Choose an application

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

This book includes papers in cross-disciplinary applications of mathematical modelling: from medicine to linguistics, social problems, and more. Based on cutting-edge research, each chapter is focused on a different problem of modelling human behaviour or engineering problems at different levels. The reader would find this book to be a useful reference in identifying problems of interest in social, medicine and engineering sciences, and in developing mathematical models that could be used to successfully predict behaviours and obtain practical information for specialised practitioners. This book is a must-read for anyone interested in the new developments of applied mathematics in connection with epidemics, medical modelling, social issues, random differential equations and numerical methods.

uncertainty quantification --- neutron diffusion equation --- discrete dynamical systems --- organisational risk --- computational efficiency --- AHP --- random power series --- order of convergence --- IPV --- multi-criteria decision-making --- random non-autonomous second order linear differential equation --- game of life --- immune system --- parameter estimation --- cytokines --- model --- stem cells --- Voynich Manuscript --- uncertainty modelling --- ode --- bottling process --- anti-torpedo decoy --- decision-making --- exponential polynomial --- Hidden Markov models --- systems of nonlinear equations --- iterative methods --- modified block Newton method --- mathematical linguistics --- DEMATEL --- convergence --- F-110 frigate --- Chikungunya disease --- nonlinear dynamical systems --- cellular automata --- mean square analytic solution --- basin of attraction --- violence index --- macrophages --- Markov chain Monte Carlo --- human behaviour --- block preconditioner --- generalized eigenvalue problem --- bone repair --- numerical simulations --- ASW --- Newton’s method --- independence index --- mathematical modeling --- brain dynamics

Choose an application

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

Based on a seminar sponsored by the Institute for Advanced Study in 1977-1978, this set of papers introduces micro-local analysis concisely and clearly to mathematicians with an analytical background. The papers treat the theory of microfunctions and applications such as boundary values of elliptic partial differential equations, propagation of singularities in the vicinity of degenerate characteristics, holonomic systems, Feynman integrals from the hyperfunction point of view, and harmonic analysis on Lie groups.

Mathematical analysis --- Differential geometry. Global analysis --- 517.98 --- -Advanced calculus --- Analysis (Mathematics) --- Algebra --- Functional analysis and operator theory --- Addresses, essays, lectures --- Mathematical analysis. --- Addresses, essays, lectures. --- -517.1 Mathematical analysis --- 517.98 Functional analysis and operator theory --- -Functional analysis and operator theory --- -517.98 Functional analysis and operator theory --- 517.1 Mathematical analysis --- 517.1. --- 517.1 --- Addition. --- Analytic function. --- Analytic manifold. --- Asymptotic analysis. --- Bernhard Riemann. --- Boundary value problem. --- Bounded operator. --- Cartan subgroup. --- Characterization (mathematics). --- Class function (algebra). --- Closed-form expression. --- Codimension. --- Cohomology. --- Compact space. --- Comparison theorem. --- Contact geometry. --- Continuous function. --- Continuous linear operator. --- Convex hull. --- Cotangent bundle. --- D-module. --- Degenerate bilinear form. --- Diagonal matrix. --- Differentiable manifold. --- Differential operator. --- Dimension (vector space). --- Dimension. --- Elliptic partial differential equation. --- Equation. --- Existence theorem. --- Fourier integral operator. --- Generic point. --- Group theory. --- Harmonic analysis. --- Holomorphic function. --- Holonomic. --- Homogeneous space. --- Hyperfunction. --- Hypersurface. --- Identity element. --- Irreducible representation. --- Killing form. --- Lagrangian (field theory). --- Lie algebra. --- Lie group. --- Linear differential equation. --- Locally compact space. --- Masaki Kashiwara. --- Maximal ideal. --- Monodromy. --- Natural number. --- Neighbourhood (mathematics). --- Ordinary differential equation. --- Orthogonal complement. --- Partial differential equation. --- Path integral formulation. --- Proper map. --- Pseudo-differential operator. --- Regularity theorem. --- Sigurdur Helgason (mathematician). --- Submanifold. --- Subset. --- Summation. --- Symmetric space. --- Symplectic geometry. --- Tangent cone. --- Theorem. --- Topological space. --- Vector bundle. --- Victor Guillemin. --- Weyl group. --- Analyse microlocale

Choose an application

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

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.

