10 August 2010, Volume 26 Issue 8

    

• Select all
  |

Articles
• Select
  Smallest Close to Regular Bipartite Graphs without an Almost Perfect Matching

  Lutz VOLKMANN, Axel ZINGSEM

  Acta Mathematica Sinica. 2010, 26(8): 1403-1412. https://doi.org/10.1007/s10114-010-9124-1

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  A graph G is close to regular or more precisely a(d,d+k)-graph,if the degree of eachvertex of G is between d and d+k.Let d≥2 be an integer,and let G be a connected bipartite(d,d+k)-graph with partite sets X and Y such that|X|=|Y|+1.If G is of order n without an almostperfect matching,then we show in this paper that•n≥6d+7 when k=1,•n≥4d+5 when k=2,•n≥4d+3 when k≥3.Examples will demonstrate that the given bounds on the order of G are the best possible.
• Select
  Realization of Numbers As the Degrees of Maps between Manifolds

  Young Min LEE, Fei XU

  Acta Mathematica Sinica. 2010, 26(8): 1413-1424. https://doi.org/10.1007/s10114-010-9102-7

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We determine the set of degrees between some classes of oriented closed(n-1)-connected2n-manifolds by using the arithmetic theory of quadratic forms.
• Select
  On Quasi-Reduced Quadratic Forms

  E.DUBOIS, C.LEVESQUE

  Acta Mathematica Sinica. 2010, 26(8): 1425-1448. https://doi.org/10.1007/s10114-010-8214-4

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  With the help of continued fractions,we plan to list all the elements of the setQ_Δ={aX²+bX Y+cY²:a,b,c∈Z,b²-ac=Δwith 0≤b<√Δ}of quasi-reduced quadratic forms of fundamental discriminantΔ.As a matter of fact,we show that foreach reduced quadratic form f=aX²+bX Y+cY²=a,b,c of discriminantΔ>0(and of signσ(f)equal to the sign of a),the quadratic forms associated with f and defined by are all dierent from one another and build a set I(f)whose cardinality isIf f and g are two dierent reduced quadratic forms,we show that I(f)∩I(g)=Φ.Our main resultis that the set Q_Δis given by the disjoint union of all I(f)with f running through the set of reducedquadratic forms of discriminantΔ>0.This allows us to deduce a formula for#(Q_Δ)involving sumsof partial quotients of certain continued fractions.
• Select
  Vector Fields with Stable Shadowable Property on Closed Surfaces

  Sheng Zhi ZHU

  Acta Mathematica Sinica. 2010, 26(8): 1449-1456. https://doi.org/10.1007/s10114-010-9418-3

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We prove that the set of vector fields satisfying the C¹ stable shadowable property on closedsurfaces is characterized as the set of Morse–Smale vector fields.Hence,the vector fields satisfyingshadowing property on closed surfaces are C¹ dense.
• Select
  The Signature of Generalized Flag Manifolds and Applications

  Ping LI, Yang SU

  Acta Mathematica Sinica. 2010, 26(8): 1457-1462. https://doi.org/10.1007/s10114-010-9014-6

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let G be a linear algebraic group over C and P be a parabolic subgroup.We determine thesignatures of the flag manifold G/P.As an application,we prove that the nonsingular hypersurfacesof degree 2 in CPⁿ are prime if n satisfies certain conditions.
• Select
  Weighted Endpoint Estimates for Maximal Commutators Associated with the Sections

  Jie Cheng CHEN, Yan Dan ZHANG

  Acta Mathematica Sinica. 2010, 26(8): 1463-1474. https://doi.org/10.1007/s10114-010-8606-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We prove endpoint estimates for maximal commutators for a class of singular integraloperators related to the real analysis of the Monge–Ampere equation.
• Select
  Correction of CT Burst Array Errors in the Generalized-Lee-RT Spaces

  Sapna JAIN, K.P.SHUM

  Acta Mathematica Sinica. 2010, 26(8): 1475-1484. https://doi.org/10.1007/s10114-010-8508-6

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In[Jain,S.:Array codes in the generalized-Lee-RT-pseudo-metric(the GLRTP-metric),toappear in Algebra Colloq.],Jain introduced a new pseudo-metric on the space Mat_m×s(Z_q),the modulespace of all m×s matrices with entries from the finite ring Z_q,generalized the classical Lee metric[Lee,C.Y.:Some properties of non-binary error correcting codes.IEEE Trans.Inform.Theory,IT-4,77–82(1958)]and array RT-metric[Rosenbloom,M.Y.,Tsfasman,M.A.:Codes for m-metric.Prob.Inf.Transm.,33,45–52(1997)]and named this pseudo-metric as the Generalized-Lee-RT-Pseudo-Metric(or the GLRTP-Metric).In this paper,we obtain some lower bounds for two-dimensional array codescorrecting CT burst array errors[Jain,S.:CT bursts—from classical to array coding.Discrete Math.,308–309,1489–1499(2008)]with weight constraints under the GLRTP-metric.
• Select
  On Non-normal Arc-Transitive 4-Valent Dihedrants

  Istvan KOVACS, Bostjan KUZMAN, Aleksander MALNIC

  Acta Mathematica Sinica. 2010, 26(8): 1485-1498. https://doi.org/10.1007/s10114-010-8271-8

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let X be a connected non-normal 4-valent arc-transitive Cayley graph on a dihedral groupD_n such that X is bipartite,with the two bipartition sets being the two orbits of the cyclic subgroupwithin D_n.It is shown that X is isomorphic either to the lexicographic product C_n[2K₁]with n≥4even,or to one of the five sporadic graphs on 10,14,26,28 and 30 vertices,respectively.
• Select
  A Note on Generalized Twisted Anomaly Cancellation Formulas

