Fractional Statistics in terms of the r-Generalized Fibonacci Sequences

We develop the basis of the two dimensional generalized quantum statistical systems by using results on $r$-generalized Fibonacci sequences. According to the spin value $s$ of the 2d-quasiparticles, we distinguish four classes of quantum statistical systems indexed by $s=0,1/2:mod(1)$, $s=1/M:mod(1)$, $s=n/M:mod(1)$ and $0\leq s\leq 1:mod(1)$. For quantum gases of quasiparticles with $s=1/M:mod(1)$, $M\geq 2,$, we show that the statistical weights densities $\rho_M$ are given by the integer hierarchies of Fibonacci sequences. This is a remarkable result which envelopes naturally the Fermi and Bose statistics and may be thought of as an alternative way to the Haldane interpolating statistical method.Comment: Late

An Effective EMTR-Based High-Impedance Fault Location Method for Transmission Lines

This paper summarizes the electromagnetic time reversal (EMTR) technique for fault location, and further numerically validates its effectiveness when the fault impedance is negligible. In addition, a specific EMTR model considering the fault impedance is derived, and the correctness of the model derivation is verified by various calculation methods. Based on this, we found that when the fault impedance is large, the existing EMTR methods might fail to accurately locate the fault. We propose an EMTR method that improves the location effect of high-impedance faults by injecting double-ended signals simultaneously. Theoretical calculations show that this method can achieve accurate location for high-impedance faults. To further illustrate the effectiveness, the proposed method is compared with the existing EMTR methods and the most commonly used traveling wave-based method using wavelet transform. The simulation results show that the proposed double-ended EMTR method can effectively locate high-impedance faults, and it is more robust against synchronization errors compared to the traveling wave method. In addition, the proposed method does not require the knowledge or the a priori guess of the unknown fault impedance