floquet  dynamical mean field theory  nonequilibrium  starkeffect  semiconductors  light–matter interaction  integrable systems  global spectrum  n/a
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This book is focused on fractional order systems. Historically, fractional calculus has been recognized since the inception of regular calculus, with the first written reference dated in September 1695 in a letter from Leibniz to L’Hospital. Nowadays, fractional calculus has a wide area of applications in areas such as physics, chemistry, bioengineering, chaos theory, control systems engineering, and many others. In all those applications, we deal with fractional order systems in general. Moreover, fractional calculus plays an important role even in complex systems and therefore allows us to develop better descriptions of realworld phenomena. On that basis, fractional order systems are ubiquitous, as the whole real world around us is fractional. Due to this reason, it is urgent to consider almost all systems as fractional order systems.
anomalous diffusion  complexity  magnetic resonance imaging  fractional calculus  fractional complex networks  adaptive control  pinning synchronization  timevarying delays  impulses  reaction–diffusion terms  fractional calculus  mass absorption  diffusionwave equation  Caputo derivative  harmonic impact  Laplace transform  Fourier transform  MittagLeffler function  fractional calculus  fractionalorder system  long memory  time series  Hurst exponent  fractional  control  PID  parameter  meaning  audio signal processing  linear prediction  fractional derivative  musical signal  optimal randomness  swarmbased search  cuckoo search  heavytailed distribution  global optimization
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For the 250th birthday of Joseph Fourier, born in 1768 in Auxerre, France, this MDPI Special Issue will explore modern topics related to Fourier Analysis and Heat Equation. Modern developments of Fourier analysis during the 20th century have explored generalizations of Fourier and Fourier–Plancherel formula for noncommutative harmonic analysis, applied to locallycompact, nonAbelian groups. In parallel, the theory of coherent states and wavelets has been generalized over Lie groups. One should add the developments, over the last 30 years, of the applications of harmonic analysis to the description of the fascinating world of aperiodic structures in condensed matter physics. The notions of model sets, introduced by Y. Meyer, and of almost periodic functions, have revealed themselves to be extremely fruitful in this domain of natural sciences. The name of Joseph Fourier is also inseparable from the study of the mathematics of heat. Modern research on heat equations explores the extension of the classical diffusion equation on Riemannian, subRiemannian manifolds, and Lie groups. In parallel, in geometric mechanics, JeanMarie Souriau interpreted the temperature vector of Planck as a spacetime vector, obtaining, in this way, a phenomenological model of continuous media, which presents some interesting properties. One last comment concerns the fundamental contributions of Fourier analysis to quantum physics: Quantum mechanics and quantum field theory. The content of this Special Issue will highlight papers exploring noncommutative Fourier harmonic analysis, spectral properties of aperiodic order, the hypoelliptic heat equation, and the relativistic heat equation in the context of Information Theory and Geometric Science of Information.
WeylHeisenberg group  affine group  Weyl quantization  Wigner function  covariant integral quantization  Fourier analysis  special functions  rigged Hilbert spaces  quantum mechanics  signal processing  nonFourier heat conduction  thermal expansion  heat pulse experiments  pseudotemperature  GuyerKrumhansl equation  higher order thermodynamics  Lie groups thermodynamics  homogeneous manifold  polysymplectic manifold  dynamical systems  nonequivariant cohomology  Lie group machine learning  SouriauFisher metric  Born–Jordan quantization  shorttime propagators  timeslicing  Van Vleck determinant  thermodynamics  symplectization  metrics  nonequilibrium processes  interconnection  discrete multivariate sine transforms  orthogonal polynomials  cubature formulas  nonequilibrium thermodynamics  variational formulation  nonholonomic constraints  irreversible processes  discrete thermodynamic systems  continuum thermodynamic systems  fourier transform  rigid body motions  partial differential equations  Lévy processes  Lie Groups  homogeneous spaces  stochastic differential equations  harmonic analysis on abstract space  heat equation on manifolds and Lie Groups
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Sol–gel technology is a contemporary advancement in science that requires taking a multidisciplinary approach with regard to its various applications. This book highlights some applications of the sol–gel technology, including protective coatings, catalysts, piezoelectric devices, wave guides, lenses, highstrength ceramics, superconductors, synthesis of nanoparticles, and insulating materials. In particular, for biotechnological applications, biomolecules or the incorporation of bioactive substances into the sol–gel matrix has been extensively studied and has been a challenge for many researchers. Some sol–gel materials are widely applied in lightemitting diodes, solar cells, sensing, catalysis, integration in photovoltaic devices, and more recently in biosensing, bioimaging, or medical diagnosis; others can be considered excellent drug delivery systems. The goal of an ideal drug delivery system is the prompt delivery of a therapeutic amount of the drug to the proper site in the body, where the desired drug concentration can be maintained. The interactions between drugs and the sol–gel system can affect the release rate. In conclusion, the sol–gel synthesis method offers mixing at the molecular level and is able to improve the chemical homogeneity of the resulting composite. This opens new doors not only regarding
solgel method  Fourier transform infrared spectroscopy (FTIR) analysis  bioactivity  biocompatibility  sol–gel method  organicinorganic hybrids  chlorogenic acid  cytotoxicity  biocompatibility  silsesquioxanes  thiolene click reaction  in situ water production  hydrophobic coatings  cotton fabric  paper  NMR  wettability  solgel  hollow sphere  1D structure  solgel  thindisk laser  Ybdoped glasses  aluminosilicate glasses  photoluminescence  ultrasonic spray deposition  tungsten oxide  lithium lanthanum titanium oxide  conformal coating  Liion batteries  solgel technique  biomaterials  cell proliferation  cell cycle  one transistor and one resistor (1T1R)  organic thinfilm transistor (OTFT)  resistive random access memory (RRAM)  solgel  lithiumion battery  LiMnxFe(1?x)PO4  carbon coating  pseudodiffusion coefficient  potential step voltammetry  electrochemical impedance spectroscopy  solgel  oxyfluoride glassceramics  nanocrystal  optical properties  solgel method  SiO2–based hybrids  poly(?caprolactone)  TGDSC  TGFTIR  Xray diffraction analysis  computeraided design (CAD)  mechanical analysis  finite element analysis (FEA)  composites  organic–inorganic hybrid materials  biomedical applications  metal oxides  multilayer  surface plasmon resonance  optical sensors  computeraided design (CAD)  mechanical analysis  finite element analysis (FEA)  composites  hybrid materials  biomedical applications
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Researches and investigations involving the theory and applications of integral transforms and operational calculus are remarkably widespread in many diverse areas of the mathematical, physical, chemical, engineering and statistical sciences.
