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The classical Melnikov method provides information on the behavior of deterministic planar systems that may exhibit transitions, i.e. escapes from and captures into preferred regions of phase space. This book develops a unified treatment of deterministic and stochastic systems that extends the applicability of the Melnikov method to physically realizable stochastic planar systems with additive, state-dependent, white, colored, or dichotomous noise. The extended Melnikov method yields the novel result that motions with transitions are chaotic regardless of whether the excitation is deterministic or stochastic. It explains the role in the occurrence of transitions of the characteristics of the system and its deterministic or stochastic excitation, and is a powerful modeling and identification tool. The book is designed primarily for readers interested in applications. The level of preparation required corresponds to the equivalent of a first-year graduate course in applied mathematics. No previous exposure to dynamical systems theory or the theory of stochastic processes is required. The theoretical prerequisites and developments are presented in the first part of the book. The second part of the book is devoted to applications, ranging from physics to mechanical engineering, naval architecture, oceanography, nonlinear control, stochastic resonance, and neurophysiology.

Differentiable dynamical systems. --- Chaotic behavior in systems. --- Stochastic systems. --- Systems, Stochastic --- Stochastic processes --- System analysis --- Chaos in systems --- Chaos theory --- Chaotic motion in systems --- Differentiable dynamical systems --- Dynamics --- Nonlinear theories --- System theory --- Differential dynamical systems --- Dynamical systems, Differentiable --- Dynamics, Differentiable --- Differential equations --- Global analysis (Mathematics) --- Topological dynamics --- Affine transformation. --- Amplitude. --- Arbitrarily large. --- Attractor. --- Autocovariance. --- Big O notation. --- Central limit theorem. --- Change of variables. --- Chaos theory. --- Coefficient of variation. --- Compound Probability. --- Computational problem. --- Control theory. --- Convolution. --- Coriolis force. --- Correlation coefficient. --- Covariance function. --- Cross-covariance. --- Cumulative distribution function. --- Cutoff frequency. --- Deformation (mechanics). --- Derivative. --- Deterministic system. --- Diagram (category theory). --- Diffeomorphism. --- Differential equation. --- Dirac delta function. --- Discriminant. --- Dissipation. --- Dissipative system. --- Dynamical system. --- Eigenvalues and eigenvectors. --- Equations of motion. --- Even and odd functions. --- Excitation (magnetic). --- Exponential decay. --- Extreme value theory. --- Flow velocity. --- Fluid dynamics. --- Forcing (recursion theory). --- Fourier series. --- Fourier transform. --- Fractal dimension. --- Frequency domain. --- Gaussian noise. --- Gaussian process. --- Harmonic analysis. --- Harmonic function. --- Heteroclinic orbit. --- Homeomorphism. --- Homoclinic orbit. --- Hyperbolic point. --- Inference. --- Initial condition. --- Instability. --- Integrable system. --- Invariant manifold. --- Iteration. --- Joint probability distribution. --- LTI system theory. --- Limit cycle. --- Linear differential equation. --- Logistic map. --- Marginal distribution. --- Moduli (physics). --- Multiplicative noise. --- Noise (electronics). --- Nonlinear control. --- Nonlinear system. --- Ornstein–Uhlenbeck process. --- Oscillation. --- Parameter space. --- Parameter. --- Partial differential equation. --- Perturbation function. --- Phase plane. --- Phase space. --- Poisson distribution. --- Probability density function. --- Probability distribution. --- Probability theory. --- Probability. --- Production–possibility frontier. --- Relative velocity. --- Scale factor. --- Shear stress. --- Spectral density. --- Spectral gap. --- Standard deviation. --- Stochastic process. --- Stochastic resonance. --- Stochastic. --- Stream function. --- Surface stress. --- Symbolic dynamics. --- The Signal and the Noise. --- Topological conjugacy. --- Transfer function. --- Variance. --- Vorticity.

