The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability eval...The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability evaluation of systems is important to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of graph G(V, E) is a kind of measure for the reliability of interconnection systems, which is defined as the minimum cardinality of a subset of edge set, if any, whose deletion disconnects G and such that every remaining component has at least h vertices. This paper shows that the h-extra edge-connectivity of the hypercube Qn is a constant 2^(n-1) for2^(n-1)/3< h ≤ 2^(n-1), and n ≥ 4, which extends the result of ["Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes, Discrete Applied Mathematics, 2013, 161(16): 2753-2757"].展开更多
Let A be a unital algebra and M be a unital A-bimodule. A linear map δ : A →M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ? B + A ? δ(B) =δ(A ? B) for any A, B ∈ A with A ? B = P, he...Let A be a unital algebra and M be a unital A-bimodule. A linear map δ : A →M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ? B + A ? δ(B) =δ(A ? B) for any A, B ∈ A with A ? B = P, here A ? B = AB + BA is the usual Jordan product. In this article, we show that if A = Alg N is a Hilbert space nest algebra and M = B(H), or A = M = B(X), then, a linear map δ : A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B(X) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.展开更多
In this paper, we consider a class of Sine-Gordon equations which arise from the model of the thermoelastic coupled rod. Firstly, by virtue of the classical semigroup theory, we prove the existence and uniqueness of t...In this paper, we consider a class of Sine-Gordon equations which arise from the model of the thermoelastic coupled rod. Firstly, by virtue of the classical semigroup theory, we prove the existence and uniqueness of the mild solution under certain initial-boundary value for above-mentioned equations. Secondly, we obtain the boundedness of solutions by the priori estimates. Lastly, we prove the existence of a global attractor.展开更多
Simultaneously, considering the viscous effect of material, damping of medium, geometrical nonlinearity, physical nonlinearity, we set up a more general equation of beam subjected to axial force and external load. We ...Simultaneously, considering the viscous effect of material, damping of medium, geometrical nonlinearity, physical nonlinearity, we set up a more general equation of beam subjected to axial force and external load. We prove the existence and uniqueness of global solutions under non-linear boundary conditions which the model is added one damping mechanism at l end. What is more, we also prove the exponential decay property of the energy of above mentioned system.展开更多
Two families F and G of k-subsets of {1, 2,..., n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F, G ∈ G and | ∩ {F : F ∈ F}| < t, | ∩ {G : G ∈ G}| < t. In the present paper,we det...Two families F and G of k-subsets of {1, 2,..., n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F, G ∈ G and | ∩ {F : F ∈ F}| < t, | ∩ {G : G ∈ G}| < t. In the present paper,we determine the maximum product of the sizes of two non-trivial cross t-intersecting families of k-subsets of{1, 2,..., n} for n≥4(t + 2)2k2, k≥5, which is a product version of the Hilton-Milner-Frankl theorem.展开更多
Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was...Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was proposed by Ding et al.In this paper,we establish the non-inclusive diagnosability of a class of regular graphs under the PMC model and the MM^(*)model.As applications,the non-inclusive diagnosabilities of hypercubes,hierarchical hypercubes,folded hypercubes,star graphs,bubble-sort graphs,pancake graphs and dual cubes are determined under the PMC model and the[Math Processing Error]model.展开更多
The PHC criterion and the realignment criterion for pure states in infinite-dimensional bipartite quantum systems are given. Furthermore, several equivalent conditions for pure states to be separable are generalized t...The PHC criterion and the realignment criterion for pure states in infinite-dimensional bipartite quantum systems are given. Furthermore, several equivalent conditions for pure states to be separable are generalized to infinite-dimensional systems.展开更多
