Finite Groups as the Union of Proper Subgroups

2000 Mathematics Subject Classification: 20D60,20E15.As is known, if a finite solvable group G is an n-sum group then n − 1 is a prime power. It is an interesting problem in group theory to study for which numbers n with n-1 > 1 and not a prime power there exists a finite n-sum group. In this paper we mainly study finite nonsolvable n-sum groups and show that 15 is the first such number. More precisely, we prove that there exist no finite 11-sum or 13-sum groups and there is indeed a finite 15-sum group. Results by J. H. E. Cohn and M. J. Tomkinson are thus extended and further generalizations are possible

On linear groups of degrees at most ¦P¦ − 1

AbstractIn this paper, we determine the structure of complex linear groups G of degree at most ¦P¦ − 1, where P is a T.I. Sylow p-subgroup of G

Power system dynamic enhancement using phase imbalance series capacitive compensation and doubly fed induction generator-based wind farms

ABSTRACT Wind energy is among the fastest growing renewable energy technologies in the world that has been increasing by about 30% a year globally. Wind energy has proven to be a clean, abundant and completely renewable source of energy. Owing to the rapidly increasing use of wind power, the aspect of integrating high level of penetrations wind power into the grid is becoming more and more of reality. Examples of large wind farms in the United States are the 781.5 MW Roscoe wind farm in Texas, the 735.5 MW Horse Hollow Wind Energy Center in Taylor and Nolan County, Texas, the 845 MW Shepherds Flat wind farm in Oregon and the 1550 MW Alta wind farm being developed in California. As most large wind farms in North America employ Doubly-fed Induction Generator (DFIG) wind turbines, their voltage-sourced converter-based back-to-backs offer independent control of the real and reactive power. The use of these control capabilities have been recently proposed for damping power swings, inter-area oscillations as well as subsynchronous resonance. There is, however, a question that is always associated with the use of voltage-sourced converter -based back-to-back wind farms for damping power system oscillations: what happens when there is no wind? The keyword to the answer is “combined”. The potential benefit of using these types of wind farms for damping power system oscillations should always be combined with conventional damping devices (power system stabilizers, thyristor controlled series capacitor, static synchronous series compensator, high voltage dc systems, etc.). This thesis reports the results of digital time-domain simulation studies that are carried out to investigate the potential use of supplemental controls of DFIG-based wind farms combined with a phase imbalanced hybrid series capacitive compensation scheme for damping power system oscillations. The thesis also addresses the recent concern over the case of large share of wind power generation which results in reducing the total inertia of the synchronous generators and degrading the system transient stability. In this regards, the results of the investigations have shown that in such a case; properly designed supplemental controllers for the wind farm converters could be an asset in improving the system transient stability rather than degrading it. Time-domain simulations are conducted on a benchmark model using the ElectroMagnetic Transients program (EMTP-RV)

On the Diameter of a Graph Related to p-Regular Conjugacy Classes of Finite Groups

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A Computationally Efficient Bi-level Coordination Framework for CAVs at Unsignalized Intersections

In this paper, we investigate cooperative vehicle coordination for connected and automated vehicles (CAVs) at unsignalized intersections. To support high traffic throughput while reducing computational complexity, we present a novel collision region model and decompose the optimal coordination problem into two sub-problems: \textit{centralized} priority scheduling and \textit{distributed} trajectory planning. Then, we propose a bi-level coordination framework which includes: (i) a Monte Carlo Tree Search (MCTS)-based high-level priority scheduler aims to find high-quality passing orders to maximize traffic throughput, and (ii) a priority-based low-level trajectory planner that generates optimal collision-free control inputs. Simulation results demonstrate that our bi-level strategy achieves near-optimal coordination performance, comparable to state-of-the-art centralized strategies, and significantly outperform the traffic signal control systems in terms of traffic throughput. Moreover, our approach exhibits good scalability, with computational complexity scaling linearly with the number of vehicles. Video demonstrations can be found online at \url{https://youtu.be/WYAKFMNnQfs}