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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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The climate changes that are becoming visible today are a challenge for the global research community. In this context, renewable energy sources, fuel cell systems and other energy generating sources must be optimally combined and connected to the grid system using advanced energy transaction methods. As this reprint presents the latest solutions in the implementation of fuel cell and renewable energy in mobile and stationary applications such as hybrid and microgrid power systems based on the Energy Internet, blockchain technology and smart contracts, we hope that they will be of interest to readers working in the related fields mentioned above.

Research & information: general --- Physics --- constant power load --- microgrid --- dynamic stability --- optimization --- PLL --- power-sharing control --- solid oxide fuel cell --- parameter identification --- backstepping control --- event-triggered control --- Lyapunov stability theorem --- networked control system --- nonlinear system --- autonomous driving vehicles --- vehicular communication --- intelligent driver model --- data-driven control model --- 3PL logistics --- decision making --- ARAS --- entropy --- CRITIC --- maximum power point tracking --- photovoltaic system --- partial shading conditions --- surface-based polynomial fitting --- Differential Evolution --- metaheuristic algorithms --- DC–DC converter --- islanding detection --- local islanding --- remote islanding --- signal processing --- hybrid microgrids --- renewable energies --- energy management --- electricity system --- vibration control --- dynamic vibration absorbers --- aerial vehicles --- quadrotor --- motion tracking control --- autonomous power system --- generating power consumer --- hydroelectric power plant --- optimal power consumption --- wind power plant --- solar photovoltaic power plant --- energy storage --- microgrids --- university campus --- battery energy storage --- renewable energy --- simulation --- optimal behavioral modeling --- automotive --- low-dropout linear voltage regulator --- power supply rejection ratio

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This book discusses some aspects of the theory of partial differential equations from the viewpoint of probability theory. It is intended not only for specialists in partial differential equations or probability theory but also for specialists in asymptotic methods and in functional analysis. It is also of interest to physicists who use functional integrals in their research. The work contains results that have not previously appeared in book form, including research contributions of the author.

Partial differential equations --- Differential equations, Partial. --- Probabilities. --- Integration, Functional. --- Functional integration --- Functional analysis --- Integrals, Generalized --- Probability --- Statistical inference --- Combinations --- Mathematics --- Chance --- Least squares --- Mathematical statistics --- Risk --- A priori estimate. --- Absolute continuity. --- Almost surely. --- Analytic continuation. --- Axiom. --- Big O notation. --- Boundary (topology). --- Boundary value problem. --- Bounded function. --- Calculation. --- Cauchy problem. --- Central limit theorem. --- Characteristic function (probability theory). --- Chebyshev's inequality. --- Coefficient. --- Comparison theorem. --- Continuous function (set theory). --- Continuous function. --- Convergence of random variables. --- Cylinder set. --- Degeneracy (mathematics). --- Derivative. --- Differential equation. --- Differential operator. --- Diffusion equation. --- Diffusion process. --- Dimension (vector space). --- Direct method in the calculus of variations. --- Dirichlet boundary condition. --- Dirichlet problem. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Elliptic operator. --- Elliptic partial differential equation. --- Equation. --- Existence theorem. --- Exponential function. --- Feynman–Kac formula. --- Fokker–Planck equation. --- Function space. --- Functional analysis. --- Fundamental solution. --- Gaussian measure. --- Girsanov theorem. --- Hessian matrix. --- Hölder condition. --- Independence (probability theory). --- Integral curve. --- Integral equation. --- Invariant measure. --- Iterated logarithm. --- Itô's lemma. --- Joint probability distribution. --- Laplace operator. --- Laplace's equation. --- Lebesgue measure. --- Limit (mathematics). --- Limit cycle. --- Limit point. --- Linear differential equation. --- Linear map. --- Lipschitz continuity. --- Markov chain. --- Markov process. --- Markov property. --- Maximum principle. --- Mean value theorem. --- Measure (mathematics). --- Modulus of continuity. --- Moment (mathematics). --- Monotonic function. --- Navier–Stokes equations. --- Nonlinear system. --- Ordinary differential equation. --- Parameter. --- Partial differential equation. --- Periodic function. --- Poisson kernel. --- Probabilistic method. --- Probability space. --- Probability theory. --- Probability. --- Random function. --- Regularization (mathematics). --- Schrödinger equation. --- Self-adjoint operator. --- Sign (mathematics). --- Simultaneous equations. --- Smoothness. --- State-space representation. --- Stochastic calculus. --- Stochastic differential equation. --- Stochastic. --- Support (mathematics). --- Theorem. --- Theory. --- Uniqueness theorem. --- Variable (mathematics). --- Weak convergence (Hilbert space). --- Wiener process.