Let N and M be nests on Banach spaces X and Y over the real or complex field F,respectively,with the property that if M∈M such that M-=M,then M is complemented in Y.Let AlgN and AlgM be the associated nest algebras.A...Let N and M be nests on Banach spaces X and Y over the real or complex field F,respectively,with the property that if M∈M such that M-=M,then M is complemented in Y.Let AlgN and AlgM be the associated nest algebras.Assume that Φ:AlgN→AlgM is a bijective map.It is proved that,if dim X=∞ and if there is a nontrivial element in N which is complemented in X,then Φ is Lie multiplicative (i.e.Φ([A,B])=[Φ(A),Φ(B)] for all A,B∈AlgN) if and only if Φ has the form Φ(A)=-TA*T-1+τ(A) for all A∈AlgN or Φ(A)=TAT-1+τ(A) for all A∈AlgN,where T is an invertible linear or conjugate linear operator and τ:AlgN→FI is a map with τ([A,B])=0 for all A,B∈AlgN.The Lie multiplicative maps are also characterized for the case dim X<∞.展开更多
In this article,we study the following fractional Schrodinger equation with electromagnetic fields and critical growth(-Δ)^sAu+V(x)u=|u|^2^*s-2)u+λf(x,|u|^2)u,x∈R^n,where(-Δ)^sA is the fractional magnetic operator...In this article,we study the following fractional Schrodinger equation with electromagnetic fields and critical growth(-Δ)^sAu+V(x)u=|u|^2^*s-2)u+λf(x,|u|^2)u,x∈R^n,where(-Δ)^sA is the fractional magnetic operator with 0<s<1,N>2s,λ>0,2^*s=2N/(N-2s),f is a continuous function,V∈C(R^n,R)and A∈C(R^n,R^n)are the electric and magnetic potentials,respectively.When V and f are asymptotically periodic in x,we prove that the equation has a ground state solution for largeλby Nehari method.展开更多
Let H be a Hilbert space with dim H≥2 and Z∈B(H) be an arbitrary but fixed operator.In this paper we show that an additive map Φ:B(H)→B(H) satisfies Φ(AB)=Φ(A)B=AΦ(B)for any A,B∈B(H) with AB=Z if and only if ...Let H be a Hilbert space with dim H≥2 and Z∈B(H) be an arbitrary but fixed operator.In this paper we show that an additive map Φ:B(H)→B(H) satisfies Φ(AB)=Φ(A)B=AΦ(B)for any A,B∈B(H) with AB=Z if and only if Φ(AB)=Φ(A)B=AΦ(B),A,B ∈B(H),that is,Φ is a centralizer.Similar results are obtained for Hilbert space nest algebras.In addition,we show that Φ(A^2)=AΦ(A)=Φ(A)A for any A∈B(H) with A^2=0 if and only if Φ(A)=AΦ(I)=Φ(I)A,A∈B(H),and generalize main results in Linear Algebra and its Application,450,243–249(2014) to infinite dimensional case.New equivalent characterization of centralizers on B(H) is obtained.展开更多
这篇论文被奉献给学习系统的唯一和存在由使用 C 0-semigroup 理论并且由分析讨论它的指数的稳定性的动态答案光谱系统操作员和它的伪紧密的分发。一些主要可靠性索引与系统操作员和最佳的假期时间的特徵函数被讨论得到最大的系统利润...这篇论文被奉献给学习系统的唯一和存在由使用 C 0-semigroup 理论并且由分析讨论它的指数的稳定性的动态答案光谱系统操作员和它的伪紧密的分发。一些主要可靠性索引与系统操作员和最佳的假期时间的特徵函数被讨论得到最大的系统利润在纸的结束被分析。展开更多
Let N be a nest on a Banach space X,and AlgN be the associated nest algebra.It is shown that if there exists a non-trivial element in N which isc omplemented in X,then D=(Ln)n∈N is a Lie higher derivation of AlgN if ...Let N be a nest on a Banach space X,and AlgN be the associated nest algebra.It is shown that if there exists a non-trivial element in N which isc omplemented in X,then D=(Ln)n∈N is a Lie higher derivation of AlgN if and only if each Ln has the form Ln(A)=τn(A)+hn(A)I for all A∈AlgN,where(τn)n∈N is a higher derivation and(hn)n∈N is a sequence of additive functionals satisfying hn([A,B])=0 for all A,B∈AlgN and all n∈N.展开更多
We discuss the fidelity of states in the infinite-dimensional systems and give an elementary proof of the infinite-dimensional version of Uhlmann's theorem.This theorem is used to generalize several properties of ...We discuss the fidelity of states in the infinite-dimensional systems and give an elementary proof of the infinite-dimensional version of Uhlmann's theorem.This theorem is used to generalize several properties of the fidelity of the finite-dimensional case to the infinite-dimensional case.These are somewhat different from those for the finite-dimensional case.展开更多
For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium,a system of coupled equations is analytically studied in this paper.Painleve analysis shows that this system admitsthe ...For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium,a system of coupled equations is analytically studied in this paper.Painleve analysis shows that this system admitsthe Painleve property under some constraints.By means of the Ablowitz-Kaup-Newell-Segur procedure,the Laxpair of this system is derived,and the Darboux transformation (DT) is constructed with the help of the obtainedLax pair.With symbolic computation,the soliton solutions are obtained by virtue of the DT algorithm.Figures areplotted to illustrate the dynamical features of the soliton solutions.Characteristics of the solitons propagating in aninhomogeneous multi-component nonlinear medium are discussed:(ⅰ) Propagation of one soliton and two-peak soliton;(ⅱ) Elastic interactions of the parabolic two solitons;(ⅲ) Overlap phenomenon between two solitons;(ⅳ) Collision oftwo head-on solitons and two head-on two-peak solitons;(ⅴ) Two different types of interactions of the three solitons;(ⅵ) Decomposition phenomenon of one soliton into two solitons.The results might be useful in the study on theultrashort-pulse propagation in the inhomogeneous multi-component nonlinear media.展开更多