Choose an application

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

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The differential field of transseries plays a central role in the subject. Besides powers of the variable, these series may contain exponential and logarithmic terms. Over the last thirty years, transseries emerged variously as super-exact asymptotic expansions of return maps of analytic vector fields, in connection with Tarski's problem on the field of reals with exponentiation, and in mathematical physics. Their formal nature also makes them suitable for machine computations in computer algebra systems.This self-contained book validates the intuition that the differential field of transseries is a universal domain for asymptotic differential algebra. It does so by establishing in the realm of transseries a complete elimination theory for systems of algebraic differential equations with asymptotic side conditions. Beginning with background chapters on valuations and differential algebra, the book goes on to develop the basic theory of valued differential fields, including a notion of differential-henselianity. Next, H-fields are singled out among ordered valued differential fields to provide an algebraic setting for the common properties of Hardy fields and the differential field of transseries. The study of their extensions culminates in an analogue of the algebraic closure of a field: the Newton-Liouville closure of an H-field. This paves the way to a quantifier elimination with interesting consequences.

Series, Arithmetic. --- Divergent series. --- Asymptotic expansions. --- Differential algebra. --- Algebra, Differential --- Differential fields --- Algebraic fields --- Differential equations --- Asymptotic developments --- Asymptotes --- Convergence --- Difference equations --- Divergent series --- Functions --- Numerical analysis --- Series, Divergent --- Series --- Arithmetic series --- Progressions, Arithmetic --- Equalizer Theorem. --- H-asymptotic couple. --- H-asymptotic field. --- H-field. --- Hahn Embedding Theorem. --- Hahn space. --- Johnson's Theorem. --- Krull's Principal Ideal Theorem. --- Kähler differentials. --- Liouville closed H-field. --- Liouville closure. --- Newton degree. --- Newton diagram. --- Newton multiplicity. --- Newton tree. --- Newton weight. --- Newton-Liouville closure. --- Riccati transform. --- Scanlon's extension. --- Zariski topology. --- algebraic differential equation. --- algebraic extension. --- angular component map. --- asymptotic couple. --- asymptotic differential algebra. --- asymptotic field. --- asymptotic relation. --- asymptotics. --- closed H-asymptotic couple. --- closure properties. --- coarsening. --- commutative algebra. --- commutative ring. --- compositional conjugation. --- constant. --- continuity. --- d-henselian. --- d-henselianity. --- decomposition. --- derivation. --- differential field extension. --- differential field. --- differential module. --- differential polynomial. --- differential-hensel. --- differential-henselian field. --- differential-henselianity. --- differential-valued extension. --- differentially closed field. --- dominant part. --- equivalence. --- eventual quantities. --- exponential integral. --- extension. --- filtered module. --- gaussian extension. --- grid-based transseries. --- henselian valued field. --- homogeneous differential polynomial. --- immediate extension. --- integral. --- integrally closed domain. --- linear differential equation. --- linear differential operator. --- linear differential polynomial. --- mathematics. --- maximal immediate extension. --- model companion. --- monotonicity. --- noetherian ring. --- ordered abelian group. --- ordered differential field. --- ordered set. --- pre-differential-valued field. --- pseudocauchy sequence. --- pseudoconvergence. --- quantifier elimination. --- rational asymptotic integration. --- regular local ring. --- residue field. --- simple differential ring. --- small derivation. --- special cut. --- specialization. --- substructure. --- transseries. --- triangular automorphism. --- triangular derivation. --- valuation topology. --- valuation. --- value group. --- valued abelian group. --- valued differential field. --- valued field. --- valued vector space.

