The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application,...The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.展开更多
Bosonization approach is applied in solving the most general ;N= 1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a （sKdV-a） equation. By introducing some fermionic parameters in the expansion...Bosonization approach is applied in solving the most general ;N= 1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a （sKdV-a） equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosoNic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonie equations are simply obtained for all values of a, Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously.展开更多
Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems....Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems.In this paper,a novel penalty function(called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed.Based on the M-objective penalty function,an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems,with its convergence proved under some conditions.Furthermore,numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters,and is efficient in choosing a penalty parameter in a large range in Matlab software.展开更多
基金Project supported by the Outstanding Youth Grant of Natural Science Foundation of China (No. 60225002), the National Basic Research Program (973) of China (No. 2004CB318000), the National Natural Science Foundation of China (Nos. 60533060 and 60473132)
文摘The problem of spherical parametrization is that of mapping a genus-zero mesh onto a spherical surface. For a given mesh, different parametrizations can be obtained by different methods. And for a certain application, some parametrization results might behave better than others. In this paper, we will propose a method to parametrize a genus-zero mesh so that a surface fitting algorithm with PHT-splines can generate good result. Here the parametrization results are obtained by minimizing discrete har- monic energy subject to spherical constraints. Then some applications are given to illustrate the advantages of our results. Based on PHT-splines, parametric surfaces can be constructed efficiently and adaptively to fit genus-zero meshes after their spherical parametrization has been obtained.
基金Supported by the National Natural Science Foundation of China under Nos.11175092,11275123 and 10905038Scientific Research Fund of Zhejiang Provincial Education Department under Grant No.Y201017148K.C.Wong Magna Fund in Ningbo University
文摘Bosonization approach is applied in solving the most general ;N= 1 supersymmetric Korteweg de-Vries equation with an arbitrary parameter a （sKdV-a） equation. By introducing some fermionic parameters in the expansion of the superfield, the sKdV-a equation is transformed to a new coupled bosoNic system. The Lie point symmetries of this model are considered and similarity reductions of it are conducted. Several types of similarity reduction solutions of the coupled bosonie equations are simply obtained for all values of a, Some kinds of exact solutions of the sKdV-a equation are discussed which was not considered integrable previously.
基金supported by the National Natural Science Foundation of China under Grant No.11271329
文摘Some classical penalty function algorithms may not always be convergent under big penalty parameters in Matlab software,which makes them impossible to find out an optimal solution to constrained optimization problems.In this paper,a novel penalty function(called M-objective penalty function) with one penalty parameter added to both objective and constrained functions of inequality constrained optimization problems is proposed.Based on the M-objective penalty function,an algorithm is developed to solve an optimal solution to the inequality constrained optimization problems,with its convergence proved under some conditions.Furthermore,numerical results show that the proposed algorithm has a much better convergence than the classical penalty function algorithms under big penalty parameters,and is efficient in choosing a penalty parameter in a large range in Matlab software.
