中国科学院数学与系统科学研究院期刊网

15 February 2010, Volume 26 Issue 2
    

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  • Bohui CHEN
    Acta Mathematica Sinica. 2010, 26(2): 209-240. https://doi.org/10.1007/s10114-010-8221-5
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    The bubble tree compactified instanton moduli spaceMK(X)is introduced.Its singularity set SingK(X)is described.By the standard gluing theory,one can show thatMK(X) SingK(X)is a topological orbifold.In this paper,we give an argument to construct smooth structures on it.
  • J.M.CALABUIG, J.RODRíGUEZ, E.A.SáNCHEZ-PéREZ
    Acta Mathematica Sinica. 2010, 26(2): 241-248. https://doi.org/10.1007/s10114-010-7382-6
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    In general,Banach space-valued Riemann integrable functions defined on[0,1](equipped with the Lebesgue measure)need not be weakly continuous almost everywhere.A Banach space is said to have the weak Lebesgue property if every Riemann integrable function taking values in it is weakly continuous almost everywhere.In this paper we discuss this property for the Banach space L1X of all Bochner integrable functions from[0,1]to the Banach space X.We show thatL1X has the weak Lebesgue property whenever X has the Radon–Nikodym property and X*is separable.This generalizes the result by Chonghu Wang and Kang Wan[Rocky Mountain J.Math.,31(2),697–703 (2001)]that L1[0,1]has the weak Lebesgue property.
  • Lucian BEZNEA, Nicu BOBOC
    Acta Mathematica Sinica. 2010, 26(2): 249-264. https://doi.org/10.1007/s10114-010-7671-0
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    We study the Schrödinger equation(q-L)u+μu=f,where L is the generator ofa Borel right process and μ is a signed measure on the state space.We prove the existence and uniqueness results in Lp,1≤p<∞.Since we consider measuresμ charging no polar set,we have to use new tools:the Revuz formula with fine versions and the appropriate Revuz correspondence,the perturbation(subordination)operators(in the sense of G.Mokobodzki)induced by the regular strongly supermedian kernels.We extend the results on the Schro¨dinger equation to the case of a strongly continuous sub-Markovian resolvent of contractions on Lp.If the measureμis positive then the perturbed process solves the martingale problem for L-μand its transition semigroup is given by the Feynman–Kac formula associated with the left continuous additive functional havingμas Revuz measure.
  • Lian Rong DING
    Acta Mathematica Sinica. 2010, 26(2): 265-276. https://doi.org/10.1007/s10114-010-8073-z
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    In this paper,we study the dynamics of the family of rational maps fλ(z)=zn+λ /zm,n≥2,m≥1,λ∈C.We construct an example of buried Sierpinski curve Julia set in this family.We also give an estimate of the location of bifurcation locus of fλ.
  • Dong Xiang CHEN, Shan Zhen LU
    Acta Mathematica Sinica. 2010, 26(2): 277-286. https://doi.org/10.1007/s10114-010-8267-4
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    This paper is primarily concerned with the proof of the Lp boundedness of parabolic Littlewood–Paley operators with kernels belonging to certain block spaces.Some known results are essentially extended and improved.
  • Run Ling AN, Jin Chuan HOU
    Acta Mathematica Sinica. 2010, 26(2): 287-294. https://doi.org/10.1007/s10114-010-8634-1
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    Let H be a Hilbert space and A be a standard *-subalgebra of B(H).We show that a bijective mapΦ:AA preserves the Lie-skew product AB-BA* if and only if there is a unitary or conjugate unitary operator UB(H) such thatΦ(A)=UAU*for all AA,that is,Φis a linear *-isomorphism or a conjugate linear *-isomorphism.
  • Wen Bin GUO, A.N.SKIBA
    Acta Mathematica Sinica. 2010, 26(2): 295-304. https://doi.org/10.1007/s10114-010-8034-6
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    In this paper,the famous Hall theorem and the famous Schur–Zassenhaus theorem are generalized.
  • A.AIZPURU, M.NICASIO-LLACH, F.RAMBLA-BARRENO
    Acta Mathematica Sinica. 2010, 26(2): 305-310. https://doi.org/10.1007/s10114-010-7472-5
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    In this paper we obtain a new version of the Orlicz–Pettis theorem by using statistical convergence.To obtain this result we prove a theorem of uniform convergence on matrices related to the statistical convergence.
