DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improve...DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improves the results of[Discrete Math.,2018,341(7):1983–1986]and[Discrete Appl.Math.,2020,277:245–251].展开更多
In order to obtain the accurate sonic conductance of solenoid valves, the polytropic exponent is used in the data processing of the discharge method for measuring the flow rate characteristics of pneumatic components....In order to obtain the accurate sonic conductance of solenoid valves, the polytropic exponent is used in the data processing of the discharge method for measuring the flow rate characteristics of pneumatic components. Three data processing principles are first introduced, and then the discharge pressure data obtained from the measured solenoid valve are processed to obtain the sonic conductance with three methods： the partial polytropic exponent method, the complete polytropic exponent method and the adiabatic method. By comparison of the obtained results it indicates that the complete polytropic exponent method is the most accurate. However, the partial polytropic exponent method is of a high applicable value, because it is easy and simple to measure and the obtained results are relatively accurate.展开更多
In this paper,nitrogen dielectric barrier discharge（DBD） plasma was generated in a quartz tube with coaxial wire-cylinder electrodes at atmospheric pressure.By varying the nitrogen gas flow（FN） in the range of 0-1...In this paper,nitrogen dielectric barrier discharge（DBD） plasma was generated in a quartz tube with coaxial wire-cylinder electrodes at atmospheric pressure.By varying the nitrogen gas flow（FN） in the range of 0-1 m3/h,the plasma optical emission spectra（OES） were measured and studied.The vibration（T_（vib）） and rotation temperature（T_（rot）） of nitrogen were obtained,by fitting the rovibronic bands of N_2（C^3∏_u-B^3∏_g,0-1）,and by the Boltzmann plot method for purposes of comparison.T_（vib） increased up to 2481 K with increasing nitrogen flow till0.2 m3/h,and then decreased with further increasing FN,while Trot decreased monotonously and approached to-350 K for FN ≥ 0.6 m^3/h.The intensity of N_2（C^3∏_u-B^3∏_g,0-0,1-0,0-3） and N_2~＋（B^2∑_u~＋-X^2Σ_g~＋,0-0） exhibited similar evolution with increasing FN to those of the T_（vib） and Trot,respectively.The discharge photos revealed that the discharge filaments gradually decreased with increasing FN,and eventually disappeared,which implied that a discharge mode transition emerged with increasing FN.The possible mechanism for the discharge mode transition is studied in detail according to the vibration（T_（vib）） and rotation temperature（T_（rot）） of nitrogen.展开更多
Given a simple graph G=(V,E)and its(proper)total coloringϕwith elements of the set{1,2,⋯,k},let wϕ(v)denote the sum of the color of v and the colors of all edges incident with v.If for each edge uv∈E,wϕ(u)≠wϕ(v),we ...Given a simple graph G=(V,E)and its(proper)total coloringϕwith elements of the set{1,2,⋯,k},let wϕ(v)denote the sum of the color of v and the colors of all edges incident with v.If for each edge uv∈E,wϕ(u)≠wϕ(v),we callϕa neighbor sum distinguishing total coloring of G.Let L={Lx∣x∈V⋃E}be a set of lists of real numbers,each of size k.The neighbor sum distinguishing total choosability of G is the smallest k for which for any specified collection of such lists,there exists a neighbor sum distinguishing total coloring using colors from Lx for each x∈V⋃E,and we denote it by[Math Processing Error].The known results of neighbor sum distinguishing total choosability are mainly about planar graphs.In this paper,we focus on 1-planar graphs.A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge.We prove that[Math Processing Error]for any 1-planar graph G withΔ≥15,whereΔis the maximum degree of G.展开更多
A neighbor sum distinguishing(NSD)total coloringφof G is a proper total coloring of G such thatΣz∈EG(u)U{u}φ(z)≠Σz∈EG(v)U{v}φ(z)for each edge uv∈E(G),where EG(u)is the set of edges incident with a vertex u.In...A neighbor sum distinguishing(NSD)total coloringφof G is a proper total coloring of G such thatΣz∈EG(u)U{u}φ(z)≠Σz∈EG(v)U{v}φ(z)for each edge uv∈E(G),where EG(u)is the set of edges incident with a vertex u.In 2015,Pilśniak and Wozniak conjectured that every graph with maximum degreeΔhas an NSD total(Δ+3)-coloring.Recently,Yang et al.proved that the conjecture holds for planar graphs withΔ≥10,and Qu et al.proved that the list version of the conjecture also holds for planar graphs withΔ≥13.In this paper,we improve their results and prove that the list version of the conjecture holds for planar graphs withΔ≥10.展开更多
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we verify the total coloring conjecture for every 1-planar graph G if either △（G） ≥9 and g...A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we verify the total coloring conjecture for every 1-planar graph G if either △（G） ≥9 and g（G）≥ 4, or △（G） ≥ 7 and g（G）≥5, where △（G） is the maximum degree of G and g（G） is the girth of G.展开更多
