A digraph D is k-ordered if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a cycle C such that C encounters the vertices of S in the specified order.In particular,we say that D is k-ordered h...A digraph D is k-ordered if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a cycle C such that C encounters the vertices of S in the specified order.In particular,we say that D is k-ordered hamiltonian if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a hamiltonian cycle C such that the vertices of S are encountered on C in the specified order.In this paper,sufficient conditions for digraphs to be ordered and ordered hamiltonian have been given.展开更多
The strong product digraph G1■G2 is constructed by the known digraph G1 and G2 of small order. The digraph G1■G2 constructed by the strong product method contain G1 and G2 as its sub-graphs. Therefore, the topologic...The strong product digraph G1■G2 is constructed by the known digraph G1 and G2 of small order. The digraph G1■G2 constructed by the strong product method contain G1 and G2 as its sub-graphs. Therefore, the topological structure and properties of these small digraphs G1 and G2 must affect the topological structure and properties of the large digraph. By using group theory, we prove some algebraic properties of strong product of digraphs, such as commutative law, associative law and so on.展开更多
Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix...Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix A_(α)(D),which is defined as Aα(D)=αW(D)+(1−α)A(D),0≤α≤1.The spectral radius of A_(α)(D)is called the Aαspectral radius of D,denoted byλα(D).We obtain some upper bounds on the Aαspectral radius of strongly connected irregular weighted digraphs.展开更多
Concurrent engineering(CE)involves the consideration during the design phase of the various factors associated with the life cycle of the product.Using the principle of CE,a feature-based CAPP system is proposed.On th...Concurrent engineering(CE)involves the consideration during the design phase of the various factors associated with the life cycle of the product.Using the principle of CE,a feature-based CAPP system is proposed.On the basis of feature modeling,the system is able to reason feature relationships,produce feature digraph of a part,and decide the machining sequence of features.展开更多
Rational measuring design of the tree length is a course to optimize all position of it before bucking. This paper offers the weighted digraph in the digrams and theories to solve the optimal problem of rational measu...Rational measuring design of the tree length is a course to optimize all position of it before bucking. This paper offers the weighted digraph in the digrams and theories to solve the optimal problem of rational measuring of tree length based on experts researches in home and foreign. Sawlines are defined as apexes xd log between two sawlines as a side yn the price of log as weight Wij. It can describe the digraph of the rational measuring design of the tree length T=(X. Y.Wij), which consists of point -set and side-set. Oweing to Wij≥0, using Mr. E. W. Dijkstra's theory, we can obtain the 'path' of maximum profit of the tree length under the best availability of the tree length.展开更多
With the rapid development of machine learning,artificial neural networks provide a powerful tool to represent or approximate many-body quantum states.It was proved that every graph state can be generated by a neural ...With the rapid development of machine learning,artificial neural networks provide a powerful tool to represent or approximate many-body quantum states.It was proved that every graph state can be generated by a neural network.Here,we introduce digraph states and explore their neural network representations(NNRs).Based on some discussions about digraph states and neural network quantum states(NNQSs),we construct explicitly an NNR for any digraph state,implying every digraph state is an NNQS.The obtained results will provide a theoretical foundation for solving the quantum manybody problem with machine learning method whenever the wave-function is known as an unknown digraph state or it can be approximated by digraph states.展开更多
Maximizing the utilization of lithium-ion battery capacity is an important means to alleviate the range anxiety of electric vehicles.Battery pack inconsistency is the main limiting factor for improving battery pack ca...Maximizing the utilization of lithium-ion battery capacity is an important means to alleviate the range anxiety of electric vehicles.Battery pack inconsistency is the main limiting factor for improving battery pack capacity utilization,and poses major safety hazards to energy storage systems.To solve this problem,a maximum capacity utilization scheme based on a path planning algorithm is proposed.Specifically,the reconfigurable topology proposed is highly flexible and fault-tolerant,enabling battery pack consistency through alternating cell discharge and reducing the increased risk of short circuits due to relay error.The Dijkstra algorithm is used to find the optimal energy path,which can effectively remove faulty cells and find the current path with the best consistency of the battery pack and the lowest relay loss.Finally,the effectiveness of the scheme is verified by hardware-in-the-loop experiments,and the experimental results show that the state-of-charge SOC consistency of the battery pack at the end of discharge is increased by 34.18%,the relay energy loss is reduced by 0.16%,and the fault unit is effectively isolated.展开更多
