Introduction The inverse Galois problem asks whether every finite group G occurs as a Galois group over the field Q of rational numbers. We then say that G is realizable over Q. This problem goes back to Hilbert [Hil] who realized Sn and An over Q. Many more groups have been realized over Q since 1892. For example, Shafarevich [Sha] finished in 1958 the work started by Scholz 1936 [Slz] and Rei...

For a given partial solution, the partial inverse problem is to modify the coefficients such that there is a full solution containing the partial solution, while the full solution becomes optimal under new coefficients, and the total modification is minimum. In this paper, we show that the partial inverse assignment problem and the partial inverse minimum cut problem are NP-hard if there are bo...

in this paper, newton harmonic balance method (nhbm) is applied to obtain the analytical solution for an electron beam injected into a plasma tube where the magnetic field is cylindrical and increases towards the axis in inverse proportion to the radius. periodic solution is analytically verified and consequently the relation between the natural frequency and the amplitude is obtained in an ana...

In this paper, two inverse problems of Stephen kind with local (Dirichlet) boundary conditions are investigated. In the first problem only a part of boundary is unknown and in the second problem, the whole of boundary is unknown. For the both of problems, at first, analytic expressions for unknown boundary are presented, then by using these analytic expressions for unknown boundaries and bounda...

In this study, inverse nodal problem is solved for the p-Laplacian operator with two potential functions. We present some asymptotic formulas which have been proved in [17,18] for the eigenvalues, nodal points and nodal lengths, provided that a potential function is unknown. Then, using the nodal points we reconstruct the potential function and its derivatives. We also introduce a solution of i...

The inverse problems play an important role in MEG reconstructions [3, 4, 5, 6, 7]. In this paper, a partially described inverse eigenvalue problem and an associated optimal approximation problem for J-centrosymmetric matrices are considered respectively. It is shown under which conditions the inverse eigenproblem has a solution. An expression of its general solution is given. In case a solutio...