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Numerical linear algebra is a very important topic in mathematics and has important recent applications in deep learning, machine learning, image processing, applied statistics, artificial intelligence and other interesting modern applications in many fields. The purpose of this Special Issue in Mathematics is to present the latest contributions and recent developments in numerical linear algebra and applications in different real domains. We invite authors to submit original and new papers and high-quality reviews related to the following topics: applied linear algebra, linear and nonlinear systems of equations, large matrix equations, numerical tensor problems with applications, ill-posed problems and image processing, linear algebra and applied statistics, model reduction in dynamic systems, and other related subjects. The submitted papers will be reviewed in line with the traditional submission process. This Special Issue will be dedicated to the inspired mathematician Constantin Petridi, who has devoted his life to mathematics.

Information technology industries --- inverse scattering --- reciprocity gap functional --- chiral media --- mixed boundary conditions --- non-linear matrix equations --- perturbation bounds --- Lyapunov majorants --- fixed-point principle --- nonsymmetric differential matrix Riccati equation --- cosine product --- Golub–Kahan algorithm --- Krylov subspaces --- PCA --- SVD --- tensors --- quadratic form --- estimates --- upper bounds --- networks --- perron vector --- power method --- lanczos method --- pseudospectra --- eigenvalues --- matrix polynomial --- perturbation --- Perron root --- large-scale matrices --- approximation algorithm --- high-dimensional --- minimum norm solution --- regularisation --- Tikhonov --- ℓp-ℓq --- variable selection --- inverse scattering --- reciprocity gap functional --- chiral media --- mixed boundary conditions --- non-linear matrix equations --- perturbation bounds --- Lyapunov majorants --- fixed-point principle --- nonsymmetric differential matrix Riccati equation --- cosine product --- Golub–Kahan algorithm --- Krylov subspaces --- PCA --- SVD --- tensors --- quadratic form --- estimates --- upper bounds --- networks --- perron vector --- power method --- lanczos method --- pseudospectra --- eigenvalues --- matrix polynomial --- perturbation --- Perron root --- large-scale matrices --- approximation algorithm --- high-dimensional --- minimum norm solution --- regularisation --- Tikhonov --- ℓp-ℓq --- variable selection

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Polynomial and its applications are well known for their proven properties and excellent applicability in interdisciplinary fields of science. Until now, research on polynomial and its applications has been done in mathematics, applied mathematics, and sciences. This book is based on recent results in all areas related to polynomial and its applications. This book provides an overview of the current research in the field of polynomials and its applications. The following papers have been published in this volume: ‘A Parametric Kind of the Degenerate Fubini Numbers and Polynomials’; ‘On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals’; ‘Fractional Supersymmetric Hermite Polynomials’; ‘Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation’; ‘Iterating the Sum of Möbius Divisor Function and Euler Totient Function’; ‘Differential Equations Arising from the Generating Function of the (r, β)-Bell Polynomials and Distribution of Zeros of Equations’; ‘Truncated Fubini Polynomials’; ‘On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights’; ‘Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity’; ‘Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials’; ‘Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from Differential Equations and Location of Their Zeros.’

