Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Fourier series. --- Series, Taylor's. --- De Taylor, Séries. --- De Fourier, Séries.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book introduces novel results on mathematical modelling, parameter identification, and automatic control for a wide range of applications of mechanical, electric, and mechatronic systems, where undesirable oscillations or vibrations are manifested. The six chapters of the book written by experts from international scientific community cover a wide range of interesting research topics related to: algebraic identification of rotordynamic parameters in rotor-bearing system using finite element models; model predictive control for active automotive suspension systems by means of hydraulic actuators; model-free data-driven-based control for a Voltage Source Converter-based Static Synchronous Compensator to improve the dynamic power grid performance under transient scenarios; an exact elasto-dynamics theory for bending vibrations for a class of flexible structures; motion profile tracking control and vibrating disturbance suppression for quadrotor aerial vehicles using artificial neural networks and particle swarm optimization; and multiple adaptive controllers based on B-Spline artificial neural networks for regulation and attenuation of low frequency oscillations for large-scale power systems. The book is addressed for both academic and industrial researchers and practitioners, as well as for postgraduate and undergraduate engineering students and other experts in a wide variety of disciplines seeking to know more about the advances and trends in mathematical modelling, control and identification of engineering systems in which undesirable oscillations or vibrations could be presented during their operation.

Technology: general issues --- History of engineering & technology --- B-spline neural networks --- adaptive power system control --- coordinated multiple controllers --- StatCom --- exact plate theory --- thick plate --- bending vibration --- partial differential operator theory --- gauge condition --- data-driven control --- reactive power compensation --- STATCOM --- voltage control --- voltage source converter --- quadrotor UAV --- artificial neural networks --- robust control --- Taylor series --- B-splines --- particle swarm optimization --- active suspension --- model predictive control --- linear parameter varying --- ellipsoidal set --- attraction sets --- quadratic stability --- algebraic identification --- rotor-bearing system --- finite element model --- rotordynamic coefficients --- B-spline neural networks --- adaptive power system control --- coordinated multiple controllers --- StatCom --- exact plate theory --- thick plate --- bending vibration --- partial differential operator theory --- gauge condition --- data-driven control --- reactive power compensation --- STATCOM --- voltage control --- voltage source converter --- quadrotor UAV --- artificial neural networks --- robust control --- Taylor series --- B-splines --- particle swarm optimization --- active suspension --- model predictive control --- linear parameter varying --- ellipsoidal set --- attraction sets --- quadratic stability --- algebraic identification --- rotor-bearing system --- finite element model --- rotordynamic coefficients

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

This book presents a new result in 3-dimensional topology. It is well known that any closed oriented 3-manifold can be obtained by surgery on a framed link in S 3. In Global Surgery Formula for the Casson-Walker Invariant, a function F of framed links in S 3 is described, and it is proven that F consistently defines an invariant, lamda (l), of closed oriented 3-manifolds. l is then expressed in terms of previously known invariants of 3-manifolds. For integral homology spheres, l is the invariant introduced by Casson in 1985, which allowed him to solve old and famous questions in 3-dimensional topology. l becomes simpler as the first Betti number increases. As an explicit function of Alexander polynomials and surgery coefficients of framed links, the function F extends in a natural way to framed links in rational homology spheres. It is proven that F describes the variation of l under any surgery starting from a rational homology sphere. Thus F yields a global surgery formula for the Casson invariant.

Chirurgie (Topologie) --- Drie-menigvuldigheden (Topologie) --- Heelkunde (Topologie) --- Surgery (Topology) --- Three-manifolds (Topology) --- Trois-variétés (Topologie) --- 3-manifolds (Topology) --- Manifolds, Three dimensional (Topology) --- Three-dimensional manifolds (Topology) --- Low-dimensional topology --- Topological manifolds --- Differential topology --- Homotopy equivalences --- Manifolds (Mathematics) --- Topology --- 515.16 --- 515.16 Topology of manifolds --- Topology of manifolds --- 3-manifold. --- Addition. --- Alexander polynomial. --- Ambient isotopy. --- Betti number. --- Casson invariant. --- Change of basis. --- Change of variables. --- Cobordism. --- Coefficient. --- Combination. --- Combinatorics. --- Computation. --- Conjugacy class. --- Connected component (graph theory). --- Connected space. --- Connected sum. --- Cup product. --- Determinant. --- Diagram (category theory). --- Disk (mathematics). --- Empty set. --- Exterior (topology). --- Fiber bundle. --- Fibration. --- Function (mathematics). --- Fundamental group. --- Homeomorphism. --- Homology (mathematics). --- Homology sphere. --- Homotopy sphere. --- Indeterminate (variable). --- Integer. --- Klein bottle. --- Knot theory. --- Manifold. --- Morphism. --- Notation. --- Orientability. --- Permutation. --- Polynomial. --- Prime number. --- Projective plane. --- Scientific notation. --- Seifert surface. --- Sequence. --- Summation. --- Symmetrization. --- Taylor series. --- Theorem. --- Topology. --- Tubular neighborhood. --- Unlink.

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

One of the most exciting new subjects in Algebraic Number Theory and Arithmetic Algebraic Geometry is the theory of Euler systems. Euler systems are special collections of cohomology classes attached to p-adic Galois representations. Introduced by Victor Kolyvagin in the late 1980's in order to bound Selmer groups attached to p-adic representations, Euler systems have since been used to solve several key problems. These include certain cases of the Birch and Swinnerton-Dyer Conjecture and the Main Conjecture of Iwasawa Theory. Because Selmer groups play a central role in Arithmetic Algebraic Geometry, Euler systems should be a powerful tool in the future development of the field. Here, in the first book to appear on the subject, Karl Rubin presents a self-contained development of the theory of Euler systems. Rubin first reviews and develops the necessary facts from Galois cohomology. He then introduces Euler systems, states the main theorems, and develops examples and applications. The remainder of the book is devoted to the proofs of the main theorems as well as some further speculations. The book assumes a solid background in algebraic Number Theory, and is suitable as an advanced graduate text. As a research monograph it will also prove useful to number theorists and researchers in Arithmetic Algebraic Geometry.

