in this paper, a nonlinear inverse problem of parabolic type, is considered. by reducing this inverse problem to a system of volterra integral equations the existence, uniqueness, and stability of the solution will be shown.

background: we have validated the monitor unit calculations from a commercially available treatment planning system (tps) for three intensity modulated radiotherapy (imrt) planning techniques for tangential breast irradiation by using ionization chamber measurements. materials and methods: treatment plans were generated for forty-two breast patients by a forward planned field in field technique...

where A is some set of multiindices α. A first crucial question is whether there is enough data to (uniquely) find f . Let u0 be a function in the Sobolev space H(Ω) with zero Cauchy data u0 = ∂νu0 = 0 on Γ0 and let f0 = −∆u0. Due to linearity, −∆(u+ u0) = f + f0. Obviously, u and u+ u0 have the same Cauchy data on Γ0, so f and f+f0 produce the same data (2), but they are different in Ω. It is ...

Nonnegative matrices have long been a sorce of interesting and challenging mathematical problems. They are real matrices with all their entries being nonnegative and arise in a num‐ ber of important application areas: communications systems, biological systems, economics, ecology, computer sciences, machine learning, and many other engineering systems. Inverse eigenvalue problems constitute an ...

1 Introduction The inverse spectral problem on a Riemannian manifold (M, g), possibly with boundary, is to determine as much as possible of the geometry of (M, g) from the spectrum of its Laplacian ∆ g (with some given boundary conditions). The special inverse problem of Kac is to determine a Euclidean domain Ω ⊂ R n up to isometry from the spectrum Spec B (Ω) of its Laplacian ∆ B with Dirichle...

The purpose of this paper is to present inverse optimal control as a promising approach to transfer biological motions to robots. Inverse optimal control helps (a) to understand and identify the underlying optimality criteria of biological motions based on measurements, and (b) to establish optimal control models that can be used to control robot motion. The aim of inverse optimal control probl...

This paper studies the application of an inverse methodology for problem solving in fracture mechanics using the finite element analysis. The method was applied to both detection of subsurface cracks and the study of propagating cracks. The procedure for detection of subsurface cracks uses a first order optimization analysis coupled with a penalty function to solve for the unknown geometric par...

The purpose of this paper is to explain how to compute the function Í2 which interpolates values of a function of one variable fix) at n distinct points x, ik) < x2 < ■ • • < *n_i < x„, and which, whenever ll/v 'H^ is bounded and the value of the bound is unknown, provides the smallest possible value of Bix) in the error bound \fix) Í2(x)l < B(*)ll/(fc)lloo

Stereology is the part of imaging science in which the three-dimensional structure of a body is determined from two-dimensional views. Although it is relatively easy to determine volume information from 2-D slices, it is nontrivial in general to determine other physical properties such as internal surface areas unless the medium is known to have some simple symmetry such as isotropy. For this r...