We study the matching of LRS spatially homogeneous collapsing dust space-times with non-stationary vacuum exteriors in cylindrical symmetry. Given an interior with diagonal metric we prove existence and uniqueness results for the exterior. The matched solutions contain trapped surfaces, singularities and Cauchy horizons. The solutions cannot be asymptotically flat and we present evidence that t...

In this paper, we are dealing with the ill-posed Cauchy problem for an elliptic operator. To do this, interpret as inverse problem, and therefore a controllability problem. This point of view induces regularization method that makes it possible, on one hand, to characterize existence regular solution On other possible obtain singular optimality system optimal control, without resorting any addi...

In this paper, the solution of an isotropic hollow cylinder, with an isotropic coating, weakened by multiple radial cracks is studied. The hollow cylinder and its coating are under Saint-Venant torsional loading. The series solution is then derived for displacement and stress fields in the cross section of the cylinder containing a Volterra-type screw dislocation. The dislocation solution is em...

A class of boundary value problems arising in the study of scattering of surface water waves by barriers, under the assumption of the linearized theory, is reduced to singular integral equations of the first kind, involving only ”weakly singular” kernels. The unified treatment presented here is observed to be most suitable to handle the class of scattering problems under consideration and it is...

For one class of the singular integro-differential equations with Cauchy kernel on an interval, a Galerkin method is justified. The convergence is proved and the error estimation is given.

An efficient Singular Value Decomposition (SVD) algorithm is an important tool for distributed and streaming computation in big data problems. It is observed that update of singular vectors of a rank-1 perturbed matrix is similar to a Cauchy matrix-vector product. With this observation, in this paper, we present an efficient method for updating Singular Value Decomposition of rank1 perturbed ma...