In this paper ill-posed linear inverse problems that arises in many applications is considered. The instability of special kind of these problems and it's relation to the kernel, is described. For finding a stable solution to these problems we need some kind of regularization that is presented. The results have been applied for a singular equation.

In this paper we show that inverting problems of higher complexity is easier than inverting problems of lower complexity. While inverting Σ i 3CNFSAT is known to be coNP-complete [6] for i = 1 we prove that it remains coNP-complete for i = 2 and is in P for all i ≥ 3. Relatedly, we show that inverting Σ i 3DNFSAT is in P for all i ≥ 1.

this paper deals with the boundary value problem involving the differential equationbegin{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  real, $qin l...