中国科学院数学与系统科学研究院期刊网

15 September 2009, Volume 25 Issue 9
    

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  • Anton BETTEN, Anne DELANDTSHEER
    Acta Mathematica Sinica. 2009, 25(9): 1399-1436. https://doi.org/10.1007/s10114-009-9275-0
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    The paper summarises existing theory and classifications for finite line-transitive linearspaces,develops the theory further,and organises it in a way that enables its effective application.Thestarting point is a theorem of Camina and the fifth author that identifies three kinds of line-transitiveautomorphism groups of linear spaces.In two of these cases the group may be imprimitive on points,that is,the group leaves invariant a nontrivial partition of the point set.In the first of these casesthe group is almost simple with point-transitive simple socle,and may or may not be point-primitive,while in the second case the group has a non-trivial point-intransitive normal subgroup and hence isdefinitely point-imprimitive.The theory presented here focuses on point-imprimitive groups.As anon-trivial application a classification is given of the point-imprimitive,line-transitive groups,and thecorresponding linear spaces,for which the greatest common divisor gcd(k,v-1)≤8,where v is thenumber of points,and k is the line size.Motivation for this classification comes from a result of WeidongFang and Huiling Li in 1993,that there are only finitely many non-trivial point-imprimitive,line-transitive linear spaces for a given value of gcd(k,v-1).The classification strengthens the classificationby Camina and Mischke under the much stronger restriction k≤8:no additional examples arise.The paper provides the backbone for future computer-based classifications of point-imprimitive,line-transitive linear spaces with small parameters.Several suggestions for further investigations are made.
  • George E.ANDREWS
    Acta Mathematica Sinica. 2009, 25(9): 1437-1442. https://doi.org/10.1007/s10114-009-6292-y
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    A variety of interesting connections with modular forms,mock theta functions and Rogers–Ramanujan type identities arise in consideration of partitions in which the smaller integers are repeatedas summands more often than the larger summands.In particular,this concept leads to new interpre-tations of the Rogers–Selberg identities and Bailey’s modulus 9 identities.
  • Meirav AMRAM, Michael FRIEDMAN, Mina TEICHER
    Acta Mathematica Sinica. 2009, 25(9): 1443-1458. https://doi.org/10.1007/s10114-009-6473-8
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    Denoting by T the complex projective torus,we can embed the surface CP1×T in CP5.Inthis paper we compute the fundamental group of the complement of the branch curve of this surface.Since the embedding is not“ample enough”,the embedded surface does not belong to the classes ofsurfaces where the fundamental group is virtually solvable:a property which holds for these groupsfor“ample enough”embeddings.On the other hand,as it is the first example of this computation fornon simply-connected surfaces,the structure of this group(as shown in this paper)give rise to theextension of the conjecture regarding the structure of those fundamental groups of any surface.
  • Jae-Young CHUNG
    Acta Mathematica Sinica. 2009, 25(9): 1459-1468. https://doi.org/10.1007/s10114-009-8254-9
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    We consider the Hyers–Ulam stability problem of the generalized quadratic functionaοequatioοuοA+vοBο2wοP1ο2κοP2=0οwhich is a distributional version of the classical generalized quadratic functional equatioοf(x+y)+g(x-y)-2h(x)-2k(y)=0ο
  • Jian LIU, Jian Guo SI
    Acta Mathematica Sinica. 2009, 25(9): 1469-1482. https://doi.org/10.1007/s10114-009-8489-5
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    In this paper,the diffierential equation involving iterates of the unknown function,x(z)=[a2-x2(z)]x[m](z)with a complex parameter a,is investigated in the complex field C for the existence of analytic solutions.First of all,we discuss the existence and the continuous dependence on the parameter a of analyticsolution for the above equation,by making use of Banach fixed point theorem.Then,as well as inmany previous works,we reduce the equation with the Schroder transformation x(z)=y(αy-1(z))tothe following another functional differential equation without iteration of the unknown functionαy(αz)=[a2-y2(αz)]y(z)y(αmz),which is called an auxiliary equation.By constructing local invertible analytic solutions of the auxiliaryequation,analytic solutions of the form y(αy-1(z))for the original iterative diffierential equation areobtained.We discuss not only theseαgiven in Schroder transformation in the hyperbolic case 0<|α|<1 and resonance,i.e.,at a root of the unity,but also thoseαnear resonance(i.e.,near a rootof the unity)under Brjuno condition.Finally,we introduce explicit analytic solutions for the originaliterative diffierential equation by means of a recurrent formula,and give some particular solutions inthe form of power functions when a=0.
