Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But th...Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices. In order to construct these asymmetrical orthogonal arrays, a class of special matrices, so-called generalized difference matrices, were discovered by Zhang（1989, 1990, 1993） by the orthogonal decompositions of projective matrices. In this article, an interesting equivalent relationship between the orthogonal arrays and the generalized difference matrices is presented. As an application, a family of orthogonal arrays of run sizes 4p2, such as L36（6^13^42^10）, are constructed.展开更多
The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensio...The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.展开更多
In the research of bistatic tomography imaging of translating object, we get a class of generalized Radon transformation. In this paper, first we prove the existence and uniguenness of its solution in theory and poin...In the research of bistatic tomography imaging of translating object, we get a class of generalized Radon transformation. In this paper, first we prove the existence and uniguenness of its solution in theory and point out this problem is ill-posed with an especial example.Secondly by means of multiplicative interpolation functions to approximate models, we constracted regularizing functional. Finally we simplify calculation by Fourier transformation,get regularizing solutions that converge to accurate solution.展开更多
基金the National Science Foundations of China(10571045)the National Science Foundations of Henan Province(02243700510211063100)
文摘Nowadays orthogonal arrays play important roles in statistics, computer science, coding theory and cryptography. The usual difference matrices are essential for the construction of many mixed orthogonal arrays. But there are also many orthogonal arrays, especially mixed-level or asymmetrical which can not be obtained by the usual difference matrices. In order to construct these asymmetrical orthogonal arrays, a class of special matrices, so-called generalized difference matrices, were discovered by Zhang（1989, 1990, 1993） by the orthogonal decompositions of projective matrices. In this article, an interesting equivalent relationship between the orthogonal arrays and the generalized difference matrices is presented. As an application, a family of orthogonal arrays of run sizes 4p2, such as L36（6^13^42^10）, are constructed.
文摘The improved tanh function method [Commun. Theor. Phys. （Beijing, China） 43 （2005） 585] is further improved by generalizing the ansatz solution of the considered equation. As its application, the （2＋1）-dimensional Broer-Kaup equations are considered and abundant new exact non-travelling wave solutions are obtained.
文摘In the research of bistatic tomography imaging of translating object, we get a class of generalized Radon transformation. In this paper, first we prove the existence and uniguenness of its solution in theory and point out this problem is ill-posed with an especial example.Secondly by means of multiplicative interpolation functions to approximate models, we constracted regularizing functional. Finally we simplify calculation by Fourier transformation,get regularizing solutions that converge to accurate solution.
