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15 December 2009, Volume 25 Issue 12
    

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  • Pfaffians and Representations of the Symmetric Group
    Alain LASCOUX
    Acta Mathematica Sinica. 2009, 25(12): 1929-1950. https://doi.org/10.1007/s10114-009-6535-y
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    Pfaffans of matrices with entries z[i,j]/(xi+xj),or determinants of matrices with entriesz[i,j]/(xi+xj),where the antisymmetrical indeterminates z[i,j]satisfy the Plucker relations,can be identified with a trace in an irreducible representation of a product of two symmetric groups.Using Young’s orthogonal bases,one can write explicit expressions of such Pfaffians and determinants,and recover in particular the evaluation of Pfaffans which appeared in the recent literature.
  • Strong Labelings of Linear Forests
    Martin BA?A, Yu Qing LIN, Francesc A.MUNTANER-BATLE, Miquel RIUS-FONT
    Acta Mathematica Sinica. 2009, 25(12): 1951-1964. https://doi.org/10.1007/s10114-009-8284-3
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    A(p,q)-graph G is called super edge-magic if there exists a bijective function f:V(G)∪ E(G)→{1,2,...,p+q}such that f(u)+f(v)+f(uv)is a constant for each uv∈E(G)and f(V(G))={1,2,...,p}.In this paper,we introduce the concept of strong super edge-magic labeling as a particular class of super edge-magic labelings and we use such labelings in order to show that the number of super edge-magic labelings of an odd union of path-like trees(mT),all of them of the same order,grows at least exponentially with m.
  • Generalized Derivations as Jordan Homomorphisms on Lie Ideals and Right Ideals
    Vincenzo DE FILIPPIS
    Acta Mathematica Sinica. 2009, 25(12): 1965-1974. https://doi.org/10.1007/s10114-009-7343-0
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    Let R be a prime ring,L a non-central Lie ideal of R and g a non-zero generalized derivation of R.If g acts as a Jordan homomorphism on L,then either g(x)=x for all x∈R,or char(R)=2,R satisfies the standard identity s4(x1,x2,x3,x4),L is commutative and u2∈Z(R),for any u∈L.We also examine some consequences of this result related to generalized derivations which act as Jordan homomorphisms on the set[I,I],where I is a non-zero right ideal of R.
  • A Note on the Stability of Jordan Triple Higher Ring Derivations
    Jaiok ROH, Yong-Soo JUNG, Ick-Soon CHANG
    Acta Mathematica Sinica. 2009, 25(12): 1975-1986. https://doi.org/10.1007/s10114-009-8417-8
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    In the present paper,we establish the stability and the superstability of a functional inequality corresponding to the functional equation fn(xyx)=Σ
    i+j+k=nfi(x)fj(y)fk(x).In addition,we take account of the problem of Jacobson radical ranges for such functional inequality.
  • Classification of Lagrangian Surfaces of Curvatureε in Non-flat Lorentzian Complex Space Form M21(4ε)
    Bang Yen CHEN
    Acta Mathematica Sinica. 2009, 25(12): 1987-2022. https://doi.org/10.1007/s10114-009-7450-y
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    It is well known that a totally geodesic Lagrangian surface in a Lorentzian complex space formM21(4ε)of constant holomorphic sectional curvature 4εis of constant curvatureε.A natural question is“Besides totally geodesic ones how many Lagrangian surfaces of constant curvatureεin M21(4ε)are there?”In an earlier paper an answer to this question was obtained for the case=0 by Chen and Fastenakels.In this paper we provide the answer to this question for the caseε=0.Our main result states that there exist thirty-five families of Lagrangian surfaces of curvatureεinM21(4ε) withε=0.Conversely,every Lagrangian surface of curvatureε=0 inM21(4ε)is locally congruent to one of the Lagrangian surfaces given by the thirty-five families.
  • On Holomorphic Sections in Teichmuller Spaces
    Ming Feng SUN, Yu Liang SHEN
    Acta Mathematica Sinica. 2009, 25(12): 2023-2034. https://doi.org/10.1007/s10114-009-0445-x
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    It is proved that,for any elementary torsion free Fuchsian groupΓ,the natural projection from the Teichmuller curve V(Γ)to the Teichmuller space T(Γ)has no holomorphic section.
  • Geometry of Rectangular Block Triangular Matrices
    Li Ping HUANG
    Acta Mathematica Sinica. 2009, 25(12): 2035-2054. https://doi.org/10.1007/s10114-009-8601-x
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    Let D be any division ring,and let T(mi,ni,k)be the set of k×k(k≥2)rectangular block triangular matrices over D.For A,B∈T(mi,ni,k),if rank(A-B)=1,then A and B are said to be adjacent and denoted by A～B.A mapφ:T(mi,ni,k)→T(mi,ni,k)is said to be an adjacency preserving map in both directions if A～B if and only ifφ(A)～φ(B).Let G be the transformation group of all adjacency preserving bijections in both directions on T(mi,ni,k).When m1,nk≥2,we characterize the algebraic structure of G,and obtain the fundamental theorem of rectangular block triangular matrices over D.