Research & information: general --- Mathematics & science --- differential equations, heat equation --- Hermite Kampé de Fériet polynomials --- Hermite polynomials --- generating functions --- degenerate Bernstein polynomials --- degenerate Bernstein operators --- degenerate Euler polynomials --- variational methods --- fractional Choquard equation --- ground state solution --- vanishing potential --- positively quadratically hyponormal --- quadratically hyponormal --- unilateral weighted shift --- recursively generated --- Fubini polynomials --- Euler polynomials --- Bernoulli polynomials --- truncated exponential polynomials --- Stirling numbers of the second kind --- differential equations --- Bell polynomials --- r-Bell polynomials --- (r, β)-Bell polynomials --- zeros --- Möbius function --- divisor functions --- Euler totient function --- hydraulic resistance --- pipe flow friction --- Colebrook equation --- Colebrook–White experiment --- floating-point computations --- approximations --- Padé polynomials --- symbolic regression --- orthogonal polynomials --- difference-differential operator --- supersymmetry --- Konhauser matrix polynomial --- generating matrix function --- integral representation --- fractional integral --- degenerate Fubini polynomials --- Stirling numbers --- differential equations, heat equation --- Hermite Kampé de Fériet polynomials --- Hermite polynomials --- generating functions --- degenerate Bernstein polynomials --- degenerate Bernstein operators --- degenerate Euler polynomials --- variational methods --- fractional Choquard equation --- ground state solution --- vanishing potential --- positively quadratically hyponormal --- quadratically hyponormal --- unilateral weighted shift --- recursively generated --- Fubini polynomials --- Euler polynomials --- Bernoulli polynomials --- truncated exponential polynomials --- Stirling numbers of the second kind --- differential equations --- Bell polynomials --- r-Bell polynomials --- (r, β)-Bell polynomials --- zeros --- Möbius function --- divisor functions --- Euler totient function --- hydraulic resistance --- pipe flow friction --- Colebrook equation --- Colebrook–White experiment --- floating-point computations --- approximations --- Padé polynomials --- symbolic regression --- orthogonal polynomials --- difference-differential operator --- supersymmetry --- Konhauser matrix polynomial --- generating matrix function --- integral representation --- fractional integral --- degenerate Fubini polynomials --- Stirling numbers

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Polynomial and its applications are well known for their proven properties and excellent applicability in interdisciplinary fields of science. Until now, research on polynomial and its applications has been done in mathematics, applied mathematics, and sciences. This book is based on recent results in all areas related to polynomial and its applications. This book provides an overview of the current research in the field of polynomials and its applications. The following papers have been published in this volume: ‘A Parametric Kind of the Degenerate Fubini Numbers and Polynomials’; ‘On 2-Variables Konhauser Matrix Polynomials and Their Fractional Integrals’; ‘Fractional Supersymmetric Hermite Polynomials’; ‘Rational Approximation for Solving an Implicitly Given Colebrook Flow Friction Equation’; ‘Iterating the Sum of Möbius Divisor Function and Euler Totient Function’; ‘Differential Equations Arising from the Generating Function of the (r, β)-Bell Polynomials and Distribution of Zeros of Equations’; ‘Truncated Fubini Polynomials’; ‘On Positive Quadratic Hyponormality of a Unilateral Weighted Shift with Recursively Generated by Five Weights’; ‘Ground State Solutions for Fractional Choquard Equations with Potential Vanishing at Infinity’; ‘Some Identities on Degenerate Bernstein and Degenerate Euler Polynomials’; ‘Some Identities Involving Hermite Kampé de Fériet Polynomials Arising from Differential Equations and Location of Their Zeros.’

differential equations, heat equation --- Hermite Kampé de Fériet polynomials --- Hermite polynomials --- generating functions --- degenerate Bernstein polynomials --- degenerate Bernstein operators --- degenerate Euler polynomials --- variational methods --- fractional Choquard equation --- ground state solution --- vanishing potential --- positively quadratically hyponormal --- quadratically hyponormal --- unilateral weighted shift --- recursively generated --- Fubini polynomials --- Euler polynomials --- Bernoulli polynomials --- truncated exponential polynomials --- Stirling numbers of the second kind --- differential equations --- Bell polynomials --- r-Bell polynomials --- (r, β)-Bell polynomials --- zeros --- Möbius function --- divisor functions --- Euler totient function --- hydraulic resistance --- pipe flow friction --- Colebrook equation --- Colebrook–White experiment --- floating-point computations --- approximations --- Padé polynomials --- symbolic regression --- orthogonal polynomials --- difference-differential operator --- supersymmetry --- Konhauser matrix polynomial --- generating matrix function --- integral representation --- fractional integral --- degenerate Fubini polynomials --- Stirling numbers

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This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods.

