In chemical graph theory, a topological index is a numerical representation of a chemical network, while a topological descriptor correlates certain physicochemical characteristics of underlying chemical compounds besides its chemical representation. The graph plays a vital role in modeling and designing any chemical network. Simonraj et al. derived a new type of graphs, which is named a third type of hex-derived networks. In our work, we discuss the third type of hex-derived networks $HDN3(r)$ , $THDN3(r)$ , $RHDN3(r)$ , $CHDN3(r)$ , and compute exact results for topological indices which are based on degrees of end vertices.

To address the issues of low detection accuracy and poor effect caused by small Oncomelania hupensis data samples and small target sizes. This article proposes the O. hupensis snails detection algorithm, the YOLOv5s-ECA-vfnet based on improved YOLOv5s, by using YOLOv5s as the basic target detection model and optimizing the loss function to improve target learning ability for specific regions. The experimental findings show that the snail detection method of the YOLOv5s-ECA-vfnet, the precision (P), the recall (R) and the mean Average Precision (mAP) of the algorithm are improved by 1.3%, 1.26%, and 0.87%, respectively. It shows that this algorithm has a good effect on snail detection. The algorithm is capable of accurately and rapidly identifying O. hupensis snails on different conditions of lighting, sizes, and densities, and further providing a new technology for precise and intelligent investigation of O. hupensiss snails for schistosomiasis prevention institutions.

In recent years, holographic projection technology has been integrated into the real society, which brings a new visual experience to people and meets their high requirements for audiovisual experience. With the development of holographic technology, the hologram from holographic technology has also attracted people’s attention. The application of holograms in the fields of art, science, and technology conforms to the trend of the times and will become an indispensable part of people’s life in the future. In this paper, it mainly studies the hologram to analyze its algorithm and production process and its application prospects.

This article discusses a class SIQS epidemic model with constant input and nonlinear incidence, puts forward the equilibrium model and demonstrates the globally asymptotic stability of disease-free equilibrium and the endemic equilibrium.