This paper deals with the Gevreg-hypoellipticity for a class of totally characteristic operators with the elliptic condition and the discrete boundary spectrum condition respectively.
In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities.Firstly,we introduce the corner t...In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities.Firstly,we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality,the Poincare′inequality,and the Hardy inequality.Then,by using the potential well method and the inequality mentioned above,we obtain an existence theorem of global solutions with exponential decay and show the blow-up in finite time of solutions for both cases with low initial energy and critical initial energy.Significantly,the relation between the above two phenomena is derived as a sharp condition.Moreover,we show that the global existence also holds for the case of a potential well family.展开更多
This paper introduces an improved convolutional neural network based on the conventional U-Net for simulating built-up land expansion.The proposed method hires a pixel-wise semantic segmentation approach considering t...This paper introduces an improved convolutional neural network based on the conventional U-Net for simulating built-up land expansion.The proposed method hires a pixel-wise semantic segmentation approach considering the spatial drivers affecting urbanization as data cubes.Independent variables including altitude,slope,and distance from barren,crop,greenery,roads,and urban areas for 1998,2008,and 2018 were considered as covariates for the simulation of built-up land expansion in Tehran and Karaj regions in Iran.The proposed method was compared with the random forest(RF)algorithm as the baseline model.Evaluation using the area under the total operating characteristic indicated the superiority of our modified U-Net(0.87)over the RF(0.82)algorithm.Furthermore,evaluation using the percent correct metric indicated that our proposed model is capable of learning neighborhood effects effectively leading to simulate built-up land expansion accurately,independent from applying a cellular automata(CA)model.Therefore,the modified U-Net independent from the CA which can consider the neighborhood effects is recommended for the simulation of built-up land expansion precisely.展开更多
文摘This paper deals with the Gevreg-hypoellipticity for a class of totally characteristic operators with the elliptic condition and the discrete boundary spectrum condition respectively.
文摘In this article,we study the initial boundary value problem of coupled semi-linear degenerate parabolic equations with a singular potential term on manifolds with corner singularities.Firstly,we introduce the corner type weighted p-Sobolev spaces and the weighted corner type Sobolev inequality,the Poincare′inequality,and the Hardy inequality.Then,by using the potential well method and the inequality mentioned above,we obtain an existence theorem of global solutions with exponential decay and show the blow-up in finite time of solutions for both cases with low initial energy and critical initial energy.Significantly,the relation between the above two phenomena is derived as a sharp condition.Moreover,we show that the global existence also holds for the case of a potential well family.
文摘This paper introduces an improved convolutional neural network based on the conventional U-Net for simulating built-up land expansion.The proposed method hires a pixel-wise semantic segmentation approach considering the spatial drivers affecting urbanization as data cubes.Independent variables including altitude,slope,and distance from barren,crop,greenery,roads,and urban areas for 1998,2008,and 2018 were considered as covariates for the simulation of built-up land expansion in Tehran and Karaj regions in Iran.The proposed method was compared with the random forest(RF)algorithm as the baseline model.Evaluation using the area under the total operating characteristic indicated the superiority of our modified U-Net(0.87)over the RF(0.82)algorithm.Furthermore,evaluation using the percent correct metric indicated that our proposed model is capable of learning neighborhood effects effectively leading to simulate built-up land expansion accurately,independent from applying a cellular automata(CA)model.Therefore,the modified U-Net independent from the CA which can consider the neighborhood effects is recommended for the simulation of built-up land expansion precisely.