In this paper,the authors consider the asymptotic behavior of the monic polynomials orthogonal with respect to the weight function w(x) = |x|^(2α)e^(-(x^4+tx^2)),x ∈ R,where α is a constant larger than -1/2 and t i...In this paper,the authors consider the asymptotic behavior of the monic polynomials orthogonal with respect to the weight function w(x) = |x|^(2α)e^(-(x^4+tx^2)),x ∈ R,where α is a constant larger than -1/2 and t is any real number. They consider this problem in three separate cases:(i) c >-2,(ii) c =-2,and(iii) c <-2,where c := t N^(-1/2) is a constant,N = n + α and n is the degree of the polynomial. In the first two cases,the support of the associated equilibrium measure μ_t is a single interval,whereas in the third case the support of μ_t consists of two intervals. In each case,globally uniform asymptotic expansions are obtained in several regions. These regions together cover the whole complex plane. The approach is based on a modified version of the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou(1993).展开更多
It is difficult to characterize graphs which contain no a 2-connected graph as a minor in graph theory.Let V_(8)be a graph constructed from an 8-cycle by connecting the antipodal vertices.There are thirteen 2-connecte...It is difficult to characterize graphs which contain no a 2-connected graph as a minor in graph theory.Let V_(8)be a graph constructed from an 8-cycle by connecting the antipodal vertices.There are thirteen 2-connected spanning subgraphs of V_(8).In particular,one of them is obtained from the Petersen graph by deleting two vertices and it is also a hard problem to characterize Petersen-minor-free graphs.In this paper,we characterize internally 4-connected graphs which contain a 2-connected spanning subgraph of V_(8)as a forbidden minor.展开更多
In this paper, we show that if an injective map on symmetric matrices Sn(C) satisfies then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and Af is the image of A under f applied...In this paper, we show that if an injective map on symmetric matrices Sn(C) satisfies then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and Af is the image of A under f applied entrywise.展开更多
Let U = Tri(A,M,B) be a triangular ring, where A and B are unital rings, and M is a faithful (A, B)-bimodule. It is shown that an additive map Φ on U is centralized at zero point (i.e., Φ(A)B = AΦ(B) = 0 whenever A...Let U = Tri(A,M,B) be a triangular ring, where A and B are unital rings, and M is a faithful (A, B)-bimodule. It is shown that an additive map Φ on U is centralized at zero point (i.e., Φ(A)B = AΦ(B) = 0 whenever AB = 0) if and only if it is a centralizer. Let δ : U → U be an additive map. It is also shown that the following four conditions are equivalent: (1) δ is specially generalized derivable at zero point, i.e., δ(AB) = δ(A)B + Aδ(B) Aδ(I)B whenever AB = 0; (2) δ is generalized derivable at zero point, i.e., there exist additive maps τ1 and τ2 on U derivable at zero point such that δ(AB) = δ(A)B + Aτ1 (B) = τ2 (A)B + Aδ(B) whenever AB = 0; (3) δ is a special generalized derivation; (4) δ is a generalized derivation. These results are then applied to nest algebras of Banach space.展开更多
基金Supported by the National Natural Science Foundation of China(11171283,11471273,11461038,11301440)Natural Sciences Foundation of Shanxi Province(2014021010-2)
文摘The classical hypercube structure is a popular topological architecture in parallel computing environments and a large number of variations based on the hypercube were posed in the past three decades. Reliability evaluation of systems is important to the design and maintenance of multiprocessor systems. The h-extra edge-connectivity of graph G(V, E) is a kind of measure for the reliability of interconnection systems, which is defined as the minimum cardinality of a subset of edge set, if any, whose deletion disconnects G and such that every remaining component has at least h vertices. This paper shows that the h-extra edge-connectivity of the hypercube Qn is a constant 2^(n-1) for2^(n-1)/3< h ≤ 2^(n-1), and n ≥ 4, which extends the result of ["Bounding the size of the subgraph induced by m vertices and extra edge-connectivity of hypercubes, Discrete Applied Mathematics, 2013, 161(16): 2753-2757"].
