Agricultural science and technology parks(ASTPs) represent an important growth pole in China’s agricultural modernization.Clarifying their diffusion laws can optimize the technological diffusion process and improve i...Agricultural science and technology parks(ASTPs) represent an important growth pole in China’s agricultural modernization.Clarifying their diffusion laws can optimize the technological diffusion process and improve its efficiency. Our study uses disaggregated spatial information in its model to analyze ASTP technology diffusion in a heterogeneous space. We constructed a comprehensive index system to evaluate the diffusion environmental quality and introduced the heterogeneous diffusion equation to calculate the technological diffusion probability. We applied this framework to a real-world scenario: the apple planting technology diffusion of the Yangling ASTP in the Loess Plateau, China. The results indicated: (1)the technological diffusion environment of the Loess Plateau advantageous apple producing area showed strong spatial heterogeneity caused by climate, topography, and external transportation links.(2) Under the combined effects of distance and spatial heterogeneity, the spatial diffusion pattern of the Yangling ASTP apple technology was expansion diffusion supplemented by hierarchical diffusion and banded diffusion, and (3) ASTP technology diffusion showed a strong distance attenuation effect, and the frictional effect of distance can be decreased by improving the diffusion environmental quality. These laws can promote regional balanced ASTP-driven development.展开更多
We propose and analyze a posteriori energy-norm error estimates for weighted interior penalty discontinuous Galerkin approximations of advection-diffusion-reaction equations with heterogeneous and anisotropic diffusio...We propose and analyze a posteriori energy-norm error estimates for weighted interior penalty discontinuous Galerkin approximations of advection-diffusion-reaction equations with heterogeneous and anisotropic diffusion. The weights, which play a key role in the analysis, depend on the diffusion tensor and are used to formulate the consistency terms in the discontinuous Galerkin method. The error upper bounds, in which all the constants are specified, consist of three terms： a residual estimator which depends only on the elementwise fluctuation of the discrete solution residual, a diffusive flux estimator where the weights used in the method enter explicitly, and a non-conforming estimator which is nonzero because of the use of discontinuous finite element spaces. The three estimators can be bounded locally by the approximation error. A particular attention is given to the dependency on problem parameters of the constants in the local lower error bounds. For moderate advection, it is shown that full robustness with respect to diffusion heterogeneities is achieved owing to the specific design of the weights in the discontinuous Galerkin method, while diffusion anisotropies remain purely local and impact the constants through the square root of the condition number of the diffusion tensor. For dominant advection, it is shown, in the spirit of previous work by Verfiirth on continuous finite elements, that the local lower error bounds can be written with constants involving a cut-off for the ratio of local mesh size to the reciprocal of the square root of the lowest local eignevalue of the diffusion tensor.展开更多
Weibo,China’s largest microblogging platform,has become one of the key information-sharing platforms in modern society.This study examines topic propagation in relation to microblogging from the perspective of the“p...Weibo,China’s largest microblogging platform,has become one of the key information-sharing platforms in modern society.This study examines topic propagation in relation to microblogging from the perspective of the“peer effect.”Using data of hot topics from Weibo,we analyze how the social effect and propagation pathway influence the topic propagation process.We propose a spatial and temporal heterogeneity diffusion model that includes endogenous and exogenous social effects and is based on but different from the Bass diffusion model.We find that most propagation pathways end after a single level of propagation.The endogenous social effect in microblogs primarily influences the inflow of topics.Such endogenous social effect,combined with the multiplier effect,motivates most users to share a microblog topic in a short period of time.The exogenous social effect primarily influences the outflow of topics,and therefore,the microblog topics of a small number of popular users’account for most of the share volume.Our results are robust to potential serial correlation,reflection problem,and potential self-selection due to user status.The findings reveal that group characteristics affect individuals’behaviors and choices in relation to the topic propagation process on microblogging platforms.The use of a spatial and temporal heterogeneity diffusion model and the robustness of the analysis process provide new information for scholars in this field.展开更多