Research & information: general --- Mathematics & science --- mathematical modeling --- infiltration well --- differential equations --- porous medium --- fractal conductivity model --- incomplete rankings --- Kendall's tau --- permutation graph --- competitive balance --- Spotify --- collocation --- volterra integral equation --- highly oscillatory --- convergence --- areal porosity --- volumetric porosity --- fractal area-volume relationship --- tortuosity factor --- joint probability --- corrugated box printing machine --- modified Delphi method --- analytic network process (ANP) --- supplier --- nonlinear system --- iterative method --- divided difference operator --- stability --- parameter plane --- dynamical plane --- random hyperbolic model --- random laplace transform --- numerical integration --- monte carlo method --- numerical simulation --- talbot algorithm --- stochastic perturbations --- random nonlinear oscillator --- maximum entropy principle --- probability density function --- stationary Gaussian noise --- random mean square parabolic model --- finite degree of randomness --- random finite difference scheme --- relativistic harmonic oscillator --- kinematics of a particle --- special relativity --- nonlinear problems in mechanics --- equations of motion in gravitational theory --- virus propagation --- stochastic modeling --- Gillespie algorithm --- conservative formulation --- multidimensional fragmentation equation --- weight functions --- finite volume scheme --- contamination plume --- advection-diffusion --- universal curves --- Dirichlet-to-Neumann map --- Schrödinger operator --- contagion effect --- difference equation --- elections --- labor condition --- mathematical compartmental discrete model --- political corruption --- revolving doors --- sensitivity analysis --- simulation --- numerical methods --- integro-interpolation method --- splitting method --- convergence of models --- standard deviation of the error --- diabetic retinopathy --- ocular fundus --- laser coagulation --- optical coherence tomography --- image processing --- segmentation --- safe treatment --- Hermite interpolation --- nodal systems --- unit circle --- circular membrane --- fluid-structure interaction --- differential-integral equations --- power series method --- closed-form solution --- time series model --- wavelet transform --- ARIMA model --- neural network NARX --- ionospheric parameters --- courtyard --- climate change --- microclimate --- Support Vector Regression (SVR) --- machine learning --- matrix functions --- matrix hyperbolic tangent --- matrix exponential --- Taylor series --- matrix polynomial evaluation --- mathematical modeling --- infiltration well --- differential equations --- porous medium --- fractal conductivity model --- incomplete rankings --- Kendall's tau --- permutation graph --- competitive balance --- Spotify --- collocation --- volterra integral equation --- highly oscillatory --- convergence --- areal porosity --- volumetric porosity --- fractal area-volume relationship --- tortuosity factor --- joint probability --- corrugated box printing machine --- modified Delphi method --- analytic network process (ANP) --- supplier --- nonlinear system --- iterative method --- divided difference operator --- stability --- parameter plane --- dynamical plane --- random hyperbolic model --- random laplace transform --- numerical integration --- monte carlo method --- numerical simulation --- talbot algorithm --- stochastic perturbations --- random nonlinear oscillator --- maximum entropy principle --- probability density function --- stationary Gaussian noise --- random mean square parabolic model --- finite degree of randomness --- random finite difference scheme --- relativistic harmonic oscillator --- kinematics of a particle --- special relativity --- nonlinear problems in mechanics --- equations of motion in gravitational theory --- virus propagation --- stochastic modeling --- Gillespie algorithm --- conservative formulation --- multidimensional fragmentation equation --- weight functions --- finite volume scheme --- contamination plume --- advection-diffusion --- universal curves --- Dirichlet-to-Neumann map --- Schrödinger operator --- contagion effect --- difference equation --- elections --- labor condition --- mathematical compartmental discrete model --- political corruption --- revolving doors --- sensitivity analysis --- simulation --- numerical methods --- integro-interpolation method --- splitting method --- convergence of models --- standard deviation of the error --- diabetic retinopathy --- ocular fundus --- laser coagulation --- optical coherence tomography --- image processing --- segmentation --- safe treatment --- Hermite interpolation --- nodal systems --- unit circle --- circular membrane --- fluid-structure interaction --- differential-integral equations --- power series method --- closed-form solution --- time series model --- wavelet transform --- ARIMA model --- neural network NARX --- ionospheric parameters --- courtyard --- climate change --- microclimate --- Support Vector Regression (SVR) --- machine learning --- matrix functions --- matrix hyperbolic tangent --- matrix exponential --- Taylor series --- matrix polynomial evaluation

