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Ordinary differential equations --- Partial differential equations --- Difference equations --- Equations aux différences --- Periodicals --- Périodiques --- Mathématiques --- Difference equations. --- Mathematical Sciences --- Applied Mathematics --- Calculus --- Differential Geometry --- differential equations --- applicable analysis --- Mathématiques --- Calculus of differences --- Differences, Calculus of --- Equations, Difference --- Mathematics --- Équations aux différences --- Mathematics. --- Science --- Math
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Ordinary differential equations --- Differential equations --- Equations différentielles --- Periodicals --- Périodiques --- Mathematical Sciences --- General and Others --- Applied Mathematics --- Mathematical Sciences. --- General and Others. --- Equations différentielles --- Périodiques --- EJMATHE ELSEVIER-E EPUB-ALPHA-J EPUB-PER-FT --- Gewone differentiaalvergelijkingen --- Periodicals. --- Differential equations. --- Equations, Differential --- Bessel functions --- Calculus --- 517.91 Differential equations
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This open access book presents a comprehensive survey of modern operator techniques for boundary value problems and spectral theory, employing abstract boundary mappings and Weyl functions. It includes self-contained treatments of the extension theory of symmetric operators and relations, spectral characterizations of selfadjoint operators in terms of the analytic properties of Weyl functions, form methods for semibounded operators, and functional analytic models for reproducing kernel Hilbert spaces. Further, it illustrates these abstract methods for various applications, including Sturm-Liouville operators, canonical systems of differential equations, and multidimensional Schrödinger operators, where the abstract Weyl function appears as either the classical Titchmarsh-Weyl coefficient or the Dirichlet-to-Neumann map. The book is a valuable reference text for researchers in the areas of differential equations, functional analysis, mathematical physics, and system theory. Moreover, thanks to its detailed exposition of the theory, it is also accessible and useful for advanced students and researchers in other branches of natural sciences and engineering.
Operator theory. --- Differential equations. --- Partial differential equations. --- System theory. --- Operator Theory. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Systems Theory, Control. --- Systems, Theory of --- Systems science --- Science --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Functional analysis --- Philosophy --- Mathematics --- Operator theory --- System theory
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The book serves both as a reference for various scaled models with corresponding dimensionless numbers, and as a resource for learning the art of scaling. A special feature of the book is the emphasis on how to create software for scaled models, based on existing software for unscaled models. Scaling (or non-dimensionalization) is a mathematical technique that greatly simplifies the setting of input parameters in numerical simulations. Moreover, scaling enhances the understanding of how different physical processes interact in a differential equation model. Compared to the existing literature, where the topic of scaling is frequently encountered, but very often in only a brief and shallow setting, the present book gives much more thorough explanations of how to reason about finding the right scales. This process is highly problem dependent, and therefore the book features a lot of worked examples, from very simple ODEs to systems of PDEs, especially from fluid mechanics. The text is easily accessible and example-driven. The first part on ODEs fits even a lower undergraduate level, while the most advanced multiphysics fluid mechanics examples target the graduate level. The scientific literature is full of scaled models, but in most of the cases, the scales are just stated without thorough mathematical reasoning. This book explains how the scales are found mathematically. This book will be a valuable read for anyone doing numerical simulations based on ordinary or partial differential equations.
Mathematics. --- Computer simulation. --- Differential equations. --- Partial differential equations. --- Computer mathematics. --- Mathematical models. --- Ordinary Differential Equations. --- Partial Differential Equations. --- Mathematical Modeling and Industrial Mathematics. --- Computational Science and Engineering. --- Simulation and Modeling. --- Math --- Models, Mathematical --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Partial differential equations --- 517.91 Differential equations --- Differential equations --- Computer modeling --- Computer models --- Modeling, Computer --- Models, Computer --- Simulation, Computer --- Mathematics --- Science --- Simulation methods --- Electromechanical analogies --- Mathematical models --- Model-integrated computing --- Differential Equations. --- Differential equations, partial. --- Computer science. --- Informatics --- Simulation and modeling
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This book appeals to scientists, teachers and graduate students in mathematics, and will be of interest for scholars in applied sciences as well, in particular in medicine, biology and social sciences. The models in this connection apply, in particular, to the study of the immune system response and to the predator–prey dynamic. The efficiency of public transport is also considered and blast waves in explosions are studied. Other contributions concern pure mathematics, in particular Pythagorean means, sequences of matrices and Markov chains, and these give evidence of deep links with Symmetry.
