Asymptotic analysis, ISSN 0921-7134, 1988

Journal

2016, Graduate studies in mathematics, ISBN 9780821848418, Volume 172, xi, 461

Random matrices (probabilistic aspects; for algebraic aspects see 15B52) | Equations of mathematical physics and other areas of application | Partial differential equations | Approximations and expansions | Probability theory and stochastic processes | Special matrices | Operator theory | Probability theory on algebraic and topological structures | Riemann-Hilbert problems | Exact enumeration problems, generating functions | Convex and discrete geometry | Special classes of linear operators | Combinatorics | Asymptotic approximations, asymptotic expansions (steepest descent, etc.) | Time-dependent statistical mechanics (dynamic and nonequilibrium) | Enumerative combinatorics | Exactly solvable dynamic models | Linear and multilinear algebra; matrix theory | Special processes | Statistical mechanics, structure of matter | Toeplitz operators, Hankel operators, Wiener-Hopf operators | Tilings in $2$ dimensions | Interacting random processes; statistical mechanics type models; percolation theory | Discrete geometry | Random matrices | Combinatorial analysis

Book

2011, Cambridge texts in applied mathematics, ISBN 9781107664104, Volume 47, xiv, 348

The field of nonlinear dispersive waves has developed enormously since the work of Stokes, Boussinesq and Korteweg–de Vries (KdV) in the nineteenth century. In...

Wave equation | Nonlinear waves | Asymptotic expansions | Solitons

Wave equation | Nonlinear waves | Asymptotic expansions | Solitons

Book

4.
Full Text
Light-by-light-type corrections to the muon anomalous magnetic moment at four-loop order

Physical Review D - Particles, Fields, Gravitation and Cosmology, ISSN 1550-7998, 10/2015, Volume 92, Issue 7

The numerically dominant QED contributions to the anomalous magnetic moment of the muon stem from Feynman diagrams with internal electron loops. We consider...

4 LOOPS | DIAGRAMS | FEYNMAN-INTEGRALS | ELECTRON | HADRONIC CONTRIBUTIONS | FORM | G-2 EXPERIMENT | ASTRONOMY & ASTROPHYSICS | ASYMPTOTIC-EXPANSION | REGIONS | VACUUM POLARIZATION INSERTIONS | PHYSICS, PARTICLES & FIELDS | Asymptotic expansions | Integrals | Mathematical analysis | Cosmology | Photons | Feynman diagrams | Muons | Magnetic moment | Physics - High Energy Physics - Phenomenology

4 LOOPS | DIAGRAMS | FEYNMAN-INTEGRALS | ELECTRON | HADRONIC CONTRIBUTIONS | FORM | G-2 EXPERIMENT | ASTRONOMY & ASTROPHYSICS | ASYMPTOTIC-EXPANSION | REGIONS | VACUUM POLARIZATION INSERTIONS | PHYSICS, PARTICLES & FIELDS | Asymptotic expansions | Integrals | Mathematical analysis | Cosmology | Photons | Feynman diagrams | Muons | Magnetic moment | Physics - High Energy Physics - Phenomenology

Journal Article

Fatigue & Fracture of Engineering Materials & Structures, ISSN 8756-758X, 08/2016, Volume 39, Issue 8, pp. 939 - 949

Three‐dimensional elastic–plastic problems for a power‐law hardening material are solved using the finite element method. Distributions of the J‐integral in...

three‐term elastic–plastic asymptotic expansion | finite element method | elastic–plastic crack tip field | constraint parameter | three-term elastic–plastic asymptotic expansion | elastic-plastic crack tip field | three-term elastic-plastic asymptotic expansion | MATERIALS SCIENCE, MULTIDISCIPLINARY | ASYMPTOTIC-EXPANSION | CRACK-TIP FIELDS | LAW HARDENING MATERIAL | FRONT | 3-DIMENSIONAL CRACK | STRESS | ENGINEERING, MECHANICAL | Fractures | Strain hardening | Alloys | Crack propagation | Finite element method | Stresses | Fracture mechanics | Compact tension | Mathematical analysis | Small scale | Deviation | Fatigue cracks

three‐term elastic–plastic asymptotic expansion | finite element method | elastic–plastic crack tip field | constraint parameter | three-term elastic–plastic asymptotic expansion | elastic-plastic crack tip field | three-term elastic-plastic asymptotic expansion | MATERIALS SCIENCE, MULTIDISCIPLINARY | ASYMPTOTIC-EXPANSION | CRACK-TIP FIELDS | LAW HARDENING MATERIAL | FRONT | 3-DIMENSIONAL CRACK | STRESS | ENGINEERING, MECHANICAL | Fractures | Strain hardening | Alloys | Crack propagation | Finite element method | Stresses | Fracture mechanics | Compact tension | Mathematical analysis | Small scale | Deviation | Fatigue cracks

Journal Article

Applied Mathematics and Computation, ISSN 0096-3003, 03/2019, Volume 344-345, pp. 183 - 190

•A method is considered for computing oscillatory Bessel transforms.•The relation between the multiple integral and simple integral is used.•The order is...

