A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of ...A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C_4-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the(combinatorial)展开更多
Let kn be the class of bipartite graphs with n vertices and k cut edges.The extremal graphs with the first and the second largest Laplacian spectral radius among all graphs in kn are presented.The bounds of the Laplac...Let kn be the class of bipartite graphs with n vertices and k cut edges.The extremal graphs with the first and the second largest Laplacian spectral radius among all graphs in kn are presented.The bounds of the Laplacian spectral radius of these extremal graphs are also obtained.展开更多
A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The...A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted graph. In this paper, a brief overview of the notation and concepts of weighted graphs that will be used throughout this study is given. In Section 2, the weighted signless Laplacian matrix of simple connected weighted graphs is considered, some upper bounds for the spectral radius of the weighted signless Laplacian matrix are obtained and some results on weighted and unweighted graphs are found.展开更多
Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bou...Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.展开更多
Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching ...Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching m-d edges at vertex u_[d/2]+1.In this paper,we mainly determine S1(m,d,k)with the largest signless Laplacian spectral radius in S(m,d,k)for 3≤d≤m-1.We also determine the supertree with the second largest signless Laplacian spectral radius in S(m,3,k).Furthermore,we determine the unique/c-uniform supertree with the largest signless Laplacian spectral radius among all fc-uniform supertrees with n vertices and pendent edges(vertices).展开更多
The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph.It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,a...The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph.It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph.In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius,where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.展开更多
Let T(n,i) be the set of all trees with order n and matching number i.We determine the third to sixth trees in T(2i + 1,i) and the third to fifth trees in T(n,i) for n ≥ 2i + 2 with the largest Laplacian spectral rad...Let T(n,i) be the set of all trees with order n and matching number i.We determine the third to sixth trees in T(2i + 1,i) and the third to fifth trees in T(n,i) for n ≥ 2i + 2 with the largest Laplacian spectral radius.展开更多
Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalv...Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.展开更多
The celebrated Erdos-Ko-Rado theorem states that given n≥2k,every intersecting k-uni-n-1 form hypergraph G on n vertices has at most(n-1 k-1)edges.This paper states spectral versions of the Erd6s-_Ko--Rado theorem:le...The celebrated Erdos-Ko-Rado theorem states that given n≥2k,every intersecting k-uni-n-1 form hypergraph G on n vertices has at most(n-1 k-1)edges.This paper states spectral versions of the Erd6s-_Ko--Rado theorem:let G be an intersecting k-uniform hypergraph on n vertices with n≥2k.Then,the sharp upper bounds for the spectral radius of Aα(G)and 2*(G)are presented,where Aα(G)=αD(G)+(1-α).A(G)is a convex linear combination of the degree diagonal tensor D(G)and the adjacency tensor A(G)for 0≤α<1,and Q^(*)(G)is the incidence Q-tensor,respectively.Furthermore,when n>2k,the extremal hypergraphs which attain the sharp upper bounds are characterized.The proof mainly relies on the Perron-Frobenius theorem for nonnegative tensor and the property of the maximizing connected hypergraphs.展开更多
The spectral radius of a graph is the maximum eigenvalues of its adjacency matrix. In this paper, using the property of quotient graph, the sharp upper bounds for the spectral radii of some adhesive graphs are determi...The spectral radius of a graph is the maximum eigenvalues of its adjacency matrix. In this paper, using the property of quotient graph, the sharp upper bounds for the spectral radii of some adhesive graphs are determined.展开更多