paradox of enrichment --- prey–predator system --- persistence of predators --- extinction of predators --- blast waves --- non-ideal gas --- Rankine–Hugoniot conditions --- magnetogasdynamics --- dynamic model --- immune system response --- immune cells --- abnormal cells --- nonlinear ordinary differential equations --- stability --- diet --- Aggregation dynamic system --- Discrete system --- Epidemic model --- Cauchy’s interlacing theorem --- Output-feedback control --- Stability --- Antistable/Stable matrix --- onboard comfort level --- Markow chain --- bus passenger occupancy prediction --- Chebyshev inequality --- Tracy-Singh product --- continuous field of operators --- Bochner integral --- weighted Pythagorean mean
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This Special Issue collects original research articles discussing cutting-edge work as well as perspectives on future directions in the whole range of theoretical and practical aspects in these research areas: i) Theory of fuzzy systems and soft computing; ii) Learning procedures; iii) Decision-making applications employing fuzzy logic and soft computing.
Research & information: general --- Mathematics & science --- fuzzy partition --- fuzzy transform --- new iterative method --- Cauchy problems --- ANFIS --- basmati rice --- image processing --- grading --- quality assessment --- fuzzy inference system --- causality --- statistics --- concept-mapping --- causal graph --- numerical methods --- systems of ordinary differential equations --- NIM --- fuzzy logics --- linear motion blur --- fuzzy deblurring --- electron beam calibration --- signal and image processing --- propagation modeling --- adaptive-network-based fuzzy system --- LoRa & --- LoRaWAN --- radio wave propagation --- artificial neural networks --- subtracting clustering --- dual double fuzzy semi-metric --- double fuzzy semi-metric --- fuzzy semi-metric space --- triangle inequality --- triangular norm --- eye gaze tracking --- interval type-2 fuzzy logic --- vision system --- mobile robots --- intelligent control --- ordered fuzzy number --- fuzzy relation --- preorder --- strict order --- equivalence relation --- variable neighborhood search --- experimental comparison --- statistical analysis --- traveling salesman problem --- soft computing --- modeling --- vector optimization --- methods of solution of vector problems --- optimal decision-making --- numerical realization of decision-making --- n/a
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The use of scientific computing tools is currently customary for solving problems at several complexity levels in Applied Sciences. The great need for reliable software in the scientific community conveys a continuous stimulus to develop new and better performing numerical methods that are able to grasp the particular features of the problem at hand. This has been the case for many different settings of numerical analysis, and this Special Issue aims at covering some important developments in various areas of application.
