In this article we obtain weighted norm estimates for multilinear singular integrals with non-smooth kernels and the boundedness of certain multilinear commutators by making use of a sharp maximal function.
Faults in rotating machine are difficult to detect and identify,especially when the system is complex and nonlinear.In order to solve this problem,a novel performance monitoring and fault diagnosis method based on ker...Faults in rotating machine are difficult to detect and identify,especially when the system is complex and nonlinear.In order to solve this problem,a novel performance monitoring and fault diagnosis method based on kernel generalized discriminant analysis(kernel GDA,KGDA)was proposed.Through KGDA,the data were mapped from the original space to the high-dimensional feature space.Then the statistic distance between normal data and test data was constructed to detect whether a fault was occurring.If a fault had occurred,similar analysis was used to identify the type of faults.The effectiveness of the proposed method was evaluated by simulation results of vibration signal fault dataset in the rotating machinery,which was scalable to different rotating machinery.展开更多
To deal with the nonlinear separable problem, the generalized noise clustering （GNC） algorithm is extended to a kernel generalized noise clustering （KGNC） model. Different from the fuzzy c-means （FCM） model and ...To deal with the nonlinear separable problem, the generalized noise clustering （GNC） algorithm is extended to a kernel generalized noise clustering （KGNC） model. Different from the fuzzy c-means （FCM） model and the GNC model which are based on Euclidean distance, the presented model is based on kernel-induced distance by using kernel method. By kernel method the input data are nonlinearly and implicitly mapped into a high-dimensional feature space, where the nonlinear pattern appears linear and the GNC algorithm is performed. It is unnecessary to calculate in high-dimensional feature space because the kernel function can do it just in input space. The effectiveness of the proposed algorithm is verified by experiments on three data sets. It is concluded that the KGNC algorithm has better clustering accuracy than FCM and GNC in clustering data sets containing noisy data.展开更多
The present article is devoted to developing new finite difference schemes with a higher order of the convergence for the generalized time-fractional diffusion equations(GTFDEs)that are characterized by a weight funct...The present article is devoted to developing new finite difference schemes with a higher order of the convergence for the generalized time-fractional diffusion equations(GTFDEs)that are characterized by a weight function w(t).Three different discrete analogs with different orders of approximations are designed for the generalized Caputo derivative.The major contribution of this paper is the development of an L2 type difference scheme that results in the(3−α)order of convergence in time.The spatial direction is discretized using a second-order difference operator.Fundamental properties of the coefficients of the L2 difference operator are examined and proved theoretically.The stability and convergence analysis of the developed L2 scheme are established theoretically using the energy method.An efficient algorithm is developed and implemented on numerical test problems to prove the numerical accuracy of the scheme.展开更多
Let L =-△+V(x) be a Schrodinger operator, where △ is the Laplacian on R^n,while nonnegative potential V(x) belonging to the reverse Holder class. The aim of this paper is to give generalized weighted Morrey estimate...Let L =-△+V(x) be a Schrodinger operator, where △ is the Laplacian on R^n,while nonnegative potential V(x) belonging to the reverse Holder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schrodinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.展开更多
文摘In this article we obtain weighted norm estimates for multilinear singular integrals with non-smooth kernels and the boundedness of certain multilinear commutators by making use of a sharp maximal function.
基金National Natural Science Foundation of China(No.60504033)
文摘Faults in rotating machine are difficult to detect and identify,especially when the system is complex and nonlinear.In order to solve this problem,a novel performance monitoring and fault diagnosis method based on kernel generalized discriminant analysis(kernel GDA,KGDA)was proposed.Through KGDA,the data were mapped from the original space to the high-dimensional feature space.Then the statistic distance between normal data and test data was constructed to detect whether a fault was occurring.If a fault had occurred,similar analysis was used to identify the type of faults.The effectiveness of the proposed method was evaluated by simulation results of vibration signal fault dataset in the rotating machinery,which was scalable to different rotating machinery.
基金The 15th Plan National Defence Preven-tive Research Project (No.413030201)
文摘To deal with the nonlinear separable problem, the generalized noise clustering （GNC） algorithm is extended to a kernel generalized noise clustering （KGNC） model. Different from the fuzzy c-means （FCM） model and the GNC model which are based on Euclidean distance, the presented model is based on kernel-induced distance by using kernel method. By kernel method the input data are nonlinearly and implicitly mapped into a high-dimensional feature space, where the nonlinear pattern appears linear and the GNC algorithm is performed. It is unnecessary to calculate in high-dimensional feature space because the kernel function can do it just in input space. The effectiveness of the proposed algorithm is verified by experiments on three data sets. It is concluded that the KGNC algorithm has better clustering accuracy than FCM and GNC in clustering data sets containing noisy data.
基金financial support from the Russian Science Foundation under Grant No.22-21-00363funding support from the Science and Engineering Research Board,India,sanctioned under Project No.CRG/2022/000813.
文摘The present article is devoted to developing new finite difference schemes with a higher order of the convergence for the generalized time-fractional diffusion equations(GTFDEs)that are characterized by a weight function w(t).Three different discrete analogs with different orders of approximations are designed for the generalized Caputo derivative.The major contribution of this paper is the development of an L2 type difference scheme that results in the(3−α)order of convergence in time.The spatial direction is discretized using a second-order difference operator.Fundamental properties of the coefficients of the L2 difference operator are examined and proved theoretically.The stability and convergence analysis of the developed L2 scheme are established theoretically using the energy method.An efficient algorithm is developed and implemented on numerical test problems to prove the numerical accuracy of the scheme.
文摘Let L =-△+V(x) be a Schrodinger operator, where △ is the Laplacian on R^n,while nonnegative potential V(x) belonging to the reverse Holder class. The aim of this paper is to give generalized weighted Morrey estimates for the boundedness of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators.Moreover, the boundedness of the commutator operators formed by BMO functions and Marcinkiewicz integrals with rough kernel associated with Schrodinger operators is discussed on the generalized weighted Morrey spaces. As its special cases, the corresponding results of Marcinkiewicz integrals with rough kernel associated with Schrodinger operator and their commutators have been deduced, respectively. Also, Marcinkiewicz integral operators, rough Hardy-Littlewood(H-L for short) maximal operators, Bochner-Riesz means and parametric Marcinkiewicz integral operators which satisfy the conditions of our main results can be considered as some examples.