基金Supported by National Natural Foundation of China(11001194)Provincial International Cooperation Project of Shanxi(2014081027-2)
文摘Let A be a unital algebra and M be a unital A-bimodule. A linear map δ : A →M is said to be Jordan derivable at a nontrivial idempotent P ∈ A if δ(A) ? B + A ? δ(B) =δ(A ? B) for any A, B ∈ A with A ? B = P, here A ? B = AB + BA is the usual Jordan product. In this article, we show that if A = Alg N is a Hilbert space nest algebra and M = B(H), or A = M = B(X), then, a linear map δ : A → M is Jordan derivable at a nontrivial projection P ∈ N or an arbitrary but fixed nontrivial idempotent P ∈ B(X) if and only if it is a derivation. New equivalent characterization of derivations on these operator algebras was obtained.
文摘In this paper, we consider a class of Sine-Gordon equations which arise from the model of the thermoelastic coupled rod. Firstly, by virtue of the classical semigroup theory, we prove the existence and uniqueness of the mild solution under certain initial-boundary value for above-mentioned equations. Secondly, we obtain the boundedness of solutions by the priori estimates. Lastly, we prove the existence of a global attractor.
文摘Simultaneously, considering the viscous effect of material, damping of medium, geometrical nonlinearity, physical nonlinearity, we set up a more general equation of beam subjected to axial force and external load. We prove the existence and uniqueness of global solutions under non-linear boundary conditions which the model is added one damping mechanism at l end. What is more, we also prove the exponential decay property of the energy of above mentioned system.
基金supported by National Natural Science Foundation of China (Grant No. 11701407)
文摘Two families F and G of k-subsets of {1, 2,..., n} are called non-trivial cross t-intersecting if|F ∩ G|≥t for all F ∈ F, G ∈ G and | ∩ {F : F ∈ F}| < t, | ∩ {G : G ∈ G}| < t. In the present paper,we determine the maximum product of the sizes of two non-trivial cross t-intersecting families of k-subsets of{1, 2,..., n} for n≥4(t + 2)2k2, k≥5, which is a product version of the Hilton-Milner-Frankl theorem.
基金supported by the National Natural Science Foundation of China(No.11571044)the Natural Science Foundation of Shanxi Province(No.201901D211106)。
文摘Fault diagnosis is an important area of study with regard to the design and maintenance of multiprocessor systems.A new measure for fault diagnosis of systems,namely,non-inclusive diagnosability(denoted by MM^(*)),was proposed by Ding et al.In this paper,we establish the non-inclusive diagnosability of a class of regular graphs under the PMC model and the MM^(*)model.As applications,the non-inclusive diagnosabilities of hypercubes,hierarchical hypercubes,folded hypercubes,star graphs,bubble-sort graphs,pancake graphs and dual cubes are determined under the PMC model and the[Math Processing Error]model.
基金supported by the National Natural Science Foundation of China (10771157 and 10871111)TianYuan Foundation of China (11026161)+1 种基金Research Fund of Shanxi for Returned Scholars (2007-38)Research Fund of Shanxi University
文摘The PHC criterion and the realignment criterion for pure states in infinite-dimensional bipartite quantum systems are given. Furthermore, several equivalent conditions for pure states to be separable are generalized to infinite-dimensional systems.
