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Intended for researchers in Riemann surfaces, this volume summarizes a significant portion of the work done in the field during the years 1966 to 1971.

Riemann surfaces --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Surfaces, Riemann --- Functions --- Congresses --- Differential geometry. Global analysis --- RIEMANN SURFACES --- congresses --- Congresses. --- MATHEMATICS / Calculus. --- Affine space. --- Algebraic function field. --- Algebraic structure. --- Analytic continuation. --- Analytic function. --- Analytic set. --- Automorphic form. --- Automorphic function. --- Automorphism. --- Beltrami equation. --- Bernhard Riemann. --- Boundary (topology). --- Canonical basis. --- Cartesian product. --- Clifford's theorem. --- Cohomology. --- Commutative diagram. --- Commutative property. --- Complex multiplication. --- Conformal geometry. --- Conformal map. --- Coset. --- Degeneracy (mathematics). --- Diagram (category theory). --- Differential geometry of surfaces. --- Dimension (vector space). --- Dirichlet boundary condition. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Eisenstein series. --- Euclidean space. --- Existential quantification. --- Explicit formulae (L-function). --- Exterior (topology). --- Finsler manifold. --- Fourier series. --- Fuchsian group. --- Function (mathematics). --- Generating set of a group. --- Group (mathematics). --- Hilbert space. --- Holomorphic function. --- Homeomorphism. --- Homology (mathematics). --- Homotopy. --- Hyperbolic geometry. --- Hyperbolic group. --- Identity matrix. --- Infimum and supremum. --- Inner automorphism. --- Intersection (set theory). --- Intersection number (graph theory). --- Isometry. --- Isomorphism class. --- Isomorphism theorem. --- Kleinian group. --- Limit point. --- Limit set. --- Linear map. --- Lorentz group. --- Mapping class group. --- Mathematical induction. --- Mathematics. --- Matrix (mathematics). --- Matrix multiplication. --- Measure (mathematics). --- Meromorphic function. --- Metric space. --- Modular group. --- Möbius transformation. --- Number theory. --- Osgood curve. --- Parity (mathematics). --- Partial isometry. --- Poisson summation formula. --- Pole (complex analysis). --- Projective space. --- Quadratic differential. --- Quadratic form. --- Quasiconformal mapping. --- Quotient space (linear algebra). --- Quotient space (topology). --- Riemann mapping theorem. --- Riemann sphere. --- Riemann surface. --- Riemann zeta function. --- Scalar multiplication. --- Scientific notation. --- Selberg trace formula. --- Series expansion. --- Sign (mathematics). --- Square-integrable function. --- Subgroup. --- Teichmüller space. --- Theorem. --- Topological manifold. --- Topological space. --- Uniformization. --- Unit disk. --- Variable (mathematics). --- Riemann, Surfaces de --- RIEMANN SURFACES - congresses --- Fonctions d'une variable complexe --- Surfaces de riemann

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This book offers the first comprehensive introduction to wave scattering in nonstationary materials. G. F. Roach's aim is to provide an accessible, self-contained resource for newcomers to this important field of research that has applications across a broad range of areas, including radar, sonar, diagnostics in engineering and manufacturing, geophysical prospecting, and ultrasonic medicine such as sonograms. New methods in recent years have been developed to assess the structure and properties of materials and surfaces. When light, sound, or some other wave energy is directed at the material in question, "imperfections" in the resulting echo can reveal a tremendous amount of valuable diagnostic information. The mathematics behind such analysis is sophisticated and complex. However, while problems involving stationary materials are quite well understood, there is still much to learn about those in which the material is moving or changes over time. These so-called non-autonomous problems are the subject of this fascinating book. Roach develops practical strategies, techniques, and solutions for mathematicians and applied scientists working in or seeking entry into the field of modern scattering theory and its applications. Wave Scattering by Time-Dependent Perturbations is destined to become a classic in this rapidly evolving area of inquiry.

