The biorthogonality condition for Stokes flow in annular trenches bounded by horizontal parallel planes and concentric vertical cylinders is derived. This condition, is needed to compute the coefficients of the eigenfunction expansion solution of the corresponding Stokes flow problem.

An alternative method for deriving water wave dispersion relations and evolution equations is to use a weak formulation. The free-surface displacement η is written as an eigenfunction expansion,

We propose a new method to solve the Hartree-Fock-Bogoliubov equations for weakly bound nuclei whose purpose is to improve the treatment of the continuum when a finite range two-body interaction is used. We replace the traditional expansion on a discrete harmonic oscillator basis by a mixed eigenfunction expansion associated with a potential that explicitely includes a continuous spectrum. We o...

In the presented paper, the governing equations of a vibratory beam with moderately large deflection are derived using the first order shear deformation theory. The beam is homogenous, isotropic and it is subjected to the dynamic transverse and axial loads. The kinematic of the problem is according to the Von-Karman strain-displacement relations and the Hook's law is used as the constitutive eq...

Marseille Cedex 9 France One-dimensional quantum scattering for potentials de ned as measures Charles-Antoine GUERIN1 Abstract We generalize the basic one-dimensional scattering formalism to potentials de ned as measures and retrieve the classical results that hold for smooth potentials. We introduce a set of generalized eigenfunctions for the corresponding Schr odinger operator and study thei...

In this paper, we investigate some properties of eigenvalues and eigenfunctions of boundary value problems with separated boundary conditions. Also, we obtain formal series solutions for some partial differential equations associated with the second order differential equation, and study necessary and sufficient conditions for the negative and positive eigenvalues of the boundary value problem....