15 October 2009, Volume 25 Issue 10

    

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Articles
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  Distortion Theorem for Bloch Mappings on the Unit Ball Bⁿ

  Jian Fei WANG, Tai Shun LIU

  Acta Mathematica Sinica. 2009, 25(10): 1583-1590. https://doi.org/10.1007/s10114-009-6677-y

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  In this paper,we obtain a version of subordination lemma for hyperbolic disk relative tohyperbolic geometry on the unit disk D.This subordination lemma yields the distortion theorem forBloch mappings f∈H(Bⁿ)satisfying‖f‖⁰=1 and det f(0)=α∈(0,1],where‖f‖⁰=sup{(1-|z|²)^n+1/2n|det(f(z))|^1/n:z∈Bⁿ}.Here we establish the distortion theorem from a unified perspective and generalize some known results.This distortion theorem enables us to obtain a lower bound for theradius of the largest univalent ball in the image of f centered at f(0).Whenα=1,the lower boundreduces to that of Bloch constant found by Liu.When n=1,our distortion theorem coincides withthat of Bonk,Minda and Yanagihara.‖
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  On a Kaehler Hypersurface with the Cyclic Ricci Semi-symmetric Tensor

  Norifumi YOKOYAMA, Yoshio MATSUYAMA

  Acta Mathematica Sinica. 2009, 25(10): 1591-1594. https://doi.org/10.1007/s10114-009-7185-9

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  The purpose of the present paper is to prove that a Kaehler hypersurface with the cyclicRicci semi-symmetric tensor is locally symmetric.
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  Refined Functional Equations Stemming from Cubic,Quadratic and Additive Mappings

  Ick-Soon CHANG, Eunyoung SON, Hark-Mahn KIM

  Acta Mathematica Sinica. 2009, 25(10): 1595-1608. https://doi.org/10.1007/s10114-009-7190-z

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  Let n≥2 be an integer.In this paper,we investigate the generalized Hyers–Ulam stabilityproblem for the following functional equationwhich contains as solutions cubic,quadratic or additive mappings.
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  Symmetry and Transitive Properties of Monohedral f-triangulations of the Riemannian Sphere

  Ana M.BREDA, J.M.SIGARRETA

  Acta Mathematica Sinica. 2009, 25(10): 1609-1616. https://doi.org/10.1007/s10114-009-7496-x

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  Here we give the complete description of the symmetry group and transitive properties ofthe set of all of monohedral triangulations of the Riemannian sphere by f-tilings.We shall also showthat each monohedral f-tiling of the Riemannian sphere can be seen,up to a spherical isometry,as thesingular set of a spherical isometric folding.
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  Two Operators Related to Marcinkiewicz Integrals

  Hui Xia MO, Shan Zhen LU

  Acta Mathematica Sinica. 2009, 25(10): 1617-1634. https://doi.org/10.1007/s10114-009-8038-2

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  In this paper,the authors consider the boundedness of generalized higher commutator ofMarcinkiewicz integral,multilinear Marcinkiewicz integralμ^A_Ωand its variationμ^A_Ωon Herz-typeHardy spaces,hereΩis homogeneous of degree zero and satisfies a class of L^s-Dini condition.And asa special case,they also get the boundedness of commutators of Marcinkiewicz integrals on Herz-typeHardy spaces.
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  A Generalization of the Concept of ^q-fractional Integrals

  Predrag M.RAJKOVIC, Sladjana D.MARINKOVIC, Miomir S.STANKOVIC

  Acta Mathematica Sinica. 2009, 25(10): 1635-1646. https://doi.org/10.1007/s10114-009-8253-x

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  In this paper,we consider the fractional q-integral with variable lower limit of integration.We prove the semigroup property of these integrals,and a formula of Leibniz type.Finally,we evaluatefractional q-integrals of some functions.The consideration of q-exponential function in that sense leadsto q-analogs of Mittag–Le?er function.
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  On a Class of Prime Entire Functions

  Kuldeep Singh CHARAK, Ilpo LAINE

  Acta Mathematica Sinica. 2009, 25(10): 1647-1652. https://doi.org/10.1007/s10114-009-7572-2

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  In this note it is proved that entire functions of the formFa(z)=H(z)-aα(z),where H andαare entire functions,withαhaving at least one zero,H andαhaving no commonzeros and T(r,α)=S(r,H),are prime in entire sense for most values of a.The class of these functionsis seen to contain examples of both periodic and non-periodic prime entire functions found by Noda,Qiao,Urabe and by Singh and Charak.Another result due to Singh and Charak will be improved aswell.
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  Abundant Semigroups with a Quasi-ideal Quasi-adequate Transversal

  Xiang Fei NI, Yan Feng LUO, Hai Zhou CHAO

  Acta Mathematica Sinica. 2009, 25(10): 1653-1664. https://doi.org/10.1007/s10114-009-8014-x

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  Characterization theorems for abundant semigroups having a quasi-ideal quasi-adequatetransversal are obtained.Our results generalize and amplify the related results of Satio on regularsemigroup obtained in 1985 and Kong obtained in 2007 respectively.Some recent results on this topicgiven by Guo–Shum are strengthened.In particular,the structure of such an abundant semigroup isdescribed.
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  Self-converse Large Sets of Pure Mendelsohn Triple Systems