Algebraic number theory. --- p-adic numbers. --- Numbers, p-adic --- Number theory --- p-adic analysis --- Galois cohomology --- Cohomologie galoisienne. --- Algebraic number theory --- p-adic numbers --- Abelian extension. --- Abelian variety. --- Absolute Galois group. --- Algebraic closure. --- Barry Mazur. --- Big O notation. --- Birch and Swinnerton-Dyer conjecture. --- Cardinality. --- Class field theory. --- Coefficient. --- Cohomology. --- Complex multiplication. --- Conjecture. --- Corollary. --- Cyclotomic field. --- Dimension (vector space). --- Divisibility rule. --- Eigenvalues and eigenvectors. --- Elliptic curve. --- Error term. --- Euler product. --- Euler system. --- Exact sequence. --- Existential quantification. --- Field of fractions. --- Finite set. --- Functional equation. --- Galois cohomology. --- Galois group. --- Galois module. --- Gauss sum. --- Global field. --- Heegner point. --- Ideal class group. --- Integer. --- Inverse limit. --- Inverse system. --- Karl Rubin. --- Local field. --- Mathematical induction. --- Maximal ideal. --- Modular curve. --- Modular elliptic curve. --- Natural number. --- Orthogonality. --- P-adic number. --- Pairing. --- Principal ideal. --- R-factor (crystallography). --- Ralph Greenberg. --- Remainder. --- Residue field. --- Ring of integers. --- Scientific notation. --- Selmer group. --- Subgroup. --- Tate module. --- Taylor series. --- Tensor product. --- Theorem. --- Upper and lower bounds. --- Victor Kolyvagin. --- Courbes elliptiques --- Nombres, Théorie des

Choose an application

• Reference Manager
• EndNote
• RefWorks (Direct export to RefWorks)

Rabinowitz's classical global bifurcation theory, which concerns the study in-the-large of parameter-dependent families of nonlinear equations, uses topological methods that address the problem of continuous parameter dependence of solutions by showing that there are connected sets of solutions of global extent. Even when the operators are infinitely differentiable in all the variables and parameters, connectedness here cannot in general be replaced by path-connectedness. However, in the context of real-analyticity there is an alternative theory of global bifurcation due to Dancer, which offers a much stronger notion of parameter dependence. This book aims to develop from first principles Dancer's global bifurcation theory for one-parameter families of real-analytic operators in Banach spaces. It shows that there are globally defined continuous and locally real-analytic curves of solutions. In particular, in the real-analytic setting, local analysis can lead to global consequences--for example, as explained in detail here, those resulting from bifurcation from a simple eigenvalue. Included are accounts of analyticity and implicit function theorems in Banach spaces, classical results from the theory of finite-dimensional analytic varieties, and the links between these two and global existence theory. Laying the foundations for more extensive studies of real-analyticity in infinite-dimensional problems and illustrating the theory with examples, Analytic Theory of Global Bifurcation is intended for graduate students and researchers in pure and applied analysis.

Differential geometry. Global analysis --- Bifurcation theory. --- Differential equations, Nonlinear --- Stability --- Numerical solutions --- Addition. --- Algebraic equation. --- Analytic function. --- Analytic manifold. --- Atmospheric pressure. --- Banach space. --- Bernhard Riemann. --- Bifurcation diagram. --- Boundary value problem. --- Bounded operator. --- Bounded set (topological vector space). --- Boundedness. --- Canonical form. --- Cartesian coordinate system. --- Codimension. --- Compact operator. --- Complex analysis. --- Complex conjugate. --- Complex number. --- Connected space. --- Coordinate system. --- Corollary. --- Curvature. --- Derivative. --- Diagram (category theory). --- Differentiable function. --- Differentiable manifold. --- Dimension (vector space). --- Dimension. --- Direct sum. --- Eigenvalues and eigenvectors. --- Elliptic integral. --- Embedding. --- Equation. --- Euclidean division. --- Euler equations (fluid dynamics). --- Existential quantification. --- First principle. --- Fredholm operator. --- Froude number. --- Functional analysis. --- Hilbert space. --- Homeomorphism. --- Implicit function theorem. --- Integer. --- Linear algebra. --- Linear function. --- Linear independence. --- Linear map. --- Linear programming. --- Linear space (geometry). --- Linear subspace. --- Linearity. --- Linearization. --- Metric space. --- Morse theory. --- Multilinear form. --- N0. --- Natural number. --- Neumann series. --- Nonlinear functional analysis. --- Nonlinear system. --- Numerical analysis. --- Open mapping theorem (complex analysis). --- Operator (physics). --- Ordinary differential equation. --- Parameter. --- Parametrization. --- Partial differential equation. --- Permutation group. --- Permutation. --- Polynomial. --- Power series. --- Prime number. --- Proportionality (mathematics). --- Pseudo-differential operator. --- Puiseux series. --- Quantity. --- Real number. --- Resultant. --- Singularity theory. --- Skew-symmetric matrix. --- Smoothness. --- Solution set. --- Special case. --- Standard basis. --- Sturm–Liouville theory. --- Subset. --- Symmetric bilinear form. --- Symmetric group. --- Taylor series. --- Taylor's theorem. --- Theorem. --- Total derivative. --- Two-dimensional space. --- Union (set theory). --- Variable (mathematics). --- Vector space. --- Zero of a function.