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数学研究及应用
数学研究及应用

王仁宏

双月刊

2095-2651

jmre@dlut.edu.cn

0411-84707392

116024

大连理工大学应用数学系

数学研究及应用/Journal Journal of mathematical research with applicationsCSCD北大核心CSTPCD
查看更多>>本刊是国家教育部主管、大连理工大学主办的数学类学术性刊物。其宗旨是推进数学研究、评论数学研究、及时报道数学理论成果与应用数学成果。主要刊载有关数学的原创性的高质量的论文、研究简报、研究通讯；国内外数学著作的评论；数学方法论、数理哲学方面的文章。还介绍某些新兴边缘学科的数学研究方法及数学新分支，反映国内外数学工作者提出的未解决问题及国内外重要数学学术研究动态。读者对象是数学工作者、大专院校数学教师、理工科研究生、数学和力学专业高年级学生、有关科技工作者以及其他数学爱好者。
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    Enumerating Pattern-avoiding Fishburn Permutations Subject to Seven Statistics

    Yujie DUPhilip B.ZHANG
    427-436页
    查看更多>>摘要：Fishburn permutations are in bijection with several important combinatorial struc-tures including interval orders.In this paper,we use the method of generating trees to enumerate two classes of pattern-avoiding Fishburn permutations subject to 7 classical statistics simulta-neously.The classes of our interest are(321,312)-avoiding and(321,4123)-avoiding Fishburn permutations.The statistics of our interest are ascents,descents,inversions,right-to-left maxi-ma,right-to-left minima,left-to-right maxima and left-to-right minima.Our results generalize a result by Egge.
      原文链接:
    • NETL
    • NSTL
    • 万方数据

    An Involution over Dyck Paths Related with Stirling Statistics

    Peng CAOJoanna N.CHEN
    437-443页
    查看更多>>摘要：We construct an involution over Dyck paths,which implies the distribution of s-tatistics"the number of peak","the number of returns"and"the height of the last peak".As an application,equidistributions of several Stirling statistics over 132-avoiding and 321-avoiding permutations are presented.
      原文链接:
    • NETL
    • NSTL
    • 万方数据

    On Integral Graphs which Belong to the Class(αKa,a,a ∪ βKb,b,b)

    Mirko LEPOVI?
    444-464页
    查看更多>>摘要：Let G be a simple graph and let (G) denote its complement.We say that G is integral if its spectrum consists entirely of integers.In this work we establish a characterization of integral graphs which belong to the class(αKa,a,a ∪ βKb,b,b),where mG denotes the m-fold union of the graph G.
      原文链接:
    • NETL
    • NSTL
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    Multicolor Ramsey Number of Stars Versus a Path

    Xuejun ZHANGXinmin HOU
    465-469页
    查看更多>>摘要：For given simple graphs H1,H2,…,Hc,the multicolor Ramsey number R(H1,H2,...,Hc)is defined as the smallest positive integer n such that for an arbitrary edge-decomposition{Gi}ci=1 of the complete graph Kn,at least one Gi has a subgraph isomorphic to Hi.Let m,n1,n2,...,nc be positive integers and Σ=Σci=1(ni-1).Some bounds and exact values of R(K1,n1,...,K1,nc,Pm)have been obtained in literature.Wang(Graphs Combin.,2020)conjec-tured that if Σ(≠)0(mod m-1)and Σ+1 ≥(m-3)2,then R(K1,n1,...,K1,nc,Pm)=Σ+m-1.In this note,we give a new lower bound and some exact values of R(K1,n1,...,K1,nc,Pm)pro-vided m ≤ Σ,Σ ≡ k(mod m-1),and 2 ≤ k ≤ m-2.These results partially confirm Wang's conjecture.
      原文链接:
    • NETL
    • NSTL
    • 万方数据

