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Dajun Liu,Guiqiu Wang,Xixian Luo,Hongming Yin,Yaochuan Wang 한국광학회 2016 Current Optics and Photonics Vol.20 No.6
The analytical expressions for a partially coherent flat-topped vortex hollow beam propagating in uniaxialcrystals orthogonal to the optical axis are derived, and the intensity and coherent vortex properties ofpartially coherent flat-topped vortex hollow beam propagation in uniaxial crystals orthogonal to the opticalaxis are analyzed by numerical examples. The influence of beam order parameter N, topological chargeM, the coherence length and the ratio of refractive indices ne/no of uniaxial crystals on the normalizedintensity distribution and coherent vortex of a partially coherent flat-topped vortex hollow beam propagatingin uniaxial crystals are discussed in detail.
Dajun Liu,Yaochuan Wang,Guiqiu Wang,Xixian Luo 한국광학회 2017 Current Optics and Photonics Vol.1 No.4
Based on the extended Huygens-Fresnel principle, the analytical propagation formulae for spectrallypartially coherent Gaussian Schell-model pulsed (SPGSMP) beams propagating in turbulent atmospherehave been derived. The influences of the parameters for turbulent atmosphere and SPGSMP beams onthe on-axis and off-axis spectral shift and degree of coherence for SPGSMP beams propagating in turbulentatmosphere have been analyzed, using numerical calculations. The obtained results have potential applicationsfor SPGSMP beams in free-space optical communication and laser lidar.
Spreading of a Lorentz-Gauss vortex beam propagating through oceanic turbulence
Dajun Liu,Hongming Yin,Guiqiu Wang,Yaochuan Wang 한국광학회 2019 Current Optics and Photonics Vol.3 No.2
Based on the extended Huygens-Fresnel principle, the analytical equation for a Lorentz-Gauss vortex beam propagating through oceanic turbulence has been derived. The spreading properties of a Lorentz-Gauss vortex beam propagating through oceanic turbulence are analyzed in detail using numerical examples. The results show that a Lorentz-Gauss vortex beam propagating through stronger oceanic turbulence will spread more rapidly, and the Lorentz-Gauss vortex beam with higher topological charge M will lose its initial dark center more slowly.
Distributed CSMA Algorithms for Link Scheduling in Multihop MIMO Networks Under SINR Model
Dajun Qian,Dong Zheng,Junshan Zhang,Shroff, N. B.,Changhee Joo IEEE 2013 IEEE/ACM transactions on networking Vol.21 No.3
<P>In this paper, we study distributed scheduling in multihop multiple-input-multiple-output (MIMO) networks. We first develop a “MIMO-pipe” model that provides the upper layers a set of rates and signal-to-interference-plus-noise ratio (SINR) requirements that capture the rate-reliability tradeoff in MIMO communications. The main thrust of this paper is then dedicated to developing distributed carrier sense multiple access (CSMA) algorithms for MIMO-pipe scheduling under the SINR interference model. We choose the SINR model over the extensively studied protocol-based interference models because it more naturally captures the impact of interference in wireless networks. The coupling among the links caused by the interference under the SINR model makes the problem of devising distributed scheduling algorithms very challenging. To that end, we explore the CSMA algorithms for MIMO-pipe scheduling from two perspectives. We start with an idealized continuous-time CSMA network, where control messages can be exchanged in a collision-free manner, and devise a CSMA-based link scheduling algorithm that can achieve throughput optimality under the SINR model. Next, we consider a discrete-time CSMA network, where the message exchanges suffer from collisions. For this more challenging case, we develop a “conservative” scheduling algorithm by imposing a more stringent SINR constraint on the MIMO-pipe model. We show that the proposed conservative scheduling achieves an efficiency ratio bounded from below.</P>
Dajun Liu,Yaochuan Wang,Guiqiu Wang,Hongming Yin 한국광학회 2016 Current Optics and Photonics Vol.20 No.1
Using coherence theory, the partially coherent flat-topped vortex hollow beam is introduced. The analyticalequation for propagation of a partially coherent flat-topped vortex hollow beam in turbulent atmosphereis derived, using the extended Huygens-Fresnel diffraction integral formula. The influence of coherencelength, beam order N, topological charge M, and structure constant of the turbulent atmosphere on theaverage intensity of this beam propagating in turbulent atmosphere are analyzed using numerical examples.
Homological properties of semi-Wakamatsu-tilting modules
Dajun Liu,Jiaqun Wei 대한수학회 2020 대한수학회보 Vol.57 No.3
For a fixed semi-Wakamatsu-tilting module $_{A}T$, we generalize the concepts of Auslander class, Bass class, and investigate many homological properties of such classes. Moreover, we establish an equivalence between the class of $\infty$-$T$-cotorsionfree modules and a subclass of the class of $T$-adstatic modules. Finally, a similar version of Auslander-Bridger approximation theorem and a nice property of relative cotranspose are obtained.
Dajun Liu,Jiaqun Wei 대한수학회 2020 대한수학회보 Vol.57 No.4
We introduce the concept of $S$-exchange rings to unify various subclass of exchange rings, where $S$ is a subset of the ring. Many properties on $S$-exchange rings are obtained. For instance, we show that a ring $R$ is clean if and only if $R$ is left $U(R)$-exchange, a ring $R$ is nil clean if and only if $R$ is left $(N(R)-1)$-exchange, and that a ring $R$ is $J$-clean if and only if $R$ is left $(J(R)-1)$-exchange. As a conclusion, we obtain a sufficient condition such that clean (nil clean property, respectively) can pass to corners and reprove that $J$-clean passes to corners by a different way.
HOMOLOGICAL PROPERTIES OF SEMI-WAKAMATSU-TILTING MODULES
Liu, Dajun,Wei, Jiaqun Korean Mathematical Society 2020 대한수학회보 Vol.57 No.3
For a fixed semi-Wakamatsu-tilting module <sub>A</sub>T, we generalize the concepts of Auslander class, Bass class, and investigate many homological properties of such classes. Moreover, we establish an equivalence between the class of ∞-T-cotorsionfree modules and a subclass of the class of T-adstatic modules. Finally, a similar version of Auslander-Bridger approximation theorem and a nice property of relative cotranspose are obtained.