structured matrices --- numerical methods --- time fractional differential equations --- hierarchical splines --- finite difference methods --- null-space --- highly oscillatory problems --- stochastic Volterra integral equations --- displacement rank --- constrained Hamiltonian problems --- hyperbolic partial differential equations --- higher-order finite element methods --- continuous geometric average --- spectral (eigenvalue) and singular value distributions --- generalized locally Toeplitz sequences --- Volterra integro–differential equations --- B-spline --- discontinuous Galerkin methods --- adaptive methods --- Cholesky factorization --- energy-conserving methods --- order --- collocation method --- Poisson problems --- time harmonic Maxwell’s equations and magnetostatic problems --- tree --- multistep methods --- stochastic differential equations --- optimal basis --- finite difference method --- elementary differential --- gradient system --- curl–curl operator --- conservative problems --- line integral methods --- stochastic multistep methods --- Hamiltonian Boundary Value Methods --- limited memory --- boundary element method --- convergence --- analytical solution --- preconditioners --- asymptotic stability --- collocation methods --- histogram specification --- local refinement --- Runge–Kutta --- edge-preserving smoothing --- numerical analysis --- THB-splines --- BS methods --- barrier options --- stump --- shock waves and discontinuities --- mean-square stability --- Volterra integral equations --- high order discontinuous Galerkin finite element schemes --- B-splines --- vectorization and parallelization --- initial value problems --- one-step methods --- scientific computing --- fractional derivative --- linear systems --- Hamiltonian problems --- low rank completion --- ordinary differential equations --- mixed-index problems --- edge-histogram --- Hamiltonian PDEs --- matrix ODEs --- HBVMs --- floating strike Asian options --- Hermite–Obreshkov methods --- generalized Schur algorithm --- Galerkin method --- symplecticity --- high performance computing --- isogeometric analysis --- discretization of systems of differential equations
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There are many applications of mathematical physics in several fields of basic science and engineering. Thus, we have tried to provide the Special Issue “Modern Problems of Mathematical Physics and Their Applications” to cover the new advances of mathematical physics and its applications. In this Special Issue, we have focused on some important and challenging topics, such as integral equations, ill-posed problems, ordinary differential equations, partial differential equations, system of equations, fractional problems, linear and nonlinear problems, fuzzy problems, numerical methods, analytical methods, semi-analytical methods, convergence analysis, error analysis and mathematical models. In response to our invitation, we received 31 papers from more than 17 countries (Russia, Uzbekistan, China, USA, Kuwait, Bosnia and Herzegovina, Thailand, Pakistan, Turkey, Nigeria, Jordan, Romania, India, Iran, Argentina, Israel, Canada, etc.), of which 19 were published and 12 rejected.
cauchy problem --- regularization --- factorization --- regular solution --- fundamental solution --- road section --- IMF SWARA --- traffic safety --- fuzzy MARCOS --- DEA --- ordinary differential equations --- analytical methods --- mathematical models --- Riccati equation --- radial Schrödinger equation --- transformations --- hyper-singular integrals --- Navier–Stokes problem --- product user experience --- enterprise network public opinion --- identification of high-risk users --- random forest algorithm --- user portrait --- controlled second-order Lagrangian --- Euler–Lagrange equations --- isoperimetric constraints --- curvilinear integral --- differential 1-form --- partition functions --- analytical extensions --- guelfand’s and gradshteyn’s --- classical gravity --- internal waves in rotating ocean --- fractional derivative --- q-Homotopy analysis transform technique --- fixed point theorem --- minimal sensitivity --- optimization --- power transform --- critical index --- secant method --- generalized secant method --- complex roots --- cressman method --- EICM --- ENSO --- SSTA --- immune system --- virus-infected cell --- effector cell --- autoimmune disease --- time-delay virus-immune model --- differential equations --- differential operators --- non-local boundary value problems --- general conditions --- integral conditions --- multipoint conditions --- composition of operators --- pseudo-differential equation --- conjugation problem --- wave factorization --- solvability condition --- measure of noncompactness --- random effect --- random operator --- Mönch’s fixed point theorem --- multi-term fractional differential equation --- Carathéodory condition --- resolvent family theory --- multi-dimensional public opinion --- topic derivation --- complex network dynamics model --- online comments --- hot events --- fluid --- flows --- dynamic --- structure --- axiomatics --- fundamental equations --- dissipation --- complete solution --- ligaments --- waves --- vortices --- plate --- wake --- drop --- impact --- boundary element method --- barrier options --- multi-asset options --- basket options --- spread options --- thrid-order differential equations --- delay --- oscillation criteria --- n/a --- radial Schrödinger equation --- Navier-Stokes problem --- Euler-Lagrange equations --- guelfand's and gradshteyn's --- Mönch's fixed point theorem --- Carathéodory condition
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