Bessel function integrals | Multiple integral | Asymptotic expansion | Hankel transforms | INTEGRALS | MATHEMATICS, APPLIED | ASYMPTOTIC EXPANSIONS | BESSEL TRANSFORMS

Bessel function integrals | Multiple integral | Asymptotic expansion | Hankel transforms | INTEGRALS | MATHEMATICS, APPLIED | ASYMPTOTIC EXPANSIONS | BESSEL TRANSFORMS

Journal Article

2017, Annals of mathematics studies, ISBN 9780691175423, Volume number 195, xxi, 849 pages

Asymptotic differential algebra seeks to understand the solutions of differential equations and their asymptotics from an algebraic point of view. The...

Series, Arithmetic | Asymptotic expansions | Divergent series | Differential algebra | MATHEMATICS | Abstract | Algebra | Mathematics

Series, Arithmetic | Asymptotic expansions | Divergent series | Differential algebra | MATHEMATICS | Abstract | Algebra | Mathematics

Book

Applied Mathematics and Computation, ISSN 0096-3003, 01/2018, Volume 317, pp. 121 - 128

In this paper, we investigate certain asymptotic series used by Hirschhorn to prove an asymptotic expansion of Ramanujan for the nth harmonic number. We give a...

Euler–Mascheroni constant | Asymptotic expansion | Harmonic number | MATHEMATICS, APPLIED | Euler-Mascheroni constant | SERIES | ASYMPTOTIC-EXPANSION

Euler–Mascheroni constant | Asymptotic expansion | Harmonic number | MATHEMATICS, APPLIED | Euler-Mascheroni constant | SERIES | ASYMPTOTIC-EXPANSION

Journal Article

1988, ISBN 9780201156744, xv, 560

Book

1990, Technical report, Volume no. 9003, 39 p. --

Book

2010, 2 ed., Cambridge series in statistical and probabilistic mathematics, ISBN 9780521877220, xii, 386

Exact statistical inference may be employed in diverse fields of science and technology. As problems become more complex and sample sizes become larger,...

Asymptotic expansions | Mathematical statistics | Probabilities | Estimation theory | Mathematics

Asymptotic expansions | Mathematical statistics | Probabilities | Estimation theory | Mathematics

Book

Communications in Partial Differential Equations, ISSN 0360-5302, 05/2016, Volume 41, Issue 5, pp. 812 - 837

We investigate the behavior of the solution of a mixed problem in a domain with two moderately close holes. We introduce a positive parameter ε and we define a...

Laplace operator | moderately close holes | mixed problem | Asymptotic expansion | singularly perturbed perforated domain | real analytic continuation in Banach space | REAL ANALYTIC FAMILIES | MATHEMATICS | MATHEMATICS, APPLIED | PLANAR DOMAIN | EXPANSIONS | HARMONIC-FUNCTIONS | End users | Partial differential equations | Asymptotic expansions | Operators | Maps | Perforations | Mathematical analysis | Laplace equation | Mathematics - Analysis of PDEs

Laplace operator | moderately close holes | mixed problem | Asymptotic expansion | singularly perturbed perforated domain | real analytic continuation in Banach space | REAL ANALYTIC FAMILIES | MATHEMATICS | MATHEMATICS, APPLIED | PLANAR DOMAIN | EXPANSIONS | HARMONIC-FUNCTIONS | End users | Partial differential equations | Asymptotic expansions | Operators | Maps | Perforations | Mathematical analysis | Laplace equation | Mathematics - Analysis of PDEs

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 02/2017, Volume 311, pp. 11 - 37

Our aim in this paper is to approximate the price of an American call option written on a dividend-paying stock close to expiry using an asymptotic analytic...

Transparent boundary conditions | Repeated integral of the complementary error functions | Black–Scholes equation | American call option | Poincaré asymptotic expansion | Free boundary value problem | ARTIFICIAL BOUNDARY METHOD | MATHEMATICS, APPLIED | APPROXIMATIONS | Black-Scholes equation | VALUATION | MODEL | Poincare asymptotic expansion | DIVIDENDS | Numerical analysis | Pricing | Differential equations | Asymptotic expansions | Equivalence | Asymptotic properties | Mathematical analysis | Exact solutions | Mathematical models

Transparent boundary conditions | Repeated integral of the complementary error functions | Black–Scholes equation | American call option | Poincaré asymptotic expansion | Free boundary value problem | ARTIFICIAL BOUNDARY METHOD | MATHEMATICS, APPLIED | APPROXIMATIONS | Black-Scholes equation | VALUATION | MODEL | Poincare asymptotic expansion | DIVIDENDS | Numerical analysis | Pricing | Differential equations | Asymptotic expansions | Equivalence | Asymptotic properties | Mathematical analysis | Exact solutions | Mathematical models

Journal Article

Journal of Computational and Applied Mathematics, ISSN 0377-0427, 07/2019, Volume 354, pp. 86 - 95

An expansion of the ratio of two gamma functions is used to obtain an adequate representation for the product of ratios of gamma functions which enables the...

