Let a,b be two positive integers such that a≤b and a≡b(mod 2).We say that a graph G has an(a,b)-parity factor if G has a spanning subgraph F such that dF(v)≡b(mod 2)and a≤dF(v)≤b for all v∈V(G).In this paper,we ...Let a,b be two positive integers such that a≤b and a≡b(mod 2).We say that a graph G has an(a,b)-parity factor if G has a spanning subgraph F such that dF(v)≡b(mod 2)and a≤dF(v)≤b for all v∈V(G).In this paper,we provide a tight spectral radius condition for a graph to have(a,b)-parity factors.展开更多
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 T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d...Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T) ≤p(Pd,r,n-d-1),and equality holds if and only if T≌ Pd,r,n-d-1展开更多
Some sharp upper bounds of Laplacian spectral radius of trees in terms of order,diameter,pendant vertex number,covering number,edge covering number or total independence number are given.And the ninth to thirteenth la...Some sharp upper bounds of Laplacian spectral radius of trees in terms of order,diameter,pendant vertex number,covering number,edge covering number or total independence number are given.And the ninth to thirteenth largest values of Laplacian spectral radius over the class of trees on a given order are also given.展开更多
Let （V, U） be the vertex-partition of tree T as a bipartite graph. T is called an （m, n）-tree if ｜V｜ = m and ｜U｜ = n. For given positive integers m, n and d, the maximum spectral radius of all （m, n）-trees o...Let （V, U） be the vertex-partition of tree T as a bipartite graph. T is called an （m, n）-tree if ｜V｜ = m and ｜U｜ = n. For given positive integers m, n and d, the maximum spectral radius of all （m, n）-trees on diameter d are obtained, and all extreme graphs are determined.展开更多
The soft fault induced by parameter variation is one of the most challenging problems in the domain of fault diagnosis for analog circuits.A new fault location and parameter prediction approach for soft-faults diagnos...The soft fault induced by parameter variation is one of the most challenging problems in the domain of fault diagnosis for analog circuits.A new fault location and parameter prediction approach for soft-faults diagnosis in analog circuits is presented in this paper.The proposed method extracts the original signals from the output terminals of the circuits under test（CUT） by a data acquisition board.Firstly,the phase deviation value between fault-free and faulty conditions is obtained by fitting the sampling sequence with a sine curve.Secondly,the sampling sequence is organized into a square matrix and the spectral radius of this matrix is obtained.Thirdly,the smallest error of the spectral radius and the corresponding component value are obtained through comparing the spectral radius and phase deviation value with the trend curves of them,respectively,which are calculated from the simulation data.Finally,the fault location is completed by using the smallest error,and the corresponding component value is the parameter identification result.Both simulated and experimental results show the effectiveness of the proposed approach.It is particularly suitable for the fault location and parameter identification for analog integrated circuits.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
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
Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual ...Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.展开更多
The authors study recursive structures with ＂finite memory＂ in Euclidean matric space and the multifractal decomposition of the corresponding fractals. For any two positive numbers q,β, and such a recursive structu...The authors study recursive structures with ＂finite memory＂ in Euclidean matric space and the multifractal decomposition of the corresponding fractals. For any two positive numbers q,β, and such a recursive structure, a linear operator V^q,β in finite dimensional space is defined. The multifractal spectrum is given by the spectral radius of Vq,^β.展开更多
By using the properties of nonnegative matrices and techniques of differential inequalities,some sufficient conditions for the global exponential stability of cellular neural networks with time delays were obtained.Th...By using the properties of nonnegative matrices and techniques of differential inequalities,some sufficient conditions for the global exponential stability of cellular neural networks with time delays were obtained.The criteria do not require such conditions as boundedness and differentiability of activation functions.The conditions of the theorem were verified.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
The preconditioned methods for solving linear system are discussed. The convergence rate of accelerated overrelaxation (AOR) method can be enlarged by using the preconditioned method when the classical AOR method conv...The preconditioned methods for solving linear system are discussed. The convergence rate of accelerated overrelaxation (AOR) method can be enlarged by using the preconditioned method when the classical AOR method converges, and the preconditioned method is invalid when the classical iterative method does not converge. The results in corresponding references are improved and perfected.展开更多
This paper presents a comparison theorem of the generalized TOR method for solving linear systems. By applying this theorem, some recent results are derived.
