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This collection of new and original papers on mathematical aspects of nonlinear dispersive equations includes both expository and technical papers that reflect a number of recent advances in the field. The expository papers describe the state of the art and research directions. The technical papers concentrate on a specific problem and the related analysis and are addressed to active researchers. The book deals with many topics that have been the focus of intensive research and, in several cases, significant progress in recent years, including hyperbolic conservation laws, Schrödinger operators, nonlinear Schrödinger and wave equations, and the Euler and Navier-Stokes equations.

Differential equations, Nonlinear --- Nonlinear partial differential operators --- Nonlinear operators --- Partial differential operators --- Absolute value. --- Addition. --- Analysis. --- Analytical technique. --- Average. --- Commutator. --- Conservation law. --- Continuous spectrum. --- Critical focus. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Equation. --- Exponential decay. --- Fourier transform. --- Lecture. --- Manifold. --- Medium frequency. --- Nature. --- Navier–Stokes equations. --- Nonlinear system. --- Scattering theory. --- Sloan Fellowship. --- Spectral method. --- Subset. --- Support (mathematics). --- Theory. --- Three-dimensional space (mathematics). --- Volume. --- Wave equation.

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This book presents an overview of recent developments in the area of localization for quasi-periodic lattice Schrödinger operators and the theory of quasi-periodicity in Hamiltonian evolution equations. The physical motivation of these models extends back to the works of Rudolph Peierls and Douglas R. Hofstadter, and the models themselves have been a focus of mathematical research for two decades. Jean Bourgain here sets forth the results and techniques that have been discovered in the last few years. He puts special emphasis on so-called "non-perturbative" methods and the important role of subharmonic function theory and semi-algebraic set methods. He describes various applications to the theory of differential equations and dynamical systems, in particular to the quantum kicked rotor and KAM theory for nonlinear Hamiltonian evolution equations. Intended primarily for graduate students and researchers in the general area of dynamical systems and mathematical physics, the book provides a coherent account of a large body of work that is presently scattered in the literature. It does so in a refreshingly contained manner that seeks to convey the present technological "state of the art."

Schrödinger operator. --- Green's functions. --- Hamiltonian systems. --- Evolution equations. --- Evolutionary equations --- Equations, Evolution --- Equations of evolution --- Hamiltonian dynamical systems --- Systems, Hamiltonian --- Functions, Green's --- Functions, Induction --- Functions, Source --- Green functions --- Induction functions --- Source functions --- Operator, Schrödinger --- Differential equations --- Differentiable dynamical systems --- Potential theory (Mathematics) --- Differential operators --- Quantum theory --- Schrödinger equation --- Almost Mathieu operator. --- Analytic function. --- Anderson localization. --- Betti number. --- Cartan's theorem. --- Chaos theory. --- Density of states. --- Dimension (vector space). --- Diophantine equation. --- Dynamical system. --- Equation. --- Existential quantification. --- Fundamental matrix (linear differential equation). --- Green's function. --- Hamiltonian system. --- Hermitian adjoint. --- Infimum and supremum. --- Iterative method. --- Jacobi operator. --- Linear equation. --- Linear map. --- Linearization. --- Monodromy matrix. --- Non-perturbative. --- Nonlinear system. --- Normal mode. --- Parameter space. --- Parameter. --- Parametrization. --- Partial differential equation. --- Periodic boundary conditions. --- Phase space. --- Phase transition. --- Polynomial. --- Renormalization. --- Self-adjoint. --- Semialgebraic set. --- Special case. --- Statistical significance. --- Subharmonic function. --- Summation. --- Theorem. --- Theory. --- Transfer matrix. --- Transversality (mathematics). --- Trigonometric functions. --- Trigonometric polynomial. --- Uniformization theorem.

