Existence and asymptotic behavior of least energy sign-changing solutions for Schrodinger-Poisson systems with doubly critical exponents

In this paper, we are concerned with the following Schr\"{o}dinger-Poisson system with critical nonlinearity and critical nonlocal term due to the Hardy-Littlewood-Sobolev inequality \begin{equation}\begin{cases} -\Delta u+u+\lambda\phi |u|^3u =|u|^4u+ |u|^{q-2}u,\ \ &\ x \in \mathbb{R}^{3},\\[2mm] -\Delta \phi=|u|^5, \ \ &\ x \in \mathbb{R}^{3}, \end{cases} \end{equation} where $\lambda\in \mathbb{R}$ is a parameter and $q\in(2,6)$. If $\lambda\ge (\frac{q+2}{8})^2$ and $q\in(2,6)$, the above system has no nontrivial solution. If $\lambda\in (\lambda^*,0)$ for some $\lambda^*<0$, we obtain a least energy radial sign-changing solution $u_\lambda$ to the above system. Furthermore, we consider $\lambda$ as a parameter and analyze the asymptotic behavior of $u_\lambda$ as $\lambda\to 0^-$

catena-Poly[[trimeth­yl(4-sulfanylphen­yl)aza­nium] [(chloridocadmate)-di-μ-chlorido]]

The title compound, {(C9H14NS)[CdCl3]}n, consists of a linear [CdCl3]nn − polyanion and a trimeth­yl(4-sulfanylphen­yl)aza­nium cation. The CdII atom is penta­coordinated by four μ2-Cl atoms and one terminal Cl atom in a trigonal–bipyramidal geometry. The trigonal–bipyramidal units are linked by two opposite shared faces, giving rise to infinite [CdCl3]n chains parallel to the a axis. The cations surround the chain and are linked to them by S—H⋯Cl and C—H⋯Cl hydrogen bonds, forming a three-dimensional network

Cooperative Multi-Type Multi-Agent Deep Reinforcement Learning for Resource Management in Space-Air-Ground Integrated Networks

The Space-Air-Ground Integrated Network (SAGIN), integrating heterogeneous devices including low earth orbit (LEO) satellites, unmanned aerial vehicles (UAVs), and ground users (GUs), holds significant promise for advancing smart city applications. However, resource management of the SAGIN is a challenge requiring urgent study in that inappropriate resource management will cause poor data transmission, and hence affect the services in smart cities. In this paper, we develop a comprehensive SAGIN system that encompasses five distinct communication links and propose an efficient cooperative multi-type multi-agent deep reinforcement learning (CMT-MARL) method to address the resource management issue. The experimental results highlight the efficacy of the proposed CMT-MARL, as evidenced by key performance indicators such as the overall transmission rate and transmission success rate. These results underscore the potential value and feasibility of future implementation of the SAGIN

A Fractal Model for the Maximum Droplet Diameter in Gas-Liquid Mist Flow

Distribution characteristics of liquid droplet size are described using the fractal theory for liquid droplet size distribution in gas-liquid mist flow. Thereby, the fractal expression of the maximum droplet diameter is derived. The fractal model for maximum droplet diameter is obtained based on the internal relationship between maximum droplet diameter and the droplet fractal dimension, which is obtained by analyzing the balance between total droplet surface energy and total gas turbulent kinetic energy. Fractal model predictions of maximum droplet diameter agree with the experimental data. Maximum droplet diameter and droplet fractal dimension are both found to be related to the superficial velocity of gas and liquid. Maximum droplet diameter decreases with an increase in gas superficial velocity but increases with an increase in liquid superficial velocity. Droplet fractal dimension increases with an increase in gas superficial velocity but decreases with an increase in liquid superficial velocity. These are all consistent with the physical facts

Pressure Transient Analysis of Dual Fractal Reservoir

A dual fractal reservoir transient flow model was created by embedding a fracture system simulated by a tree-shaped fractal network into a matrix system simulated by fractal porous media. The dimensionless bottom hole pressure model was created using the Laplace transform and Stehfest numerical inversion methods. According to the model's solution, the bilogarithmic type curves of the dual fractal reservoirs are illustrated, and the influence of different fractal factors on pressure transient responses is discussed. This semianalytical model provides a practical and reliable method for empirical applications