  Jian Guo LEI, Cui Ling FAN, Jun Ling ZHOU

  Acta Mathematica Sinica. 2009, 25(10): 1665-1680. https://doi.org/10.1007/s10114-009-7381-7

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  A Mendelsohn triple system of order v(MTS(v))is a pair(X,B)where X is a v-set andB is a collection of cyclic triples on X such that every ordered pair of X belongs to exactly one tripleof B.An MTS(v)(X,B)is called pure and denoted by PMTS(v)if x,y,z∈B implies z,y,x∈B.A large set of MTS(v)s(LMTS(v))is a collection of v-2 pairwise disjoint MTS(v)s on a v-set.Aself-converse large set of PMTS(v)s,denoted by LPMTS^*(v),is an LMTS(v)containing [v-2/2]conversepairs of PMTS(v)s.In this paper,some results about the existence and non-existence for LPMTS^*(v)are obtained.
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  A Note on Jensen’s Inequality for BSDEs

  Sheng Jun FAN

  Acta Mathematica Sinica. 2009, 25(10): 1681-1692. https://doi.org/10.1007/s10114-009-7350-1

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  Under the Lipschitz assumption and square integrable assumption on g,Jiang proved thatJensen’s inequality for BSDEs with generator g holds in general if and only if g is independent of y,g issuper homogenous in z and g(t,0)=0,a.s.,a.e..In this paper,based on Jiang’s results,under the sameassumptions as Jiang’s,we investigate the necessary and su?cient condition on g under which Jensen’sinequality for BSDEs with generator g holds for some specific convex functions,which generalizes someknown results on Jensen’s inequality for BSDEs.
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  Hochschild(Co)homology of Galois Coverings of Grassmann Algebras

  Yun Ge XU, Xin TANG

  Acta Mathematica Sinica. 2009, 25(10): 1693-1702. https://doi.org/10.1007/s10114-009-7346-x

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  LetΛbe the Z2-Galois covering of the Grassmann algebraΛover a field k of characteristicnot equal to 2.In this paper,the dimensional formulae of Hochschild homology and cohomology groupsofΛare calculated explicitly.And the cyclic homology ofΛcan also be calculated when the underlyingfield is of characteristic zero.As a result,we prove that there is an isomorphism from⊕_i≥1H Hⁱ(Λ)to⊕_i≥1H Hⁱ(Λ).
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  Global Existence of the Radially Symmetric Strong Solution to Navier–Stokes–Poisson Equations for Isentropic Compressible Fluids

  Jun Ping YIN, Zhong TAN

  Acta Mathematica Sinica. 2009, 25(10): 1703-1720. https://doi.org/10.1007/s10114-009-6595-z

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  We prove the two existence results of the radially symmetric strong solutions to the Navier–Stokes–Poisson equations for isentropic compressible fluids.The important point in this paper is thatthe initial density is vacuum.It is di?erent from weak solutions.Now we need some compatibilitycondition.
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  On Spinors

  Yan Lin YU, Lin ZHU, Xiu Hong FENG

  Acta Mathematica Sinica. 2009, 25(10): 1721-1728. https://doi.org/10.1007/s10114-009-6605-1

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  For a 2ⁿ-dimensional complex Hermitian vector space S,we prove that any unitary basisof S can be explained as an augmented spinor structure on S.By using this explanation,a Spin^c(2n)-action on S is equivalent to an action on a subset of augmented spinor structures.The latter action isa little easy to be understood,and is shown in the last part of this paper.Such kind of understandingcould be of use to the discussions of Hermitian manifolds and spin manifolds,especially could help tofind connections and elliptical operators.
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  The Quasi-Representation Theorem of the Conjugate Cone[L^β(μ,X)]^*_β(0<β<1)

  Jian Yong WANG

  Acta Mathematica Sinica. 2009, 25(10): 1729-1740. https://doi.org/10.1007/s10114-009-6104-4

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  For 0<β<1,the author once wrote a paper to deal with the representation problemof the conjugate cone[L^β[0,1]]^*_βof complexβ-Banach space Lβ[0,1].In this paper,replacing[0,1]with a Borel finite measure space(Ω,M,μ)and replacing the complex field C with a Banach spaceX,we study the representation problem of the conjugate cone[L^β(μ,X)]^*_βof L^β(μ,X),and obtain[L^β(μ,X)]^*_β=L^∞M⁺(μ,S),called the Quasi-Representation Theorem of[L^β(μ,X)]^*_β.
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  On Gauss–Weierstrass Semigroups and Inversion of Potentials Associated with the Bessel Differential Operator

  Mehmet Zeki SARIKAYA, Hűseyin YILDIRIM

  Acta Mathematica Sinica. 2009, 25(10): 1741-1758. https://doi.org/10.1007/s10114-009-6458-7

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  In this paper,we define the generalized Gauss–Weierstrass semigroups with Weierstrasskernel,and give some of their properties.Using them,we study the inversion formulas for the general-ized Riesz and Bessel potentials,generated by the generalized shift operators and associated with theLaplace Bessel Differential operator.