In MEC-enabled vehicular network with limited wireless resource and computation resource,stringent delay and high reliability requirements are challenging issues.In order to reduce the total delay in the network as we...In MEC-enabled vehicular network with limited wireless resource and computation resource,stringent delay and high reliability requirements are challenging issues.In order to reduce the total delay in the network as well as ensure the reliability of Vehicular UE(VUE),a Joint Allocation of Wireless resource and MEC Computing resource(JAWC)algorithm is proposed.The JAWC algorithm includes two steps:V2X links clustering and MEC computation resource scheduling.In the V2X links clustering,a Spectral Radius based Interference Cancellation scheme(SR-IC)is proposed to obtain the optimal resource allocation matrix.By converting the calculation of SINR into the calculation of matrix maximum row sum,the accumulated interference of VUE can be constrained and the the SINR calculation complexity can be effectively reduced.In the MEC computation resource scheduling,by transforming the original optimization problem into a convex problem,the optimal task offloading proportion of VUE and MEC computation resource allocation can be obtained.The simulation further demonstrates that the JAWC algorithm can significantly reduce the total delay as well as ensure the communication reliability of VUE in the MEC-enabled vehicular network.展开更多
Let {an}∞n=0be a weight sequence and let W denote the associated unilateral weighted shift on H. In this paper, we consider the connection between the M-hyponormal and hyponormalizable weighted shift operator. Main r...Let {an}∞n=0be a weight sequence and let W denote the associated unilateral weighted shift on H. In this paper, we consider the connection between the M-hyponormal and hyponormalizable weighted shift operator. Main results are Theorems 4.1 and Theorems4.2. Theorem 4.1 gives the sufficient condition that a weighted shifts M-hyponormal operator is hyponormalizable. Theorem 4.2 gives the sufficient condition that a hyponormalizable weighted shift operator is M-hyponormal. Finally, invariant subspaces of such operators are discussed.展开更多
A simulation model based on nonlinear ordinary differential equations to interpret the transmission dynamics of Zika Virus (ZIKV), is formulated and analyzed, integrating the asymptomatic human population and coupled ...A simulation model based on nonlinear ordinary differential equations to interpret the transmission dynamics of Zika Virus (ZIKV), is formulated and analyzed, integrating the asymptomatic human population and coupled to the Aedes aegypti dynamics, the epidemic threshold Basic Reproduction Number R0 is determined, as the spectral radius of Next-Generation Matrix and the system is simulated with MAPLE computing program taking the parameter values from literature.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
A supertree is a connected and acyclic hypergraph.We investigate the supertrees with the extremal spectral radii among several kinds of r-uniform supertrees.First,by using the matching polynomials of supertrees,a new ...A supertree is a connected and acyclic hypergraph.We investigate the supertrees with the extremal spectral radii among several kinds of r-uniform supertrees.First,by using the matching polynomials of supertrees,a new and useful grafting operation is proposed for comparing the spectral radii of supertrees,and its applications are shown to obtain the supertrees with the extremal spectral radi among some kinds of r-uniform supertrees.Second,the supertree with the third smallest spectral radius among the r-uniform supertrees is deduced.Third,among the r-uniform supertrees with a given maximum degree,the supertree with the smallest spectral radius is derived.At last,among the r-uniform starlike supert rees,the supertrees with the smallest and the largest spectral radii are characterized.展开更多
In this paper,we present several sharper upper bounds for the M-spectral radius and Z-spectral radius based on the eigenvalues of some unfolding matrices of nonnegative tensors.Meanwhile,we show that these bounds coul...In this paper,we present several sharper upper bounds for the M-spectral radius and Z-spectral radius based on the eigenvalues of some unfolding matrices of nonnegative tensors.Meanwhile,we show that these bounds could be tight for some special tensors.For a general nonnegative tensor which can be transformed into a matrix,we prove the maximal singular value of this matrix is an upper bound of its Z-eigenvalues.Some examples are provided to show these proposed bounds greatly improve some existing ones.展开更多
