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This book gives a new foundation for the theory of links in 3-space modeled on the modern developmentby Jaco, Shalen, Johannson, Thurston et al. of the theory of 3-manifolds. The basic construction is a method of obtaining any link by "splicing" links of the simplest kinds, namely those whose exteriors are Seifert fibered or hyperbolic. This approach to link theory is particularly attractive since most invariants of links are additive under splicing.Specially distinguished from this viewpoint is the class of links, none of whose splice components is hyperbolic. It includes all links constructed by cabling and connected sums, in particular all links of singularities of complex plane curves. One of the main contributions of this monograph is the calculation of invariants of these classes of links, such as the Alexander polynomials, monodromy, and Seifert forms.

Algebraic geometry --- Differential geometry. Global analysis --- Link theory. --- Curves, Plane. --- SINGULARITIES (Mathematics) --- Curves, Plane --- Invariants --- Link theory --- Singularities (Mathematics) --- Geometry, Algebraic --- Low-dimensional topology --- Piecewise linear topology --- Higher plane curves --- Plane curves --- Invariants. --- 3-sphere. --- Alexander Grothendieck. --- Alexander polynomial. --- Algebraic curve. --- Algebraic equation. --- Algebraic geometry. --- Algebraic surface. --- Algorithm. --- Ambient space. --- Analytic function. --- Approximation. --- Big O notation. --- Call graph. --- Cartesian coordinate system. --- Characteristic polynomial. --- Closed-form expression. --- Cohomology. --- Computation. --- Conjecture. --- Connected sum. --- Contradiction. --- Coprime integers. --- Corollary. --- Curve. --- Cyclic group. --- Determinant. --- Diagram (category theory). --- Diffeomorphism. --- Dimension. --- Disjoint union. --- Eigenvalues and eigenvectors. --- Equation. --- Equivalence class. --- Euler number. --- Existential quantification. --- Exterior (topology). --- Fiber bundle. --- Fibration. --- Foliation. --- Fundamental group. --- Geometry. --- Graph (discrete mathematics). --- Ground field. --- Homeomorphism. --- Homology sphere. --- Identity matrix. --- Integer matrix. --- Intersection form (4-manifold). --- Isolated point. --- Isolated singularity. --- Jordan normal form. --- Knot theory. --- Mathematical induction. --- Monodromy matrix. --- Monodromy. --- N-sphere. --- Natural transformation. --- Newton polygon. --- Newton's method. --- Normal (geometry). --- Notation. --- Pairwise. --- Parametrization. --- Plane curve. --- Polynomial. --- Power series. --- Projective plane. --- Puiseux series. --- Quantity. --- Rational function. --- Resolution of singularities. --- Riemann sphere. --- Riemann surface. --- Root of unity. --- Scientific notation. --- Seifert surface. --- Set (mathematics). --- Sign (mathematics). --- Solid torus. --- Special case. --- Stereographic projection. --- Submanifold. --- Summation. --- Theorem. --- Three-dimensional space (mathematics). --- Topology. --- Torus knot. --- Torus. --- Tubular neighborhood. --- Unit circle. --- Unit vector. --- Unknot. --- Variable (mathematics).

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The ever-increasing need for higher efficiency, smaller size, and lower cost make the analysis, understanding, and design of energy conversion systems extremely important, interesting, and even imperative. One of the most neglected features in the study of such systems is the effect of the inherent nonlinearities on the stability of the system. Due to these nonlinearities, these devices may exhibit undesirable and complex dynamics, which are the focus of many researchers. Even though a lot of research has taken place in this area during the last 20 years, it is still an active research topic for mainstream power engineers. This research has demonstrated that these systems can become unstable with a direct result in increased losses, extra subharmonics, and even uncontrollability/unobservability. The detailed study of these systems can help in the design of smaller, lighter, and less expensive converters that are particularly important in emerging areas of research like electric vehicles, smart grids, renewable energy sources, and others. The aim of this Special Issue is to cover control and nonlinear aspects of instabilities in different energy conversion systems: theoretical, analysis modelling, and practical solutions for such emerging applications. In this Special Issue, we present novel research works in different areas of the control and nonlinear dynamics of energy conversion systems.

multi-clearance --- neural network --- zero average dynamics --- Cable3D --- variable bus voltage MG --- explosion-magnetic generator --- quadratic boost --- matrix norm --- coordinated control system --- permanent magnet synchronous motor (PMSM) --- photovoltaic (PV) --- power conversion --- capacitance current pulse train control --- air gap eccentricity --- high step-up voltage gain --- voltage ripple --- offset-free --- goal representation heuristic dynamic programming (GrHDP) --- current mode control --- sliding mode observer (SMO) --- multi-model predictive control --- combined heat and power unit --- discontinuous conduction mode (DCM) --- current-pulse formation --- sliding mode control --- single artificial neuron goal representation heuristic dynamic programming (SAN-GrHDP) --- subharmonic oscillations --- DC micro grid --- supply air temperature --- air-handling unit (AHU) --- vibration characteristics --- magnetic saturation --- slope compensation --- fixed-point inducting control --- the load of suspension point in the z direction --- variable switching frequency DC-DC converters --- droop control --- Helmholtz number --- plasma accelerator --- contraction analysis --- sliding control --- bifurcations in control parameter --- disturbance observer --- DC motor --- multiphysics --- virtual impedance --- pulverizing system --- ultrahigh voltage conversion ratio --- corrugated pipe --- DC-DC converters --- maximum power point tracking (MPPT) --- dynamic model --- nonlinear dynamics --- new step-up converter --- micro-grid --- global stability --- extended back electromotive force (EEMF) --- small-signal model --- electromagnetic vibration --- nonlinear dynamic model --- excited modes --- data-driven --- rigid body rotation --- position sensorless --- prediction --- centralized vs. decentralized control --- inferential control --- boost-flyback converter --- calculation method --- switched reluctance generator --- monodromy matrix --- bridgeless converter --- decoupling control --- distributed architecture --- wave --- buck converter --- soft sensor --- model–plant mismatches --- whistling noise --- efficiency optimization --- steel catenary riser --- moving horizon estimation --- single artificial neuron (SAN) --- space mechanism --- two-stage bypass --- electrical machine --- harmonic suppression --- local vs. global optimization --- performance recovery --- reinforcement learning (RL) --- adaptive dynamic programming (ADP) --- overvoltage --- planetary gears --- maximum power point tracking --- DC-DC buck converter --- power quality --- average-current mode control --- feedback coefficient --- power factor correction (PFC) --- capacitance current --- predictive control --- rotor dynamics