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Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a nontrivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.
point projection  intersection  parametric curve  ndimensional Euclidean space  Newton’s second order method  fixed point theorem  nonlinear equations  multiple zeros  optimal iterative methods  higher order of convergence  nonlinear operator equation  Fréchet derivative  ?continuity condition  Newtonlike method  Frédholm integral equation  nonlinear equations  Padé approximation  iterative method  order of convergence  numerical experiment  fourth order iterative methods  local convergence  banach space  radius of convergence  nonlinear equation  iterative process  nondifferentiable operator  Lipschitz condition  high order  sixteenth order convergence method  local convergence  dynamics  Banach space  Newton’s method  semilocal convergence  Kantorovich hypothesis  iterative methods  Steffensen’s method  Rorder  with memory  computational efficiency  nonlinear equation  basins of attraction  optimal order  higher order method  computational order of convergence  nonlinear equations  multiple roots  Chebyshev–Halleytype  optimal iterative methods  efficiency index  Banach space  semilocal convergence  ?continuity condition  Jarratt method  error bound  Fredholm integral equation  Newton’s method  global convergence  variational inequality problem  split variational inclusion problem  multivalued quasinonexpasive mappings  Hilbert space  sixteenthorder optimal convergence  multipleroot finder  asymptotic error constant  weight function  purely imaginary extraneous fixed point  attractor basin  drazin inverse  generalized inverse  iterative methods  higher order  efficiency index  integral equation  efficiency index  nonlinear models  iterative methods  higher order  nonlinear equations  optimal iterative methods  multiple roots  efficiency index  iterative methods  nonlinear equations  Newtontype methods  smooth and nonsmooth operators  heston model  Hull–White  option pricing  PDE  finite difference (FD)  iteration scheme  Moore–Penrose  rectangular matrices  rate of convergence  efficiency index  nonlinear equations  conjugate gradient method  projection method  convex constraints  signal and image processing  nonlinear monotone equations  conjugate gradient method  projection method  signal processing  nonlinear systems  multipoint iterative methods  divided difference operator  order of convergence  Newton’s method  computational efficiency index  system of nonlinear equations  Newton method  NewtonHSS method  nonlinear HSSlike method  PicardHSS method  convexity  least square problem  accretive operators  signal processing  point projection  intersection  planar algebraic curve  Newton’s iterative method  the improved curvature circle algorithm  systems of nonlinear equations  King’s family  order of convergence  multipoint iterative methods  nonlinear equations  Potra–Pták method  optimal methods  weight function  basin of attraction  engineering applications  Kung–Traub conjecture  multipoint iterations  nonlinear equation  optimal order  basins of attraction
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Developing techniques for assessing various risks and calculating probabilities of ruin and survival are exciting topics for mathematicallyinclined academics. For practicing actuaries and financial engineers, the resulting insights have provided enormous opportunities but also created serious challenges to overcome, thus facilitating closer cooperation between industries and academic institutions. In this book, several renown researchers with extensive interdisciplinary research experiences share their thoughts that, in one way or another, contribute to the betterment of practice and theory of decision making under uncertainty. Behavioral, cultural, mathematical, and statistical aspects of risk assessment and modelling have been explored, and have been often illustrated using real and simulated data. Topics range from financial and insurance risks to securitytype risks, from onedimensional to multi and even infinitedimensional risks.
aggregate discounted claims  Markovian arrival process  partial integrodifferential equation  covariance  multivariate gamma distribution  multiplicative background risk model  aggregate risk  individual risk model  collective risk model  risk measure  cumulative Parisian ruin  stochastic orders  surplus process  renewal process  discounted aggregate claims  copulas  archimedean copulas  background risk  systematic risk  transfer function  information processing  order statistic  concomitant  ruin probability  dual risk model  constant interest rate  integral equation  Laplace transform  numerical approximation  maximal tail dependence  clustering  financial time series  weighted cuts  copula  national culture  survival analysis  hazard model  rating migrations  advanced measurement approach  confidence interval  Monte Carlo  operational risk  valueatrisk  central limit theorem  insurance  maxstable random fields  rate of spatial diversification  reinsurance  risk management  risk theory  spatial dependence  spatial risk measures and corresponding axiomatic approach  n/a
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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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