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According to the National Research Council, the use of embedded systems throughout society could well overtake previous milestones in the information revolution. Mechatronics is the synergistic combination of electronic, mechanical engineering, controls, software and systems engineering in the design of processes and products. Mechatronic systems put “intelligence” into physical systems. Embedded sensors/actuators/processors are integral parts of mechatronic systems. The implementation of mechatronic systems is consistently on the rise. However, manufacturers are working hard to reduce the implementation cost of these systems while trying avoid compromising product quality. One way of addressing these conflicting objectives is through new automatic control methods, virtual sensing/estimation, and new innovative hardware topologies.

independent-wheel drive --- steering assistance --- nonlinear system --- active disturbance rejection control --- smooth road feeling --- city bus transport --- electric vehicles --- electrification --- software tool --- planning --- control --- charging management --- simulation --- analysis --- energy management --- hybrid electric vehicle --- powertrain electrification --- equivalent consumption minimization --- supercharging --- hardware-in-the-loop experiments --- driving force distribution --- decentralized traction system --- 4WD electric vehicle --- energy efficiency --- traction control --- efficiency optimization --- air mobility --- fuel cell hybrid aircraft --- stochastic optimal control --- drift counteraction optimal control --- normal force estimation --- unbiased minimum variance estimation --- controller output observer --- youla parameterization --- adaptive cruise control --- automated driving --- energy-saving --- fuel-saving --- optimal control --- passenger comfort --- new energy vehicles --- speed prediction --- macroscopic traffic model --- traffic big-data --- deep learning --- vehicle lateral dynamic and control --- unresolved issues --- application of speed prediction --- electric vehicle --- hybrid vehicle --- lithium ion --- ultracapacitor --- battery aging --- EHB --- EMB --- EWB --- system modeling --- bond graph --- optimization --- control design --- Youla parameterization --- robust control --- nonlinear optimization --- brake-by-wire --- actuator --- electro-mechanical brake --- electronic wedge brake --- electro-hydraulic brake --- n/a

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According to the National Research Council, the use of embedded systems throughout society could well overtake previous milestones in the information revolution. Mechatronics is the synergistic combination of electronic, mechanical engineering, controls, software and systems engineering in the design of processes and products. Mechatronic systems put “intelligence” into physical systems. Embedded sensors/actuators/processors are integral parts of mechatronic systems. The implementation of mechatronic systems is consistently on the rise. However, manufacturers are working hard to reduce the implementation cost of these systems while trying avoid compromising product quality. One way of addressing these conflicting objectives is through new automatic control methods, virtual sensing/estimation, and new innovative hardware topologies.

Technology: general issues --- History of engineering & technology --- independent-wheel drive --- steering assistance --- nonlinear system --- active disturbance rejection control --- smooth road feeling --- city bus transport --- electric vehicles --- electrification --- software tool --- planning --- control --- charging management --- simulation --- analysis --- energy management --- hybrid electric vehicle --- powertrain electrification --- equivalent consumption minimization --- supercharging --- hardware-in-the-loop experiments --- driving force distribution --- decentralized traction system --- 4WD electric vehicle --- energy efficiency --- traction control --- efficiency optimization --- air mobility --- fuel cell hybrid aircraft --- stochastic optimal control --- drift counteraction optimal control --- normal force estimation --- unbiased minimum variance estimation --- controller output observer --- youla parameterization --- adaptive cruise control --- automated driving --- energy-saving --- fuel-saving --- optimal control --- passenger comfort --- new energy vehicles --- speed prediction --- macroscopic traffic model --- traffic big-data --- deep learning --- vehicle lateral dynamic and control --- unresolved issues --- application of speed prediction --- electric vehicle --- hybrid vehicle --- lithium ion --- ultracapacitor --- battery aging --- EHB --- EMB --- EWB --- system modeling --- bond graph --- optimization --- control design --- Youla parameterization --- robust control --- nonlinear optimization --- brake-by-wire --- actuator --- electro-mechanical brake --- electronic wedge brake --- electro-hydraulic brake --- independent-wheel drive --- steering assistance --- nonlinear system --- active disturbance rejection control --- smooth road feeling --- city bus transport --- electric vehicles --- electrification --- software tool --- planning --- control --- charging management --- simulation --- analysis --- energy management --- hybrid electric vehicle --- powertrain electrification --- equivalent consumption minimization --- supercharging --- hardware-in-the-loop experiments --- driving force distribution --- decentralized traction system --- 4WD electric vehicle --- energy efficiency --- traction control --- efficiency optimization --- air mobility --- fuel cell hybrid aircraft --- stochastic optimal control --- drift counteraction optimal control --- normal force estimation --- unbiased minimum variance estimation --- controller output observer --- youla parameterization --- adaptive cruise control --- automated driving --- energy-saving --- fuel-saving --- optimal control --- passenger comfort --- new energy vehicles --- speed prediction --- macroscopic traffic model --- traffic big-data --- deep learning --- vehicle lateral dynamic and control --- unresolved issues --- application of speed prediction --- electric vehicle --- hybrid vehicle --- lithium ion --- ultracapacitor --- battery aging --- EHB --- EMB --- EWB --- system modeling --- bond graph --- optimization --- control design --- Youla parameterization --- robust control --- nonlinear optimization --- brake-by-wire --- actuator --- electro-mechanical brake --- electronic wedge brake --- electro-hydraulic brake

