Accurate gradient computations at interfaces using finite element methods

New finite element methods are proposed for elliptic interface problems in one and two dimensions. The main motivation is not only to get an accurate solution but also an accurate first order derivative at the interface (from each side). The key in 1D is to use the idea from \cite{wheeler1974galerkin}. For 2D interface problems, the idea is to introduce a small tube near the interface and introduce the gradient as part of unknowns, which is similar to a mixed finite element method, except only at the interface. Thus the computational cost is just slightly higher than the standard finite element method. We present rigorous one dimensional analysis, which show second order convergence order for both of the solution and the gradient in 1D. For two dimensional problems, we present numerical results and observe second order convergence for the solution, and super-convergence for the gradient at the interface

Culture shapes how we look: Comparison between Chinese and African university students

Previous cross-cultural studies find that cultures can shape how we look during scene perception, but don’t mention its condition and limited to the East and West. This study recruited Chinese and African students to testify the cultural effects on two phases. In free-viewing phase: Africans fixated more on the focal objects than Chinese, while Chinese payed more attention to the backgrounds than Africans especially on the first fourth and fifth fixations. In recognition phase, there was no cultural difference on perception, but Chinese recognized more objects than Africans. Based on chosen subjects, we conclude that cultural differences exit on scene perception under conditions of no task and more clearly in its later period, but that differences may be hidden in a deeper way (e.g. memory) in task condition

Multicell Edge Coverage Enhancement Using Mobile UAV-Relay

Unmanned aerial vehicle (UAV)-assisted communication is a promising technology in future wireless communication networks. UAVs can not only help offload data traffic from ground base stations (GBSs) but also improve the Quality of Service (QoS) of cell-edge users (CEUs). In this article, we consider the enhancement of cell-edge communications through a mobile relay, i.e., UAV, in multicell networks. During each transmission period, GBSs first send data to the UAV, and then the UAV forwards its received data to CEUs according to a certain association strategy. In order to maximize the sum rate of all CEUs, we jointly optimize the UAV mobility management, including trajectory, velocity, and acceleration, and association strategy of CEUs to the UAV, subject to minimum rate requirements of CEUs, mobility constraints of the UAV, and causal buffer constraints in practice. To address the mixed-integer nonconvex problem, we transform it into two convex subproblems by applying tight bounds and relaxations. An iterative algorithm is proposed to solve the two subproblems in an alternating manner. Numerical results show that the proposed algorithm achieves higher rates of CEUs as compared with the existing benchmark schemes