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This paper is concerned with the new method for solving the coefficient inverse problem in the reproducing kernel space. It is different from the previous studies. This method gives accurate results and shows that it is valid by the numerical example.

This paper is intended to discuss the problems of solving system of linear operator equations and a kind of nonlinear operator equation A u B u + C u = f . For system of linear operator equations, we obtain a criterion about the existence of solutions. If it has solutions, we get the analytic representation of its minimum norm solution and the structure of its solution space; for nonlinear operator equation A u B u + C u = f , with the help of the discussion on how to solve the system of linear operator equations, the exact solution is given. Besides, we obtain the representation of all its solutions.

This paper is concerned with the new algorithm for giving the approximate solution of a class of nonlinear integro-differential equations in the reproducing kernel space. Two integro-differential equations are solved using the algorithm. It turns out that this algorithm is valid.

In this paper, we will introduce the concept of affine frame in wavelet analysis to the field of p-adic number, hence provide new mathematic tools for application of p-adic analysis.

The paper proposed a new encryption algorithm of one dimension chaotic map, which based on parameter randomly changing. Through the randomly changing of parameter and iteration times, the complicated degree of chaotic sequences and cryptographic specific property are strengthened, and improved algorithm has n times long cycle compared to original function. Theory analysis to the mapping is well-distributed, and self-correlation and mutual-correlation is also good property. Through encryption test, it shows that new algorithm has high security , is realized easily ,and the encryption speed is very fast.

In this work, we give a new method for solving a nonlinear partial differential equation in the reproducing kernel space. Through numerical example, it is proved to be valid.