In this paper we consider the Cauchy problem for the singular semilinear parabolic equation u t-Δu+V 1(x)u=V 2(x)u p,x∈R n\{0},t>0, where V 1(x),V 2(x) may have singularities at the origin. Using functions...In this paper we consider the Cauchy problem for the singular semilinear parabolic equation u t-Δu+V 1(x)u=V 2(x)u p,x∈R n\{0},t>0, where V 1(x),V 2(x) may have singularities at the origin. Using functions of the Kato class and the Green tight functions we got the existence of the positive solution being singular at the origin.展开更多
The Circle algorithm was proposed for large datasets.The idea of the algorithm is to find a set of vertices that are close to each other and far from other vertices.This algorithm makes use of the connection between c...The Circle algorithm was proposed for large datasets.The idea of the algorithm is to find a set of vertices that are close to each other and far from other vertices.This algorithm makes use of the connection between clustering aggregation and the problem of correlation clustering.The best deterministic approximation algorithm was provided for the variation of the correlation of clustering problem,and showed how sampling can be used to scale the algorithms for large datasets.An extensive empirical evaluation was given for the usefulness of the problem and the solutions.The results show that this method achieves more than 50% reduction in the running time without sacrificing the quality of the clustering.展开更多
In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and dualit...In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and duality results for a vector optimization problem with functions defined on a Banach space.展开更多
Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method fo...Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method for flood classification, which is based on the mathematical theorem of dialectics basic laws. This newly proposed method explores a novel way to analyze and solve engineering problems by utilizing a dialectical thinking. In this paper, the Tuwei River basin, located in the Yellow River tributary, is taken as an example for flood classification. The results obtained in this study reveal the problems in a previous method—Set Pair Analysis classification method. The variable sets method is proven to be theoretically rigorous, computationally simple. The classification results are objective, accurate and consistent with the actual situations. This study demonstrates the significant importance of using a scientifically sound method in solving engineering problems.展开更多
This paper proposes robust version to unsupervised classification algorithm based on modified robust version of primal problem of standard SVMs, which directly relaxes it with label variables to a semi-definite progra...This paper proposes robust version to unsupervised classification algorithm based on modified robust version of primal problem of standard SVMs, which directly relaxes it with label variables to a semi-definite programming. Numerical results confirm the robustness of the proposed method.展开更多
For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a sm...For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.展开更多
文摘In this paper we consider the Cauchy problem for the singular semilinear parabolic equation u t-Δu+V 1(x)u=V 2(x)u p,x∈R n\{0},t>0, where V 1(x),V 2(x) may have singularities at the origin. Using functions of the Kato class and the Green tight functions we got the existence of the positive solution being singular at the origin.
基金Projects(60873265,60903222) supported by the National Natural Science Foundation of China Project(IRT0661) supported by the Program for Changjiang Scholars and Innovative Research Team in University of China
文摘The Circle algorithm was proposed for large datasets.The idea of the algorithm is to find a set of vertices that are close to each other and far from other vertices.This algorithm makes use of the connection between clustering aggregation and the problem of correlation clustering.The best deterministic approximation algorithm was provided for the variation of the correlation of clustering problem,and showed how sampling can be used to scale the algorithms for large datasets.An extensive empirical evaluation was given for the usefulness of the problem and the solutions.The results show that this method achieves more than 50% reduction in the running time without sacrificing the quality of the clustering.
基金Foundation item： Supported by the National Natural Science Foundation of China（60574075） University, engaged in optimization theory and application.
文摘In this note,new classes of generalized type-I functions are introduced for functions between Banach spaces.These generalized type-I functions are then utilized to establish sufficient optimality conditions and duality results for a vector optimization problem with functions defined on a Banach space.
基金supported by the National Natural Science Foundation of China (Grant Nos. 51209032, 50779005)
文摘Flood classification is an effective way to improve flood forecasting accuracy. According to the opposite unity mathematical theorem in Variable Sets theory, this paper proposes a Variable Sets principle and method for flood classification, which is based on the mathematical theorem of dialectics basic laws. This newly proposed method explores a novel way to analyze and solve engineering problems by utilizing a dialectical thinking. In this paper, the Tuwei River basin, located in the Yellow River tributary, is taken as an example for flood classification. The results obtained in this study reveal the problems in a previous method—Set Pair Analysis classification method. The variable sets method is proven to be theoretically rigorous, computationally simple. The classification results are objective, accurate and consistent with the actual situations. This study demonstrates the significant importance of using a scientifically sound method in solving engineering problems.
基金supported by the Key Project of the National Natural Science Foundation of China under Grant No.10631070
文摘This paper proposes robust version to unsupervised classification algorithm based on modified robust version of primal problem of standard SVMs, which directly relaxes it with label variables to a semi-definite programming. Numerical results confirm the robustness of the proposed method.
基金supported by the National Natural Science Foundation of China under Grant Nos.10971118, 10701047 and 10901096the Natural Science Foundation of Shandong Province under Grant Nos. ZR2009AL019 and BS2010SF010
文摘For the semi-infinite programming （SIP） problem, the authors first convert it into an equivalent nonlinear programming problem with only one inequality constraint by using an integral function, and then propose a smooth penalty method based on a class of smooth functions. The main feature of this method is that the global solution of the penalty function is not necessarily solved at each iteration, and under mild assumptions, the method is always feasible and efficient when the evaluation of the integral function is not very expensive. The global convergence property is obtained in the absence of any constraint qualifications, that is, any accumulation point of the sequence generated by the algorithm is the solution of the SIP. Moreover, the authors show a perturbation theorem of the method and obtain several interesting results. Furthermore, the authors show that all iterative points remain feasible after a finite number of iterations under the Mangasarian-Fromovitz constraint qualification. Finally, numerical results are given.
