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In this work we explore the Floquet theory for evolution equations of the form u'(t)+A_t u(t)=0 (t real) where the operators A_t periodically depend on t and the function u takes values in a UMD Banach space X.We impose a suitable condition on the operator family (A_t) and their common domain, in particular a decay condition for certain resolvents, to obtain the central result that all exponentially bounded solutions can be described as a superposition of a fixed family of Floquet solutions.

Bloch solution --- Lp setting --- Floquet theory --- periodic evolution equation --- superposition principle

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The use of lightweight structures across several industries has become inevitable in today’s world given the ever-rising demand for improved fuel economy and resource efficiency. In the automotive industry, composites, reinforced plastics, and lightweight materials, such as aluminum and magnesium are being adopted by many OEMs at increasing rates to reduce vehicle mass and develop efficient new lightweight designs. Automotive weight reduction with high-strength steel is also witnessing major ongoing efforts to design novel damage-controlled forming processes for a new generation of efficient, lightweight steel components. Although great progress has been made over the past decades in understanding the thermomechanical behavior of these materials, their extensive use as lightweight solutions is still limited due to numerous challenges that play a key role in cost competitiveness. Hence, significant research efforts are still required to fully understand the anisotropic material behavior, failure mechanisms, and, most importantly, the interplay between industrial processing, microstructure development, and the resulting properties. This Special Issue reprint book features concise reports on the current status in the field. The topics discussed herein include areas of manufacturing and processing technologies of materials for lightweight applications, innovative microstructure and process design concepts, and advanced characterization techniques combined with modeling of material’s behavior.

n/a --- microstructure --- Mg-Al-Ba-Ca alloy --- strength --- severe plastic deformation --- hot working --- surface roughness --- high pressure torsion extrusion --- optimization --- fatigue fracture behavior --- magnesium alloys --- de-coring --- formability --- multilayered sheets --- HPDC --- spring-back --- contact heat transfer --- mechanical properties --- bending --- in-die quenching --- equivalent strain --- light metals --- processing --- heat transfer --- damage --- creep aging --- thin-walled profile --- rolling --- aluminum alloy --- transmission line fittings --- ceramic core --- processing map --- automated void recognition --- FEA --- multi-output porthole extrusion --- density --- kinetic analysis --- texture --- non-ferrous alloys --- material characterization --- stress superposition --- hot stamping --- metal flow --- hybrid composite material --- V-bending test --- finite element model --- aluminium alloy --- shear lap test --- Al-Cu-Mg alloy --- characterization

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The Special Issue book focuses on highlighting current research and developments in the automation and control field for autonomous systems as well as showcasing state-of-the-art control strategy approaches for autonomous platforms. The book is co-edited by distinguished international control system experts currently based in Sweden, the United States of America, and the United Kingdom, with contributions from reputable researchers from China, Austria, France, the United States of America, Poland, and Hungary, among many others. The editors believe the ten articles published within this Special Issue will be highly appealing to control-systems-related researchers in applications typified in the fields of ground, aerial, maritime vehicles, and robotics as well as industrial audiences.

Technology: general issues --- History of engineering & technology --- neuron PID --- Kalman filtering --- omnidirectional mobile robot --- implementations --- anti-windup --- fault tolerance --- reconfigurable control --- Maglev --- neural networks --- artificial intelligence --- unmanned tracked vehicle --- inertial parameters --- vehicle-terrain interaction --- identification --- recursive least square with exponential forgetting --- generalized Newton–Raphson --- Unscented Kalman Filter --- lane keeping control (LKC) --- non-smooth finite-time control --- previewed tracking --- error weight superposition --- electric vehicle (EV) --- ODD-based AD function design --- path tracking --- path planning --- software architecture --- interface design --- autonomous vehicle --- advanced driver-assistance system --- LPV approach --- robust control --- cruise control --- semi-active suspension control --- passenger comfort --- automated vehicles --- ADAS/AD functions --- C-ITS --- IVIM --- infrastructure assistance --- routing recommendations --- autonomous driving --- active learning --- formal methods --- model-based engineering --- automata learning --- unmanned vehicle --- nonlinear model prediction controller --- trajectory tracking --- outdoor field test --- vehicle following --- path following --- splines --- spline approximation --- n/a --- generalized Newton-Raphson

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Quantum field theory has achieved some extraordinary successes over the past sixty years; however, it retains a set of challenging problems. It is not yet able to describe gravity in a mathematically consistent manner. CP violation remains unexplained. Grand unified theories have been eliminated by experiment, and a viable unification model has yet to replace them. Even the highly successful quantum chromodynamics, despite significant computational achievements, struggles to provide theoretical insight into the low-energy regime of quark physics, where the nature and structure of hadrons are determined. The only proposal for resolving the fine-tuning problem, low-energy supersymmetry, has been eliminated by results from the LHC. Since mathematics is the true and proper language for quantitative physical models, we expect new mathematical constructions to provide insight into physical phenomena and fresh approaches for building physical theories.