highly oscillatory  convolution quadrature rule  volterra integral equation  Bessel kernel  convergence  higher order Schwarzian derivatives  Janowski starlike function  Janowski convex function  bound on derivatives  tangent numbers  tangent polynomials  Carlitztype qtangent numbers  Carlitztype qtangent polynomials  (p,q)analogue of tangent numbers and polynomials  (p,q)analogue of tangent zeta function  symmetric identities  zeros  Lommel functions  univalent functions  starlike functions  convex functions  inclusion relationships  analytic function  Hankel determinant  exponential function  upper bound  nonlinear boundary value problems  fractionalorder differential equations  RiemannStieltjes functional integral  LiouvilleCaputo fractional derivative  infinitepoint boundary conditions  advanced and deviated arguments  existence of at least one solution  Fredholm integral equation  Schauder fixed point theorem  Hölder condition  generalized Kuramoto–Sivashinsky equation  modified Kudryashov method  exact solutions  Maple graphs  analytic function  Hadamard product (convolution)  partial sum  Srivastava–Tomovski generalization of Mittag–Leffler function  subordination  differential equation  differential inclusion  Liouville–Caputotype fractional derivative  fractional integral  existence  fixed point  Bernoulli spiral  Grandi curves  Chebyshev polynomials  pseudoChebyshev polynomials  orthogonality property  symmetric  encryption  password  hash  cryptography  PBKDF  q–Bleimann–Butzer–Hahn operators  (p,q)integers  (p,q)Bernstein operators  (p,q)Bleimann–Butzer–Hahn operators  modulus of continuity  rate of approximation  Kfunctional  HurwitzLerch zeta function  generalized functions  analytic number theory  ?generalized HurwitzLerch zeta functions  derivative properties  series representation  basic hypergeometric functions  generating functions  qpolynomials  analytic functions  Mittag–Leffler functions  starlike functions  convex functions  Hardy space  vibrating string equation  initial conditions  spectral decomposition  regular solution  the uniqueness of the solution  the existence of a solution  analytic  ?convex function  starlike function  stronglystarlike function  subordination  q Sheffer–Appell polynomials  generating relations  determinant definition  recurrence relation  q Hermite–Bernoulli polynomials  q Hermite–Euler polynomials  q Hermite–Genocchi polynomials  Volterra integral equations  highly oscillatory Bessel kernel  Hermite interpolation  direct Hermite collocation method  piecewise Hermite collocation method  differential operator  qhypergeometric functions  meromorphic function  Mittag–Leffler function  Hadamard product  differential subordination  starlike functions  Bell numbers  radius estimate  (p, q)integers  Dunkl analogue  generating functions  generalization of exponential function  Szász operator  modulus of continuity  function spaces and their duals  distributions  tempered distributions  Schwartz testing function space  generalized functions  distribution space  wavelet transform of generalized functions  Fourier transform  analytic function  subordination  Dziok–Srivastava operator  nonlinear boundary value problem  nonlocal  multipoint  multistrip  existence  Ulam stability  functions of bounded boundary and bounded radius rotations  subordination  functions with positive real part  uniformly starlike and convex functions  analytic functions  univalent functions  starlike and qstarlike functions  qderivative (or qdifference) operator  sufficient conditions  distortion theorems  Janowski functions  analytic number theory  ?generalized Hurwitz–Lerch zeta functions  derivative properties  recurrence relations  integral representations  Mellin transform  natural transform  Adomian decomposition method  Caputo fractional derivative  generalized mittagleffler function  analytic functions  Hadamard product  starlike functions  qderivative (or qdifference) operator  Hankel determinant  qstarlike functions  fuzzy volterra integrodifferential equations  fuzzy general linear method  fuzzy differential equations  generalized Hukuhara differentiability  spectrum symmetry  DCT  MFCC  audio features  anuran calls  analytic functions  convex functions  starlike functions  strongly convex functions  strongly starlike functions  uniformly convex functions  Struve functions  truncatedexponential polynomials  monomiality principle  generating functions  Apostoltype polynomials and Apostoltype numbers  Bernoulli, Euler and Genocchi polynomials  Bernoulli, Euler, and Genocchi numbers  operational methods  summation formulas  symmetric identities  Euler numbers and polynomials  qEuler numbers and polynomials  HurwitzEuler eta function  multiple HurwitzEuler eta function  higher order qEuler numbers and polynomials  (p, q)Euler numbers and polynomials of higher order  symmetric identities  symmetry of the zero
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