A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G with maximum degree △（G） 〉 12 and girth at least five...A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G with maximum degree △（G） 〉 12 and girth at least five is totally （△（G）＋1）-colorable.展开更多
This paper presents a smart electrical car park model where the power flows among electrical vehicles(EVs)as well as between EVs and the main grid.Based on this model,an optimal charging/discharging scheme is proposed...This paper presents a smart electrical car park model where the power flows among electrical vehicles(EVs)as well as between EVs and the main grid.Based on this model,an optimal charging/discharging scheme is proposed.The fluctuation of hourly electricity rates is considered in this strategy to select a proper charging/discharging rate for each EV with less expenditure during each charging period.The proposed smart electrical car park is able to buy or sell electricity in the form of active and/or reactive power,i.e.kWh and/or kVARh,from or to the main grid to improve the power quality.According to the current state of charge of the EV’s battery bank,customers and the grid demands,a control center makes the decisions and sends the instructions of specific charging/discharging mode to each charging station.The performance of the proposed charging/discharging algorithm is simulated in Matlab.A comparison between the proposed and the unregulated charging/discharging strategies has been implemented.The results demonstrate that the proposed scheme can achieve better economic profits for EV customers and increase the commercial benefits for the car park owner.展开更多
Given a graph G=(V,E)and a positive integer k,a k-total-coloring of G is a mappingφ:V⋃E→{1,2,⋯,k}such that no two adjacent or incident elements receive the same color.The central problem of the total-colorings is th...Given a graph G=(V,E)and a positive integer k,a k-total-coloring of G is a mappingφ:V⋃E→{1,2,⋯,k}such that no two adjacent or incident elements receive the same color.The central problem of the total-colorings is the Total Coloring Conjecture,which asserts that every graph of maximum degreeΔadmits a(Δ+2)-total-coloring.More precisely,this conjecture has been verified forΔ≤5,and it is still open whenΔ=6,even for planar graphs.Let mad(G)denote the maximum average degree of the graph G.In this paper,we prove that every graph G withΔ(G)=6 and mad(G)<23/5 admits an 8-total-coloring.展开更多
基金Partially supported by NSFC(No.12301436)NSF of Guangxi Province(No.2025GXNSFAA069811)。
文摘DP-coloring as a generalization of list coloring was introduced recently by Dvo˘r´ak and Postle.In this paper,we show that planar graphs without 5-cycles adjacent to two triangles are DP-4-colorable,which improves the results of[Discrete Math.,2018,341(7):1983–1986]and[Discrete Appl.Math.,2020,277:245–251].
文摘In order to obtain the accurate sonic conductance of solenoid valves, the polytropic exponent is used in the data processing of the discharge method for measuring the flow rate characteristics of pneumatic components. Three data processing principles are first introduced, and then the discharge pressure data obtained from the measured solenoid valve are processed to obtain the sonic conductance with three methods： the partial polytropic exponent method, the complete polytropic exponent method and the adiabatic method. By comparison of the obtained results it indicates that the complete polytropic exponent method is the most accurate. However, the partial polytropic exponent method is of a high applicable value, because it is easy and simple to measure and the obtained results are relatively accurate.
基金supported by National Natural Science Foundation of China(Nos.11475040,11375041)the Fundamental Research Funds for the Central Universities(No.DUT14ZD[G]04)
文摘In this paper,nitrogen dielectric barrier discharge（DBD） plasma was generated in a quartz tube with coaxial wire-cylinder electrodes at atmospheric pressure.By varying the nitrogen gas flow（FN） in the range of 0-1 m3/h,the plasma optical emission spectra（OES） were measured and studied.The vibration（T_（vib）） and rotation temperature（T_（rot）） of nitrogen were obtained,by fitting the rovibronic bands of N_2（C^3∏_u-B^3∏_g,0-1）,and by the Boltzmann plot method for purposes of comparison.T_（vib） increased up to 2481 K with increasing nitrogen flow till0.2 m3/h,and then decreased with further increasing FN,while Trot decreased monotonously and approached to-350 K for FN ≥ 0.6 m^3/h.The intensity of N_2（C^3∏_u-B^3∏_g,0-0,1-0,0-3） and N_2~＋（B^2∑_u~＋-X^2Σ_g~＋,0-0） exhibited similar evolution with increasing FN to those of the T_（vib） and Trot,respectively.The discharge photos revealed that the discharge filaments gradually decreased with increasing FN,and eventually disappeared,which implied that a discharge mode transition emerged with increasing FN.The possible mechanism for the discharge mode transition is studied in detail according to the vibration（T_（vib）） and rotation temperature（T_（rot）） of nitrogen.
