This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Und...This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.展开更多
A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Four...A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum展开更多
We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the...We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.展开更多
We developed a system for monitoring the ionosphere, which uses the GNSS network located in the western part of Ukraine. The system is based on determining the ionosphere parameters from GNSS observations performed at...We developed a system for monitoring the ionosphere, which uses the GNSS network located in the western part of Ukraine. The system is based on determining the ionosphere parameters from GNSS observations performed at an individual station. We are proposed algorithm for restoring the spatial position of the ionospheric state or its ionization field according to the regular definitions of the TEC parameter. The description below shows one of the possible solutions that are based on the application of the regularized approximation of functions with numerous variables. To experimentally determine the changes in the ionization field in time, we took measurements from 272 days in 2013 that were determined during the GNSS observations at 17 continuously operating stations of the ZAKPOS network. The resulting error indicators show that the developed algorithm gives consistent results for ionization field restoration that do not depend on the ionosphere state, satellites positions and changes in number of stations in the network used for computations.展开更多
A stable skeleton is very important to some applications such as vehicle navigation, object represent and pattern recognition. The connection skeleton is just one that not only can be computed stably but also can figu...A stable skeleton is very important to some applications such as vehicle navigation, object represent and pattern recognition. The connection skeleton is just one that not only can be computed stably but also can figure the connectivity structure of contour. A new method named continuous connectivity detection and a new model named approximate regular polygon (ARP) were proposed for connection skeleton extraction. Both the method and the model were tested by the real maps of road network including flyovers, interchanges and other common object contours. Satisfactory results were obtained.展开更多
基金supported by the Natural Science Foundation of China(11801108)the Natural Science Foundation of Guangdong Province(2021A1515010314)the Science and Technology Planning Project of Guangzhou City(202201010111)。
文摘This paper deals with the forward and backward problems for the nonlinear fractional pseudo-parabolic equation ut+(-Δ)^(s1)ut+β(-Δ)^(s2)u=F(u,x,t)subject o random Gaussian white noise for initial and final data.Under the suitable assumptions s1,s2andβ,we first show the ill-posedness of mild solutions for forward and backward problems in the sense of Hadamard,which are mainly driven by random noise.Moreover,we propose the Fourier truncation method for stabilizing the above ill-posed problems.We derive an error estimate between the exact solution and its regularized solution in an E‖·‖Hs22norm,and give some numerical examples illustrating the effect of above method.
文摘A new method for approximating the inerse Laplace transform is presented. We first change our Laplace transform equation into a convolution type integral equation, where Tikhonov regularization techniques and the Fourier transformation are easily applied. We finally obtain a regularized approximation to the inverse Laplace transform as finite sum
基金Supported by NSF(No. 10531020) of Chinathe Program of 985 Innovation Engineering on Information in Xiamen University (2004-2007) and NCETXMU
文摘We consider the questions of boundary regularity for weak solutions of second-order nonlinear elliptic systems under the natural growth condition. We obtain a general criterion for a weak solution to be regular in the neighborhood of a given boundary point. The proof yields directly the optimal regularity for the solution in this neighborhood. This result is new for the situation under the natural growth conditions.
文摘We developed a system for monitoring the ionosphere, which uses the GNSS network located in the western part of Ukraine. The system is based on determining the ionosphere parameters from GNSS observations performed at an individual station. We are proposed algorithm for restoring the spatial position of the ionospheric state or its ionization field according to the regular definitions of the TEC parameter. The description below shows one of the possible solutions that are based on the application of the regularized approximation of functions with numerous variables. To experimentally determine the changes in the ionization field in time, we took measurements from 272 days in 2013 that were determined during the GNSS observations at 17 continuously operating stations of the ZAKPOS network. The resulting error indicators show that the developed algorithm gives consistent results for ionization field restoration that do not depend on the ionosphere state, satellites positions and changes in number of stations in the network used for computations.
文摘A stable skeleton is very important to some applications such as vehicle navigation, object represent and pattern recognition. The connection skeleton is just one that not only can be computed stably but also can figure the connectivity structure of contour. A new method named continuous connectivity detection and a new model named approximate regular polygon (ARP) were proposed for connection skeleton extraction. Both the method and the model were tested by the real maps of road network including flyovers, interchanges and other common object contours. Satisfactory results were obtained.
