中国科学院数学与系统科学研究院期刊网

10 July 2010, Volume 26 Issue 7
    

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  • Jeong Ja BAE
    Acta Mathematica Sinica. 2010, 26(7): 1197-1206. https://doi.org/10.1007/s10114-010-8058-y
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    In this paper we consider the large time behavior of solutions to an n-dimensional trans-mission problem for two Kirchho-type viscoelastic wave equations,that is,the wave propagation overbodies consisting of two physically different types of materials.One component is a simple elastic partwhile the other is a viscoelastic component endowed with a long range memory.We show that thedissipation produced by the viscoelastic part is strong enough to produce exponential or polynomialdecay of the solution
  • Serkan DEMIRIZ, Celal CAKAN
    Acta Mathematica Sinica. 2010, 26(7): 1207-1222. https://doi.org/10.1007/s10114-010-8334-x
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    In this paper,the sequence spaces er0(u,p)and erc(u,p)of non-absolute type which are thegeneralization of the Maddox sequence spaces have been introduced and it is proved that the spaceser0(u,p)and erc(u,p)are linearly isomorphic to spaces c0(p)and c(p),respectively.Furthermore,theα-,β-andγ-duals of the spaces er0(u,p)and erc(u,p)have been computed and their bases have beenconstructed and some topological properties of these spaces have been investigated.Besides this,theclass of matrices(er0(u,p):μ)has been characterized,whereμis one of the sequence spaces∞,c andc0 and derives the other characterizations for the special cases ofμ.In the last section,Euler Core ofa complex-valued sequence has been introduced,and we prove some inclusion theorems related to thisnew type of core.
  • Shang Quan BU
    Acta Mathematica Sinica. 2010, 26(7): 1223-1232. https://doi.org/10.1007/s10114-010-9231-z
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    We study the well-posedness of the equations with fractional derivative Dαu(t)=Au(t)+f(t),0≤t≤2π,where A is a closed operator in a Banach space X,α>0 and Dαis the fractionalderivative in the sense of Weyl.Using known results on Lp-multipliers,we give necessary and/orsuffcient conditions for the Lp-well-posedness of this problem.The conditions we give involve theresolvent of A and the Rademacher boundedness.Corresponding results on the well-posedness of thisproblem in periodic Besov spaces,periodic Triebel–Lizorkin spaces and periodic Hardy spaces are alsoobtained.
  • Wai Chee SHIU, Man Ho LING
    Acta Mathematica Sinica. 2010, 26(7): 1233-1244. https://doi.org/10.1007/s10114-010-8517-5
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    Let G=(V,E)be a connected simple graph.A labeling f-1:V→Z2 induces an edgelabeling f-1*:E→Z2 def-1ined by f-1*(xy)=f-1(x)+f-1(y)f-1or each xy∈E.f-1or i∈Z2,let vf-1(i)=|f-1-1(i)|and ef-1(i)=|f-1*-1(i)|.A labeling f-1 is called f-1riendly if-1|vf-1(1)-vf-1(0)|≤1.f-1or a f-1riendly labeling f-1 of-1a graph G,we def-1ine the f-1riendly index of-1 G under f-1 by if-1(G)=ef-1(1)-ef-1(0).The set{if-1(G)|f-1 is af-1riendly labeling of-1 G}is called the f-1ull f-1riendly index set of-1 G,denoted by f-1f-1I(G).In this paper,wewill determine the f-1ull f-1riendly index set of-1 every Cartesian product of-1 two cycles.
  • Shan Zhen LU, Fa You ZHAO
    Acta Mathematica Sinica. 2010, 26(7): 1245-1254. https://doi.org/10.1007/s10114-010-8603-8
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    The purpose of this paper is to study the multilinear Hardy operators in higher dimensionalcases and establish the CBMO estimates for multilinear Hardy operators on some function spaces,suchas the Lebesgue spaces,the Herz spaces and the Morrey–Herz spaces.
  • Kil Woung JUN, Sang Baek LEE, Won Gil PARK
    Acta Mathematica Sinica. 2010, 26(7): 1255-1262. https://doi.org/10.1007/s10114-010-8621-6
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    In this paper,we investigate the general solution and the stability of a cubic functionalequationf(x+ny)+f(x-ny)+f(nx)=n2f(x+y)+n2f(x-y)+(n3-2n2+2)f(x),where n≥2 is an integer.Furthermore,we prove the stability by the fixed point method.
  • Yu Xia GUO, Guang Zhong CHEN
    Acta Mathematica Sinica. 2010, 26(7): 1263-1276. https://doi.org/10.1007/s10114-010-8042-6
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    In this note,we prove the existence of positive solutions to a class of biharmonical systems.Our main ingredients are proving a Liouville type result for biharmonical system in RN+via the methodof moving plane combined with integral inequality,and establishing a prior estimates for positivesolutions of the system via the blowing-up method.
  • Xiao Huan MO, Fang SUN
    Acta Mathematica Sinica. 2010, 26(7): 1277-1286. https://doi.org/10.1007/s10114-010-8599-0
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    We show that any harmonic sequence determined by a harmonic map from a compactRiemannian surface M to CPn has a terminating holomorphic(or anti-holomorphic)map from M toCPn,or a“bubble tree limit”consisting of a harmonic map f:M→CPn and a tree of bubbleshμλ:S2→CPn.
  • Gang MENG, Mei Rong ZHANG
    Acta Mathematica Sinica. 2010, 26(7): 1287-1298. https://doi.org/10.1007/s10114-010-8103-x
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    In this paper we study important quantities defined from solutions of first order linearsystems of ordinary differential equations.It will be proved that many quantities,such as solutions,eigenvalues of one-dimensional Dirac operators,Lyapunov exponents and rotation numbers,depend onthe coeffcients in a very strong way.That is,they are not only continuous in coeffcients with respect tothe usual Lp topologies,but also with respect to the weak topologies of the Lp spaces.The continuityresults of this paper are a basis to study these quantities in a quantitative way.