Choose an application

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

The application by Fadeev and Pavlov of the Lax-Phillips scattering theory to the automorphic wave equation led Professors Lax and Phillips to reexamine this development within the framework of their theory. This volume sets forth the results of that work in the form of new or more straightforward treatments of the spectral theory of the Laplace-Beltrami operator over fundamental domains of finite area; the meromorphic character over the whole complex plane of the Eisenstein series; and the Selberg trace formula.CONTENTS: 1. Introduction. 2. An abstract scattering theory. 3. A modified theory for second order equations with an indefinite energy form. 4. The Laplace-Beltrami operator for the modular group. 5. The automorphic wave equation. 6. Incoming and outgoing subspaces for the automorphic wave equations. 7. The scattering matrix for the automorphic wave equation. 8. The general case. 9. The Selberg trace formula.

Harmonic analysis. Fourier analysis --- Automorphic functions --- Scattering (Mathematics) --- Fonctions automorphes --- Dispersion (Mathématiques) --- Automorphic functions. --- Scattering (Mathematics). --- Dispersion (Mathématiques) --- Selberg, Formule de trace de --- Selberg trace formula --- Eisenstein series --- Eisenstein, Séries d' --- Scattering theory (Mathematics) --- Boundary value problems --- Differential equations, Partial --- Scattering operator --- Fuchsian functions --- Functions, Automorphic --- Functions, Fuchsian --- Functions of several complex variables --- Absolute continuity. --- Algebra. --- Analytic continuation. --- Analytic function. --- Annulus (mathematics). --- Asymptotic distribution. --- Automorphic function. --- Bilinear form. --- Boundary (topology). --- Boundary value problem. --- Bounded operator. --- Calculation. --- Cauchy sequence. --- Change of variables. --- Complex plane. --- Conjugacy class. --- Convolution. --- Cusp neighborhood. --- Cyclic group. --- Derivative. --- Differential equation. --- Differential operator. --- Dimension (vector space). --- Dimensional analysis. --- Dirichlet integral. --- Dirichlet series. --- Eigenfunction. --- Eigenvalues and eigenvectors. --- Eisenstein series. --- Elliptic operator. --- Elliptic partial differential equation. --- Equation. --- Equivalence class. --- Even and odd functions. --- Existential quantification. --- Explicit formula. --- Explicit formulae (L-function). --- Exponential function. --- Fourier transform. --- Function space. --- Functional analysis. --- Functional calculus. --- Fundamental domain. --- Harmonic analysis. --- Hilbert space. --- Hyperbolic partial differential equation. --- Infinitesimal generator (stochastic processes). --- Integral equation. --- Integration by parts. --- Invariant subspace. --- Laplace operator. --- Laplace transform. --- Lebesgue measure. --- Linear differential equation. --- Linear space (geometry). --- Matrix (mathematics). --- Maximum principle. --- Meromorphic function. --- Modular group. --- Neumann boundary condition. --- Norm (mathematics). --- Null vector. --- Number theory. --- Operator theory. --- Orthogonal complement. --- Orthonormal basis. --- Paley–Wiener theorem. --- Partial differential equation. --- Perturbation theory (quantum mechanics). --- Perturbation theory. --- Primitive element (finite field). --- Principal component analysis. --- Projection (linear algebra). --- Quadratic form. --- Removable singularity. --- Representation theorem. --- Resolvent set. --- Riemann hypothesis. --- Riemann surface. --- Riemann zeta function. --- Riesz representation theorem. --- Scatter matrix. --- Scattering theory. --- Schwarz reflection principle. --- Selberg trace formula. --- Self-adjoint. --- Semigroup. --- Sign (mathematics). --- Spectral theory. --- Subgroup. --- Subsequence. --- Summation. --- Support (mathematics). --- Theorem. --- Trace class. --- Trace formula. --- Unitary operator. --- Wave equation. --- Weighted arithmetic mean. --- Winding number. --- Eisenstein, Séries d'. --- Analyse harmonique