Waves --- Scattering (Physics) --- Perturbation (Mathematics) --- Perturbation equations --- Perturbation theory --- Approximation theory --- Dynamics --- Functional analysis --- Mathematical physics --- Atomic scattering --- Atoms --- Nuclear scattering --- Particles (Nuclear physics) --- Scattering of particles --- Wave scattering --- Collisions (Nuclear physics) --- Particles --- Collisions (Physics) --- Cycles --- Hydrodynamics --- Benjamin-Feir instability --- Mathematics. --- Scattering --- Acoustic wave equation. --- Acoustic wave. --- Affine space. --- Angular frequency. --- Approximation. --- Asymptotic analysis. --- Asymptotic expansion. --- Banach space. --- Basis (linear algebra). --- Bessel's inequality. --- Boundary value problem. --- Bounded operator. --- C0-semigroup. --- Calculation. --- Characteristic function (probability theory). --- Classical physics. --- Codimension. --- Coefficient. --- Continuous function (set theory). --- Continuous function. --- Continuous spectrum. --- Convolution. --- Differentiable function. --- Differential equation. --- Dimension (vector space). --- Dimension. --- Dimensional analysis. --- Dirac delta function. --- Dirichlet problem. --- Distribution (mathematics). --- Duhamel's principle. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Electromagnetism. --- Equation. --- Existential quantification. --- Exponential function. --- Floquet theory. --- Fourier inversion theorem. --- Fourier series. --- Fourier transform. --- Fredholm integral equation. --- Frequency domain. --- Helmholtz equation. --- Hilbert space. --- Initial value problem. --- Integral equation. --- Integral transform. --- Integration by parts. --- Inverse problem. --- Inverse scattering problem. --- Lebesgue measure. --- Linear differential equation. --- Linear map. --- Linear space (geometry). --- Locally integrable function. --- Longitudinal wave. --- Mathematical analysis. --- Mathematical physics. --- Metric space. --- Operator theory. --- Ordinary differential equation. --- Orthonormal basis. --- Orthonormality. --- Parseval's theorem. --- Partial derivative. --- Partial differential equation. --- Phase velocity. --- Plane wave. --- Projection (linear algebra). --- Propagator. --- Quantity. --- Quantum mechanics. --- Reflection coefficient. --- Requirement. --- Riesz representation theorem. --- Scalar (physics). --- Scattering theory. --- Scattering. --- Scientific notation. --- Self-adjoint operator. --- Self-adjoint. --- Series expansion. --- Sine wave. --- Spectral method. --- Spectral theorem. --- Spectral theory. --- Square-integrable function. --- Subset. --- Theorem. --- Theory. --- Time domain. --- Time evolution. --- Unbounded operator. --- Unitarity (physics). --- Vector space. --- Volterra integral equation. --- Wave function. --- Wave packet. --- Wave propagation.

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Electromagnetic (EM) waves carry energy through propagation in space. This radiation associates with entangled electric and magnetic fields which must exist simultaneously. Although all EM waves travel at the speed of light in vacuum, they cover a wide range of frequencies called the EM spectrum. The various portions of the EM spectrum are referred to by various names based on their different attributes in the emission, transmission, and absorption of the corresponding waves and also based on their different practical applications. There are no certain boundaries separating these various portions, and the ranges tend to overlap. Overall, the EM spectrum, from the lowest to the highest frequency (longest to shortest wavelength) contains the following waves: radio frequency (RF), microwaves, millimeter waves, terahertz, infrared, visible light, ultraviolet, X-rays, and gamma rays. This Special Issue consists of sixteen papers covering a broad range of topics related to the applications of EM waves, from the design of filters and antennas for wireless communications to biomedical imaging and sensing and beyond.

History of engineering & technology --- bonding wire --- S parameters --- electromagnetic simulation --- port embedding --- balanced bandpass filter --- common mode suppression --- spurline --- source–load coupling --- stepped impedance resonator (SIR) --- open-ended waveguide --- slow-wave --- endfire --- radiation --- dispersion --- gain --- energy verification --- Hall probe --- dipole --- movable slit --- Goubau line --- non-invasive blood glucose measurement --- Acu-check --- lancet --- leaky waves --- surface waves --- ultra-wideband --- THz absorber --- high absorption --- polarization independent --- holography --- microwave imaging --- microwave measurement system --- nondestructive testing --- electromagnetic compatibility --- protection of information --- electromagnetic emissions --- computers and information processing --- data acquisition --- image recognition --- pattern recognition --- image processing --- graphic information --- LED array --- laser printer --- compromising emanations --- electromagnetic infiltration --- reconstruction --- non-invasive data acquisition --- Fourier series expansion --- nanorod --- multimode --- propagation characteristics --- guided wave --- bandpass filter --- half-wavelength resonator --- insertion loss --- phantom measurement system --- bone lesion detection --- ground penetrating radar --- reverse time migration --- Tibetan Plateau --- permafrost active layer --- internal structure --- Chebyshev filter --- cavity --- metamaterial --- waveguide --- X-band --- meta-resonator --- machine learning --- material identification --- microwave sensor array --- microwave waveguide --- dipole and horn antennas --- carbon-composite material --- graphene --- antenna measurements --- electromagnetic waves --- n/a --- source-load coupling

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In the past, when elements in sructures were composed of perishable materials, such as wood, the maintenance of houses, bridges, etc., was considered of vital importance for their safe use and to preserve their efficiency. With the advent of materials such as reinforced concrete and steel, given their relatively long useful life, periodic and constant maintenance has often been considered a secondary concern. When it was realized that even for structures fabricated with these materials that the useful life has an end and that it was being approached, planning maintenance became an important and non-negligible aspect. Thus, the concept of structural health monitoring (SHM) was introduced, designed, and implemented as a multidisciplinary method. Computational mechanics, static and dynamic analysis of structures, electronics, sensors, and, recently, the Internet of Things (IoT) and artificial intelligence (AI) are required, but it is also important to consider new materials, especially those with intrinsic self-diagnosis characteristics, and to use measurement and survey methods typical of modern geomatics, such as satellite surveys and highly sophisticated laser tools.