The over-current capacity of half-bridge modular multi-level converter(MMC)is quite weak,which requests protections to detect faults accurately and reliably in several milliseconds after DC faults.The sensitivity and ...The over-current capacity of half-bridge modular multi-level converter(MMC)is quite weak,which requests protections to detect faults accurately and reliably in several milliseconds after DC faults.The sensitivity and reliability of the existing schemes are vulnerable to high resistance and data errors.To improve the insufficiencies,this paper proposes a pilot protection scheme by using the random matrix for DC lines in the symmetrical bipolar MMC high-voltage direct current(HVDC)grid.Firstly,the 1-mode voltage time-domain characteristics of the line end,DC bus,and adjacent line end are analyzed by the inverse Laplace transform to find indicators of fault direction.To combine the actual model with the data-driven method,the methods to construct the data expansion matrix and to calculate additional noise are proposed.Then,the mean spectral radiuses of two random matrices are used to detect fault directions,and a novel pilot protection criterion is proposed.The protection scheme only needs to transmit logic signals,decreasing the communication burden.It performs well in high-resistance faults,abnormal data errors,measurement errors,parameters errors,and different topology conditions.Numerous simulations in PSCAD/EMTDC confirm the effectiveness and reliability of the proposed protection scheme.展开更多
Given a graph G,the adjacency matrix and degree diagonal matrix of G are denoted by A(G)and D(G),respectively.In 2017,Nikiforov~([24])proposed the A_(α)-matrix:A_α(G)=αD(G)+(1-α)A(G),whereα∈[0,1].The largest eig...Given a graph G,the adjacency matrix and degree diagonal matrix of G are denoted by A(G)and D(G),respectively.In 2017,Nikiforov~([24])proposed the A_(α)-matrix:A_α(G)=αD(G)+(1-α)A(G),whereα∈[0,1].The largest eigenvalue of this novel matrix is called the A_(α)-index of G.In this paper,we characterize the graphs with minimum A_(α)-index among n-vertex graphs with independence number i forα∈[0,1),where i=1,[n/2],[n/2],[n/2]+1,n-3,n-2,n-1,whereas for i=2 we consider the same problem forα∈[0,3/4].Furthermore,we determine the unique graph(resp.tree)on n vertices with given independence number having the maximum A_(α)-index withα∈[0,1),whereas for the n-vertex bipartite graphs with given independence number,we characterize the unique graph having the maximum A_α-index withα∈[1/2,1).展开更多
基金Supported by the National Natural Science Foundation of China（11171273） Supported by the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical Uni- versity（Z2016170）
文摘A k-cyclic graph is a connected graph of order n and size n + k-1. In this paper, we determine the maximal signless Laplacian spectral radius and the corresponding extremal graph among all C_4-free k-cyclic graphs of order n. Furthermore, we determine the first three unicycles and bicyclic, C_4-free graphs whose spectral radius of the signless Laplacian is maximal. Similar results are obtained for the(combinatorial)
基金Fundamental Research Funds for the Central Universities of China(No. 11D10902,No. 11D10913)
文摘Let kn be the class of bipartite graphs with n vertices and k cut edges.The extremal graphs with the first and the second largest Laplacian spectral radius among all graphs in kn are presented.The bounds of the Laplacian spectral radius of these extremal graphs are also obtained.
文摘A weighted graph is a graph that has a numeric label associated with each edge, called the weight of edge. In many applications, the edge weights are usually represented by nonnegative integers or square matrices. The weighted signless Laplacian matrix of a weighted graph is defined as the sum of adjacency matrix and degree matrix of same weighted graph. In this paper, a brief overview of the notation and concepts of weighted graphs that will be used throughout this study is given. In Section 2, the weighted signless Laplacian matrix of simple connected weighted graphs is considered, some upper bounds for the spectral radius of the weighted signless Laplacian matrix are obtained and some results on weighted and unweighted graphs are found.