  • Hong Xin GUO
    Acta Mathematica Sinica. 2010, 26(7): 1299-1308. https://doi.org/10.1007/s10114-010-9266-1
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    In this paper,we derive evolution equation of the integral of the Gauss curvature on anevolving hypersurface.As an application,we obtain a monotone quantity on the level surface of thepotential function on a 3-dimensional steady gradient Ricci soliton with positive sectional curvature,and prove that such a soliton is rotationally symmetric outside of a compact set under a curvaturedecaying assumption.Along the way we will also apply our evolution equation to some other cases.
  • Javier CILLERUELO
    Acta Mathematica Sinica. 2010, 26(7): 1309-1314. https://doi.org/10.1007/s10114-010-8272-7
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    We use the probabilistic method to prove that for any positive integer g there exists aninfinite B2[g]sequence A={ak}such that ak≤k2+1/g(log k)1/g+o(1)as k→∞.The exponent 2+1/gimproves the previous one,2+2/g,obtained by Erdffos and Renyi in 1960.We obtain a similar resultfor B2[g]sequences of squares.
  • Min XU
    Acta Mathematica Sinica. 2010, 26(7): 1315-1322. https://doi.org/10.1007/s10114-010-8581-x
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    The twisted cube T Qn is a variant of the hypercube Qn.It has been shown by Chang,Wang and Hsu[Topological properties of twisted cube.Information Science,113,147–167(1999)]thatT Qn contains a cycle of every length from 4 to 2n.In this paper,we improve this result by showingthat every edge of T Qn lies on a cycle of every length from 4 to 2n inclusive.We also show that thetwisted cube are Hamiltonian connected.
  • Wei HE, Mao Kang LUO
    Acta Mathematica Sinica. 2010, 26(7): 1323-1330. https://doi.org/10.1007/s10114-010-7511-2
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    In this paper,a more general concept of quantum space is given by modifying the originalconcept defined by Borceux and Bossche.We show that a quantum space is a topological analogueof a quantale defined by Mulvey,and also a non-commutative generalization of the Zariski spectrumof a commutative ring.But quantum spaces are not good enough to have much of the properties oftopological spaces,such as product spaces and quotient spaces.
  • Jun Wu DONG
    Acta Mathematica Sinica. 2010, 26(7): 1331-1344. https://doi.org/10.1007/s10114-010-7442-y
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    Let M be a subset of r-dimensional vector space Vr(F2)over a finite field F2,consisting ofn nonzero vectors,such that every t vectors of M are linearly independent over F2.Then M is called(n,t)-linearly independent array of length n over Vr(F2).The(n,t)-linearly independent array M thathas the maximal number of elements is called the maximal(r,t)-linearly independent array,and themaximal number is denoted by M(r,t).It is an interesting combinatorial structure,which has manyapplications in cryptography and coding theory.It can be used to construct orthogonal arrays,strongpartial balanced designs.It can also be used to design good linear codes.In this paper,we constructa class of maximal(r,t)-linearly independent arrays of length r+2,and provide some enumeratortheorems.
  • Tao HAO
    Acta Mathematica Sinica. 2010, 26(7): 1345-1354. https://doi.org/10.1007/s10114-010-7566-0
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    In this paper,the existence of sign-changing solutions for p-Laplacian equation is obtainedvia a new linking theorem.
  • You Jun WANG, Yao Tian SHEN
    Acta Mathematica Sinica. 2010, 26(7): 1355-1368. https://doi.org/10.1007/s10114-010-7383-5
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    In this paper we study a class of subsets of the general Sierpinski carpets for which twogroups of allowed digits occur in the expansions with proportional frequency.We calculate the Hausdor?and Box dimensions of these subsets and give necessary and su?cient conditions for the correspondingHausdor?measure to be positive and finite.
  • Yong Xin GUI
    Acta Mathematica Sinica. 2010, 26(7): 1369-1382. https://doi.org/10.1007/s10114-010-7191-y
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    We investigate the contact process on random graphs generated from the configurationmodel for scale-free complex networks with the power law exponentβ∈(2,3].Using the neighborhoodexpansion method,we show that,with positive probability,any disease with an infection rateλ>0can survive for exponential time in the number of vertices of the graph.This strongly supports theview that stochastic scale-free networks are remarkably different from traditional regular graphs,suchas Zd and classical Erdffos–Renyi random graphs.
  • Dayue CHEN, Qi LIU
    Acta Mathematica Sinica. 2010, 26(7): 1383-1392. https://doi.org/10.1007/s10114-010-6611-3
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    Suppose f(z)is a quadratic rational map with two Siegel disks.If the rotation numbers ofthe Siegel disks are both of bounded type,the Hausdor?dimension of the Julia set satisfies Dim(J(f))<2.
  • Liang SHEN, Sheng Jian WU
    Acta Mathematica Sinica. 2010, 26(7): 1393-1402. https://doi.org/10.1007/s10114-010-7582-0
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    In this paper,we introduce the notion of g-variance and study some properties of thisoperator.We find the nonlinear variance operator,g-variance,does not preserve some basic propertiesof traditional mathematic variance.We also consider the relationship Dμ[ξ]and supQ∈P1TVarQ[ξ](D[ξ]and infQ∈P1TVarQ[ξ]).The result shows that the maximum(minimum)variance is not alwaysequal to Dμ[·](D[·]).If g satisfies some restrictive conditions,we get the uniqueness theorem andthe comparison theorem via g-variance.