In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It ...In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.展开更多
A fractional matching of a graph G is a function f: E(G)→[0,1] such that for each vertex v, ∑eϵΓG(v)f(e)≤1.. The fractional matching number of G is the maximum value of ∑e∈E(G)f(e) over all fractional matchings ...A fractional matching of a graph G is a function f: E(G)→[0,1] such that for each vertex v, ∑eϵΓG(v)f(e)≤1.. The fractional matching number of G is the maximum value of ∑e∈E(G)f(e) over all fractional matchings f. Tian et al. (Linear Algebra Appl 506:579–587, 2016) determined the extremal graphs with minimum distance Laplacian spectral radius among n-vertex graphs with given matching number. However, a natural problem is left open: among all n-vertex graphs with given fractional matching number, how about the lower bound of their distance Laplacian spectral radii and which graphs minimize the distance Laplacian spectral radii? In this paper, we solve these problems completely.展开更多
To achieve accurate positioning of autonomous underwater vehicles, an appropriate underwater terrain database storage format for underwater terrain-matching positioning is established using multi-beam data as underwat...To achieve accurate positioning of autonomous underwater vehicles, an appropriate underwater terrain database storage format for underwater terrain-matching positioning is established using multi-beam data as underwater terrainmatching data. An underwater terrain interpolation error compensation method based on fractional Brownian motion is proposed for defects of normal terrain interpolation, and an underwater terrain-matching positioning method based on least squares estimation（LSE） is proposed for correlation analysis of topographic features. The Fisher method is introduced as a secondary criterion for pseudo localization appearing in a topographic features flat area, effectively reducing the impact of pseudo positioning points on matching accuracy and improving the positioning accuracy of terrain flat areas. Simulation experiments based on electronic chart and multi-beam sea trial data show that drift errors of an inertial navigation system can be corrected effectively using the proposed method. The positioning accuracy and practicality are high, satisfying the requirement of underwater accurate positioning.展开更多
对于环境中存在的各种类型能量源,其往往具有不同的阻抗特性以及输出功率范围。为了提高能量收集系统的能量萃取能力,合理的接口电路设计是关键。基于此,通过对环境中光伏(Photovoltaic,PV)能量源微弱直流特性以及高效率收集和转化的研...对于环境中存在的各种类型能量源,其往往具有不同的阻抗特性以及输出功率范围。为了提高能量收集系统的能量萃取能力,合理的接口电路设计是关键。基于此,通过对环境中光伏(Photovoltaic,PV)能量源微弱直流特性以及高效率收集和转化的研究,在传统开路电压法(Open-Circuit Voltage,OCV)的基础上,结合输入电压纹波控制,提出了一种可实时最大功率点追踪(Maximum Power Point Tracking,MPPT)的预估算法。该预估算法根据能量源的输出特性,采用了分数开路电压法(Fractional Open-Circuit Voltage,FOCV),并根据纹波大小动态调节变换器的工作模式,实现阻抗匹配。为了尽可能减小因采样带来的能量损失,采用可片上全集成的较小的采样电容,并逐周期的进行开路电压采样和计算,实现了对源功率变化的高精度追踪。仿真结果表明,所提出的追踪算法能够实时监测能量源的状态,具有高的追踪速度和追踪精度,且采样时间仅需100 ns。能量源功率在1μW~10 mW范围内变化时,最短的追踪时间仅需4.37μs,追踪精度可达99.7%。展开更多
文摘In this paper, we consider the relationship between the binding number and the existence of fractional k-factors of graphs. The binding number of G is defined by Woodall as bind(G)=min{ | NG(X) || X |:∅≠X⊆V(G) }. It is proved that a graph G has a fractional 1-factor if bind(G)≥1and has a fractional k-factor if bind(G)≥k−1k. Furthermore, it is showed that both results are best possible in some sense.
基金This work is supported by the Science and Technology Program of Guangzhou,China(No.202002030183)the Guangdong Province Natural Science Foundation(No.2021A1515012045)the Qinghai Province Natural Science Foundation(No.2020-ZJ-924).
文摘A fractional matching of a graph G is a function f: E(G)→[0,1] such that for each vertex v, ∑eϵΓG(v)f(e)≤1.. The fractional matching number of G is the maximum value of ∑e∈E(G)f(e) over all fractional matchings f. Tian et al. (Linear Algebra Appl 506:579–587, 2016) determined the extremal graphs with minimum distance Laplacian spectral radius among n-vertex graphs with given matching number. However, a natural problem is left open: among all n-vertex graphs with given fractional matching number, how about the lower bound of their distance Laplacian spectral radii and which graphs minimize the distance Laplacian spectral radii? In this paper, we solve these problems completely.
基金financially supported by the National Natural Science Foundation of China(Grant Nos.51179035 and 51279221)the Natural Science Foundation of Heilongjiang Province(Grant No.E201121)
文摘To achieve accurate positioning of autonomous underwater vehicles, an appropriate underwater terrain database storage format for underwater terrain-matching positioning is established using multi-beam data as underwater terrainmatching data. An underwater terrain interpolation error compensation method based on fractional Brownian motion is proposed for defects of normal terrain interpolation, and an underwater terrain-matching positioning method based on least squares estimation（LSE） is proposed for correlation analysis of topographic features. The Fisher method is introduced as a secondary criterion for pseudo localization appearing in a topographic features flat area, effectively reducing the impact of pseudo positioning points on matching accuracy and improving the positioning accuracy of terrain flat areas. Simulation experiments based on electronic chart and multi-beam sea trial data show that drift errors of an inertial navigation system can be corrected effectively using the proposed method. The positioning accuracy and practicality are high, satisfying the requirement of underwater accurate positioning.
文摘对于环境中存在的各种类型能量源,其往往具有不同的阻抗特性以及输出功率范围。为了提高能量收集系统的能量萃取能力,合理的接口电路设计是关键。基于此,通过对环境中光伏(Photovoltaic,PV)能量源微弱直流特性以及高效率收集和转化的研究,在传统开路电压法(Open-Circuit Voltage,OCV)的基础上,结合输入电压纹波控制,提出了一种可实时最大功率点追踪(Maximum Power Point Tracking,MPPT)的预估算法。该预估算法根据能量源的输出特性,采用了分数开路电压法(Fractional Open-Circuit Voltage,FOCV),并根据纹波大小动态调节变换器的工作模式,实现阻抗匹配。为了尽可能减小因采样带来的能量损失,采用可片上全集成的较小的采样电容,并逐周期的进行开路电压采样和计算,实现了对源功率变化的高精度追踪。仿真结果表明,所提出的追踪算法能够实时监测能量源的状态,具有高的追踪速度和追踪精度,且采样时间仅需100 ns。能量源功率在1μW~10 mW范围内变化时,最短的追踪时间仅需4.37μs,追踪精度可达99.7%。
