Développement asymptotique d'intégrales oscillantes lentement convergentes à l'infini
Eine Verallgemeinerung eines Approximations-Satzes von C. Franchetti.
Equivalent Boundary Conditions for an Elasto-Acoustic Problem set in a Domain with a Thin Layer
We present equivalent conditions and asymptotic models for the diffraction problem of elastic and acoustic waves in a solid medium surrounded by a thin layer of fluid medium. Due to the thinness of the layer with respect to the wavelength, this problem is well suited for the notion of equivalent conditions and the effect of the fluid medium on the solid is as a first approximation local. We derive and validate equivalent conditions up to the fourth order for the elastic displacement. These conditions...
Estimating powers with base close to unity and large exponents.
Existence and convergence of the expansion in the asymptotic theory of elastic thin plates
Existence of an instanton singularity in . Euclidean field theory
Extensions of asymptotic expansions from Chapter 15 of Ramanujan's second notebook.
From multi-instantons to exact results
In these notes, conjectures about the exact semi-classical expansion of eigenvalues of hamiltonians corresponding to potentials with degenerate minima, are recalled. They were initially motivated by semi-classical calculations of quantum partition functions using a path integral representation and have later been proven to a large extent, using the theory of resurgent functions. They take the form of generalized Bohr--Sommerfeld quantization formulae. We explain here their...
Further Generalization of Kobayashi's Gamma Function
In this paper, we introduce a further generalization of the gamma function involving Gauss hypergeometric function 2F1 (a, b; c; z)
Generalizing the arithmetic geometric mean - a hapless computer experiment.
Global existence of smooth solutions for the Vlasov-Fokker-Planck equation in and space dimensions
Heat Equation Asymptotics for Singular Sturm-Liouville Operators.
High order corrections to the time-independent Born-Oppenheimer approximation. — I. Smooth potentials
High order transmission conditions for thin conductive sheets in magneto-quasistatics
We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...
High order transmission conditions for thin conductive sheets in magneto-quasistatics
We propose transmission conditions of order 1, 2 and 3 approximating the shielding behaviour of thin conducting curved sheets for the magneto-quasistatic eddy current model in 2D. This model reduction applies to sheets whose thicknesses ε are at the order of the skin depth or essentially smaller. The sheet has itself not to be resolved, only its midline is represented by an interface. The computation is directly in one step with almost no additional cost. We prove the well-posedness w.r.t. to...
Laplace asymptotic expansions for Gaussian functional integrals.
Lipschitz-Nikolskii constants and asymptotic simultaneous approximation of the Mn-operators. (Short Communication).
Lipschitz-Nikolskii constants and asymptotic simultaneous approximation of the Mn-operators.
Multivariate asymptotics for products of large powers with applications to Lagrange inversion.
Non-perturbative asymptotic improvement of perturbation theory and Mellin-Barnes representation.