15 June 2008, Volume 24 Issue 6

    

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  A New Quasi-local Mass and Positivity

  Xiao ZHANG

  Acta Mathematica Sinica. 2008, 24(6): 881-890. https://doi.org/10.1007/s10114-007-7153-1

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  A new definition of quasi-local mass is proposed and its positivity is proved under certain conditions
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  A Note on the Illposedness for Anisotropic Nonlinear Schrödinger Equation

  Xiao Yi ZHANG

  Acta Mathematica Sinica. 2008, 24(6): 891-900. https://doi.org/10.1007/s10114-007-5418-3

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  In this short note,we show the illposedness of anisotropic Schrödinger equation in L² if the growth of nonlinearity is larger than a threshold power p_c which is also the critical power for blowup,as Fibich,Ilan and Schochet have pointed out recently.The illposedness in anisotropic Sobolev space H_k,d-k^2s,s where 0<s<s_c,s_c=d/2-k/4-2/p-1,and the illposedness in Sobolev space of negative order H^s,s<0 are also proved
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  Moduli of Continuity of a Class of N-parameter Gaussian Processes and Their Fast Points

  Zheng Yan LIN, Zong Mao CHENG

  Acta Mathematica Sinica. 2008, 24(6): 901-910. https://doi.org/10.1007/s10114-007-5533-1

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  We study the moduli of continuity of a class of N-parameter Gaussian processes and get some results on the packing dimension of the set of their fast points.
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  On the Ricci Curvature of a Randers Metric of Isotropic S-curvature

  Xiao Huan MO, Chang Tao YU

  Acta Mathematica Sinica. 2008, 24(6): 911-916. https://doi.org/10.1007/s10114-007-6058-3

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  We derive the integral inequality of a Randers metric with isotropic S-curvature in terms of its navigation representation.Using the obtained inequality we give some rigidity results under the condition of Ricci curvature.In particular,we show the following result: Assume that an n-dimensional compact Randers manifold (M,F) has constant S-curvature c.Then (M,F) must be Riemannian if its Ricci curvature satisfies that Ric<-(n-1)c².
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  On the Diophantine System a²+b²=c³ and a^x+b^y=c^z for b is an Odd Prime

  Mao Hua LE

  Acta Mathematica Sinica. 2008, 24(6): 917-924. https://doi.org/10.1007/s10114-007-6140-x

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  Let a,b and c be fixed coprime positive integers.In this paper we prove that if a²+b²=c³ and b is an odd prime,then the equation a^x+b^y=c^z has only the positive integer solution (x,y,z)=(2,2,3).
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  New Oscillation Criteria for Second Order Linear Matrix Differential Equations with Damping

  Yan Cong XU, Ming De ZHU

  Acta Mathematica Sinica. 2008, 24(6): 925-936. https://doi.org/10.1007/s10114-007-6148-2

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  By using the positive linear functional and the monotone subhomogeneous functional,including the general means and Riccati technique,some new oscillation criteria are established for the second order linear matrix differential system
  (P(t)X'(t))'+R(t)X'(t)+Q(t)X(t)=0,t≥t⁰>0,
  where P(t),R(t),Q(t) are n × n real continuous matrix functions,P(t) and R(t) are commutative.The results improve and generalize those given in some previous papers,which can be seen by the examples given at the end of this paper.
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  A Census of Petal Bundles by Genus

  Yan XU, Yan Pei LIU

  Acta Mathematica Sinica. 2008, 24(6): 937-946. https://doi.org/10.1007/s10114-007-6213-x

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  This paper provides the uniform enumerative functional equation of orientable (nonorientable) rooted petal bundles with more parameters,and deduces two recursion formulas for calculation.Accordingly,an explicit expression of rooted petal bundles with up to two parameters on nonorientable surface of genus 4 is also obtained.
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  Browder Spectra and Essential Spectra of Operator Matrices

  Yun Nan ZHANG, Huai Jie ZHONG, Li Qiong LIN

  Acta Mathematica Sinica. 2008, 24(6): 947-954. https://doi.org/10.1007/s10114-007-6339-x

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  Let M_C=be a 2×2 upper triangular operator matrix acting on the Banach space X×Y.We prove tha
  σ_t(A)∪σ_t(B)=σ_t(M_C)∪W,where W is the union of certain of the holes in στ(MC) which happen to be subsets of στ(A)∩στ (B),and στ(A),στ(B),στ(MC) can be equal to the Browder or essential spectra of A,B,MC,respectively.We also show that the above result isn't true for the Kato spectrum,left (right) essential spectrum and left (right) spectrum.
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  Partition Identities Arising from Theta Function Identities

  Nayandeep Deka BARUAH, Bruce C. BERNDT

  Acta Mathematica Sinica. 2008, 24(6): 955-970. https://doi.org/10.1007/s10114-007-0960-6