基金supported by Deutsche Forschungsgemeinschaft (DFG) (Grant No. ME 4473/2-1)the Centre Henri Lebesgue (CHL) (Grant No. ANR-11-LABX-0020-01)National Natural Science Foundation of China (Grants Nos. 11971063, 11731012, 12271062 and 12288201)。
文摘Let(g_(n))_(n≥1) be a sequence of independent and identically distributed positive random d×d matrices and consider the matrix product G_(n)=g_(n)…g_1.Under suitable conditions,we establish the Berry-Esseen bounds on the rate of convergence in the central limit theorem and Cramer-type moderate deviation expansions,for any matrix norm ‖G_(n)‖ of G_(n),its entries G_(n)^(i,j) and its spectral radius ρ(G_(n)).Extended versions of their joint law with the direction of the random walk G_(n)x are also established,where x is a starting point in the unit sphere of R~d.
基金supported in part by the National Natural Science Foundation of China(Grant No.11871398)the Natural Science Foundation of Shaanxi Province(Nos.2020JQ-107,2020JQ-696)the Seed Foundation of Innovation and Creation for Graduate Students in Northwestern Polytechnical University(Nos.ZZ2018171,CX2020190).
文摘Let S(m,d,k)be the set of k-uniform supertrees with m edges and diameter d,and S1(m,d,k)be the k-uniform supertree obtained from a loose path u_(1),e_(1),u_(2),e_(2),...,u_(d),e_(d),u_(d+1),with length d by attaching m-d edges at vertex u_[d/2]+1.In this paper,we mainly determine S1(m,d,k)with the largest signless Laplacian spectral radius in S(m,d,k)for 3≤d≤m-1.We also determine the supertree with the second largest signless Laplacian spectral radius in S(m,3,k).Furthermore,we determine the unique/c-uniform supertree with the largest signless Laplacian spectral radius among all fc-uniform supertrees with n vertices and pendent edges(vertices).
基金Natural Science Foundation of China(Grant Nos.11871073,11871077)NSF of Department of Education of Anhui Province(Grant No.KJ2017A362)。
文摘The spectral radius of a uniform hypergraph is defined to be that of the adjacency tensor of the hypergraph.It is known that the unique unicyclic hypergraph with the largest spectral radius is a nonlinear hypergraph,and the unique linear unicyclic hypergraph with the largest spectral radius is a power hypergraph.In this paper we determine the unique linear unicyclic hypergraph with the second or third largest spectral radius,where the former hypergraph is a power hypergraph and the latter hypergraph is a non-power hypergraph.
基金Supported by the National Natural Science Foundation of China (Grant No.10871204)
文摘Let T(n,i) be the set of all trees with order n and matching number i.We determine the third to sixth trees in T(2i + 1,i) and the third to fifth trees in T(n,i) for n ≥ 2i + 2 with the largest Laplacian spectral radius.
文摘Let G be a graph and A(G) the adjacency matrix of G. The spectrum of G is the eigenvalues together with their multiplicities of A(G). Chang et al. (2011) characterized the structures of all graphs with rank 4. Monsalve and Rada (2021) gave the bound of spectral radius of all graphs with rank 4. Based on these results as above, we further investigate the spectral properties of graphs with rank 4. And we give the expressions of the spectral radius and energy of all graphs with rank 4. In particular, we show that some graphs with rank 4 are determined by their spectra.
基金the National Natural Science Foundation of China(Nos.11971311,11531001)the Montenegrin-Chinese Science and Technology Cooperation Project(No.3-12).
文摘The celebrated Erdos-Ko-Rado theorem states that given n≥2k,every intersecting k-uni-n-1 form hypergraph G on n vertices has at most(n-1 k-1)edges.This paper states spectral versions of the Erd6s-_Ko--Rado theorem:let G be an intersecting k-uniform hypergraph on n vertices with n≥2k.Then,the sharp upper bounds for the spectral radius of Aα(G)and 2*(G)are presented,where Aα(G)=αD(G)+(1-α).A(G)is a convex linear combination of the degree diagonal tensor D(G)and the adjacency tensor A(G)for 0≤α<1,and Q^(*)(G)is the incidence Q-tensor,respectively.Furthermore,when n>2k,the extremal hypergraphs which attain the sharp upper bounds are characterized.The proof mainly relies on the Perron-Frobenius theorem for nonnegative tensor and the property of the maximizing connected hypergraphs.
