the leaders of the soviet :union: adopted atheist and anti-religious policies toward muslim nations during decades of ruling over central asia; the polices that posed a threat to the existence of muslims. following the outbreak of second world war, the government of the soviet :union: was forced to revise its hostile policies toward muslims and establish muslim religious department also known a...

Since the classical iterative methods for solving nonlinear ill-posed problems are locally convergent, this paper constructs a robust and widely convergent method for identifying parameter based on homotopy algorithm, and investigates this method’s convergence in the light of Lyapunov theory. Furthermore, we consider 1-D elliptic type equation to testify that the homotopy regularization can ide...

1. Introduction Various authors have explored the role of molliication in the solution of improperly posed problems such as numerical diierentiation and the numerical solution of rst kind integral equations. For example, Murio 13], exploiting earlier suggestions of Manselli and Miller 11] as well as Vasin 16], has shown how molliied numerical diierentiators can be constructed for the diierentia...

Following a discussion of the relation of these problems to applications , intended to clarify the considerations which must be handled in order to obtain genuinely useful results, we consider techniques for determining optimal approximationss and consequent optimal error bounds for certain classes of ill-posed problems with appropriate a priori information.