基金Under the auspices of the National Natural Science Foundation of China(No.41771129)Social Science Foundation of Shaanxi(No.2015D055)Social Science Research Project on Major Theoretical and Practical Issues of Shaanxi(No.2020Z026)。
文摘Agricultural science and technology parks(ASTPs) represent an important growth pole in China’s agricultural modernization.Clarifying their diffusion laws can optimize the technological diffusion process and improve its efficiency. Our study uses disaggregated spatial information in its model to analyze ASTP technology diffusion in a heterogeneous space. We constructed a comprehensive index system to evaluate the diffusion environmental quality and introduced the heterogeneous diffusion equation to calculate the technological diffusion probability. We applied this framework to a real-world scenario: the apple planting technology diffusion of the Yangling ASTP in the Loess Plateau, China. The results indicated: (1)the technological diffusion environment of the Loess Plateau advantageous apple producing area showed strong spatial heterogeneity caused by climate, topography, and external transportation links.(2) Under the combined effects of distance and spatial heterogeneity, the spatial diffusion pattern of the Yangling ASTP apple technology was expansion diffusion supplemented by hierarchical diffusion and banded diffusion, and (3) ASTP technology diffusion showed a strong distance attenuation effect, and the frictional effect of distance can be decreased by improving the diffusion environmental quality. These laws can promote regional balanced ASTP-driven development.
文摘We propose and analyze a posteriori energy-norm error estimates for weighted interior penalty discontinuous Galerkin approximations of advection-diffusion-reaction equations with heterogeneous and anisotropic diffusion. The weights, which play a key role in the analysis, depend on the diffusion tensor and are used to formulate the consistency terms in the discontinuous Galerkin method. The error upper bounds, in which all the constants are specified, consist of three terms： a residual estimator which depends only on the elementwise fluctuation of the discrete solution residual, a diffusive flux estimator where the weights used in the method enter explicitly, and a non-conforming estimator which is nonzero because of the use of discontinuous finite element spaces. The three estimators can be bounded locally by the approximation error. A particular attention is given to the dependency on problem parameters of the constants in the local lower error bounds. For moderate advection, it is shown that full robustness with respect to diffusion heterogeneities is achieved owing to the specific design of the weights in the discontinuous Galerkin method, while diffusion anisotropies remain purely local and impact the constants through the square root of the condition number of the diffusion tensor. For dominant advection, it is shown, in the spirit of previous work by Verfiirth on continuous finite elements, that the local lower error bounds can be written with constants involving a cut-off for the ratio of local mesh size to the reciprocal of the square root of the lowest local eignevalue of the diffusion tensor.
基金the National Natural Science Foundation of China(Grant Nos.70801066,71071167,7107168,71371200)Sun Yat-sen University Basic Research Funding(Grant Nos.1009028,1109115,16wkjc13)。
文摘Weibo,China’s largest microblogging platform,has become one of the key information-sharing platforms in modern society.This study examines topic propagation in relation to microblogging from the perspective of the“peer effect.”Using data of hot topics from Weibo,we analyze how the social effect and propagation pathway influence the topic propagation process.We propose a spatial and temporal heterogeneity diffusion model that includes endogenous and exogenous social effects and is based on but different from the Bass diffusion model.We find that most propagation pathways end after a single level of propagation.The endogenous social effect in microblogs primarily influences the inflow of topics.Such endogenous social effect,combined with the multiplier effect,motivates most users to share a microblog topic in a short period of time.The exogenous social effect primarily influences the outflow of topics,and therefore,the microblog topics of a small number of popular users’account for most of the share volume.Our results are robust to potential serial correlation,reflection problem,and potential self-selection due to user status.The findings reveal that group characteristics affect individuals’behaviors and choices in relation to the topic propagation process on microblogging platforms.The use of a spatial and temporal heterogeneity diffusion model and the robustness of the analysis process provide new information for scholars in this field.