基金supported by Guangdong Basic and Applied Basic Research Foundation(Natural Science Foundation of Guangdong Province,China,Grant No.2025A1515011904)the National Natural Science Foundation of China(Nos.12101285,12171222)+4 种基金the Natural Science Foundation of Xinjiang Uygur Autonomous Region(2016D01C006)Guangdong Philosophy and Social Sciences Planning Project(Grant No.GD22CXW01)Research Platforms and Projects of Colleges and Universities in Guangdong(Grant No.2022KTSCX071)Scientific Research Innovation Project of Lingnan Normal University(LT2401)Lingnan Normal University(No.LT2410).
文摘Given a simple graph G=(V,E)and its(proper)total coloringϕwith elements of the set{1,2,⋯,k},let wϕ(v)denote the sum of the color of v and the colors of all edges incident with v.If for each edge uv∈E,wϕ(u)≠wϕ(v),we callϕa neighbor sum distinguishing total coloring of G.Let L={Lx∣x∈V⋃E}be a set of lists of real numbers,each of size k.The neighbor sum distinguishing total choosability of G is the smallest k for which for any specified collection of such lists,there exists a neighbor sum distinguishing total coloring using colors from Lx for each x∈V⋃E,and we denote it by[Math Processing Error].The known results of neighbor sum distinguishing total choosability are mainly about planar graphs.In this paper,we focus on 1-planar graphs.A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge.We prove that[Math Processing Error]for any 1-planar graph G withΔ≥15,whereΔis the maximum degree of G.
基金supported by the National Natural Science Foundation of China (No.12271438, No.12071370 and U1803263)the Science Found of Qinhai Province (No.2022-ZJ-753)+2 种基金Shaanxi Fundamental Science Research Project for Mathematics and Physics (No.22JSZ009)Shangluo University Doctoral Initiation Fund Project(No.22SKY112)Shangluo University Key Disciplines Project (Discipline name:Mathematics)。
文摘A neighbor sum distinguishing(NSD)total coloringφof G is a proper total coloring of G such thatΣz∈EG(u)U{u}φ(z)≠Σz∈EG(v)U{v}φ(z)for each edge uv∈E(G),where EG(u)is the set of edges incident with a vertex u.In 2015,Pilśniak and Wozniak conjectured that every graph with maximum degreeΔhas an NSD total(Δ+3)-coloring.Recently,Yang et al.proved that the conjecture holds for planar graphs withΔ≥10,and Qu et al.proved that the list version of the conjecture also holds for planar graphs withΔ≥13.In this paper,we improve their results and prove that the list version of the conjecture holds for planar graphs withΔ≥10.
基金Supported by the scientific research program of Xinjiang Uygur Autonomous Region grant 2016D01C012 the Scientific Research Program(XJEDU2016I046)of the Higher Education Institution of Xinjiang
文摘A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we verify the total coloring conjecture for every 1-planar graph G if either △（G） ≥9 and g（G）≥ 4, or △（G） ≥ 7 and g（G）≥5, where △（G） is the maximum degree of G and g（G） is the girth of G.
基金supported by National Natural Science Foundation of China(Grant No.11271006)
文摘A graph is 1-planar if it can be drawn on the plane so that each edge is crossed by at most one other edge. In this paper, we prove that every 1-planar graph G with maximum degree △（G） 〉 12 and girth at least five is totally （△（G）＋1）-colorable.
文摘This paper presents a smart electrical car park model where the power flows among electrical vehicles(EVs)as well as between EVs and the main grid.Based on this model,an optimal charging/discharging scheme is proposed.The fluctuation of hourly electricity rates is considered in this strategy to select a proper charging/discharging rate for each EV with less expenditure during each charging period.The proposed smart electrical car park is able to buy or sell electricity in the form of active and/or reactive power,i.e.kWh and/or kVARh,from or to the main grid to improve the power quality.According to the current state of charge of the EV’s battery bank,customers and the grid demands,a control center makes the decisions and sends the instructions of specific charging/discharging mode to each charging station.The performance of the proposed charging/discharging algorithm is simulated in Matlab.A comparison between the proposed and the unregulated charging/discharging strategies has been implemented.The results demonstrate that the proposed scheme can achieve better economic profits for EV customers and increase the commercial benefits for the car park owner.
基金This work was supported by the National Natural Science Foundation of China(11471193,11631014)the Foundation for Distinguished Young Scholars of Shandong Province(JQ201501)the Fundamental Research Funds of Shandong University and Independent Innovation Foundation of Shandong University(IFYT14012).
文摘Given a graph G=(V,E)and a positive integer k,a k-total-coloring of G is a mappingφ:V⋃E→{1,2,⋯,k}such that no two adjacent or incident elements receive the same color.The central problem of the total-colorings is the Total Coloring Conjecture,which asserts that every graph of maximum degreeΔadmits a(Δ+2)-total-coloring.More precisely,this conjecture has been verified forΔ≤5,and it is still open whenΔ=6,even for planar graphs.Let mad(G)denote the maximum average degree of the graph G.In this paper,we prove that every graph G withΔ(G)=6 and mad(G)<23/5 admits an 8-total-coloring.