基金supported by National Natural Science Foundation of China (Grant No. 10871111)Tian Yuan Foundation of China (Grant No. 11026161)Foundation of Shanxi University
文摘Let N and M be nests on Banach spaces X and Y over the real or complex field F,respectively,with the property that if M∈M such that M-=M,then M is complemented in Y.Let AlgN and AlgM be the associated nest algebras.Assume that Φ:AlgN→AlgM is a bijective map.It is proved that,if dim X=∞ and if there is a nontrivial element in N which is complemented in X,then Φ is Lie multiplicative (i.e.Φ([A,B])=[Φ(A),Φ(B)] for all A,B∈AlgN) if and only if Φ has the form Φ(A)=-TA*T-1+τ(A) for all A∈AlgN or Φ(A)=TAT-1+τ(A) for all A∈AlgN,where T is an invertible linear or conjugate linear operator and τ:AlgN→FI is a map with τ([A,B])=0 for all A,B∈AlgN.The Lie multiplicative maps are also characterized for the case dim X<∞.
基金supported in part by the NationalNatural Science Foundation of China(11801153,11501403,11701322,11561072)the Honghe University Doctoral Research Programs(XJ17B11,XJ17B12,DCXL171027,201810687010)+4 种基金the Yunnan Province Applied Basic Research for Youths(2018FD085)the Yunnan Province Local University(Part)Basic Research Joint Project(2017FH001-013)the Natural Sciences Foundation of Yunnan Province(2016FB011)the Yunnan Province Applied Basic Research for General Project(2019FB001)Technology Innovation Team of University in Yunnan Province。
文摘In this article,we study the following fractional Schrodinger equation with electromagnetic fields and critical growth(-Δ)^sAu+V(x)u=|u|^2^*s-2)u+λf(x,|u|^2)u,x∈R^n,where(-Δ)^sA is the fractional magnetic operator with 0<s<1,N>2s,λ>0,2^*s=2N/(N-2s),f is a continuous function,V∈C(R^n,R)and A∈C(R^n,R^n)are the electric and magnetic potentials,respectively.When V and f are asymptotically periodic in x,we prove that the equation has a ground state solution for largeλby Nehari method.
基金Supported by National Natural Foundation of China(Grant No.11001194)Provincial International Cooperation Project of Shanxi(Grant No.2014081027–2)
文摘Let H be a Hilbert space with dim H≥2 and Z∈B(H) be an arbitrary but fixed operator.In this paper we show that an additive map Φ:B(H)→B(H) satisfies Φ(AB)=Φ(A)B=AΦ(B)for any A,B∈B(H) with AB=Z if and only if Φ(AB)=Φ(A)B=AΦ(B),A,B ∈B(H),that is,Φ is a centralizer.Similar results are obtained for Hilbert space nest algebras.In addition,we show that Φ(A^2)=AΦ(A)=Φ(A)A for any A∈B(H) with A^2=0 if and only if Φ(A)=AΦ(I)=Φ(I)A,A∈B(H),and generalize main results in Linear Algebra and its Application,450,243–249(2014) to infinite dimensional case.New equivalent characterization of centralizers on B(H) is obtained.
基金supported by NSF (10771157) of ChinaResearch Fund (2007-38) of Shanxi for Returned ScholarsFoundation of Shanxi University
文摘Let N be a nest on a Banach space X,and AlgN be the associated nest algebra.It is shown that if there exists a non-trivial element in N which isc omplemented in X,then D=(Ln)n∈N is a Lie higher derivation of AlgN if and only if each Ln has the form Ln(A)=τn(A)+hn(A)I for all A∈AlgN,where(τn)n∈N is a higher derivation and(hn)n∈N is a sequence of additive functionals satisfying hn([A,B])=0 for all A,B∈AlgN and all n∈N.
基金supported by the National Natural Science Foundation of China(Grant Nos.11171249 and 11101250)the Youth Foundation of Shanxi Province(Grant No.2012021004)the Young Talents Plan for Shanxi University and a grant from the International Cooperation Program in Sciences and Technology of Shanxi(Grant No.2011081039)
文摘We discuss the fidelity of states in the infinite-dimensional systems and give an elementary proof of the infinite-dimensional version of Uhlmann's theorem.This theorem is used to generalize several properties of the fidelity of the finite-dimensional case to the infinite-dimensional case.These are somewhat different from those for the finite-dimensional case.
基金Acknowledgements This work was supported by the Foundation of Shanxi Scholarship Council of China （2011-024）, the Foundation of Shanxi Province for Selected Returned Overseas Scholars, and the Natural Science Foundation of Shanxi Province （2013011001-2）.
