In this paper,a Cauchy problem of two-dimensional heat conduction equation is investigated.This is a severely iⅡ-posed problem.Based on the solution of Cauchy problem of two-dimensional heat conduction equation,we pr...In this paper,a Cauchy problem of two-dimensional heat conduction equation is investigated.This is a severely iⅡ-posed problem.Based on the solution of Cauchy problem of two-dimensional heat conduction equation,we propose to solve this problem by modifying the kernel,which generates a well-posed problem.Error estimates between the exact solution and the regularized solution are given.We provide a numerical experiment to illustrate the main results.展开更多
A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means ...A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means （MPCM） algorithm by using kernel methods. Different from MPCM and fuzzy c-means （FCM） model which are based on Euclidean distance, the proposed model is based on kernel-induced distance. Furthermore, with kernel methods the input data can be mapped implicitly into a high-dimensional feature space where the nonlinear pattern now appears linear. It is unnecessary to do calculation in the high-dimensional feature space because the kernel function can do it. Numerical experiments show that KMPCM outperforms FCM and MPCM.展开更多
In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive pa...In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.展开更多
基金supported by the National Natural Science Foundation of China(11101109,11271102)and the Natural Science Foundation of Heilongjiang Province of China(A201107).
文摘In this paper,a Cauchy problem of two-dimensional heat conduction equation is investigated.This is a severely iⅡ-posed problem.Based on the solution of Cauchy problem of two-dimensional heat conduction equation,we propose to solve this problem by modifying the kernel,which generates a well-posed problem.Error estimates between the exact solution and the regularized solution are given.We provide a numerical experiment to illustrate the main results.
基金Project supported by the 15th Plan for National Defence Preventive Research Project (Grant No.413030201)
文摘A novel model of fuzzy clustering using kernel methods is proposed. This model is called kernel modified possibilistic c-means （KMPCM） model. The proposed model is an extension of the modified possibilistic c-means （MPCM） algorithm by using kernel methods. Different from MPCM and fuzzy c-means （FCM） model which are based on Euclidean distance, the proposed model is based on kernel-induced distance. Furthermore, with kernel methods the input data can be mapped implicitly into a high-dimensional feature space where the nonlinear pattern now appears linear. It is unnecessary to do calculation in the high-dimensional feature space because the kernel function can do it. Numerical experiments show that KMPCM outperforms FCM and MPCM.
基金the National Natural Science Foundation of China(No.10671022)Research Foundation for Doctor Programme (No.20060027023)Henan Institute of Education Youth Scientific Research Fund (No.20070107)
文摘In this article,we consider the integral representation of harmonic functions.Using a property of the modified Poisson kernel in a half plane,we prove that a harmonic function u(z) in a half plane with its positive part u+(z)=max{u(z),0} satisfying a slowly growing condition can be represented by its integral of a measure on the boundary of the half plan.
