ICNPAA 2010: Mathematical Problems in
Engineering, Aerospace and Sciences

In this Conference, we first would like to introduce some fundamental theory for linear transforms in the framework of Hilbert spaces and its general applications with very concrete typical examples. Secondly, we introduce the construction of the approximate solutions of the equations by using the Tikhonov regularization and the theory of reproducing kernels. Thirdly, we will propose a new method that the singular integral equations may be transformed to regular and discrete integral equations. The contents will be given by the following key words: Reproducing kernel, Pythagorean theorem, inversion of the linear systems, numerical analysis, inverse problem, inverse heat conduction, observation data, discretization, noise, error estimate, generalized inverse, Tikhonov regularization, singular integral equations with shift.