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

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

DAQE: Enhancing the Quality of Compressed Images by Finding the Secret of Defocus

Image defocus is inherent in the physics of image formation caused by the optical aberration of lenses, providing plentiful information on image quality. Unfortunately, the existing quality enhancement approaches for compressed images neglect the inherent characteristic of defocus, resulting in inferior performance. This paper finds that in compressed images, the significantly defocused regions are with better compression quality and two regions with different defocus values possess diverse texture patterns. These findings motivate our defocus-aware quality enhancement (DAQE) approach. Specifically, we propose a novel dynamic region-based deep learning architecture of the DAQE approach, which considers the region-wise defocus difference of compressed images in two aspects. (1) The DAQE approach employs fewer computational resources to enhance the quality of significantly defocused regions, while more resources on enhancing the quality of other regions; (2) The DAQE approach learns to separately enhance diverse texture patterns for the regions with different defocus values, such that texture-wise one-on-one enhancement can be achieved. Extensive experiments validate the superiority of our DAQE approach in terms of quality enhancement and resource-saving, compared with other state-of-the-art approaches