Medicine --- structural health monitoring --- jointless bridge --- high-speed railway --- bearing --- expansion device --- displacement analysis --- structural reliability estimation --- modal identification --- finite element model updating --- cyber-physical systems --- crowdsourcing --- temperature effects --- time-lag effect --- Fourier series expansion --- box-girder bridges --- structural engineering --- overall deformation monitoring --- perspective transformation --- edge detection --- close-range photogrammetry --- railway embankment --- condition assessment --- ground penetrating radar --- multi-attribute utility theory --- laser scanner --- line scanner --- structure monitoring --- deformation --- dynamic measurements --- scan-to-BIM --- point cloud --- HBIM --- FEM --- Rhinoceros --- terrestrial laser scanner (TLS) --- ground-based real aperture radar (GB-RAR) --- vibration frequency --- spectral analysis --- displacement --- structural health monitoring (SHM) --- vibration-based damage detection --- system identification --- subspace system identification (SSI) --- tie rod --- natural frequencies --- mode shapes --- root-mean-square error (RMSE) --- environmental monitoring --- long-range mapping --- MMS --- sub-millimetric EDM geodetic techniques --- damage detection --- damage localization --- hybrid approach --- neural network --- timber bridges --- stress-laminated timber decks --- monitoring --- humidity-temperature sensors --- wood moisture content --- multi-phase models --- finite element method --- moving load identification --- strain influence line --- load transverse distribution --- strain integral coefficient --- identification error --- n/a

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Book 6 in the Princeton Mathematical Series.Originally published in 1941.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Laplace transformation. --- Absolute continuity. --- Absolute convergence. --- Absolute value. --- Analytic continuation. --- Analytic function. --- Antiderivative. --- Arbitrarily large. --- Arithmetic progression. --- Asymptote. --- Auxiliary function. --- Bernstein polynomial. --- Bessel function. --- Big O notation. --- Bounded function. --- Bounded variation. --- Cauchy's theorem (group theory). --- Central limit theorem. --- Change of variables. --- Complex number. --- Conjugate transpose. --- Continuous function (set theory). --- Continuous function. --- Countable set. --- Derivative. --- Determinant. --- Differential operator. --- Dirichlet integral. --- Dirichlet series. --- Entire function. --- Equation. --- Euler's theorem. --- Existential quantification. --- Finite difference. --- Fubini's theorem. --- Function (mathematics). --- Generating function. --- Hamburger moment problem. --- Hausdorff moment problem. --- Helly–Bray theorem. --- Hölder's inequality. --- Imaginary number. --- Improper integral. --- Infimum and supremum. --- Integral equation. --- Integration by parts. --- Laguerre polynomials. --- Lambert series. --- Laplace transform. --- Laurent series. --- Lebesgue integration. --- Lebesgue–Stieltjes integration. --- Leibniz integral rule. --- Limit of a sequence. --- Limit point. --- Limit superior and limit inferior. --- Lipschitz continuity. --- Mathematical induction. --- Mean value theorem. --- Moment problem. --- Monotonic function. --- Multiple integral. --- Natural number. --- Order condition. --- Order of integration (calculus). --- Order of integration. --- Parseval's theorem. --- Plancherel theorem. --- Polynomial. --- Positive polynomial. --- Positive semidefinite. --- Power series. --- Prime factor. --- Prime number theorem. --- Prime number. --- Principal value. --- Radius of convergence. --- Representation theorem. --- Resultant. --- Riemann–Stieltjes integral. --- Right half-plane. --- Series (mathematics). --- Series expansion. --- Sign (mathematics). --- Simultaneous equations. --- Singular integral. --- Special case. --- Stieltjes moment problem. --- Stone–Weierstrass theorem. --- Summation. --- Taylor's theorem. --- Theorem. --- Total variation. --- Uniform continuity. --- Uniform convergence. --- Uniqueness theorem. --- Upper and lower bounds. --- Vanish at infinity. --- Variable (mathematics). --- Without loss of generality. --- Zero of a function.