文摘The spectral radius of a graph is the maximum eigenvalues of its adjacency matrix. In this paper, using the property of quotient graph, the sharp upper bounds for the spectral radii of some adhesive graphs are determined.
基金This work was supported in part by the National Key R&D Program of China under Grant 2019YFE0114000in part by the National Natural Science Foundation of China under Grant 61701042+1 种基金in part by the 111 Project of China(Grant No.B16006)the research foundation of Ministry of EducationChina Mobile under Grant MCM20180101.
文摘In MEC-enabled vehicular network with limited wireless resource and computation resource,stringent delay and high reliability requirements are challenging issues.In order to reduce the total delay in the network as well as ensure the reliability of Vehicular UE(VUE),a Joint Allocation of Wireless resource and MEC Computing resource(JAWC)algorithm is proposed.The JAWC algorithm includes two steps:V2X links clustering and MEC computation resource scheduling.In the V2X links clustering,a Spectral Radius based Interference Cancellation scheme(SR-IC)is proposed to obtain the optimal resource allocation matrix.By converting the calculation of SINR into the calculation of matrix maximum row sum,the accumulated interference of VUE can be constrained and the the SINR calculation complexity can be effectively reduced.In the MEC computation resource scheduling,by transforming the original optimization problem into a convex problem,the optimal task offloading proportion of VUE and MEC computation resource allocation can be obtained.The simulation further demonstrates that the JAWC algorithm can significantly reduce the total delay as well as ensure the communication reliability of VUE in the MEC-enabled vehicular network.
基金Supported by the NNSF of China(11126286,11201095)Supported by the Research Fund of Heilongjiang Provincial Education Department(12541618)
文摘Let {an}∞n=0be a weight sequence and let W denote the associated unilateral weighted shift on H. In this paper, we consider the connection between the M-hyponormal and hyponormalizable weighted shift operator. Main results are Theorems 4.1 and Theorems4.2. Theorem 4.1 gives the sufficient condition that a weighted shifts M-hyponormal operator is hyponormalizable. Theorem 4.2 gives the sufficient condition that a hyponormalizable weighted shift operator is M-hyponormal. Finally, invariant subspaces of such operators are discussed.
文摘A simulation model based on nonlinear ordinary differential equations to interpret the transmission dynamics of Zika Virus (ZIKV), is formulated and analyzed, integrating the asymptomatic human population and coupled to the Aedes aegypti dynamics, the epidemic threshold Basic Reproduction Number R0 is determined, as the spectral radius of Next-Generation Matrix and the system is simulated with MAPLE computing program taking the parameter values from literature.
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supported by the National Natural Science Foundation of China(Grant Nos.11871040,11001166).
文摘A supertree is a connected and acyclic hypergraph.We investigate the supertrees with the extremal spectral radii among several kinds of r-uniform supertrees.First,by using the matching polynomials of supertrees,a new and useful grafting operation is proposed for comparing the spectral radii of supertrees,and its applications are shown to obtain the supertrees with the extremal spectral radi among some kinds of r-uniform supertrees.Second,the supertree with the third smallest spectral radius among the r-uniform supertrees is deduced.Third,among the r-uniform supertrees with a given maximum degree,the supertree with the smallest spectral radius is derived.At last,among the r-uniform starlike supert rees,the supertrees with the smallest and the largest spectral radii are characterized.
基金the National Natural Science Foundation of China(No.11271206)the Natural Science Foundation of Tianjin(No.12JCYBJC31200).
文摘In this paper,we present several sharper upper bounds for the M-spectral radius and Z-spectral radius based on the eigenvalues of some unfolding matrices of nonnegative tensors.Meanwhile,we show that these bounds could be tight for some special tensors.For a general nonnegative tensor which can be transformed into a matrix,we prove the maximal singular value of this matrix is an upper bound of its Z-eigenvalues.Some examples are provided to show these proposed bounds greatly improve some existing ones.