In this paper, we consider the properties of iteration graphs over the unit group Z*n of the residue ring Z n associated with the maps x → x p and compute the average values of tails and cycles of those iteration gra...In this paper, we consider the properties of iteration graphs over the unit group Z*n of the residue ring Z n associated with the maps x → x p and compute the average values of tails and cycles of those iteration graphs.展开更多
In 2020,Alexander Grigor'yan,Yong Lin and Shing-Tung Yau[6]introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory.Based on the analytic ...In 2020,Alexander Grigor'yan,Yong Lin and Shing-Tung Yau[6]introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory.Based on the analytic torsion for digraphs introduced in[6],we consider the notion of weighted analytic torsion for vertex-weighted digraphs.For any non-vanishing real functions f and g on the vertex set,we consider the vertex-weighted digraphs with the weights(f;g).We calculate the(f;g)-weighted analytic torsion by examples and prove that the(f;g)-weighted analytic torsion only depend on the ratio f=g.In particular,if the weight is of the diagonal form(f;f),then the weighted analytic torsion equals to the usual(un-weighted)torsion.展开更多
A majority k-coloring of a digraph D with k colors is an assignment c:V(D)→{1,2,…,k},such that for every v∈V(D),we have c(w)=c(v)for at most half of all out-neighbors w∈N^(+)(v).For a natural number k≥2,a 1/k-maj...A majority k-coloring of a digraph D with k colors is an assignment c:V(D)→{1,2,…,k},such that for every v∈V(D),we have c(w)=c(v)for at most half of all out-neighbors w∈N^(+)(v).For a natural number k≥2,a 1/k-majority coloring of a digraph is a coloring of the vertices such that each vertex receives the same color as at most a 1/k proportion of its out-neighbours.Kreutzer,Oum,Seymour,van der Zypen and Wood proved that every digraph has a majority 4-coloring and conjectured that every digraph admits a majority 3-coloring.Gireao,Kittipassorn and Popielarz proved that every digraph has a 1/k-majority 2k-coloring and conjectured that every digraph admits a 1/k majority(2k-1)-coloring.We showed that every r-regular digraph D with r>36ln(2n)has a majority 3-coloring and proved that every digraph D with minimum outdegreeδ+>2k2(2k-1)/(k-1)^(2)ln2(n)[(2k-1)n]has a 1/k-majority(2k-1)-coloring.We showed that every r-regular digraph D with r>36ln(2n)has a majority 3-coloring and proved that every digraph D with minimum outdegreeδ+>,2k^(2)(2k-1)^(2)/(k-1)^(2)ln[(2k-1)n]has a 1/k-majority(2k-1)-coloring.And we also proved that every r-regular digraph D with r>3k^(2)(2k-1)/(k-1)^2ln(2n)has a 1/k-majority(2k-1)-coloring.展开更多
基金Foundation item： Supported by the National Natural Science Foundation of China（61070229） Supported by the Natural Science Foundation of Shanxi Province（2008011010）
文摘A digraph D is k-ordered if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a cycle C such that C encounters the vertices of S in the specified order.In particular,we say that D is k-ordered hamiltonian if for every sequence S：v 1,v 2,…,v k of k distinct vertices,there exists a hamiltonian cycle C such that the vertices of S are encountered on C in the specified order.In this paper,sufficient conditions for digraphs to be ordered and ordered hamiltonian have been given.
基金Supported by National Natural Science Foundation of China(Grant No. 11551002)Natural Science Foundation of Qinghai Province (Grant No. 2019-ZJ-7093)。
文摘The strong product digraph G1■G2 is constructed by the known digraph G1 and G2 of small order. The digraph G1■G2 constructed by the strong product method contain G1 and G2 as its sub-graphs. Therefore, the topological structure and properties of these small digraphs G1 and G2 must affect the topological structure and properties of the large digraph. By using group theory, we prove some algebraic properties of strong product of digraphs, such as commutative law, associative law and so on.
基金Supported by the National Natural Science Foundation of China (Grant No.12001434)The Natural Science Basic Research Program of Shaanxi Province (Grant No.2022JM-006)Chinese Universities Scientific Fund (Grant No.2452020021)
文摘Let D be a weighted digraph with n vertices in which each arc has been assigned a positive number.Let A(D)be the adjacency matrix of D and W(D)=diag(w_(1)^(+),w_(2)^(+),...,w_(n)^(+)).In this paper,we study the matrix A_(α)(D),which is defined as Aα(D)=αW(D)+(1−α)A(D),0≤α≤1.The spectral radius of A_(α)(D)is called the Aαspectral radius of D,denoted byλα(D).We obtain some upper bounds on the Aαspectral radius of strongly connected irregular weighted digraphs.
文摘Concurrent engineering(CE)involves the consideration during the design phase of the various factors associated with the life cycle of the product.Using the principle of CE,a feature-based CAPP system is proposed.On the basis of feature modeling,the system is able to reason feature relationships,produce feature digraph of a part,and decide the machining sequence of features.
文摘Rational measuring design of the tree length is a course to optimize all position of it before bucking. This paper offers the weighted digraph in the digrams and theories to solve the optimal problem of rational measuring of tree length based on experts researches in home and foreign. Sawlines are defined as apexes xd log between two sawlines as a side yn the price of log as weight Wij. It can describe the digraph of the rational measuring design of the tree length T=(X. Y.Wij), which consists of point -set and side-set. Oweing to Wij≥0, using Mr. E. W. Dijkstra's theory, we can obtain the 'path' of maximum profit of the tree length under the best availability of the tree length.
