Double-tower Solutions for Higher Order Prescribed Curvature Problem

We consider the following higher order prescribed curvature problem on ${\mathbb{S}}^N :$ \begin{equation*} D^m \tilde u=\widetilde{K}(y) \tilde u^{m^{*}-1} \quad \mbox{on} \ {\mathbb {S}}^N, \qquad \tilde u >0 \quad \mbox{in} \ {\mathbb {S}}^N. \end{equation*} where $\widetilde{K}(y)>0$ is a radial function, $m^{*}=\frac{2N}{N-2m}$ and $D^m$ is $2m$ order differential operator given by \begin{equation*} D^m=\prod_{i=1}^m\left(-\Delta_g+\frac{1}{4}(N-2i)(N+2i-2)\right), \end{equation*} where $g=g_{{\mathbb{S}}^N}$is the Riemannian metric. We prove the existence of infinitely many double-tower type solutions, which are invariant under some non-trivial sub-groups of $O(3),$ and their energy can be made arbitrarily large.Comment: 34 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2205.14482 by other author

Collecting: a way of exploring the difficulty to leave game world

Digital games have become a part of daily life for people in recent years. they have the capacity of making game users set playing games as top priority in daily life. In this sense, playing digital games can break the balance between the virtual and the reality and it is possible that some people may get lost in the virtual world. However, this thesis argues that it can be inappropriate just equating excessive play with addiction. By discussing and connecting previous literature reviews on games and addiction, as well as adding three game case studies, this thesis finally finds collecting as a different approach to explore the difficulty to leave game world. Through discussing in-game collecting and book collecting in ancient China, this thesis helps answer how people understand the heavy use on digital games and what is hidden behind choosing to stay in game world

Flame Retardant Polymer Nanocomposites and Interfaces

The flame retardant efficiency of polymer nanocomposites is highly dependent on the dispersion of the nano-fillers within the polymer matrix. In order to control the filler dispersion, it is very essential to explore the interfacial compatibility between fillers and matrices, which provides a guide for the flame retardant nanocomposites compounding. In this short review, we mainly focus on the thermoplastic polymers and their interactions with the surfaces of the flame retardant fillers. Other physical properties of those nanocomposites such as mechanical properties, gas permeability, rheological performance and thermal conductivity are also briefly reviewed along with the flame retardancy, since they are all dispersion related

Buddhist monasteries facilitated landscape conservation on the Qinghai-Tibetan Plateau

Context: The Sanjiangyuan region of the Qinghai-Tibetan Plateau—also known as the “Three Rivers’ Headwaters”—is the origin of the Yellow, Yangtze, and Mekong Rivers and therefore the key water source for hundreds of millions of downstream residents. Protecting this region’s ecosystems is a key priority for sustainable development in China and Asia. An important social dimension of Sanjiangyuan is the long-established and widespread presence of Tibetan Buddhism, particularly as manifested in the large number of monasteries throughout the region. However, the influence of cultural factors on environmental change remains largely understudied here. / Objective: We focus on two types of spatial associations—point-point and point-area features—to quantitatively investigate the effects of Buddhist monasteries on land use/cover change (LUCC) in surrounding landscapes. / Methods: We conduct a spatially-explicit analysis of Sanjiangyuan for two periods, 1990–2000 and 2010–2015, to identify and quantify the influence of the presence and spatial distributions of Buddhist monasteries on LUCC compared to village communities that lack monasteries. / Results: We found that the presence of monasteries is highly correlated with the preservation of natural ecosystems, specifically of grasslands and forests. Within monastery buffer zones with radii between 1 and 10 km, 7.13–9.30% more grassland area and 7.14–7.47% more forest area remained around monasteries compared to villages. This contrast decreased with increasing distance to the monastery/village. Overall, built-up areas were also much smaller around monasteries than around villages, while unused land was more commonly transformed to forests and grasslands around monasteries. / Conclusions: These findings strongly support the idea that Buddhist culture, as manifested through its physical institutions and communities, are instrumental in achieving desired landscape conservation outcomes