A second-order difference scheme for a first-order elliptic system with discontinuous coefficients is derived and studied. This approximation can be viewed as an improvement of the well-known scheme with harmonic averaging of the coefficients for a second order elliptic equation, which is first-order accurate for the gradient of the solution. The numerical experiments confirm the second order c...

We establish various inequalities relating the coefficients of a polynomial with the separation of its roots. Applications are given to oscillatory integrals and sublevel sets in euclidean harmonic analysis as well as exponential sums and polynomial congruences in number theory. These applications depend on precise structural statements of sublevel sets for polynomials with coefficients in a ge...

Emission of anisotropic gravitational radiation from compact binary system leads to a flux linear momentum. This results in the recoil system. We investigate rate loss Linear momentum far zone source using various mass type and current multipole moments for inspiralling mergers quasi-elliptical orbits at 2.5 Post Newtonian order. compute accurate up $\mathcal{O}(e_t)$ harmonic coordinate. A Qua...

It is proved that the Laurent expansion of the following Gauss hypergeometric functions, are an arbitrary integer nonnegative numbers, a, b, c are an arbitrary numbers and ε is an arbitrary small parameters, are expressible in terms of the harmonic polylogarithms of Remiddi and Vermaseren with polynomial coefficients. An efficient algorithm for the calculation of the higher-order coefficients o...

We generalize a construction of Dunkl, obtaining a wide class intertwining functions on the symmetric group and a related family of multidimensional Hahn polynomials. Following a suggestion of Vilenkin and Klymik, we develop a tree-method approach for those intertwining functions. We also give a group theoretic proof of the relation between Hahn polynomials and Clebesh-Gordan coefficients, give...

Timbre can be defined as feature of an auditory stimulus that allows us to distinguish the sounds which have the same pitch and loudness. In this paper, we explore timbre based perceptual feature for singer identification. We start with a vocal detection process to extract the vocal segments from the sound. The cepstral coefficients, which reflect timbre characteristics, are then computed from ...

A cosmic ray observatory with full-sky coverage can exploit standard anisotropy analysis methods that do not work if part of the celestial sphere is never seen. In particular, the distribution of arrival directions can be fully characterized by a list of spherical harmonic coefficients. The dipole vector and quadrupole tensor are of special interest, but the full set of harmonic coefficients co...

We present and analyze a non-standard finite element method based on element-local boundary integral operators that permits polyhedral element shapes as well as meshes with hanging nodes. The method employs elementwise PDE-harmonic trial functions and can thus be interpreted as a local Trefftz method. The construction principle requires the explicit knowledge of the fundamental solution of the ...

This paper considers the common sonobuoy configuration comprising two horizontal dipoles mounted orthogonally together with an omnidirectional sensor. Under the assumption that, within a narrow frequency band of interest, the acoustic power impinging on the sonobuoy consists of uncorrelated Gaussian noise processes, the paper examines how data collected by the sensor can be used to infer the di...

Forward and adjoint Monte Carlo (MC) models of radiance are proposed for use in model-based quantitative photoacoustic tomography. A two-dimensional (2-D) radiance MC model using a harmonic angular basis is introduced and validated against analytic solutions for the radiance in heterogeneous media. A gradient-based optimization scheme is then used to recover 2-D absorption and scattering coeffi...