A new class of regularizing filters is applied to solve the first kind of opertor equation.

By using the sigular system theory of compact operator, a new regularizing filter and a new regularization method for solving ill-posed problems are established.

According to the theory of singular system of compact operators, a new family of regularizing filters is set forth, and then a new class of reegularization strategies for solving ill-posed problems of the first kind equations is constructed.

A quantum spherically symmetrical solution by using a canonical quantization based on the de Broglie-Bohm interpretation is obtained, which is in accordance with the correspondence principle.

The equivalence of motion equation and canonical quantization in the two methods has been proved, and also the correspondence relation of constraints found.

In the case of the regularization operator with Laplacian,numerical results show that the new method performs better than traditional meth-ods and yields steadily close-to-optimal resto.

Using the regularization operator and approach process and a series of prior estimates, the existence of the global weak solutions was proved under the conditions that the mobility neither equals to a constant nor satisfies velocity saturation.

We find the normalizing factorβv.

In this paper,using the Tickhonov regularizer,we give a sufficient and necessary condition for the Moore-Penrose inverses T+_x being continuous,which plays an important role in the computation.