  Yong WANG

  Acta Mathematica Sinica. 2010, 26(8): 1499-1508. https://doi.org/10.1007/s10114-010-8617-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this note,by studying modular invariance properties of some characteristic forms,weget some new twisted anomaly cancellation formulas.
• Select
  Composition of Fractional Orlicz Maximal Operators and A₁-weights on Spaces of Homogeneous Type

  Ana L.BERNARDIS, Gladis PRADOLINI, Maria LORENTE, Maria Silvina RIVEROS

  Acta Mathematica Sinica. 2010, 26(8): 1509-1518. https://doi.org/10.1007/s10114-010-8445-4

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  For a Young functionΘwith 0≤α<1,let M_α,Θbe the fractional Orlicz maximal operatordefined in the context of the spaces of homogeneous type(X,d,μ)by M_α,Θf(x)=sup_x∈Bμ(B)^α‖f‖_Θ,B,where ‖f‖_Θ,B is the mean Luxemburg norm of f on a ball B.Whenα=0 we simply denote it by M_Θ.In this paper we prove that ifΦandΨare two Young functions,there exists a third Young functionΘsuch that the composition M_α,ΨοM_Φis pointwise equivalent to M_α,Θ.As a consequence we provethat for some Young functionsΘ,if M_α,Θf<∞a.e.andδ∈(0,1)then(M_α,Θf)^δis an A₁-weight.Keywords Orlicz maximal function,spaces of homogeneous type,weights
• Select
  Isometries on the Quasi-Banach Spaces L^p(0

  Lei LI, Wei Yun REN

  Acta Mathematica Sinica. 2010, 26(8): 1519-1524. https://doi.org/10.1007/s10114-010-8225-1

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We study the extension of isometries between the unit spheres of quasi-Banach spaces L^pfor 0p(μ)into that of another L^p(ν)can be extended to be a linear isometry defined on the wholespace.
• Select
  A Generalized Existence Theorem of Backward Doubly Stochastic Differential Equations

  Qian LIN

  Acta Mathematica Sinica. 2010, 26(8): 1525-1534. https://doi.org/10.1007/s10114-010-8217-1

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper,we deal with a class of one-dimensional backward doubly stochastic differentialequations(BDSDEs).We obtain a generalized comparison theorem and a generalized existence theoremof BDSDEs.
• Select
  Subdifferential Representation of Homogeneous Functions and Extension of Smoothness in Banach spaces

  Fu Chun YANG, Zhou WEI, Dong WANG

  Acta Mathematica Sinica. 2010, 26(8): 1535-1544. https://doi.org/10.1007/s10114-010-8289-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper,we mainly consider proximal subdifferentials of lower semicontinuous func-tions defined on real Hilbert space and Clarke’s subDifferentials of locally Lipschitzian functions de-fined on Banach space respectively,and obtain the generalized Euler identity of homogenous functions.Then,by introducing a multifunctionΓ,we extend the smoothness of sphere and differentiability ofnorm function in Banach space.
• Select
  On the Perturbation of Semi-Fredholm Relations with Complemented Ranges and Null Spaces

  TeresaA LVAREZ

  Acta Mathematica Sinica. 2010, 26(8): 1545-1554. https://doi.org/10.1007/s10114-010-7700-z

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Multivalued semi-Fredholm type linear operators with complemented ranges and nullspaces are introduced.Conditions are obtained under which the classes given are stable under compact,strictly singular and strictly cosingular additive perturbations.
• Select
  On-Derivations and Local-Derivations

  Ajda FOSNER, Maja FOSNER

  Acta Mathematica Sinica. 2010, 26(8): 1555-1556. https://doi.org/10.1007/s10114-010-7650-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper,we describe-derivations in certain graded algebras by their actions onelements satisfying some special conditions.One of the main results is applied to local-derivations onsome certain graded algebras.
• Select
  Trace Class Toeplitz Operators with Unbounded Symbols on Weighted Bergman Spaces

  Sui HUANG, Guang Fu CAO

  Acta Mathematica Sinica. 2010, 26(8): 1567-1574. https://doi.org/10.1007/s10114-010-8040-8

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this note we construct a functionφin L²(B_n,dμ)which is unbounded on any neighbor-hood of each boundary point of B_n such that T_φis a trace class operator on weighted Bergman spaceL²_a(B_n,dμ)for several complex variables.
• Select
  Convergence Rates of Tail Probabilities for Sums under Dependence Assumptions

  Xiao Rong YANG, Wei Dong LIU, Ke Ang FU, Lin Xin ZHANG

  Acta Mathematica Sinica. 2010, 26(8): 1591-1600. https://doi.org/10.1007/s10114-010-7618-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Let{X,X₁,X₂,...}be a zero mean strictly stationaryφ-mixing sequence.Set S₁=Σ¹_k=1X_kand f(x^p)=Σ^∞_n=1n^r-2P(|S_n|≥x^p√ES²_n log n).Whenε>(√2^1/p),for p>1/2 and r>1,the conditions for∫^∞_εf(x^p)dx<∞to hold is established,by using coupled methods together withstrong approximation,which are dierent from the traditional symmetrization and Homan–Jrgenseninequality.
• Select
  On the Generalized 2-D Stochastic Ginzburg–Landau Equation

  De Sheng YANG

  Acta Mathematica Sinica. 2010, 26(8): 1601-1612. https://doi.org/10.1007/s10114-010-7313-6

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This paper proves the existence and uniqueness of solutions in a Banach space for thegeneralized stochastic Ginzburg–Landau equation with a multiplicative noise in two spatial dimensions.The noise is white in time and correlated in spatial variables.The condition on the parameters is thesame as in the deterministic case.The Banach contraction principle and stochastic estimates in Banachspaces are used as the main tool.