基金supported by the State Scholarship Fund of China Scholarship Council(No.202007000168).
文摘The over-current capacity of half-bridge modular multi-level converter(MMC)is quite weak,which requests protections to detect faults accurately and reliably in several milliseconds after DC faults.The sensitivity and reliability of the existing schemes are vulnerable to high resistance and data errors.To improve the insufficiencies,this paper proposes a pilot protection scheme by using the random matrix for DC lines in the symmetrical bipolar MMC high-voltage direct current(HVDC)grid.Firstly,the 1-mode voltage time-domain characteristics of the line end,DC bus,and adjacent line end are analyzed by the inverse Laplace transform to find indicators of fault direction.To combine the actual model with the data-driven method,the methods to construct the data expansion matrix and to calculate additional noise are proposed.Then,the mean spectral radiuses of two random matrices are used to detect fault directions,and a novel pilot protection criterion is proposed.The protection scheme only needs to transmit logic signals,decreasing the communication burden.It performs well in high-resistance faults,abnormal data errors,measurement errors,parameters errors,and different topology conditions.Numerous simulations in PSCAD/EMTDC confirm the effectiveness and reliability of the proposed protection scheme.
基金the Undergraduate Innovation and Entrepreneurship Grant from Central China Normal University(Grant No.20210409037)by Industry-University-Research Innovation Funding of Chinese University(Grant No.2019ITA03033)by the National Natural Science Foundation of China(Grant Nos.12171190,11671164)。
文摘Given a graph G,the adjacency matrix and degree diagonal matrix of G are denoted by A(G)and D(G),respectively.In 2017,Nikiforov~([24])proposed the A_(α)-matrix:A_α(G)=αD(G)+(1-α)A(G),whereα∈[0,1].The largest eigenvalue of this novel matrix is called the A_(α)-index of G.In this paper,we characterize the graphs with minimum A_(α)-index among n-vertex graphs with independence number i forα∈[0,1),where i=1,[n/2],[n/2],[n/2]+1,n-3,n-2,n-1,whereas for i=2 we consider the same problem forα∈[0,3/4].Furthermore,we determine the unique graph(resp.tree)on n vertices with given independence number having the maximum A_(α)-index withα∈[0,1),whereas for the n-vertex bipartite graphs with given independence number,we characterize the unique graph having the maximum A_α-index withα∈[1/2,1).
基金supported by NSF of China under Grant No.10071071
文摘我们考虑在 form$$\varphi \left ( x \right )写=\sum\limits_的精炼方程的答案{ \alpha \in \Zopf ^ s }{ a\left ( \alpha \right ) \varphi \left ({ Mx - \alpha } \right )+ g\left ( x \right )，\，\，\， x \in \Ropf ^ s } $$where 功能的向量}=(} 1 ，...，} r ) T 是未知的， g 是^ s 上的简洁地支持的功能的给定的向量，一是 2 个 r 矩阵把精炼面具称为的 r 的一个有限地支持的序列，并且 M 是 s 有 m =|detM|的 2 s 膨胀矩阵。不同类的精炼方程出现在构造多小浪和有限间隔上的小浪的构造。有面具的串联算法一， g ，和膨胀 M 产生一个序列} n ， n = 1 ， 2 ，...，由反复的 process$$\varphi _n \left ( x \right )=\sum\limits_{ \alpha \in \Zopf ^ s }{ a\left ( \alpha \right ) \varphi _{ n - 1 } \left ( Mx - \alpha \right )+ g\left ( x \right )，\，\，\， x \in \Ropf ^ s } $$from 开始的向量工作} 0 。我们描绘 Lp 集中(0 < p < 1 ) 串联算法以 p 标准关节光谱与精炼面具联系的许多线性操作员的半径。我们也获得与同类的精炼方程联系的精炼方程的答案的一个光滑性质。
