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The last few years have been characterized by a tremendous development of quantum information and probability and their applications, including quantum computing, quantum cryptography, and quantum random generators. In spite of the successful development of quantum technology, its foundational basis is still not concrete and contains a few sandy and shaky slices. Quantum random generators are one of the most promising outputs of the recent quantum information revolution. Therefore, it is very important to reconsider the foundational basis of this project, starting with the notion of irreducible quantum randomness. Quantum probabilities present a powerful tool to model uncertainty. Interpretations of quantum probability and foundational meaning of its basic tools, starting with the Born rule, are among the topics which will be covered by this issue. Recently, quantum probability has started to play an important role in a few areas of research outside quantum physics—in particular, quantum probabilistic treatment of problems of theory of decision making under uncertainty. Such studies are also among the topics of this issue.
quantum logic  groups  partially defined algebras  quasigroups  viable cultures  quantum information theory  bit commitment  protocol  entropy  entanglement  orthogonality  quantum computation  Gram–Schmidt process  quantum probability  potentiality  complementarity  uncertainty relations  Copenhagen interpretation  indefiniteness  indeterminism  causation  randomness  quantum information  quantum dynamics  entanglement  algebra  causality  geometry  probability  quantum information theory  realism  reality  entropy  correlations  qubits  probability representation  Bayes’ formula  quantum entanglement  threequbit random states  entanglement classes  entanglement polytope  anisotropic invariants  quantum random number  vacuum state  maximization of quantum conditional minentropy  quantum logics  quantum probability  holistic semantics  epistemic operations  Bell inequalities  algorithmic complexity  Borel normality  Bayesian inference  model selection  random numbers  quantumlike models  operational approach  information interpretation of quantum theory  social laser  social energy  quantum information field  social atom  Bose–Einstein statistics  bandwagon effect  social thermodynamics  resonator of social laser  master equation for socioinformation excitations  quantum contextuality  Kochen–Specker sets  MMP hypergraphs  Greechie diagrams  quantum foundations  probability  irreducible randomness  random number generators  quantum technology  entanglement  quantumlike models for social stochasticity  contextuality
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The many technical and computational problems that appear to be constantly emerging in various branches of physics and engineering beg for a more detailed understanding of the fundamental mathematics that serves as the cornerstone of our way of understanding natural phenomena. The purpose of this Special Issue was to establish a brief collection of carefully selected articles authored by promising young scientists and the world's leading experts in pure and applied mathematics, highlighting the stateoftheart of the various research lines focusing on the study of analytical and numerical mathematical methods for pure and applied sciences.
ultraparabolic equation  ultradiffusion process  probabilistic representation  mathematical finance  linear elastostatics  layer potentials  fredholmian operators  fractional differential equations  fractional derivative  Abeltype integral  time delay  distributed lag  gamma distribution  macroeconomics  Keynesian model  integral transforms  Laplace integral transform  transmutation operator  generating operator  integral equations  differential equations  operational calculus of Mikusinski type  Mellin integral transform  fractional derivative  fractional integral  Mittag–Leffler function  Riemann–Liouville derivative  Caputo derivative  Grünwald–Letnikov derivative  spacetime fractional diffusion equation  fractional Laplacian  subordination principle  MittagLeffler function  Bessel function  exterior calculus  exterior algebra  electromagnetism  Maxwell equations  differential forms  tensor calculus  Fourier Theory  DFT in polar coordinates  polar coordinates  multidimensional DFT  discrete Hankel Transform  discrete Fourier Transform  Orthogonality  multispecies biofilm  biosorption  free boundary value problem  heavy metals toxicity  method of characteristics  relativistic diffusion equation  Caputo fractional derivatives of a function with respect to another function  BesselRiesz motion  Mittag–Leffler function  matrix function  Schur decomposition  Laplace transform  fractional calculus  central limit theorem  anomalous diffusion  stable distribution  fractional calculus  power law  n/a
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This Special Issue focuses mainly on techniques and the relative formalism typical of numerical methods and therefore of numerical analysis, more generally. These fields of study of mathematics represent an important field of investigation both in the field of applied mathematics and even more exquisitely in the pure research of the theory of approximation and the study of polynomial relations as well as in the analysis of the solutions of the differential equations both ordinary and partial derivatives. Therefore, a substantial part of research on the topic of numerical analysis cannot exclude the fundamental role played by approximation theory and some of the tools used to develop this research. In this Special Issue, we want to draw attention to the mathematical methods used in numerical analysis, such as special functions, orthogonal polynomials, and their theoretical tools, such as Lie algebra, to study the concepts and properties of some special and advanced methods, which are useful in the description of solutions of linear and nonlinear differential equations. A further field of investigation is dedicated to the theory and related properties of fractional calculus with its adequate application to numerical methods.