基金supported by the National Natural Science Foundation of China(Grant Nos.12001480 and 11871318)the Applied Basic Research Program of Shanxi Province(Grant Nos.201901D211461 and 201901D211462)+2 种基金the Scientific and Technologial Innovation Programs of Higher Education Institutions in Shanxi(Grant No.2020L0554)the Excellent Doctoral Research Project of Shanxi Province(Grant No.QZX-2020001)the PhD Start-up Project of Yuncheng University(Grant No.YQ-2019021)。
文摘With the rapid development of machine learning,artificial neural networks provide a powerful tool to represent or approximate many-body quantum states.It was proved that every graph state can be generated by a neural network.Here,we introduce digraph states and explore their neural network representations(NNRs).Based on some discussions about digraph states and neural network quantum states(NNQSs),we construct explicitly an NNR for any digraph state,implying every digraph state is an NNQS.The obtained results will provide a theoretical foundation for solving the quantum manybody problem with machine learning method whenever the wave-function is known as an unknown digraph state or it can be approximated by digraph states.
基金supported in part by the National Natural Science Foundation of China(62203352,U2003110)in part by the Key Laboratory Project of Shaanxi Provincial Department of Education(20JS110)in part by the Thousand Talents Plan of Shaanxi Province for Young Professionals。
文摘Maximizing the utilization of lithium-ion battery capacity is an important means to alleviate the range anxiety of electric vehicles.Battery pack inconsistency is the main limiting factor for improving battery pack capacity utilization,and poses major safety hazards to energy storage systems.To solve this problem,a maximum capacity utilization scheme based on a path planning algorithm is proposed.Specifically,the reconfigurable topology proposed is highly flexible and fault-tolerant,enabling battery pack consistency through alternating cell discharge and reducing the increased risk of short circuits due to relay error.The Dijkstra algorithm is used to find the optimal energy path,which can effectively remove faulty cells and find the current path with the best consistency of the battery pack and the lowest relay loss.Finally,the effectiveness of the scheme is verified by hardware-in-the-loop experiments,and the experimental results show that the state-of-charge SOC consistency of the battery pack at the end of discharge is increased by 34.18%,the relay energy loss is reduced by 0.16%,and the fault unit is effectively isolated.
基金Supported by the National Natural Science Foundation of China（11271208）
Acknowledgement The authors are grateful to the referees for their careful reading of the original version of this paper, their detailed comments and suggestions that much improved the quality of this paper.
文摘In this paper, we consider the properties of iteration graphs over the unit group Z*n of the residue ring Z n associated with the maps x → x p and compute the average values of tails and cycles of those iteration graphs.
基金REN Shi-quan is supported by China Postdoctoral Science Foundation(Grant No.2022M721023)WANG Chong is supported by Science and Technology Project of Hebei Education Department(Grant No.ZD2022168)Project of Cangzhou Normal University(Grant No.XNJJLYB2021006).
文摘In 2020,Alexander Grigor'yan,Yong Lin and Shing-Tung Yau[6]introduced the Reidemeister torsion and the analytic torsion for digraphs by means of the path complex and the path homology theory.Based on the analytic torsion for digraphs introduced in[6],we consider the notion of weighted analytic torsion for vertex-weighted digraphs.For any non-vanishing real functions f and g on the vertex set,we consider the vertex-weighted digraphs with the weights(f;g).We calculate the(f;g)-weighted analytic torsion by examples and prove that the(f;g)-weighted analytic torsion only depend on the ratio f=g.In particular,if the weight is of the diagonal form(f;f),then the weighted analytic torsion equals to the usual(un-weighted)torsion.
基金Supported by the National Natural Science Foundation of China(Grant No.12071351)the Natural Science Foundation of Shandong Provence(Grant No.ZR2020MA043).
文摘A majority k-coloring of a digraph D with k colors is an assignment c:V(D)→{1,2,…,k},such that for every v∈V(D),we have c(w)=c(v)for at most half of all out-neighbors w∈N^(+)(v).For a natural number k≥2,a 1/k-majority coloring of a digraph is a coloring of the vertices such that each vertex receives the same color as at most a 1/k proportion of its out-neighbours.Kreutzer,Oum,Seymour,van der Zypen and Wood proved that every digraph has a majority 4-coloring and conjectured that every digraph admits a majority 3-coloring.Gireao,Kittipassorn and Popielarz proved that every digraph has a 1/k-majority 2k-coloring and conjectured that every digraph admits a 1/k majority(2k-1)-coloring.We showed that every r-regular digraph D with r>36ln(2n)has a majority 3-coloring and proved that every digraph D with minimum outdegreeδ+>2k2(2k-1)/(k-1)^(2)ln2(n)[(2k-1)n]has a 1/k-majority(2k-1)-coloring.We showed that every r-regular digraph D with r>36ln(2n)has a majority 3-coloring and proved that every digraph D with minimum outdegreeδ+>,2k^(2)(2k-1)^(2)/(k-1)^(2)ln[(2k-1)n]has a 1/k-majority(2k-1)-coloring.And we also proved that every r-regular digraph D with r>3k^(2)(2k-1)/(k-1)^2ln(2n)has a 1/k-majority(2k-1)-coloring.
