The compressed word problem for a finitely generated monoid M asks whether two given compressed words over the generators of M represent the same element of M . For string compression, straight-line programs, i.e., contextfree grammars that generate a single string, are used in this paper. It is shown that the compressed word problem for a free inverse monoid of finite rank at least two is comp...

A finite element method (FEM) formulation for the prediction of unknown steady boundary conditions in heat conduction for multi-domain three-dimensional solid objects is presented. The FEM formulation is capable of determining temperatures and heat fluxes on the boundaries where such quantities are unknown, provided such quantities are sufficiently over-specified on other boundaries. An inverse...

In this work, we investigate the regularized solutions and their finite element to inverse source problems governed by partial differential equations, establish stochastic convergence optimal rates of these solutions, under pointwise measurement data with random noise. Unlike most existing regularization theories, error estimates are derived without any conditions, while show explicit depende...

The tractions that cells exert on a gel substrate from the observed displacements is an increasingly attractive and valuable information in biomedical experiments. The computation of these tractions requires in general the solution of an inverse problem. Here, we resort to the discretisation with finite elements of the associated direct variational formulation, and solve the inverse analysis us...