Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satis...Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satisfies ∥V<sub>1</sub>∣ - ∣V<sub>2</sub>∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V<sub>1</sub>, V<sub>2</sub>) such that ∀v ∈ V<sub>1</sub>, at least half minuses one of the neighbors of v are in the V<sub>2</sub>;∀v ∈ V<sub>2</sub>, at least half minuses one of the neighbors of v are in the V<sub>1</sub>. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.展开更多
Ultra-high spectral purity lasers are of considerable research interests in numerous fields such as coherent optical communication,microwave photonics,distributed optical fiber sensing,gravitational wave detection,opt...Ultra-high spectral purity lasers are of considerable research interests in numerous fields such as coherent optical communication,microwave photonics,distributed optical fiber sensing,gravitational wave detection,optical clock,and so on.Herein,to deeply purify laser spectrum with compact size under normal condition,we propose a novel and practical idea to effectively suppress the spontaneous radiation of the laser cavity through weak external distributed perturbation.Subsequently,a laser configuration consisting of a main lasing cavity and an external distributed feedback cavity is proposed.The feedback signal with continuous spatio-temporal phase transition controlled by a distributed feedback structure is injected into the main cavity,which can deeply suppress the coupling rate from the spontaneous radiation to the stimulated emission and extremely purify the laser spectrum.Eventually,an ultra-narrow linewidth on-chip laser system with a side mode suppression ratio greater than 80 dB,an output linewidth of 10 Hz,and a relative intensity noise less than-150 dB/Hz is successfully obtained under normal conditions.The proposed concept in this work provides a new perspective for extreme regulation of laser parameters by using weak external distributed perturbation,which can be valid for various gain-type lasers with wide wavelength bands.展开更多
We study theoretically the effect of weak external magnetic fields on persistent spin helix states in semiconductor two-dimensional electron gases with both Rashba and linear-in-momentum Dresselhaus spin-orbit couplin...We study theoretically the effect of weak external magnetic fields on persistent spin helix states in semiconductor two-dimensional electron gases with both Rashba and linear-in-momentum Dresselhaus spin-orbit coupling.We show that in the presence of weak external magnetic fields, some basic properties of a persistent spin helix state,including the dispersion relation between the decay time and the magnitude of the wavevector, the maximum decay time and the value of the characteristic magnitude of the wavevector at which the maximum decay time occurs, will all depend sensitively on the directions of applied external magnetic fields.展开更多
文摘Let G be a graph. A bipartition of G is a bipartition of V (G) with V (G) = V<sub>1</sub> ∪ V<sub>2</sub> and V<sub>1</sub> ∩ V<sub>2</sub> = ∅. If a bipartition satisfies ∥V<sub>1</sub>∣ - ∣V<sub>2</sub>∥ ≤ 1, we call it a bisection. The research in this paper is mainly based on a conjecture proposed by Bollobás and Scott. The conjecture is that every graph G has a bisection (V<sub>1</sub>, V<sub>2</sub>) such that ∀v ∈ V<sub>1</sub>, at least half minuses one of the neighbors of v are in the V<sub>2</sub>;∀v ∈ V<sub>2</sub>, at least half minuses one of the neighbors of v are in the V<sub>1</sub>. In this paper, we confirm this conjecture for some bipartite graphs, crown graphs and windmill graphs.
基金supported by the National Natural Science Foundation of China(NSFC)(61635004)the National Science Fund for Distinguished Young Scholars(61825501)the Chongqing Natural Science Foundation of Innovative Research Groups under Grant(CSTC2020JCYJ,CXTTX0005)。
文摘Ultra-high spectral purity lasers are of considerable research interests in numerous fields such as coherent optical communication,microwave photonics,distributed optical fiber sensing,gravitational wave detection,optical clock,and so on.Herein,to deeply purify laser spectrum with compact size under normal condition,we propose a novel and practical idea to effectively suppress the spontaneous radiation of the laser cavity through weak external distributed perturbation.Subsequently,a laser configuration consisting of a main lasing cavity and an external distributed feedback cavity is proposed.The feedback signal with continuous spatio-temporal phase transition controlled by a distributed feedback structure is injected into the main cavity,which can deeply suppress the coupling rate from the spontaneous radiation to the stimulated emission and extremely purify the laser spectrum.Eventually,an ultra-narrow linewidth on-chip laser system with a side mode suppression ratio greater than 80 dB,an output linewidth of 10 Hz,and a relative intensity noise less than-150 dB/Hz is successfully obtained under normal conditions.The proposed concept in this work provides a new perspective for extreme regulation of laser parameters by using weak external distributed perturbation,which can be valid for various gain-type lasers with wide wavelength bands.
基金Supported by the National Natural Science Foundation of China under Grant No.10874049
文摘We study theoretically the effect of weak external magnetic fields on persistent spin helix states in semiconductor two-dimensional electron gases with both Rashba and linear-in-momentum Dresselhaus spin-orbit coupling.We show that in the presence of weak external magnetic fields, some basic properties of a persistent spin helix state,including the dispersion relation between the decay time and the magnitude of the wavevector, the maximum decay time and the value of the characteristic magnitude of the wavevector at which the maximum decay time occurs, will all depend sensitively on the directions of applied external magnetic fields.
