15 November 2007, Volume 23 Issue 11

    

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  Approximately Linear Mappings in Banach Modules over a C*-algebra

  Choonkil PARK, Jian Lian CUI

  Acta Mathematica Sinica. 2007, 23(11): 1919-1936. https://doi.org/10.1007/s10114-007-0964-2

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  Let X and Y be vector spaces.The authors show that a mapping f:X→Y satisfies the functional equation
  
  with f(0)=0 if and only if the mapping f:X→Y is Cauchy additive,and prove the stability of the functional equation in Banach modules over a unital C^*-algebra,and in Poisson Banach modules over a unital Poisson C^*-algebra.Let A and B be unital C^*-algebras,Poisson C^*-algebras or Poisson JC^*-algebras.As an application,the authors show that every almost homomorphism h:A →B of Ainto B is a homomorphism when h((2d-1)nuy)=h((2d-1)nu)h(y) or h((2d-1)nuoy)=h((2d-1)nu)oh(y) for all unitaries u∈A,all y∈A,n=0,1,2,....Moreover,the authors prove the stability of homomorphisms in C^*-algebras,Poisson C^*-algebras or Poisson JC^*-algebras.
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  Quasi L_p-Intersection Bodies

  Wu Yang YU, Dong Hua WU, Gang Song LENG

  Acta Mathematica Sinica. 2007, 23(11): 1937-1948. https://doi.org/10.1007/s10114-007-0958-0

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  The purpose of this paper is to generalize the notion of intersection bodies to that of quasi L_p-intersection bodies.The L_p-analogs of the Busemann intersection inequality and the Brunn-Minkowski inequality for the quasi L_p-intersection bodies are obtained.The Aleksandrov-Fenchel inequality for the mixed quasi L_p-intersection bodies is also established.
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  On the Monotonicity of the Speed of Random Walks on a Percolation Cluster of Trees

  Da Yue CHEN, Fu Xi ZHANG

  Acta Mathematica Sinica. 2007, 23(11): 1949-1954. https://doi.org/10.1007/s10114-007-0975-z

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  The authors consider the simple random walk on the in.nite cluster of the Bernoulli bond percolation of trees,and investigate the relation between the speed of the simple random walk and the retaining probability p by studying three classes of trees.A sufficient condition is established for Galton-Watson trees.
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  A Note on the Maximum Principle for Second-Order Elliptic Equations in General Domains

  Antonio VITOLO

  Acta Mathematica Sinica. 2007, 23(11): 1955-1966. https://doi.org/10.1007/s10114-007-0976-y

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  We make a further advance concerning the maximum principle for second-order elliptic operators.We investigate in particular a geometric condition,first considered by Berestycki-Nirenberg-Varadhan,that seems to be natural in view of the application of the boundary weak Harnack inequality,on which our argument is based.Setting it free from some technical assumptions,apparently needed in earlier papers,we significantly enlarge the class of unbounded domains where the maximum principle holds,compatibly with the first-order term.
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  On the Koszul Modules of Exterior Algebras

  Jin Yun GUO, Quan Hong WAN, Qiu Xian WU

  Acta Mathematica Sinica. 2007, 23(11): 1967-1984. https://doi.org/10.1007/s10114-007-0971-3

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  We prove that the Koszul modules over an exterior algebra can be filtered by the cyclic Koszul modules.We also introduce the cyclic dimension vector as invariants for studying the Koszul modules over an exterior algebra.
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  A Remark on з-Permutability of Finite Groups

  Li Fang WANG, Yan Ming WANG

  Acta Mathematica Sinica. 2007, 23(11): 1985-1990. https://doi.org/10.1007/s10114-005-0906-9

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  Let з be a complete set of Sylow subgroups of a finite group G,that is,з contains exactly one and only one Sylow p-subgroup of G for each prime p.A subgroup of a finite group G is said to be з-permutable if it permutes with every member of з.Recently,using the Classification of Finite Simple Groups,Heliel,Li and Li proved the following result:If the cyclic subgroups of prime order or order 4 (if p=2) of every member of з are з-permutable subgroups in G,then G is supersolvable.In this paper,we give an elementary proof of this theorem and generalize it in terms of formation.
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  Composition Operators on α-Bloch Spaces of the Unit Ball

  Min Zhu ZHANG, Wen XU

  Acta Mathematica Sinica. 2007, 23(11): 1991-2002. https://doi.org/10.1007/s10114-007-0993-x

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  The authors characterize the boundedness and compactness of composition operators between α-Bloch spaces of the unit ball.
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  A Class of Maximal Functions with Oscillating Kernels

  Ahmad AL-SALMAN

  Acta Mathematica Sinica. 2007, 23(11): 2003-2016. https://doi.org/10.1007/s10114-007-0936-6

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  The author studies the L^p mapping properties of a class of maximal functions that are related to oscillatory singular integral operators.L^p estimates,as well as the corresponding weighted estimates of such maximal functions,are obtained.Moreover,several applications of our results are highlighted.
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  Distributional Methods for a Class of Functional Equations and Their Stabilities

  Jae Young CHUNG

  Acta Mathematica Sinica. 2007, 23(11): 2017-2026. https://doi.org/10.1007/s10114-007-0977-x

