Simple mathematical expressions are given for the betweenness centrality of nodes in trees, forests and cycles. As application, a centrality test is given for when a network might be a forest.

In recent years, the rapid development of technologies such as virtual reality, augmented reality, and mixed reality, along with the significant increase in publications related to the Metaverse, demonstrates a sustained growth in interest in this field. Some scholars have already performed bibliometric analyses of this emerging field. However, previous analyses have not been comprehensive due to limitations such as the volume of literature, particularly lacking in co-citation analysis, which is crucial for understanding the interconnectedness and impact of research works. In this study, we used the Web of Science as a database to search for topics related to the Metaverse from 1995 to 2023. Subsequently, we employed CiteSpace for co-citation network analysis to supplement previous research. Through our analysis at the journal, author, and literature levels, we identified core journals and key authors in the Metaverse field. We discovered that Extended Reality (XR), education, user privacy, and terminologies related to the Metaverse are significant research themes within the field. This study provides clear and actionable research directions for future papers in the Metaverse field.

Yunnan is rich in cultural heritage, with its primitive pottery techniques coexisting with modern pottery techniques, and is known as the “Museum of Ceramic History”. Due to regional and socio-economic development factors, some folk pottery and craftsmen have faded out of sight or only circulated in a few small areas and specific environments. The study analyzes and summarizes the characteristics of Yunnan folk pottery and industry and evaluates the Yunnan folk pottery value based on the conditional valuation method. The study takes the folk pottery of the Bai nationality in Dali, Yunnan as an example and obtains the evaluation results of the purchasing motivation value of the pottery through a questionnaire survey. 45.26% of people pay for their existence value, 26.03% pay for their choice value, and 28.71% pay for their legacy value. Based on the evaluation results, the study proposes targeted activation paths for Yunnan folk pottery, including innovative development combined with new technologies, highlighting the functional characteristics of pottery, and brand building. This study will help Yunnan folk pottery find more suitable ways of protection and inheritance in the rapid development of materials and technology. This study can help inheritors gain the possibility of sustainable development and provide reference value for the activation path of other traditional folk.

Tropical dry forests are complex and fragile ecosystems with high anthropogenic intervention and restricted reproductive cycles. They harbor unique richness, structural, physiological and phenological diversity. This research was carried out in the upper Magdalena valley, in four forest fragments with different successional stages. In each fragment, four permanent plots of 0.25 ha were established and the light habitat associated with species richness, relative abundance and rarity was evaluated, as well as the forest dynamics that included mortality, recruitment and diameter growth for a period of 5.25 years. In mature riparian forest, species richness was found to be higher than that reported in other studies for similar areas in the Cauca Valley and the Atlantic coast. Values of species richness, heterogeneity and rarity are higher than those found in drier areas of Tolima. Forest structure, diversity and dynamics were correlated with light habitat, showing differences in canopy architecture and its role in the capture and absorption of radiation. The utilization rate of photosynthetic effective radiation in the forest underlayer with high canopy density is low, which is related to the low species richness, while the underlayer under light is more abundant and heterogeneous.

In view of the large energy consumption of the regeneration process in the chemical absorption decarburization process, on the basis of the enrichment classification flow process, the nanoscale ceramic film is used as a new heat exchanger between the enriched liquid and the regeneration gas. The porous ceramic film is capable of coupling thermal-mass transfer to effectively recover part of the water vapor and the heat carried in the regeneration gas, so as to reduce the regenerative energy consumption of the system. The effects of parameters such as regeneration temperature, flow rate, molar fraction of water vapor, and MEA enrichment temperature, flow rate, and MEA concentration of shunt on the hydrothermal recovery effect of ceramic membranes of different pore sizes and lengths were studied by using the heat recovery flux and water recovery rate as the indicators. The results show that the hydrothermal recovery performance of the ceramic membrane increases with the increase of MEA enrichment flow, but decreases significantly with the increase of the enrichment temperature. At the same time, with the increase of regenerative gas velocity and the molar fraction of water vapor in the regenerative gas, the heat recovery flux will increase. The heat recovery performance of the 10 nm ceramic membrane is better than that of the 20 nm ceramic membrane.

Due to its physicochemical properties, nanoparticles titanium dioxide (nTiO₂) is being put into mass production and widespread applications, which inevitably results in their increasing exposure to the water body. After it entering the water body, the chemical properties of nTiO₂ can be influenced by ion compositions, ion strength and pH, which affects their ecological risk. Excess of ammonium (NH₄⁺) fertilizer has contaminated soil and water environments. In this paper, the Zeta potentials and hydrodynamic radius of nTiO₂ were studied in NH₄⁺ solution compared to those in Na⁺ solution. In addition, the sedimentation rate of nTiO₂ was also investigated. The experiment results show that high pH inhibits the sedimentation of nTiO₂. Moreover, NH₄⁺ increases the stability of nTiO₂ more than Na⁺ at the same IS, which was attributed the more negative Zeta potentials and the smaller hydraulic radius. Our results provide a theoretical basis for evaluating the ecological risk of nTiO₂ in aqueous solution containing NH₄⁺.