The flavor and quark mass dependence of the in-medium q→qg, g→gg, q→gq, g→qq¯ processes is fully captured by the light-front wavefunction formalism and the color representation of the parent and daughter partons. Our splitting functions results are presented as iterative solutions to matrix equations with initial conditions set by the leading order branchings in the vacuum. In this Letter we report the first calculation of all O(αs) medium-induced branching processes to any order in opacity. It is demonstrated through simulation results that the proposed joint optimization algorithm is converges fast and shows significant improvement in terms of the sum-rate, fairness, access latency, and system capacity. By leveraging an alternating descent approach, a joint optimal solution can be obtained after a finite number of iterations. Meanwhile, a multi-level water-filling method is proposed for power allocation. Specifically, an improved Kuhn-Munkras (KM) algorithm based on graph theory is proposed for RB allocation, which guarantees the fairness. To address the formulated problem, we propose a graph-based joint optimization algorithm for resource block (RB) and power allocation. Aiming at maximizing the overall capacity of downlink transmission in an AGIN, we formulate the resource allocation problem as an optimization problem subject to both quality of service (QoS) and fairness requirements.

Motivated by this fact, we propose a novel architecture of air-ground integrated networks (AGIN), which leverages civil aircrafts and ground base stations to support terrestrial users’ service. Due to heterogeneous characteristics of different layers, it is necessary to perform efficient resource allocation. With the combined advantages of satellite communications, aerial networks and terrestrial systems, a space-air-ground integrated network has gradually become a promising architecture for the next generation wireless communication. The findings of this study are essential for resource managers to comprehend the meaning and use of reserved resources that can be utilized in small quantities to avoid resource allocation deadlocks. The essential edges, or resource demands, necessary to ensure a smooth, deadlock-free processing are identified. After getting the deadlock cycles, those edges are identified using a matrix operation, which may be deleted or postponed for a fixed period in order to prevent deadlock or locate other allocations. The ranking of vertices based on centralities is used to identify cycles with the potential to generate deadlocks. Furthermore, centrality metrics have been utilized to find cycles in the graph and after the cycles have been acquired those cycles with potential deadlocks have been found. The graph's edges have been collected as ordered pairs, with each ordered pair denoting a process’s request either for any resource or for a process's allocation of resources.

The set of resources and processes are combined in this work to provide the set of vertices for a directed graph. The purpose of this research is to provide a graph theoretic technique for allocating resources to processes in order to avoid deadlocks. Resources are necessary for process management because they enable computational methodologies and functions and offer crucial hard and soft frameworks that aid in improved process management. Processes are the actions that various components take in order to conduct analysis and deal with massive databases. Resources and Processes are two elements of the computational approach that make large-scale data analytics applications for databases and database management systems possible.

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