Research & information: general --- Physics --- semiheaps --- ternary algebras --- para-associativity --- quantum mechanics --- gravity --- Clairaut equation --- Cho–Duan–Ge decomposition --- constraintless formalism --- canonical gravity --- covariance --- black holes --- quantum foundations --- non-axiomaticity --- detector clicks --- ensembles --- superposition principle --- arithmetic --- numbers --- vector space --- abstracting --- interpretations --- self-referentiality --- direct product --- direct power --- polyadic semigroup --- arity --- polyadic ring --- polyadic field --- Maxwell’s vacuum equations --- Hamilton–Jacobi equation --- Klein–Gordon–Fock equation --- algebra of symmetry operators --- separation of variables --- linear partial differential equations --- Einstein field equation --- recursion operator --- Noether symmetry --- master symmetry --- conformable differential --- Poisson manifold --- diffeomorphism group --- current algebra symmetry --- current Lie algebra representation --- fock space --- generating functional --- distribution functions --- Lie–Poisson structure --- coherent states --- Lie-Poisson action --- Hilbert space linearization --- hamiltonian systems --- symmetry reduction --- integrability --- idiabatic states --- factorization --- heavenly type dynamical systems --- integrable dynamical systems --- dirac reduction --- hydrodynamic flows --- entropy --- vortex flows --- asymptotic conditions --- Kirchhoff’s integral theorem --- quantum gravity and the problem of the Big Bang --- hidden Hermitian formulations of quantum mechanics --- stationary Wheeler-DeWitt system --- physical Hilbert space metric --- non-stationary Wheeler-DeWitt system --- n/a --- Cho-Duan-Ge decomposition --- Maxwell's vacuum equations --- Hamilton-Jacobi equation --- Klein-Gordon-Fock equation --- Lie-Poisson structure --- Kirchhoff's integral theorem

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This book presents collective works published in the recent Special Issue (SI) entitled "Aero/Hydrodynamics and Symmetry". These works address the existence of symmetry and its breakdown in aero-/hydro-dynamics and their related applications. The presented problems are complex nonlinear, non-Newtonian fluid flow problems that are (in some cases) coupled with heat transfer, phase change, nanofluidic, and magnetohydrodynamics phenomena. The applications vary and range from polymer chain transfer in micro-channel to the evaluation of vertical axis wind turbines, as well as autonomous underwater hovering vehicles. Recent advances in numerical, theoretical, and experimental methodologies, as well as finding new physics, new methodological developments, and their limitations are presented within the scope of the current book. Among others, in the presented works, special attention is paid to validation and improving the accuracy of the presented methodologies. This book brings together a collection of inter-/multi-disciplinary works applied to many engineering applications in a coherent manner.

Savonius vertical axis wind turbine --- horizontal overlap ratio --- vertical overlap ratio --- torque coefficient --- power coefficient --- Advection–diffusion --- fractional derivative --- concentrated source --- integral transform --- Burgers’ fluid --- velocity field --- shear stress --- Laplace transform --- modified Bessel function --- Stehfest’s algorithm --- MATHCAD --- electroosmotic flow --- power law fluid --- nanoparticles --- MHD --- entropy generation --- convergence analysis --- residual error --- autonomous underwater vehicle (AUV) --- airborne-launched AUV --- autonomous underwater hovering vehicle (AUH) --- water entry impact force --- computational fluid dynamics (CFD) --- two-phase flow --- Autonomous Underwater Vehicle (AUV) --- Autonomous Underwater Hovering Vehicle (AUH) --- hydrodynamic interaction --- response amplitude operator (RAO) --- wave effects --- symmetric flying wing --- plasma flow control --- energy --- stall --- dimensionless frequency --- particle image velocimetry --- SA–NaAlg fluid --- porosity --- fractional model --- Atangana–Baleanu derivative --- large eddy simulation --- subgrid scale model --- diffuser --- dynamic one equation model --- Vreman model --- separation --- heat conduction --- non-fourier --- solution structure theorems --- superposition approach --- Buongiorno model --- unsteady flow --- nanoliquid --- special third-grade liquid --- non-linear thermal radiation --- magneto hydro-dynamics (MHD) --- dissipative particle dynamics (DPD) --- Hartmann number (Ha-value) --- harmony bond coefficient or spring constant (K)