This paper investigates data transmission in an Internet of Things (IoT) network, where multiple devices send environmental data to a remote base station through an unmanned aerial vehicle (UAV) relay. The UAV serves as an airborne intermediary that collects status information from distributed IoT devices (e.g., temperature readings in a real-time forest fire monitoring system) and forwards it to the base station. To capture the impact of data staleness, a novel Age of Information (AoI) and entropy-aware system loss is defined in terms of L-conditional cross-entropy, which quantifies the expected penalty caused by state misestimation. The scheduling problem, which aims to minimize the system loss defined by L-conditional cross-entropy, is formulated as a Restless Multi-Armed Bandit (RMAB) problem. By applying Lagrange relaxation, the objective function is decomposed into tractable sub-problems, enabling a low-complexity, gain-index-based scheduling strategy. Numerical simulations validate the effectiveness of the proposed algorithm in reducing the long-term average system loss. In particular, the gain-index-based policy achieves a significant reduction in average penalty compared to random, round-robin, periodic update, and MAX-AoI scheduling strategies, demonstrating its superior performance over these baselines.

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Owing to their high flexibility, autonomous operation, and rapid deployment capability, unmanned aerial vehicles (UAVs) serve as effective aerial platforms for sensing and communication in remote and time-critical scenarios. However, their limited onboard energy budget poses a significant bottleneck for sustained operations. This paper investigates an energy-efficient UAV-assisted integrated sensing and communication (ISAC) system, aiming to maximize the sensing energy efficiency (SEE), defined as the ratio of the total radar estimation rate to the total energy consumption. Unlike prior works focused solely on rate maximization or fairness, our design jointly optimizes the UAV’s 3D trajectory, task scheduling, and power allocation under kinematic and coverage constraints to maximize the SEE. To solve the formulated non-convex fractional programming problem, we propose an efficient iterative algorithm based on the Dinkelbach method and block coordinate descent (BCD). Simulation results demonstrate that the proposed scheme achieves a superior trade-off between sensing performance and energy consumption.

We prove new regularity criteria for a density-dependent incompressible Ginzburg–Landau–Navier–Stokes system with the Coulomb gauge in a bounded domain $\Omega \subset \mathbb R $.