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Ahmad et al. in their paper for the first time proposed to apply sharp function for classification of images. In continuation of their work, in this paper we investigate the use of sharp function as an edge detector through well known diffusion models. Further, we discuss the formulation of weak solution of nonlinear diffusion equation and prove uniqueness of weak solution of nonlinear problem. The anisotropic generalization of sharp operator based diffusion has also been implemented and tested on various types of images.
With less than 6% of total global water resources but one fifth of the global population, China is facing serious challenges for its water resources management, particularly in rural areas due to the long-standing urban-rural dualistic structure and the economic-centralized developmental policies. This paper addresses the key water crises in rural China including potable water supply, wastewater treatment and disposal, water for agricultural purposes, and environmental concerns, and then analyzes the administrative system on water resources from the perspective of characteristics of the current administrative system and regulations; finally, synthetic approaches to solve water problems in rural China are proposed with regard to institutional reform, regulation revision, economic instruments, technology innovation and capacity-building. These recommendations provide valuable insights to water managers in rural China so that they can identify the most appropriate pathways for optimizing their water resources, reducing the total wastewater discharge and improving their water-related ecosystem.