文摘Let a,b be two positive integers such that a≤b and a≡b(mod 2).We say that a graph G has an(a,b)-parity factor if G has a spanning subgraph F such that dF(v)≡b(mod 2)and a≤dF(v)≤b for all v∈V(G).In this paper,we provide a tight spectral radius condition for a graph to have(a,b)-parity factors.
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)
文摘Let T denote a tree with the diameter d(d≥2) and order n. Let Pd,r,n-d-1 denote the tree obtained by identifying the rth vertex of path Pd+1 and the center of star K1,n-d-1, where r = r(d) is the integer part about d+2/2. Then p(T) ≤p(Pd,r,n-d-1),and equality holds if and only if T≌ Pd,r,n-d-1
基金Supported by National Natural Science Foundation of China（10871204）
文摘Some sharp upper bounds of Laplacian spectral radius of trees in terms of order,diameter,pendant vertex number,covering number,edge covering number or total independence number are given.And the ninth to thirteenth largest values of Laplacian spectral radius over the class of trees on a given order are also given.
基金Supported by the Department Fund of Science and Technology in Tianjin Higher Education Institutions(20050404)
文摘Let （V, U） be the vertex-partition of tree T as a bipartite graph. T is called an （m, n）-tree if ｜V｜ = m and ｜U｜ = n. For given positive integers m, n and d, the maximum spectral radius of all （m, n）-trees on diameter d are obtained, and all extreme graphs are determined.
基金supported by the National Natural Science Foundation of China under Grant No.61371049
文摘The soft fault induced by parameter variation is one of the most challenging problems in the domain of fault diagnosis for analog circuits.A new fault location and parameter prediction approach for soft-faults diagnosis in analog circuits is presented in this paper.The proposed method extracts the original signals from the output terminals of the circuits under test（CUT） by a data acquisition board.Firstly,the phase deviation value between fault-free and faulty conditions is obtained by fitting the sampling sequence with a sine curve.Secondly,the sampling sequence is organized into a square matrix and the spectral radius of this matrix is obtained.Thirdly,the smallest error of the spectral radius and the corresponding component value are obtained through comparing the spectral radius and phase deviation value with the trend curves of them,respectively,which are calculated from the simulation data.Finally,the fault location is completed by using the smallest error,and the corresponding component value is the parameter identification result.Both simulated and experimental results show the effectiveness of the proposed approach.It is particularly suitable for the fault location and parameter identification for analog integrated circuits.
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.
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.
文摘Under a very general condition （TNC condition） we show that the spectral radius of the kernel of a general branching process is a threshold parameter and hence plays a role as the basic reproduction number in usual CMJ processes. We discuss also some properties of the extinction probability and the generating operator of general branching processes. As an application in epidemics, in the final section we suggest a generalization of SIR model which can describe infectious diseases transmission in an inhomogeneous population.
文摘The authors study recursive structures with ＂finite memory＂ in Euclidean matric space and the multifractal decomposition of the corresponding fractals. For any two positive numbers q,β, and such a recursive structure, a linear operator V^q,β in finite dimensional space is defined. The multifractal spectrum is given by the spectral radius of Vq,^β.
基金the Foundation of Technology Project of Chongqing Education Commission (No. 041503)
文摘By using the properties of nonnegative matrices and techniques of differential inequalities,some sufficient conditions for the global exponential stability of cellular neural networks with time delays were obtained.The criteria do not require such conditions as boundedness and differentiability of activation functions.The conditions of the theorem were verified.
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The preconditioned methods for solving linear system are discussed. The convergence rate of accelerated overrelaxation (AOR) method can be enlarged by using the preconditioned method when the classical AOR method converges, and the preconditioned method is invalid when the classical iterative method does not converge. The results in corresponding references are improved and perfected.
文摘This paper presents a comparison theorem of the generalized TOR method for solving linear systems. By applying this theorem, some recent results are derived.