  • A.O.MOSTAFA, M.K.AOUF
    Acta Mathematica Sinica. 2009, 25(9): 1483-1496. https://doi.org/10.1007/s10114-009-8211-7
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    Making use of the principle of differential subordination,we investigate some inclusionrelationships of certain subclasses of p-valent analytic functions which are defined by Cho–Kwon–Srivastava Operator.
  • Hao DING
    Acta Mathematica Sinica. 2009, 25(9): 1497-1506. https://doi.org/10.1007/s10114-009-8087-6
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    In this note,we give a generalization of the famous combinational identity(-1)nn!=−nk=1(nk)(-1)kkn arising from symplectic geometry.
  • Yan LIU, Gui Ying YAN
    Acta Mathematica Sinica. 2009, 25(9): 1507-1516. https://doi.org/10.1007/s10114-009-7676-8
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    The maximum matching graph M(G)of a graph G is a simple graph whose vertices arethe maximum matchings of G and where two maximum matchings are adjacent in M(G)if they diffierby exactly one edge.In this paper,we prove that if a graph is isomorphic to its maximum matchinggraph,then every block of the graph is an odd cycle.
  • Li Ping HUANG
    Acta Mathematica Sinica. 2009, 25(9): 1517-1528. https://doi.org/10.1007/s10114-009-7697-3
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    Let F be a field with|F|≥3,Km be the set of all m×m(m≥4)alternate matrices overF.The arithmetic distance of A,B∈Km is d(A,B):=rank(A-B).If d(A,B)=2,then A and B aresaid to be adjacent.The diameter of Km is max{d(A,B):A,B∈Km}.Assume thatφ:Km→Kmis a map.We prove the following are equivalent:(a)φis a diameter preserving surjection in bothdirections,(b)is both an adjacency preserving surjection and a diameter preserving map,(c)φis abijective map which preserves the arithmetic distance.
  • Abbas NAJATI
    Acta Mathematica Sinica. 2009, 25(9): 1529-1542. https://doi.org/10.1007/s10114-009-7648-z
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    In this paper,we prove the generalized Hyers–Ulam stability of homomorphisms in quasi-Banach algebras associated with the following Pexiderized Jensen functional equationf(x+y/2)+z-g(x-y/2)+z=h(y).This is applied to investigating homomorphisms between quasi-Banach algebras.The concept of thegeneralized Hyers–Ulam stability originated from Rassias’stability theorem that appeared in his paper:On the stability of the linear mapping in Banach spaces,Proc.Amer.Math.Soc.,72,297–300(1978).
  • Miloud ASSAL
    Acta Mathematica Sinica. 2009, 25(9): 1543-1560. https://doi.org/10.1007/s10114-009-7309-2
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    In this paper we introduce the homogeneous Besov type spaces•Λγp,q(K)on the dual ofLaguerre hypergroup K and we establish some new harmonic analysis results.We give some character-izations of these spaces using equivalent seminorms.Also we study the non-homogeneous Besov typespacesΛγp,q(K).We give some properties of these spaces and embeddings results with respect to theirparameters p,q andγ
  • Guang Bin REN, Uwe KAHLER
    Acta Mathematica Sinica. 2009, 25(9): 1561-1566. https://doi.org/10.1007/s10114-009-7023-0
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    In this paper we construct Almansi decompositions for powers of the ultrahyperbolicoperator.The construction will be done in a constructive way.
  • De Xu ZHOU
    Acta Mathematica Sinica. 2009, 25(9): 1567-1582. https://doi.org/10.1007/s10114-009-6385-7
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    Assume that S is an almost excellent extension of R.Using functors HomR(S,-)and-RS,we establish some connections between classes of modules CR and CR,cotorsion pairs(AR,BR)and(AS,BS).If CS is a T-extension or(and)H-extension of CR,we show that CR is a(resp.,monomorphic,epimorphic,special)preenveloping class if and only if so is CR.If(AS,BS)is a T H-extension of(AR,BR),we obtain that(AS,BS)is complete(resp.,of finite type,of cofinite type,hereditary,perfect,n-tilting)if and only if so is(AR,BR).