Our aim in this paper is to develop a Schrödinger-type identity for a Schrödinger free boundary problem in R n. As an application, we establish necessary and sufficient conditions for the product of some distributional functions to satisfy the Schrödinger-type identity. As a consequence, our results significantly improve and generalize previous work.

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In wireless sensor networks (WSNs), inefficient coverage does affect the quality of service (QoS), which the minimum exposure path (MEP) is traditionally used to handle. But intelligent mobile devices are generally of limited computation capability, local storage, and energy. Present methods cannot meet the demand of multiple target intrusion, lacking the consideration of energy consumption. Based on the Voronoi diagram in computational geometry, this paper proposed an invasion strategy of minimum risk path (MRP) to such a question. MRP is the path considered both the exposure of the moving target and energy consumption. Federated learning is introduced to figure out how to find the MRP, expressed as C t i , t j = f E , e . The value of C t i , t j can measure the success of an invasion. At the time when a single smart mobile device invades, horizontal federated learning is taken to partition the path feature, and a single target feature federated (SPF) algorithm is for calculating the MRP. Moreover, for multi smart mobile device invasion, it has imported the time variable. Vertical federated learning can partition the feature of multipath data, and the multi-target feature federated (MFF) algorithm is for solving the multipath MRP dynamically. The experimental results show that the SPF and MFF have the dominant advantage over traditional computational performance and time. It primarily applies the complex conditions of a massive amount of sensor nodes.

Abstract. Taking S-57 standard electronic chart as the research subject, the paper introduces the technology of lossless digital watermarking. Based on an in-depth analysis of the content feature of the S-57 electronic chart, the lossless digital watermarking technology is concretized. A framework model of lossless digital watermarking based on the content feature of the electronic chart is put forward in the paper, as well as a zero-bit dynamical extension technology based on the gradient algorithm with which lossless embedding can be realized. At last, based on the experiment results and corresponding comparative analysis, the robustness, invisibility, lossless content and other aspects of the watermarking algorithm are compared and verified in detail. Meanwhile, the defects of the watermarking algorithm are also pointed out, paving the way for future research.