In this paper,we study some basic properties on Lipschitz star bodies,such as the equivalence between Lipschitz star bodies and star bodies with respect to a ball,the equivalence between the convergence of Lipschitz s...In this paper,we study some basic properties on Lipschitz star bodies,such as the equivalence between Lipschitz star bodies and star bodies with respect to a ball,the equivalence between the convergence of Lipschitz star bodies with respect to Hausdorff distance and the convergence of Lipschtz star bodies with respect to radial distance,and the convergence of Steiner symmetrizations of Lipschitz star bodies.展开更多
In this paper, we study the viscosity solutions of the Neumann problem in a bounded C<sup>2</sup> domain Ω, where Δ<sup>N</sup>∞</sub> is called the normalized infinity Laplacian. The ...In this paper, we study the viscosity solutions of the Neumann problem in a bounded C<sup>2</sup> domain Ω, where Δ<sup>N</sup>∞</sub> is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory. .展开更多
In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property i...In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property if and only if it is structurally stable.展开更多
There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA...There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA) estimation system based on self-organizing map (SOM) and designed for arbitrarily distributed sensor array is proposed. The essential principle of this method is that the map from distance difference of arrival (DDOA) to DOA is Lipschitz continuity, it indicates the similar topology between them, and thus Kohonen SOM is a suitable network to classify DOA through DDOA. The simulation results show that the DOA estimation errors are less than 1° for most signals between 0° to 180°. Compared to MUSIC, Root-MUSIC, ESPRIT, and RBF, the errors of signals under signal-to-noise ratios (SNR) declines from 20 dB to 2 dB are robust, SOM is better than RBF and almost close to MUSIC. Further, the network can be trained in advance, which makes it possible to be implemented in real-time.展开更多
基金supported by the NSFC(11971080,KJQN202000838)the funds of the Basic and Advanced Research Project of CQ CSTC(cstc2018jcyj AX0790,cstc2020jcyj-msxm X0328)+1 种基金supported by Project funded by the China Postdoctoral Science Foundation(2019TQ0097)the Science and Technology Commission of Shanghai Municipality(22DZ2229014)。
文摘In this paper,we study some basic properties on Lipschitz star bodies,such as the equivalence between Lipschitz star bodies and star bodies with respect to a ball,the equivalence between the convergence of Lipschitz star bodies with respect to Hausdorff distance and the convergence of Lipschtz star bodies with respect to radial distance,and the convergence of Steiner symmetrizations of Lipschitz star bodies.
文摘In this paper, we study the viscosity solutions of the Neumann problem in a bounded C<sup>2</sup> domain Ω, where Δ<sup>N</sup>∞</sub> is called the normalized infinity Laplacian. The normalized infinity Laplacian was first studied by Peres, Shramm, Sheffield and Wilson from the point of randomized theory named tug-of-war, which has wide applications in optimal mass transportation, financial option price problems, digital image processing, physical engineering, etc. We give the Lipschitz regularity of the viscosity solutions of the Neumann problem. The method we adopt is to choose suitable auxiliary functions as barrier functions and combine the perturbation method and viscosity solutions theory. .
基金supported by National Natural Science Foundation of China(12071018)Fundamental Research Funds for the Central Universitiessupported by the National Research Foundation of Korea(NRF)funded by the Korea government(MIST)(2020R1F1A1A01051370)。
文摘In this paper,we define a generalized Lipschitz shadowing property for flows and prove that a flowΦgenerated by a C1vector field X on a closed Riemannian manifold M has this generalized Lipschitz shadowing property if and only if it is structurally stable.
文摘There are many DOA estimation methods based on different signal features, and these methods are often evaluated by experimental results, but lack the necessary theoretical basis. Therefore, a direction of arrival (DOA) estimation system based on self-organizing map (SOM) and designed for arbitrarily distributed sensor array is proposed. The essential principle of this method is that the map from distance difference of arrival (DDOA) to DOA is Lipschitz continuity, it indicates the similar topology between them, and thus Kohonen SOM is a suitable network to classify DOA through DDOA. The simulation results show that the DOA estimation errors are less than 1° for most signals between 0° to 180°. Compared to MUSIC, Root-MUSIC, ESPRIT, and RBF, the errors of signals under signal-to-noise ratios (SNR) declines from 20 dB to 2 dB are robust, SOM is better than RBF and almost close to MUSIC. Further, the network can be trained in advance, which makes it possible to be implemented in real-time.