基金Supported by the National Natural Science Foundation of China under Grant No.60772023by the Open Fund No.BUAA-SKLSDE-09KF-04+2 种基金Supported Project No.SKLSDE-2010ZX-07 of the State Key Laboratory of Software Development Environment,Beijing University of Aeronautics and Astronauticsby the National Basic Research Program of China (973 Program) under Grant No.2005CB321901by the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No.200800130006,Chinese Ministry of Education
文摘For the propagation of the ultrashort pulses in an inhomogeneous multi-component nonlinear medium,a system of coupled equations is analytically studied in this paper.Painleve analysis shows that this system admitsthe Painleve property under some constraints.By means of the Ablowitz-Kaup-Newell-Segur procedure,the Laxpair of this system is derived,and the Darboux transformation (DT) is constructed with the help of the obtainedLax pair.With symbolic computation,the soliton solutions are obtained by virtue of the DT algorithm.Figures areplotted to illustrate the dynamical features of the soliton solutions.Characteristics of the solitons propagating in aninhomogeneous multi-component nonlinear medium are discussed:(ⅰ) Propagation of one soliton and two-peak soliton;(ⅱ) Elastic interactions of the parabolic two solitons;(ⅲ) Overlap phenomenon between two solitons;(ⅳ) Collision oftwo head-on solitons and two head-on two-peak solitons;(ⅴ) Two different types of interactions of the three solitons;(ⅵ) Decomposition phenomenon of one soliton into two solitons.The results might be useful in the study on theultrashort-pulse propagation in the inhomogeneous multi-component nonlinear media.
基金supported by the National Natural Science Foundation of China(Nos.11771090,11571376)
文摘In this paper,the authors consider the asymptotic behavior of the monic polynomials orthogonal with respect to the weight function w(x) = |x|^(2α)e^(-(x^4+tx^2)),x ∈ R,where α is a constant larger than -1/2 and t is any real number. They consider this problem in three separate cases:(i) c >-2,(ii) c =-2,and(iii) c <-2,where c := t N^(-1/2) is a constant,N = n + α and n is the degree of the polynomial. In the first two cases,the support of the associated equilibrium measure μ_t is a single interval,whereas in the third case the support of μ_t consists of two intervals. In each case,globally uniform asymptotic expansions are obtained in several regions. These regions together cover the whole complex plane. The approach is based on a modified version of the steepest descent method for Riemann-Hilbert problems introduced by Deift and Zhou(1993).
基金Research Project supported by the National Natural Science Foundation of China(No.11961051)Provincial Natural Science Foundation of Shanxi(20210302123097)Shanxi Scholarship Council of China。
文摘It is difficult to characterize graphs which contain no a 2-connected graph as a minor in graph theory.Let V_(8)be a graph constructed from an 8-cycle by connecting the antipodal vertices.There are thirteen 2-connected spanning subgraphs of V_(8).In particular,one of them is obtained from the Petersen graph by deleting two vertices and it is also a hard problem to characterize Petersen-minor-free graphs.In this paper,we characterize internally 4-connected graphs which contain a 2-connected spanning subgraph of V_(8)as a forbidden minor.
文摘In this paper, we show that if an injective map on symmetric matrices Sn(C) satisfies then for all , where f is an injective homomorphism on C, S is a complex orthogonal matrix and Af is the image of A under f applied entrywise.
基金supported by National Natural Science Foundation of China (Grant No. 11101250)supported by National Natural Science Foundation of China (Grant No. 11171249)Youth Foundation of Shanxi Province (Grant No. 2012021004)
文摘Let U = Tri(A,M,B) be a triangular ring, where A and B are unital rings, and M is a faithful (A, B)-bimodule. It is shown that an additive map Φ on U is centralized at zero point (i.e., Φ(A)B = AΦ(B) = 0 whenever AB = 0) if and only if it is a centralizer. Let δ : U → U be an additive map. It is also shown that the following four conditions are equivalent: (1) δ is specially generalized derivable at zero point, i.e., δ(AB) = δ(A)B + Aδ(B) Aδ(I)B whenever AB = 0; (2) δ is generalized derivable at zero point, i.e., there exist additive maps τ1 and τ2 on U derivable at zero point such that δ(AB) = δ(A)B + Aτ1 (B) = τ2 (A)B + Aδ(B) whenever AB = 0; (3) δ is a special generalized derivation; (4) δ is a generalized derivation. These results are then applied to nest algebras of Banach space.
