On reduced Arakelov divisors of real quadratic fields

We generalize the concept of reduced Arakelov divisors and define $C$-reduced divisors for a given number $C \geq 1$. These $C$-reduced divisors have remarkable properties which are similar to the properties of reduced ones. In this paper, we describe an algorithm to test whether an Arakelov divisor of a real quadratic field $F$ is $C$-reduced in time polynomial in $\log|\Delta_F|$ with $\Delta_F$ the discriminant of $F$. Moreover, we give an example of a cubic field for which our algorithm does not work.Comment: 18 page

Multi-source in DF cooperative networks with the PSR protocol based full-duplex energy harvesting over a Rayleigh fading channel: performance analysis

Due to the tremendous energy consumption growth with ever-increasing connected devices, alternative wireless information and power transfer techniques are important not only for theoretical research but also for saving operational costs and for a sustainable growth of wireless communications. In this paper, we investigate the multi-source in decode-and-forward cooperative networks with the power splitting protocol based full-duplex energy harvesting relaying network over a Rayleigh fading channel. In this system model, the multi-source and the destination communicate with each other by both the direct link and an intermediate helping relay. First, we investigate source selection for the best system performance. Then, the closed-form expression of the outage probability and the symbol error ratio are derived. Finally, the Monte Carlo simulation is used for validating the analytical expressions in connection with all main possible system parameters. The research results show that the analytical and simulation results matched well with each other.Web of Science68327526

Topological Lifshitz phase transition in effective model of QCD with chiral symmetry non-restoration

The topological Lifshitz phase transition is studied systematically within an effective model of QCD, in which the chiral symmetry, broken at zero temperature, is not restored at high temperature and/or baryon chemical potential. It is found that during phase transition the quark system undergoes a first-order transition from low density fully-gapped state to high density state with Fermi sphere which is protected by momentum-space topology. The Lifshitz phase diagram in the plane of temperature and baryon chemical potential is established. The critical behaviors of various equations of state are determined.Comment: 8 pages, 10 figure

Energy harvesting based two-way full-duplex relaying network over a Rician fading environment: performance analysis

Full-duplex transmission is a promising technique to enhance the capacity of communication systems. In this paper, we propose and investigate the system performance of an energy harvesting based two-way full-duplex relaying network over a Rician fading environment. Firstly, we analyse and demonstrate the analytical expressions of the achievable throughput, outage probability, optimal time switching factor, and symbol error ratio of the proposed system. In the second step, the effect of various parameters of the system on its performance is presented and investigated. In the final step, the analytical results are also demonstrated by Monte Carlo simulation. The numerical results proved that the analytical results and the simulation results agreed with each other.Web of Science68112311

Multisource power splitting energy harvesting relaying network in half-duplex system over block Rayleigh fading channel: System performance analysis

Energy harvesting and information transferring simultaneously by radio frequency (RF) is considered as the novel solution for green-energy wireless communications. From that point of view, the system performance (SP) analysis of multisource power splitting (PS) energy harvesting (EH) relaying network (RN) over block Rayleigh-fading channels is presented and investigated. We investigate the system in both delay-tolerant transmission (DTT), and delay-limited transmission (DLT) modes and devices work in the half-duplex (HD) system. In this model system, the closed-form (CF) expressions for the outage probability (OP), system throughput (ST) in DLT mode and for ergodic capacity (EC) for DTT mode are analyzed and derived, respectively. Furthermore, CF expression for the symbol errors ratio (SER) is demonstrated. Then, the optimal PS factor is investigated. Finally, a Monte Carlo simulation is used for validating the analytical expressions concerning with all system parameters (SP).Web of Science81art. no. 6