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We derive an asymptotic error formula for Gauss--Legendre quadrature applied to functions with limited regularity, using the contour-integral representation of the remainder term. To address the absence of uniformly valid approximations of…

Numerical Analysis · Mathematics 2025-09-30 Pei Liu

Exactly soluble models in the theory of electromagnetic propagation and scattering are essentially restricted to horizontally stratified or spherically symmetric geometries, with results also available for certain waveguide geometries.…

Classical Physics · Physics 2012-06-06 Peter B. Weichman

A number of new problems in remote sensing and identification of buried compact metallic targets motivate the search for new models that, if not exact, at least enable extremely rapid numerical predictions of electromagnetic…

Classical Physics · Physics 2015-03-19 Peter B. Weichman

Uncertainty in physical parameters can make the solution of forward or inverse light scattering problems in astrophysical, biological, and atmospheric sensing applications, cost prohibitive for real-time applications. For example, given a…

Numerical Analysis · Mathematics 2021-12-28 Akif Khan , Murugesan Venkatapathi

In this work, we construct the Born and inverse Born approximation and series to recover two function-valued coefficients in the Helmholtz equation for inverse scattering problems from the scattering data at two different frequencies. An…

Numerical Analysis · Mathematics 2025-03-18 Fioralba Cakoni , Shixu Meng , Zehui Zhou

In the present paper we examine the accuracy of the quasiclassical approach on the example of small-angle electron elastic scattering. Using the quasiclassical approach, we derive the differential cross section and the Sherman function for…

Atomic Physics · Physics 2015-11-13 P. A. Krachkov , R. N. Lee , A. I. Milstein

A generalization of associated Legendre functions is proposed and used to describe the scattering states of the Rosen-Morse potential. The functions are then given explicit formulas in terms of the hypergeometric function, their asymptotic…

Quantum Physics · Physics 2024-01-01 F. L. Freitas

It is shown that quadrature formulas in many different applications can be derived from rational approximation of the Cauchy transform of a weight function. Since rational approximation is now a routine technology, this provides an easy new…

Numerical Analysis · Mathematics 2025-07-22 Andrew Horning , Lloyd N. Trefethen

In Radiative transfer, the intensities of radiation from the bounding faces of finite slab are obtained in terms of X- and Y- functions of Chandrasekhar . Those are non linear non homogeneous coupled integral equations . Those non linear…

Astrophysics · Physics 2007-05-23 Rabindra Nath Das

In this paper, we consider the inverse scattering problem for recovering either an isotropic or anisotropic scatterer from the measured scattered field initiated by a point source. We propose two new imaging functionals for solving the…

Analysis of PDEs · Mathematics 2021-07-20 Isaac Harris , Dinh-Liem Nguyen , Thi-Phong Nguyen

Approximation of scattered data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This approach is useful for a higher…

Numerical Analysis · Computer Science 2018-06-21 Zuzana Majdisova , Vaclav Skala

The Heckman-Opdam hypergeometric functions of type BC extend classical Jacobi functions in one variable and include the spherical functions of non-compact Grassmann manifolds over the real, complex or quaternionic numbers. There are various…

Representation Theory · Mathematics 2014-02-25 Margit Rösler , Michael Voit

We compute the scattering angle $\chi$ for hyperboliclike encounters in massless Scalar-Tensor (ST) theories up to third post-Newtonian (PN) order for the conservative part of the dynamics. To calculate the gauge-invariant scattering angle…

General Relativity and Quantum Cosmology · Physics 2023-04-19 Tamanna Jain

Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…

Graphics · Computer Science 2018-04-19 Zuzana Majdisova , Vaclav Skala

Photon transport through a diffusing slab can be described by the radiative transfer equation (RTE). When the slab is highly scattering and weakly absorbing, the RTE simplifies to the diffusion equation. In this paper, an inverse diffusion…

In this paper we discuss a new method which can be used to obtain arbitrarily accurate analytical expressions for the deflection angle of light propagating in a given metric. Our method works by mapping the integral into a rapidly…

General Relativity and Quantum Cosmology · Physics 2009-11-11 Paolo Amore , Santiago Arceo Diaz

The Glauber method is extensively used to describe the motion of a hadronic projectile in interaction with the surrounding nuclear medium. One of the main approximations consists in the linearization of the wave equation for the interacting…

Nuclear Theory · Physics 2009-10-28 A. Bianconi , M. Radici

A new method to compute the incoherent scattering function of harmonic lattices is introduced. It is based in a saddle point approximation for each term of the phonon expansion, and is simple enough to be used in practice. The method gives…

Other Condensed Matter · Physics 2018-07-20 Victor Laliena , Javier Campo

We present a new approximation scheme for the centrifugal term to solve the Schrodinger equation with the Hulthen potential for any arbitrary l state by means of a mathematical Nikiforov-Uvarov (NU) method. We obtain the bound state energy…

Quantum Physics · Physics 2009-11-13 Sameer M. Ikhdair

Approximation using Fourier features is a popular technique for scaling kernel methods to large-scale problems, with myriad applications in machine learning and statistics. This method replaces the integral representation of a…

Machine Learning · Statistics 2024-08-26 Ayoub Belhadji , Qianyu Julie Zhu , Youssef Marzouk