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Recent advancements in mechanical engineering are an essential topic for discussion. The topics relating to mechanical engineering include the following: measurements of signals of shafts, springs, belts, bearings, gears, rotors, machine elements, vibration analysis, acoustic analysis, fault diagnosis, construction, analysis of machine operation, analysis of smart-material systems, integrated systems, stresses, analysis of deformations, analysis of mechanical properties, signal processing of mechanical systems, and rotor dynamics. Mechanical engineering deals with solid and fluid mechanics, rotation, movements, materials, and thermodynamics. This book, with 15 published articles, presents the topic “Symmetry in Mechanical Engineering”. The presented topic is interesting. It is categorized into eight different sections: Deformation; Stresses; Mechanical properties; Tribology; Thermodynamic; Measurement; Fault diagnosis; Machine. The development of techniques and methods related to mechanical engineering is growing every month. The described articles have made a contribution to mechanical engineering. The proposed research can find applications in factories, oil refineries, and mines. It is essential to develop new improved methods, techniques, and devices related to mechanical engineering.

History of engineering & technology --- traveling waves --- vibration stability --- self-excited vibration --- thin spur gear --- variational mode decomposition --- signal analysis --- time-frequency analysis --- center frequency method of double thresholds --- Hilbert transform --- finite-time control --- terminal sliding mode --- chattering --- neural network --- thin-walled structures --- higher-order deformation modes --- identification --- doubly symmetric cross-sections --- shell-like deformation --- dual mass flywheel --- absolute sensitivity --- relative sensitivity --- torsional vibration --- spring --- Dempster’s rule --- evidence distance --- pattern recognition --- maritime surveillance --- customer needs --- bad parameters --- core problems --- design process --- conceptual design --- time-varying P-type IL method --- MFA control --- imprecise probability --- active control --- piezoelectric cantilever plate --- image processing --- particle --- distribution --- rolling bearings --- Fault diagnosis --- second-order tristable stochastic resonance --- seeker optimization algorithm --- output signal-to-noise ratio --- global optimization --- meta-heuristic --- butterfly optimization algorithm --- cross-entropy method --- engineering design problems --- grinding --- rheology --- breakage parameters --- relative viscosity --- tool wear state --- CNN --- BiLSTM --- attention mechanism --- signal features --- vibrations --- symmetries --- two-engine vehicle --- rear clutch --- front clutch --- vibration modes --- granulation --- on-line monitoring --- fertilizers --- parallel robot --- minimally invasive procedures --- algebraic modeling --- Study parameters --- fractional damping --- vibration --- dynamic behaviour --- hybrid mechanism --- helicopter --- abrasive belt grinding --- predictive model --- regression --- material removal --- electric vehicles --- PMSM --- auxiliary slot --- response surface methodology --- n/a --- Dempster's rule

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Recent advancements in mechanical engineering are an essential topic for discussion. The topics relating to mechanical engineering include the following: measurements of signals of shafts, springs, belts, bearings, gears, rotors, machine elements, vibration analysis, acoustic analysis, fault diagnosis, construction, analysis of machine operation, analysis of smart-material systems, integrated systems, stresses, analysis of deformations, analysis of mechanical properties, signal processing of mechanical systems, and rotor dynamics. Mechanical engineering deals with solid and fluid mechanics, rotation, movements, materials, and thermodynamics. This book, with 15 published articles, presents the topic “Symmetry in Mechanical Engineering”. The presented topic is interesting. It is categorized into eight different sections: Deformation; Stresses; Mechanical properties; Tribology; Thermodynamic; Measurement; Fault diagnosis; Machine. The development of techniques and methods related to mechanical engineering is growing every month. The described articles have made a contribution to mechanical engineering. The proposed research can find applications in factories, oil refineries, and mines. It is essential to develop new improved methods, techniques, and devices related to mechanical engineering.