Ratio of gamma functions | Asymptotic expansions | Fourier transform | Mixtures | Gamma function | Generalized Bernoulli polynomials | MATHEMATICS, APPLIED | APPROXIMATIONS | ASYMPTOTIC-EXPANSION | NEAR-EXACT DISTRIBUTIONS | Statistics | Equality

Ratio of gamma functions | Asymptotic expansions | Fourier transform | Mixtures | Gamma function | Generalized Bernoulli polynomials | MATHEMATICS, APPLIED | APPROXIMATIONS | ASYMPTOTIC-EXPANSION | NEAR-EXACT DISTRIBUTIONS | Statistics | Equality

Journal Article

Communications in Nonlinear Science and Numerical Simulation, ISSN 1007-5704, 03/2018, Volume 56, pp. 314 - 329

•The Prabhakar function is presented and its main properties are reviewed.•Integral and derivative operators of fractional-order based on the Prabhakar...

Prabhakar function | Asymptotic expansion | Nonlinear heat equation | Prabhakar derivative | Mittag–Leffler function | Fractional calculus | Havriliak–Negami model | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | Havriliak-Negami model | ASYMPTOTIC-EXPANSION | REPRESENTATION | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MODELS | Mittag-Leffler function | ANOMALOUS RELAXATION | OPERATORS | Derivatives (Financial instruments) | Electrical conductivity | Dielectrics

Prabhakar function | Asymptotic expansion | Nonlinear heat equation | Prabhakar derivative | Mittag–Leffler function | Fractional calculus | Havriliak–Negami model | MATHEMATICS, APPLIED | PHYSICS, FLUIDS & PLASMAS | Havriliak-Negami model | ASYMPTOTIC-EXPANSION | REPRESENTATION | DIFFERENTIAL-EQUATIONS | PHYSICS, MATHEMATICAL | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | MECHANICS | MODELS | Mittag-Leffler function | ANOMALOUS RELAXATION | OPERATORS | Derivatives (Financial instruments) | Electrical conductivity | Dielectrics

Journal Article

Nonlinear Analysis: Hybrid Systems, ISSN 1751-570X, 11/2019, Volume 34, p. 1

Journal Article

18.
Full Text
Asymptotic expansion of the L 2 -norm of a solution of the strongly damped wave equation

Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 267, Issue 2, pp. 902 - 937

The Fourier transform, F, on R (N≥3) transforms the Cauchy problem for the strongly damped wave equation u −Δu −Δu=0 to an ordinary differential equation in...

Wave equation | Asymptotic expansion of L | Fourier analysis | Strong damping | Asymptotic analysis | initial data | norm | Weighted L | MATHEMATICS | Asymptotic expansion of L-2-norm | Weighted L-1-initial data

Wave equation | Asymptotic expansion of L | Fourier analysis | Strong damping | Asymptotic analysis | initial data | norm | Weighted L | MATHEMATICS | Asymptotic expansion of L-2-norm | Weighted L-1-initial data

Journal Article

Journal of the Mechanics and Physics of Solids, ISSN 0022-5096, 03/2016, Volume 88, pp. 320 - 345

Discrete fine-scale models, in the form of either particle or lattice models, have been formulated successfully to simulate the behavior of quasi-brittle...

Asymptotic expansion homogenization | Asymptotic expansion | Strain softening | Size effect | Lattice models | Discrete models | Cosserat continuum | PHYSICS, CONDENSED MATTER | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | SIZE | CONCRETE DAMAGE | TENSION | COMPRESSION | FRACTURE | ELEMENT | MECHANICS | REPRESENTATIVE VOLUME | MEDIA | SHEAR LATTICE MODEL | Analysis | Models | Numerical analysis | Heterogeneity | Elastic constants | Degrees of freedom | Computer simulation | Mathematical analysis | Particulate composites | Mathematical models | Homogenizing | Physics - Materials Science

Asymptotic expansion homogenization | Asymptotic expansion | Strain softening | Size effect | Lattice models | Discrete models | Cosserat continuum | PHYSICS, CONDENSED MATTER | BEHAVIOR | MATERIALS SCIENCE, MULTIDISCIPLINARY | SIZE | CONCRETE DAMAGE | TENSION | COMPRESSION | FRACTURE | ELEMENT | MECHANICS | REPRESENTATIVE VOLUME | MEDIA | SHEAR LATTICE MODEL | Analysis | Models | Numerical analysis | Heterogeneity | Elastic constants | Degrees of freedom | Computer simulation | Mathematical analysis | Particulate composites | Mathematical models | Homogenizing | Physics - Materials Science

Journal Article

2017, Probability theory and stochastic modelling, ISBN 3662543222, Volume 80, xviii, 204 pages

Presenting tools to aid understanding of asymptotic theory and weakly dependent processes, this book is devoted to inequalities and limit theorems for...

Inequalities (Mathematics) | Markov processes | Central limit theorem | Asymptotic distribution (Probability theory) | Mathematics | Asymptotic expansions | Stochastic processes

Inequalities (Mathematics) | Markov processes | Central limit theorem | Asymptotic distribution (Probability theory) | Mathematics | Asymptotic expansions | Stochastic processes

Book

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