Novel non-hyper-singular [i.e., only strongly-singular] boundary-integral-equations for the gradients of the acoustic velocity potential, involving only O(r−2) singularities at the surface of a 3-D body, are derived, for solving problems of acoustics governed by the Helmholtz differential equation. The gradients of the fundamental solution to the Helmholtz differential equation for the velocity...

Abstract. Generalizing work of Zagier, in an important recent paper Bruinier and Funke prove that the generating functions for traces of singular values of many modular functions are weight 3 2 modular forms. Using facts about half-integral weight modular forms, we obtain identities relating traces of singular moduli for modular functions of level p and 1. These follow from a general result rel...

We investigate local convergence of an SQP method for non-linear optimal control of weakly singular Hammerstein integral equations. Suucient conditions for local quadratic convergence of the method based are discussed.

We present several coupled finite and boundary element formulations for the vibro-acoustic simulation of completely immersed bodies such as submarines. All formulations are based on the different use of standard boundary integral equations. In addition to the well known symmetric coupling we discuss two different approaches which are based on the weakly singular boundary integral equation only.

An effective technique upon linear B-spline wavelets has been developed for solving weakly singular Fredholm integral equations. Properties of these wavelets and some operational matrices are first presented. These properties are then used to reduce the computation of integral equations to some algebraic equations. The method is computationally attractive, and applications are demonstrated thro...