History of engineering & technology --- traveling waves --- vibration stability --- self-excited vibration --- thin spur gear --- variational mode decomposition --- signal analysis --- time-frequency analysis --- center frequency method of double thresholds --- Hilbert transform --- finite-time control --- terminal sliding mode --- chattering --- neural network --- thin-walled structures --- higher-order deformation modes --- identification --- doubly symmetric cross-sections --- shell-like deformation --- dual mass flywheel --- absolute sensitivity --- relative sensitivity --- torsional vibration --- spring --- Dempster’s rule --- evidence distance --- pattern recognition --- maritime surveillance --- customer needs --- bad parameters --- core problems --- design process --- conceptual design --- time-varying P-type IL method --- MFA control --- imprecise probability --- active control --- piezoelectric cantilever plate --- image processing --- particle --- distribution --- rolling bearings --- Fault diagnosis --- second-order tristable stochastic resonance --- seeker optimization algorithm --- output signal-to-noise ratio --- global optimization --- meta-heuristic --- butterfly optimization algorithm --- cross-entropy method --- engineering design problems --- grinding --- rheology --- breakage parameters --- relative viscosity --- tool wear state --- CNN --- BiLSTM --- attention mechanism --- signal features --- vibrations --- symmetries --- two-engine vehicle --- rear clutch --- front clutch --- vibration modes --- granulation --- on-line monitoring --- fertilizers --- parallel robot --- minimally invasive procedures --- algebraic modeling --- Study parameters --- fractional damping --- vibration --- dynamic behaviour --- hybrid mechanism --- helicopter --- abrasive belt grinding --- predictive model --- regression --- material removal --- electric vehicles --- PMSM --- auxiliary slot --- response surface methodology --- n/a --- Dempster's rule

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The Special Issue entitled “Remote Sensing in Vessel Detection and Navigation” comprises 15 articles on many topics related to remote sensing with navigational sensors. The sequence of articles included in this Special Issue is in line with the latest scientific trends. The latest developments in science, including artificial intelligence, were used. It can be said that navigation and vessel detection remain important and hot topics, and a lot of work will continue to be done worldwide. New techniques and methods for analyzing and extracting information from navigational sensors and data have been proposed and verified. Some of these will spark further research, and some are already mature and can be considered for industrial implementation and development.

autonomous navigation --- automatic radar plotting aid --- safe objects control --- game theory --- computer simulation --- Sentinel-2 --- multispectral --- temporal offsets --- ship --- aircraft --- velocity --- altitude --- parallax --- jet stream --- Unmanned Surface Vessel (USV) --- multi-Global Navigation Satellite System (GNSS) receiver --- bathymetric measurements --- cross track error (XTE) --- SSL --- six-degrees-of-freedom motion --- motion attitude model --- edge detection --- straight-line fitting --- visual saliency --- vessel detection --- video monitoring --- inland waterway --- real-time detection --- neural network --- target recognition --- HRRP --- residual structure --- loss function --- trajectory tracking --- unmanned surface vehicle --- navigation --- bathymetry --- hydrographic survey --- real-time communication --- maritime situational awareness --- ship detection --- Iridium --- on-board --- image processing --- flight campaign --- position estimation --- ranging mode --- single shore station --- AIS --- bag-of-words mechanism --- machine learning --- image analysis --- ship classification --- marine system --- river monitoring system --- feature extraction --- synthetic aperture radar (SAR) ship detection --- multi-stage rotational region based network (MSR2N) --- rotated anchor generation --- multi-stage rotational detection network (MSRDN) --- convolutional neural network (CNN) --- synthetic aperture radar (SAR) --- multiscale and small ship detection --- complex background --- false alarm --- farbon dioxide peaks --- midwave infrared --- FTIR --- adaptive stochastic resonance (ASR) --- matched intrawell response --- nonlinear filter --- line enhancer --- autonomous underwater vehicles (AUVs) --- target tracking --- group targets --- GLMB --- structure --- formation --- remote sensing