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  The authors show that certain theta function identities of Schröter and Ramanujan imply elegant partition identities.
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  Precise Asymptotics for Random Matrices and Random Growth Models

  Zhong Gen SU

  Acta Mathematica Sinica. 2008, 24(6): 971-982. https://doi.org/10.1007/s10114-007-6365-8

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  The author considers the largest eigenvalues of random matrices from Gaussian unitary ensemble and Laguerre unitary ensemble,and the rightmost charge in certain random growth models.We obtain some precise asymptotics results,which are in a sense similar to the precise asymptotics for sums of independent random variables in the context of the law of large numbers and complete convergence.Our proofs depend heavily upon the upper and lower tail estimates for random matrices and random growth models.The Tracy-Widom distribution plays a central role as well.
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  The Pressure in Operator Algebras

  Cheng Jun HOU

  Acta Mathematica Sinica. 2008, 24(6): 983-996. https://doi.org/10.1007/s10114-007-6370-y

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  We introduce two notions of the pressure in operator algebras, one is the pressure P_α(π, T) for an automorphism α of a unital exact C^∗-algebra A at a self-adjoint element T in A with respect to a faithful unital ∗-representation π, the other is the pressure Pτ,α(T) for an automorphism α of a hyperfinite von Neumann algebra M at a self-adjoint element T in M with respect to a faithful normal α-invariant state τ . We give some properties of the pressure, show that it is a conjugate invariant, and also prove that the pressure of the implementing inner automorphism of a crossed product A ×_αZ at a self-adjoint operator T in A equals that of α at T.
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  Strict Achirality of Prime Links up to 11-Crossing

  Shi Da WANG

  Acta Mathematica Sinica. 2008, 24(6): 997-1004. https://doi.org/10.1007/s10114-007-6372-9

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  In this paper we determine all strictly achiral prime links up to 11 crossings.There are exactly four strictly achiral non-trivial prime links up to 11 crossings.
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  Strongly Convergent Approximations to Fixed Points of Total Asymptotically Nonexpansive Mappings

  Yakov ALBER, Rafa ESPÍNOLA, Pepa LORENZO

  Acta Mathematica Sinica. 2008, 24(6): 1005-1022. https://doi.org/10.1007/s10114-007-6367-6

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  In this work we prove a new strong convergence result of the regularized successive approximation method given by
  y_n+1=q_n z₀+(1-q_n )Tⁿy_n,n=1,2,...,
  where 
  
  for T a total asymptotically nonexpansive mapping,i.e.,T is such that
  ||Tⁿx-Tⁿy||≤||x-y||+k_n⁽¹⁾Φ(||x-y||)+k_n⁽²⁾
  where kn1 and kn2 are real null convergent sequences and Φ: R+→R+ is continuous such that Φ(0)=0 and limt→∞Φ(t)/t ≤ C for a certain constant C>0.   Among other features,our results essentially generalize existing results on strong convergence for T nonexpansive and asymptotically nonexpansive.The convergence and stability analysis is given for both self-and nonself-mappings.
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  Essential Tori in 3-String Free Tangle Decompositions of Links

  Kanji MORIMOTO

  Acta Mathematica Sinica. 2008, 24(6): 1023-1030. https://doi.org/10.1007/s10114-007-6492-2

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  The author characterizes those link types which have 3-string essential free tangle decompositions and have essential tori in their exteriors.
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  L_p Boundedness of Marcinkiewicz Integrals with H¹ Kernels

  Leslie C. CHENG

  Acta Mathematica Sinica. 2008, 24(6): 1031-1038. https://doi.org/10.1007/s10114-007-5603-4

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  We establish the L^p boundedness of Marcinkiewicz integral operators with kernels in the Hardy space on a compact submanifold of finite type.Previously such boundedness properties were obtained when the submanifold is a sphere.Our result shows that what matters is not the symmetry,but a certain type of curvature property of the submanifold.
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  Parametrization of the Teichmüller Space of Bordered Surface NEC Groups

  B. ESTRADA E. MARTÍNEZ

  Acta Mathematica Sinica. 2008, 24(6): 1039-1056. https://doi.org/10.1007/s10114-007-6162-4

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  A non-Euclidean crystallographic group Γ (NEC group,for short) is a discrete subgroup of isometries of the hyperbolic plane H,with compact quotient space H/Γ.These groups uniformize Klein surfaces,surfaces endowed with dianalytic structure.These surfaces can be seen as a generalization of Riemann surfaces.

  Fundamental polygons play an important role in the study of parametrizations of the Teichmüller space of NEC groups.

  In this work we construct a class of right-angled polygons which are fundamental regions of bordered surface NEC groups.The free parameters used in the construction of the polygons give a parametrization of the Teichmüller space.From the parameters we obtain explicit matrices of the generators of the groups.Finally,we give examples to exhibit how different relations between the parameters reflect the existence of automorphisms on the quotient surfaces.