This paper deals with the boundary value problem involving the differential equation begin{equation*}     ell y:=-y''+qy=lambda y,  end{equation*}  subject to the standard boundary conditions along with the following discontinuity  conditions at a point $ain (0,pi)$  begin{equation*}     y(a+0)=a_1 y(a-0),quad y'(a+0)=a_1^{-1}y'(a-0)+a_2 y(a-0), end{equation*} where $q(x),  a_1 , a_2$ are  rea...

The task of the image reconstruction in Electrical Impedance Tomography (EIT) is highly ill-posed inverse problem. The level set method with the gradient technique is established model for our numerical problem. Interfaces between subdomains with constant conductivities are represented by the level set function. Moreover, only one function is needed to represent any numbers of phases. The itera...

Alfred Horn's conjecture on eigenvalues of sums Hermitian matrices was proved more than 20 years ago. In this note, the problem is raised of, given an $n$-tuple $\gamma$ in solution polytope, constructing with required spectra such that their sum has $\gamma$.

This paper formulates the inverse power flow problem which is to infer nodal admittance matrix (hence network structure of system) from voltage and current phasors measured at a number buses. We show that can be uniquely identified sequence measurements corresponding different steady states when every node in system equipped with measurement device, Kron-reduced determined even if some nodes ar...

This paper is focused on the application of inverse problem methodology for solving some problems that have emerged in space science. The inverse model is an implicit technique: a constrained non-linear optimization problem, in which the forward problem is iteratively solved for successive approximations of the unknown parameters. Iteration proceeds until an objective-function, representing the...