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This volume deals with novel high-quality research results of a wide class of mathematical models with applications in engineering, nature, and social sciences. Analytical and numeric, deterministic and uncertain dimensions are treated. Complex and multidisciplinary models are treated, including novel techniques of obtaining observation data and pattern recognition. Among the examples of treated problems, we encounter problems in engineering, social sciences, physics, biology, and health sciences. The novelty arises with respect to the mathematical treatment of the problem. Mathematical models are built, some of them under a deterministic approach, and other ones taking into account the uncertainty of the data, deriving random models. Several resulting mathematical representations of the models are shown as equations and systems of equations of different types: difference equations, ordinary differential equations, partial differential equations, integral equations, and algebraic equations. Across the chapters of the book, a wide class of approaches can be found to solve the displayed mathematical models, from analytical to numeric techniques, such as finite difference schemes, finite volume methods, iteration schemes, and numerical integration methods.

mathematical modeling --- infiltration well --- differential equations --- porous medium --- fractal conductivity model --- incomplete rankings --- Kendall’s tau --- permutation graph --- competitive balance --- Spotify --- collocation --- volterra integral equation --- highly oscillatory --- convergence --- areal porosity --- volumetric porosity --- fractal area-volume relationship --- tortuosity factor --- joint probability --- corrugated box printing machine --- modified Delphi method --- analytic network process (ANP) --- supplier --- nonlinear system --- iterative method --- divided difference operator --- stability --- parameter plane --- dynamical plane --- random hyperbolic model --- random laplace transform --- numerical integration --- monte carlo method --- numerical simulation --- talbot algorithm --- stochastic perturbations --- random nonlinear oscillator --- maximum entropy principle --- probability density function --- stationary Gaussian noise --- random mean square parabolic model --- finite degree of randomness --- random finite difference scheme --- relativistic harmonic oscillator --- kinematics of a particle --- special relativity --- nonlinear problems in mechanics --- equations of motion in gravitational theory --- virus propagation --- stochastic modeling --- Gillespie algorithm --- conservative formulation --- multidimensional fragmentation equation --- weight functions --- finite volume scheme --- contamination plume --- advection-diffusion --- universal curves --- Dirichlet-to-Neumann map --- Schrödinger operator --- contagion effect --- difference equation --- elections --- labor condition --- mathematical compartmental discrete model --- political corruption --- revolving doors --- sensitivity analysis --- simulation --- numerical methods --- integro-interpolation method --- splitting method --- convergence of models --- standard deviation of the error --- diabetic retinopathy --- ocular fundus --- laser coagulation --- optical coherence tomography --- image processing --- segmentation --- safe treatment --- Hermite interpolation --- nodal systems --- unit circle --- circular membrane --- fluid-structure interaction --- differential-integral equations --- power series method --- closed-form solution --- time series model --- wavelet transform --- ARIMA model --- neural network NARX --- ionospheric parameters --- courtyard --- climate change --- microclimate --- Support Vector Regression (SVR) --- machine learning --- matrix functions --- matrix hyperbolic tangent --- matrix exponential --- Taylor series --- matrix polynomial evaluation --- n/a --- Kendall's tau --- Schrödinger operator