  • Alberto DAMIANO, David EELBODE
    Acta Mathematica Sinica. 2010, 26(2): 311-330. https://doi.org/10.1007/s10114-010-7672-z
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    We introduce two new linear di?erential operators which are invariant with respect to the unitary group SU(n).They constitute analogues of the twistor and the Rarita–Schwinger operator in the orthogonal case.The natural setting for doing this is Hermitian Cli?ord Analysis.Such operators are constructed by twisting the two versions of the Hermitian Dirac operator z and z and then projecting on irreducible modules for the unitary group.We then study some properties of their spaces of nullsolutions and we find a formulation of the Hermitian Rarita–Schwinger operators in terms of Hermitian monogenic polynomials.
  • Guang Gui DING
    Acta Mathematica Sinica. 2010, 26(2): 331-336. https://doi.org/10.1007/s10114-010-8266-5
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    In this paper,we show that if V0 is a 1-Lipschitz mapping between unit spheres of two ALp-spaces with p>2 and-V0(S1(Lp))⊂V0(S1(Lp)),then V0 can be extended to a linear isometry defined on the whole space.If 1V0 is an“anti-1-Lipschitz”mapping,then V0 can also be linearly and isometrically extended.
  • Shi Sheng ZHANG
    Acta Mathematica Sinica. 2010, 26(2): 337-344. https://doi.org/10.1007/s10114-010-7610-0
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    The purpose of this paper is to study the weak convergence problems of the implicity iteration process for Lipschitzian pseudocontraction semigroups in general Banach spaces.The results presented in this paper extend and improve the corresponding results of Zhou[Nonlinear Anal.,68, 2977–983(2008)],Chen,et al.[J.Math.Anal.Appl.,314,701–709(2006)],Xu and Ori[Numer.Funct.Anal.Optim,22,767–773(2001)]and Osilike[J.Math.Anal.Appl.,294,73–81(2004)].
  • Pawel WITOWICZ
    Acta Mathematica Sinica. 2010, 26(2): 345-352. https://doi.org/10.1007/s10114-010-6574-4
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    This work gives a classification theorem for affine immersions with planar geodesics in the case where the codimension is maximal.Vrancken classified parallel affine immersions in this case and obtained,among others,generalized Veronese submanifolds.In this work it is shown that the immersions with planar geodesics are the same as the parallel ones in the considered case.A geometric interpretation of parallel immersions is also given:The affine immersions with pointwise planar normal sections(with respect to the equiaffine transversal bundle)are parallel.This result is verified for surfaces in R4 and for immersions with the maximal codimension.
  • Ping LI, Gui Zhen LIU
    Acta Mathematica Sinica. 2010, 26(2): 353-360. https://doi.org/10.1007/s10114-010-6685-y
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    Let G be the circuit graph of any connected matroid M with minimum degree δ(G).It is proved that its connectivityκ(G)≥2|E(M)-B(M)|-2.Thereforeδ(G)≥2|E(M)-B(M)|-2 and this bound is the best possible in some sense.
  • Xu Sheng LIU
    Acta Mathematica Sinica. 2010, 26(2): 361-368. https://doi.org/10.1007/s10114-010-6698-6
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    We prove the following vanishing theorem.Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and MSO0(2,2)/SO(2)×SO(2).Letπ:EM be any vector bundle.Then any E-valued L2 harmonic 1-form over M vanishes.In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.
  • Xin Xing CHEN, Jian Gang YING
    Acta Mathematica Sinica. 2010, 26(2): 369-376. https://doi.org/10.1007/s10114-010-6286-9
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    In this short note we study how two colors, red and blue, painted on a given graph are evolved randomly according to a transition rule which aims to simulate how people influence each other. We shall also calculate the probability that the evolution will be trapped eventually using the martingale method.
  • Xiao Miao WANG, Yan Xun CHANG
    Acta Mathematica Sinica. 2010, 26(2): 377-392. https://doi.org/10.1007/s10114-010-7556-2
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    In this paper, several recursive constructions for directed difference family and perfect directed difference family are presented by means of difference matrix and incomplete difference matrix.Finally the necessary and sufficient conditions for the existence of a (gv, g, 3, λ)-directed difference family in Zgv are established. As a consequence, the necessary and sufficient conditions for the existence of a cyclic directed group divisible design with block size three and type gv are obtained.
  • Rong Mao ZHANG, Zheng Yan LIN
    Acta Mathematica Sinica. 2010, 26(2): 393-404. https://doi.org/10.1007/s10114-010-6067-5
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    Let {X(t), t ∈ R+} be an integrated α stable process. In this paper, a functional law of the iterated logarithm (LIL) is derived via estimating the small ball probability of X. As a corollary, the classical Chung LIL of X is obtained. Furthermore, some results about the weighted occupation measure of X(t) are established.