Determinant inequalities concerning the solution of wave diffraction problems with several parallel Sommerfeld half planes

determinant of the hankel matrix with binomial entries

abstract in this thesis at first we comput the determinant of hankel matrix with enteries a_k (x)=?_(m=0)^k??((2k+2-m)¦(k-m)) x^m ? by using a new operator, ? and by writing and solving differential equation of order two at points x=2 and x=-2 . also we show that this determinant under k-binomial transformation is invariant.

Switching on the Sommerfeld Half-line Diffraction Problem

Talk Abstract This paper concerns the switching on of twodimensional time-harmonic scalar waves. We consider the diffraction of a time-harmonic plane wave by a halfline, determining the rate at which the solution of the time domain ‘switching on’ problem converges to the solution of the corresponding frequency domain problem (the classical ‘Sommerfeld problem’) as the time since the wave was sw...

On the Optimum Directivity of Uniformly Spaced Broadside Arrays of Parallel Half-Wave Dipoles (RESEARCH NOTES)

The nominal directivity for uniformly spaced broadside parallel half-wave dipoles associated with a uniform excitation is evaluated. The amplitude distribution for an optimized directivity is then obtained for different numbers of elements with the separations between the dipoles as a variable. The optimum and nominal directivities are compared for different spacings of the elements. While thes...

On the parallel solution of large industrial wave propagation problems

The use of Fast Multipole Methods (FMM) combined with embedded Krylov solvers preconditioned by a sparse approximate inverse is investigated for the solution of large linear systems arising in industrial acoustic and electromagnetic simulations. We use a boundary elements integral equation method to solve the Helmholtz and the Maxwell equations in the frequency domain. The resulting linear syst...

Extended Stokes ’ problems for relatively moving porous half - planes