查看更多>>摘要：Based on the residual implication of continuous triangular norms,we obtain the expression of residual operator for extended operators(type-2 triangular norms)of continuous triangular norms on convex normal upper semi-continuous fuzzy truth values,answering an open problem in[D.LI,Inf.Sci.,2015,317:259-277].
查看更多>>摘要：In this paper,we give some sufficient conditions for a graph to be traceable in terms of its order and size.As applications,the normalized Laplacian spectral conditions for a graph to be traceable are established.
查看更多>>摘要：For a simple undirected graph G with fixed size m ≥ 2k(k ∈ Z+)and maximum degree Δ(G)≤ m-k,we give an upper bound on the signless Laplacian spectral radius q(G)of G.For two connected graphs G1 and G2 with size m ≥ 8,employing this upper bound,we prove that q(G1)＞q(G2)if Δ(G1)＞Δ(G2)+1 and Δ(G1)≥ m/2+2.For triangle-free graphs,we prove two stronger results.As an application,we completely characterize the graph with maximal signless Laplacian spectral radius among all graphs with size m and circumference c for m ≥ max{2c,c+9},which partially answers the question proposed by Chen et al.in[Linear Algebra Appl.,2022,645:123-136].
查看更多>>摘要：Let (A)be an abelian category,(J)a self-orthogonal subcategory of(A)and each object in(J)admit finite projective and injective dimensions.If the left Gorenstein subcategory l(G)((J))equals to the right orthogonal class of(J)and the right Gorenstein subcategory r(G)((J))equals to the left orthogonal class of(J),we prove that the Gorenstein subcategory(G)((J))equals to the intersection of the left orthogonal class of(J)and the right orthogonal class of(J),and prove that their stable categories are triangle equivalent to the relative singularity category of(A)with respect to(J).As applications,let R be a left Noetherian ring with finite left self-injective dimension and RCs a semidualizing bimodule,and let the supremum of the flat dimensions of all injective left R-modules be finite.We prove that if RC has finite injective(or flat)dimension and the right orthogonal class of C contains R,then there exists a triangle-equivalence between the intersection of C-Gorenstein projective modules and Bass class with respect to C,and the relative singularity category with respect to C-projective modules.Some classical results are generalized.
查看更多>>摘要：In this paper,the existence and growth of entire solutions of some type of nonlinear delay-differential equations are studied.Using Cartan's second main theorem and Nevanlinna theory of meromorphic functions,we obtain the exact forms of its entire solutions with hyper-order less than one.
查看更多>>摘要：Let T,U be two Artin algebras and UMT be a U-T-bimodule.In this paper,we get a necessary and sufficient condition such that the formal triangular matrix algebra A=(TM 0U)is(m,n)-Igusa-Todorov when uM,MT are projective.We also study the Igusa-Todorov dimension of A.More specifically,it is proved that nax{IT.dim T,IT.dim U} ≤ IT.dim A ≤ min{max{gl.dim T,IT.dim U},max{gl.dim U,IT.dim T}}.
查看更多>>摘要：In this work,we study the error estimates of the fully discrete Fourier pseudo-spectral numerical scheme for solving the nonlocal volume-conserved Allen-Cahn(AC)equation.The time marching method of the numerical scheme is based on the well-known Invariant En-ergy Quadratization(IEQ)method.We demonstrate that the proposed fully discrete numerical method is uniquely solvable,unconditionally energy stable,and obtain the optimal error esti-mate of the scheme for both space and time.Additionally,we conduct several numerical tests to verify the theoretical results.
查看更多>>摘要：In this paper,the Cauchy problem of biharmonic equation is considered.This problem is ill-posed,i.e.,the solution(if exists)does not depend on the measurable data.Firstly,we give the conditional stability result under the a priori bound assumption for the exact solution.Secondly,a modified Tikhonov regularization method is used to solve this ill-posed problem.Under the a priori and the a posteriori regularization parameter choice rule,the error estimates between the regularization solutions and the exact solution are obtained.Finally,some numerical examples are presented to verify that our method is effective.
查看更多>>摘要：Let A be a commutative unital C*-algebra with the unit element e and M be a full Hilbert A-module.Denote by EndA(M)the algebra of all bounded A-linear mappings on M and by M'the set of all bounded A-linear mappings from M into A.In this paper,we prove that if there exists x0 in M and f0 in M'such that f0(x0)=e,then every A-linear Lie triple derivation on EndA(M)is standard.
查看更多>>摘要：In this paper,we mainly study fuzzy(quasi-)pseudo-b-metrics on algebraic structures.We mainly establish the following results:(1)If a group G with a topology τ,which is induced by a left invariant fuzzy quasi-pseudo-b-metric(resp.,pseudo-b-metric)on the G,is a right topological group,then G with the topology τ is a paratopological group(resp.,a topological group)and(2)If a semigroup S with a topology τ is induced by an invariant fuzzy quasi-pseudo-b-metric,then S with the topology τ is a topological semigroup.
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