risk assessment  numerical analysis  ignition hazard  effective field strength  offshore plant  Hamiltonian system  complex Lagrangian  Noether symmetries  first integrals  symplectic Runge–Kutta methods  effective order  partitioned rungekutta methods  symplecticity  hamiltonian systems  RungeKutta type methods  fourthorder ODEs  order conditions  Bseries  quadcolored trees  khypergeometric differential equations  nonhomogeneous  khypergeometric series  special function  general solution  Frobenius method  Chebyshev polynomials  pseudoChebyshev polynomials  recurrence relations  differential equations  composition properties  orthogonality properties  numerical analysis  heat generation  chemical reaction  thin needle  nanofluid  fourthorder  nonoscillatory solutions  oscillatory solutions  delay differential equations  particle accelerator  coupling impedance  dual integral equations  ClenshawCurtis quadrature  steepest descent method  logarithmic singularities  Cauchy singularity  highly oscillatory integrals  secondorder  nonoscillatory solutions  oscillatory solutions  delay differential equations  Fredholm integral equations  multiresolution analysis  unitary extension principle  oblique extension principle  Bsplines  wavelets  tight framelets  Swift–Hohenberg type of equation  surfaces  narrow band domain  closest point method  operator splitting method
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Microwave imaging techniques allow for the development of systems that are able to inspect, identify, and characterize in a noninvasive fashion under different scenarios, ranging from biomedical to subsurface diagnostics as well as from surveillance and security applications to nondestructive evaluation. Such great opportunities, though, are actually severely limited by difficulties arising from the solution of the underlying inverse scattering problem. As a result, ongoing research efforts in this area are devoted to developing inversion strategies and experimental apparatus so that they are as reliable and accurate as possible with respect to reconstruction capabilities and resolution performance, respectively. The intent of this Special Issue is to present the experiences of leading scientists in the electromagnetic inverse scattering community, as well as to serve as an assessment tool for people who are new to the area of microwave imaging and electromagnetic inverse scattering problems.
microwave imaging  tomography  inverse problems  microwave imaging  inverse scattering  Bayesian compressive sensing (BCS)  contrast source inversion (CSI)  3D  electromagnetic inverse scattering problems  magnetic resonance imaging  electricalproperty tomography  nonlinear optimization  contrastsource inversion  inverse scattering  nonlinear problem  contraction integral equation for inversion (CIEI)  imaging  inverse obstacles problem  inverse source problem  joint sparsity  linear sampling method  microwave imaging  orthogonality sampling method  antenna array  nearfield measurements  5G communication  array diagnosis  rank minimization  compressed sensing  antenna testing  breast imaging  microwave imaging  discontinuous Galerkin method (DGM)  contrast source inversion (CSI)  stopping criteria  KolmogorovSmirnov (KS) test  RCS estimation  imagebased approach  adjoint inversion methods  microwave plasma diagnostics  electromagnetic inverse scattering  microwave imaging profilometry  finitedifference methods  radarbased breast imaging  microwave imaging  breast cancer
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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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