Professor Ivan Pekov Nedialkov (1921-1984) is one of the pioneers in Bulgaria in the development and application of methods of ill-posed problems theory in different regions of science, like geophysics, elementary particle physics, astrophysics, biology, techniques. As a consequence of his more than 30 years of research are obtained results with theoretical importance and by their means are solved classes applied problems. The most important of them are:
- The method of transformed areas for analytical application of harmonic functions and its application for solving problems of geophysics for determining parameters of deep and extra-deep geological structures and in the physics of elementary particles for analytical continuation of sattering amplitude and determining parameters of short-life particles, the resonances
- Active display method for solving direct and inverse problem of potential theory.
- Method for separating potential fields. Alone or with his collaborators he created new effective methods for solving the basic geophysical problem - the inverse problem in potential theory. Part of his research in this direction has obtained a practical application.
- Works in neutrino tomography for studding the Earth structure.
- Description, regulation and optimisation of casting processes by means of ill-posed problems.
- Application of mathematical and theoretical physics achievements in studying technical and technological processes.