    On the Zeros of a Special Class of Polynomials

    Mahnaz Shafi CHISHTIVipin Kumar TYAGIMohammad Ibrahim MIR
    470-474页
    查看更多>>摘要：Let P be a complex polynomial of the form P(z)=(λz-a)m Πn-mj=1(2-zj),where|zj|≥ 1,1 ≤ j ≤ n-m.The aim of this paper is to obtain generalisation of a result due to Zargar and Manzoor and a result due to Mir,Nazir and Wani.We shall also obtain an interesting bound which contains the zeros of the second derivative of P(z).
      原文链接:
    • NETL
    • NSTL
    • 万方数据

    FI-t-Lifting Modules and T-Quasi-Dual Baer Modules

    Yu WANGYongduo WANG
    475-482页
    查看更多>>摘要：The notions of FI-t-lifting modules and t-quasi-dual Baer modules are introduced and the relations between them are studied in this paper.It is shown that an amply supplemented module M is an FI-t-lifting module if and only if every fully invariant t-coclosed submodule of M is a direct summand of M if and only if(Z)2(M)is a direct summand of M and(Z)2(M)is an FI-lifting module if and only if M is t-quasi-dual Baer and an FI-t-K-module.
      原文链接:
    • NETL
    • NSTL
    • 万方数据

    The Complementarity of Normalized Solutions for Kirchhoff Equations with Mixed Nonlinearity

    Lin XUQilin XIE
    483-494页
    查看更多>>摘要：In this paper,we study the existence of solutions for Kirchhoff equation-(a+b∫(R)3|▽u|2dx)△u=λu+μ|u|q-2u+|u|p-2u,x ∈(R)3 with mass constraint condition Sc:={u ∈ H1((R)3):∫(R)3|u|2dx=c},where a,b,c＞0,μ ∈(R),2＜q＜p＜6,and λ ∈(R)appears as a Lagrange multiplier.For the range of p and q,the Sobolev critical exponent 6 and mass critical exponent 14/3 are involved where corresponding energy functional is unbounded from below on Sc.We consider the focusing case,i.e.,μ＞0 when(p,q)belongs to a certain domain in (R)2.We prove the existence of normalized solutions by using constraint minimization,concentration compactness principle and Minimax methods.We partially extend the results which have been studied.
      原文链接:
    • NETL
    • NSTL
    • 万方数据

    Gradient Estimate for an Exponentially Harmonic Type Heat Equation on Riemannian Manifolds

    Jianyi MAOXinrong JIANG
    495-501页
    查看更多>>摘要：In this paper,we derive a Hamilton-Souplet-Zhang type gradient estimate for expo-nentially harmonic type heat equation on Riemannian manifolds.As its application,we obtain a Liouville type theorem.
      原文链接:
    • NETL
    • NSTL
    • 万方数据

    On Ideal-Derived-Set Mappings in Uniform Spaces

    Lihua LINXiangeng ZHOU
    502-510页
    查看更多>>摘要：In this paper,we introduce some ideal-derived-set mappings in uniform spaces and investigate the images of those mappings.Meanwhile,we introduce a concept of (I)-Hurewicz boundedness,study some basic topological operations of them.Finally,we obtain an equivalent characterization of(I)-Hurewicz boundedness in uniform spaces.
      原文链接:
    • NETL
    • NSTL
    • 万方数据

    Positive Solutions of Second Order Discrete Problem on Infinite Intervals

    Haiyi WUTianlan CHEN
    511-520页
    查看更多>>摘要：In this paper,by using the discrete Arzelá-Ascoli Lemma and the fixed-point theorem in cones,we discuss the existence of positive solutions of the following second order discrete Sturm-Liouville boundary value problem on infinite intervals{-△2u(x-1)=f(x,u(x),△u(x-1)),x ∈ N,u(0)-a△u(0)=B,△u(∞)=C,where △u(x)=u(x+1)-u(x)is the forward difference operator,N={1,2,...,∞},f:(N)×(R)+×(R)+→(R)+is continuous,a＞0,B and C are nonnegative constants,(R)+=[0,+∞),△u(∞)=limx→∞ △u(x).
      原文链接:
    • NETL
    • NSTL
    • 万方数据