A hypersingular integral equation in two disjoint intervals is solved by using the solution of Cauchy type singular integral equation in disjoint intervals. Also a direct function theoretic method is used to determine the solution of the same hypersingular integral equation in two disjoint intervals. Solutions by both the methods are in good agreement with… (More)
A direct function theoretic method is applied to solve a weakly singular integral equation whose kernel involves logarithmic singularity. This method avoids the occurrence of strong singularity. The solution of this integral equation is then applied to re-investigate the well known problem of water wave scattering by a partially immersed vertical barrier.
The reaction of RuCl(3)(solv.)(n) with tert-butylacetylene in methanol or ethanol leads to the formation of chloro-bridged half-sandwich complexes with sterically demanding cyclopentadienyl ligands, which are of high interest as starting materials for the synthesis of novel Ru catalysts.
In the present paper, the solution of a singular integral equation with logarithmic kernel in two disjoint intervals (0, a)4(b, ∞), (a, b are finite) is obtained by using function theoretic method. The two cases are considered when the unknown function satisfying the integral equation is unbounded or bounded at both nonzero finite end points of the… (More)