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  We consider a class of n-dimensional Pompeiu equations and that of Pexider equations and their Hyers-Ulam stability problems in the spaces of Schwartz distributions.First,reducing the given distribution version of functional equations to differential equations we.nd their solutions.Secondly,using approximate identities we prove the Hyers-Ulam stability of the equations.
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  Primal-dual Interior-point Algorithms for Second-order Cone Optimization Based on a New Parametric Kernel Function

  Yan Qin BAI, Guo Qiang WANG

  Acta Mathematica Sinica. 2007, 23(11): 2027-2042. https://doi.org/10.1007/s10114-007-0967-z

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  A class of polynomial primal-dual interior-point algorithms for second-order cone optimization based on a new parametric kernel function,with parameters p and q,is presented.Its growth term is between linear and quadratic.Some new tools for the analysis of the algorithms are proposed.The complexity bounds of O(√N log N log N/ε) for large-update methods and O(√N log N/ε) for small-update methods match the best known complexity bounds obtained for these methods.Numerical tests demonstrate the behavior of the algorithms for different results of the parameters p and q.
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  Asymptotic Smoothing Effect of Solutions to Davey-Stewartson Systems on the Whole Plane

  Cai Di ZHAO, Yong Sheng LI, Sheng Fan ZHOU

  Acta Mathematica Sinica. 2007, 23(11): 2043-2060. https://doi.org/10.1007/s10114-007-0949-1

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  This paper discusses the Cauchy problem of elliptic-elliptic-type Davey-Stewartson systems with zero-order dissipation on R².Making use of the Fourier spectral projector,together with a long time comparison between the solutions to the Davey-Stewartson systems and to an auxiliary problem,we prove that the global attractor in H¹(R²) for the addressed Davey-Stewartson systems is a compact subset of H²(R²),and thus reveal the asymptotic smoothing effect of the solutions for the systems.
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  8-ranks of Class Groups of Some Imaginary Quadratic Number Fields

  Xi Mei WU, Qin YUE

  Acta Mathematica Sinica. 2007, 23(11): 2061-2068. https://doi.org/10.1007/s10114-007-0965-1

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  Let F=Q(√-P1P2) be an imaginary quadratic field with distinct primes p₁≡p₂≡1 mod 8 and the Legendre symbol (P1/P2)=1.Then the 8-rank of the class group of F is equal to 2 if and only if the following conditions hold:(1) The quartic residue symbols (P1/P2)4=1;(2) Either both p₁ and p₂ are represented by the form a²+32b² over Z and P₂^h+(2P1)/4,x,y∈Z,or both p₁ and p₂ are not represented by the form a² +32b² over Z and P^h+(2P1)/4= ε(2x²-P1y²),x,y ∈Z,ε∈{±1},where h₊(2p₁) is the narrow class number of Q(√2P1).Moreover,we also generalize these results.
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  On Certain Distributive Lattices of Subgroups of Finite Soluble Groups

  L. M. EZQUERRO, X. SOLER-ESCRIVÀ

  Acta Mathematica Sinica. 2007, 23(11): 2069-2078. https://doi.org/10.1007/s10114-005-0925-6

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  In this paper,we prove the following result.Let F be a saturated formation and Σ a Hall system of a soluble group G.Let X be a w-solid set of maximal subgroups of G such that Σ reduces into each element of X.Consider in G the following three subgroups:the F-normalizer D of G associated with Σ;the X-prefrattini subgroup W=W(G,X) of G;and a hypercentrally embedded subgroup T of G.Then the lattice L(T,W,D)generated by T,D and W is a distributive lattice of pairwise permutable subgroups of G with the cover and avoidance property.This result remains true for the lattice L(V,W,D),where V is a subgroup of G whose Sylow subgroups are also Sylow subgroups of hypercentrally embedded subgroups of G such that Σ reduces into V.
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  A Note on Minimal Surfaces in Euclidean 3-Space

  Zu Huan YU, Qing Zhong LI

  Acta Mathematica Sinica. 2007, 23(11): 2079-2086. https://doi.org/10.1007/s10114-007-0968-y

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  In this note,a construction of minimal surfaces in Euclidean 3-space is given.By using the product of Weierstrass data of two known minimal surfaces,one gets a new Weierstrass data and a corresponding minimal surface from the Weierstrass representation.
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  On the Convergence of Broyden-Like Methods

  Ioannis K. ARGYROS

  Acta Mathematica Sinica. 2007, 23(11): 2087-2096. https://doi.org/10.1007/s10114-007-0963-3

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  The author provides a finer local as well as semilocal convergence analysis of a certain class of Broyden-like methods for solving equations containing a nondifferentiable term on the m-dimensional Euclidean space (m≥1 a natural number).
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  Strongly Singular Calderón-Zygmund Operator and Commutator on Morrey Type Spaces

  Yan LIN

  Acta Mathematica Sinica. 2007, 23(11): 2097-2110. https://doi.org/10.1007/s10114-007-0974-0

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  In this paper,the author considers the boundedness of strongly singular Calderón-Zygmund operator and commutator generated by this operator and Lipschitz function on the classical Morrey space and generalized Morrey space.Moreover,the boundedness of strongly singular Calderón-Zygmund operator on the predual of Morrey space is discussed.