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In recent years, fractional calculus has led to tremendous progress in various areas of science and mathematics. New definitions of fractional derivatives and integrals have been uncovered, extending their classical definitions in various ways. Moreover, rigorous analysis of the functional properties of these new definitions has been an active area of research in mathematical analysis. Systems considering differential equations with fractional-order operators have been investigated thoroughly from analytical and numerical points of view, and potential applications have been proposed for use in sciences and in technology. The purpose of this Special Issue is to serve as a specialized forum for the dissemination of recent progress in the theory of fractional calculus and its potential applications.

Research & information: general --- Mathematics & science --- Caputo fractional derivative --- fractional differential equations --- hybrid differential equations --- coupled hybrid Sturm-Liouville differential equation --- multi-point boundary coupled hybrid condition --- integral boundary coupled hybrid condition --- dhage type fixed point theorem --- linear fractional system --- distributed delay --- finite time stability --- impulsive differential equations --- fractional impulsive differential equations --- instantaneous impulses --- non-instantaneous impulses --- time-fractional diffusion-wave equations --- Euler wavelets --- integral equations --- numerical approximation --- coupled systems --- Riemann-Liouville fractional derivative --- Hadamard-Caputo fractional derivative --- nonlocal boundary conditions --- existence --- fixed point --- LR-p-convex interval-valued function --- Katugampola fractional integral operator --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér inequality --- space-fractional Fokker-Planck operator --- time-fractional wave with the time-fractional damped term --- Laplace transform --- Mittag-Leffler function --- Grünwald-Letnikov scheme --- potential and current in an electric transmission line --- random walk of a population --- fractional derivative --- gradient descent --- economic growth --- group of seven --- fractional order derivative model --- GPU --- a spiral-plate heat exchanger --- parallel model --- heat transfer --- nonlinear system --- stochastic epidemic model --- malaria infection --- stochastic generalized Euler --- nonstandard finite-difference method --- positivity --- boundedness --- Caputo fractional derivative --- fractional differential equations --- hybrid differential equations --- coupled hybrid Sturm-Liouville differential equation --- multi-point boundary coupled hybrid condition --- integral boundary coupled hybrid condition --- dhage type fixed point theorem --- linear fractional system --- distributed delay --- finite time stability --- impulsive differential equations --- fractional impulsive differential equations --- instantaneous impulses --- non-instantaneous impulses --- time-fractional diffusion-wave equations --- Euler wavelets --- integral equations --- numerical approximation --- coupled systems --- Riemann-Liouville fractional derivative --- Hadamard-Caputo fractional derivative --- nonlocal boundary conditions --- existence --- fixed point --- LR-p-convex interval-valued function --- Katugampola fractional integral operator --- Hermite-Hadamard type inequality --- Hermite-Hadamard-Fejér inequality --- space-fractional Fokker-Planck operator --- time-fractional wave with the time-fractional damped term --- Laplace transform --- Mittag-Leffler function --- Grünwald-Letnikov scheme --- potential and current in an electric transmission line --- random walk of a population --- fractional derivative --- gradient descent --- economic growth --- group of seven --- fractional order derivative model --- GPU --- a spiral-plate heat exchanger --- parallel model --- heat transfer --- nonlinear system --- stochastic epidemic model --- malaria infection --- stochastic generalized Euler --- nonstandard finite-difference method --- positivity --- boundedness