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Real-world systems exhibit complex behavior, therefore novel mathematical approaches or modifications of classical ones have to be employed to precisely predict, monitor, and control complicated chaotic and stochastic processes. One of the most basic concepts that has to be taken into account while conducting research in all natural sciences is symmetry, and it is usually used to refer to an object that is invariant under some transformations including translation, reflection, rotation or scaling.The following Special Issue is dedicated to investigations of the concept of dynamical symmetry in the modelling and analysis of dynamic features occurring in various branches of science like physics, chemistry, biology, and engineering, with special emphasis on research based on the mathematical models of nonlinear partial and ordinary differential equations. Addressed topics cover theories developed and employed under the concept of invariance of the global/local behavior of the points of spacetime, including temporal/spatiotemporal symmetries.

Research & information: general --- Mathematics & science --- time delay --- third order differential equations --- difference scheme --- stability --- ϕc-Laplacian --- boundary value problem --- critical point theory --- three solutions --- multiple solutions --- fixed point theory --- boundary value problems --- generalized attracting horseshoe --- strange attractors --- poincaré map --- electronic circuits --- non-canonical differential equations --- second-order --- neutral delay --- mixed type --- oscillation criteria --- cell transplantation --- cytokines --- ischemic stroke --- numerical simulation --- runge-kutta method --- stability analysis --- ambient assisted living --- AAL --- ambient intelligence --- assisted living --- user-interfaces --- fuzzy logic --- vibrations --- symmetrical structures --- eigenmodes --- building --- concrete --- partial difference equation --- infinitely many small solutions --- (p,q)-Laplacian

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Real-world systems exhibit complex behavior, therefore novel mathematical approaches or modifications of classical ones have to be employed to precisely predict, monitor, and control complicated chaotic and stochastic processes. One of the most basic concepts that has to be taken into account while conducting research in all natural sciences is symmetry, and it is usually used to refer to an object that is invariant under some transformations including translation, reflection, rotation or scaling.The following Special Issue is dedicated to investigations of the concept of dynamical symmetry in the modelling and analysis of dynamic features occurring in various branches of science like physics, chemistry, biology, and engineering, with special emphasis on research based on the mathematical models of nonlinear partial and ordinary differential equations. Addressed topics cover theories developed and employed under the concept of invariance of the global/local behavior of the points of spacetime, including temporal/spatiotemporal symmetries.

Research & information: general --- Mathematics & science --- time delay --- third order differential equations --- difference scheme --- stability --- ϕc-Laplacian --- boundary value problem --- critical point theory --- three solutions --- multiple solutions --- fixed point theory --- boundary value problems --- generalized attracting horseshoe --- strange attractors --- poincaré map --- electronic circuits --- non-canonical differential equations --- second-order --- neutral delay --- mixed type --- oscillation criteria --- cell transplantation --- cytokines --- ischemic stroke --- numerical simulation --- runge-kutta method --- stability analysis --- ambient assisted living --- AAL --- ambient intelligence --- assisted living --- user-interfaces --- fuzzy logic --- vibrations --- symmetrical structures --- eigenmodes --- building --- concrete --- partial difference equation --- infinitely many small solutions --- (p,q)-Laplacian --- time delay --- third order differential equations --- difference scheme --- stability --- ϕc-Laplacian --- boundary value problem --- critical point theory --- three solutions --- multiple solutions --- fixed point theory --- boundary value problems --- generalized attracting horseshoe --- strange attractors --- poincaré map --- electronic circuits --- non-canonical differential equations --- second-order --- neutral delay --- mixed type --- oscillation criteria --- cell transplantation --- cytokines --- ischemic stroke --- numerical simulation --- runge-kutta method --- stability analysis --- ambient assisted living --- AAL --- ambient intelligence --- assisted living --- user-interfaces --- fuzzy logic --- vibrations --- symmetrical structures --- eigenmodes --- building --- concrete --- partial difference equation --- infinitely many small solutions --- (p,q)-Laplacian

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This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.

heteroclinic solutions --- non-instantaneous impulses --- Schauder’s fixed point theory --- dichotomy --- second-order differential/difference/q-difference equation of hypergeometric type --- differential equations --- a priori estimates --- global solutions --- generalized Liouville equation --- Hilbert space --- dissipation --- collocation method --- exponential dichotomy --- Sumudu decomposition method --- three-step Taylor method --- dynamical system --- lower and upper solutions --- problems in the real line --- Nagumo condition on the real line --- SIRS epidemic model --- first order periodic systems --- regular solutions --- Clairin’s method --- coupled nonlinear systems --- Navier–Stokes equations --- Bäcklund transformation --- asymptotic stability --- Caputo fractional derivative --- exponential stability --- difference equations --- lipschitz stability --- strong nonlinearities --- polynomial solution --- integro-differentials --- kinetic energy --- Legendre wavelets --- weak solutions --- discrete Lyapunov equation --- population dynamics --- non-uniform lattices --- Korteweg-de Vries equation --- time-dependent partial differential equations --- mean curvature operator --- functional boundary conditions --- mathematical modelling --- fixed point theory --- limit-periodic solutions --- Arzèla Ascoli theorem --- Miura transformation --- state dependent delays --- ?-Laplacian operator --- divided-difference equations --- effective existence criteria

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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