查看更多>>摘要：A graph G is said to be planar if G can be drawn on the plane in such a way that its edges intersect only at their endpoints.In this paper,all the planar graphs without isolated vertices whose second largest eigenvalue smaller than√5-1/2are characterized.
查看更多>>摘要：A signed graph S=(Su,a)has an underlying graph Su and a function σ:E(Su)→{+,=}.Let E-(S)denote the set of negative edges of S.Then S is eulerian signed graph(or subeulerian signed graph,or balanced eulerian signed graph,respectively)if Su is eulerian(or subeulerian,or eulerian and |E-(S)| is even,respectively).We say that S is balanced subeulerian signed graph if there exists a balanced eulerian signed graph S'such that S'is spanned by S.The signed line graph L(S)of a signed graph S is a signed graph with the vertices of L(S)being the edges of S,where an edge eiej is in L(S)if and only if the edges ei and ej of S have a vertex in common in S such that an edge eiej in L(S)is negative if and only if both edges ei and ej are negative in S.In this paper,two families of signed graphs S and S'are identified,which are applied to characterize balanced subeulerian signed graphs and balanced subeulerian signed line graphs.In particular,it is proved that a signed graph S is balanced subeulerian if and only if S(∈)S,and that a signed line graph of signed graph S is balanced subeulerian if and only if S(∈)S'.
查看更多>>摘要：A right module M over an associative ring R with unity is a QTAG-module if every finitely generated submodule of any homomorphic image of M is a direct sum of uniserial modules.This article considers the closure of h-pure-S-high submodules of QTAG-modules.Here,we determine all submodules S of a QTAG-module M such that each closure of h-pure-S-high submodule of M is h-pure-(S)-high in (M).A few results of this theme give a comparison of some elementary properties of h-pure-S-high and S-high submodules.
查看更多>>摘要：In this paper,we study the relations between the class of A-Gorenstein projective modules and the left orthogonal class of A,also the relations between the class of A-Gorenstein injective modules and the right orthogonal class of A.Some functor characterizations of A-Gorenstein projective modules and A-Gorenstein injective modules are obtained.Using the no-tion of complete duality pair,we discuss the relations between A-Gorenstein projective modules and B-Gorenstein flat modules.Some known results are generalized.
查看更多>>摘要：We prove the existence of solutions of the system for nonlocal Neumann problems with Minkowski-curvature operator(rN-1u'/√1-u'2)'=rN-1f(r,u),r∈(0,1),u'(0)=0,u'(1)=∫01u'(s)dg(s),where k,N ≥ 1 are integers,f:[0,1]× Rk → Rk is continuous and g:[0,1]→ Rk is a function of bounded variation.Our proof is based on the perturbation method.
查看更多>>摘要：The main goal of this paper is to establish the boundedness of bilinear strongly singular operator (T) and its commutator (T)b1,b2 on generalized Morrey spaces Mup(μ)over non-homogeneous metric measure spaces.Under assumption that the Lebesgue measurable functions u,u1 and u2 belong to Wτ for τ ∈(0,2),and u1u2=u.The authors prove that (T) is bounded from product spaces Mu1p1(μ×Mu2p2(μ)into spaces Mup(μ),where 1/p=1/p1+1/p2 with 1＜p1,p2＜∞;and also bounded from product spaces Mu1p1(μ)×Mu2p2(μ)into generalized weak Morrey spaces WMup(μ).Furthermore,the author also show that commutator (T)b1,b2generated by b1,b2 ∈RBMO(μ)and (T) is bounded from product spaces Mu1p1(μ)× Mu2p2(μ)into spaces Mup(μ).
查看更多>>摘要：In this paper,we study the necessary and sufficient condition that the Toeplitz operators with respect to the conjugations of one permutation are 2-complex symmetric.Firstly,we introduce a class of conjugations called the conjugations of one permutations on the classical Hardy space.Secondly,Toeplitz operators are completely characterized as 2-complex symmetric structure under this class of conjugations.The matrix representation of Toeplitz operators in the classical regular orthogonal basis on Hardy space is used to describe this class of 2-complex symmetric Toeplitz operators.Finally,we add two preconditions fn=-f-n and fn=f-n respectively to the Toeplitz operators,and we get more simplified results.Under the second condition,we study the 3-complex symmetry of Toeplitz operators,and we get the same result for Tf is a 3-CSO with the conjugation C(i,j)and 2-CSO's.
查看更多>>摘要：In this paper,we mainly consider the long-time behavior of stochastic non-autonomous suspension bridge equation by linear multiplicative white noise with small coefficient.First step,the well-posedness for the cocycle associated with the considered system is established.Second step,the existence of random attractor for the system is investigated.Third step,the upper semi-continuity of random attractor is also provided when the coefficient of random term approaches zero.Fourth step,we prove the regularity of random attractor in a higher regular space by the"iteration"method.Finally,we give the existence of a random exponential attractor for the considered system,which implies the finiteness of fractal dimension of random attractor.
查看更多>>摘要：In this paper,we introduce the notion of a generalized weak group-like algebra which is designed to cover finite groupoid algebras and group-like algebras.Then we construct a list of examples and show that a generalized weak group-like algebra can be regarded as a generalized weak bi-Frobenius algebra.Moreover,we discuss when a generalized weak bi-Frobenius algebra is a groupoid algebra.Finally,we give the classifications of low-dimensional generalized weak group-like algebras.
查看更多>>摘要：Impulse noise removal is an important task in image restoration.In this paper,we introduce a general nonsmooth nonconvex model for recovering images degraded by blur and impulsive noise,which can easily include some prior information,such as box constraint or low rank,etc.To deal with the nonconvex problem,we employ the proximal linearized minimization algorithm.For the subproblem,we use the alternating direction method of multipliers to solve it.Furthermore,based on the assumption that the objective function satisfies the Kurdyka-Lojasiewicz property,we prove the global convergence of the proposed algorithm.Numerical experiments demonstrate that our method outperforms both the l1TV and Nonconvex TV mod-els in terms of subjective and objective quality measurements.
NETL
NSTL
万方数据