  • Lp-Poincare Inequality for General Symmetric Forms
    Yong Hua MAO
    Acta Mathematica Sinica. 2009, 25(12): 2055-2064. https://doi.org/10.1007/s10114-009-8205-5
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    Lp Poincare inequalities for general symmetric forms are established by new Cheeger’s isoperimetric constants.Lp super-Poincare inequalities are introduced to describe the equivalent con-ditions for the Lp compact embedding,and the criteria via the new Cheeger’s constants for those inequalities are presented.Finally,the concentration or the volume growth of measures for these inequalities are studied.
  • The Regularity of Local Solutions for a Generalized Camassa–Holm Type Equation
    Shao Yong LAI, Jian ZHANG
    Acta Mathematica Sinica. 2009, 25(12): 2065-2076. https://doi.org/10.1007/s10114-009-8104-9
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    The regularity of the Cauchy problem for a generalized Camassa–Holm type equation is investigated.The pseudoparabolic regularization approach is employed to obtain some prior estimates under certain assumptions on the initial value of the equation.The local existence of its solution in Sobolev space Hs(R)with 1
  • On Mobius Form and Mobius Isoparametric Hypersurfaces
    Ze Jun HU, Xiao Li TIAN
    Acta Mathematica Sinica. 2009, 25(12): 2077-2092. https://doi.org/10.1007/s10114-009-7682-x
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    An umbilic-free hypersurface in the unit sphere is called Mobius isoparametric if it satisfies two conditions,namely,it has vanishing Mobius form and has constant Mobius principal curvatures.In this paper,under the condition of having constant Mobius principal curvatures,we show that the hypersurface is of vanishing Mobius form if and only if its Mobius form is parallel with respect to the Levi-Civita connection of its Mobius metric.Moreover,typical examples are constructed to show that the condition of having constant Mobius principal curvatures and that of having vanishing Mobius form are independent of each other.
  • G-Frames and g-Frame Sequences in Hilbert Spaces
    Yan Jin WANG, Yu Can ZHU
    Acta Mathematica Sinica. 2009, 25(12): 2093-2106. https://doi.org/10.1007/s10114-009-7615-8
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    In this paper,we first determine the relations among the best bounds A and B of the g-frame,the g-frame operator S and the pre-frame operator Q and give a necessary and su?cient condition for a g-frame with bounds A and B in a complex Hilbert space.We also introduce the definition of a g-frame sequence and obtain a necessary and suffcient condition for a g-frame sequence with bounds A and B in a complex Hilbert space.Lastly,we consider the stability of a g-frame sequence for a complex Hilbert space under perturbation.
  • The Representations of Generalized Inverses of Lower Triangular Operators
    Chun Fang SHAO, Hong Ke DU, Shu Feng JI, Jun Lian XU
    Acta Mathematica Sinica. 2009, 25(12): 2107-2118. https://doi.org/10.1007/s10114-009-7562-4
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    In this note,the explicit representations of Moore–Penrose inverses of lower triangular operator matrices are established.As an application,the explicit representations of Bott–Duffn inverses f bounded linear operators on a Hilbert space with respect to a closed subspace are obtained.
  • Gauges for the Cookie-cutter Sets
    Yu Xia DAI, Sheng You WEN
    Acta Mathematica Sinica. 2009, 25(12): 2119-2126. https://doi.org/10.1007/s10114-009-7455-6
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    Let E be a cookie-cutter set with dimH E=s.It is known that the Hausdorffs-measure and the packing s-measure of the set E are positive and finite.In this paper,we prove that for a gauge function g the set E has positive and finite Hausdorff g-measure if and only if 0 t→0 g(t)/ts<∞.Also,we prove that for a doubling gauge function g the set E has positive and finite packing g-measure if and only if 0 t→0 g(t)/ts<∞.
  • On Initial Data of the Monopole Equation
    Hong Yu WANG, Xiu Juan ZHU
    Acta Mathematica Sinica. 2009, 25(12): 2127-2132. https://doi.org/10.1007/s10114-009-7427-x
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    The space-time monopole equation is the reduction of anti-self-dual Yang–Mills equations in R2,2 to R2,1.This equation is a non-linear wave equation,and can be encoded in a Lax pair.An equivalent Lax pair is used by Dai and Terng to construct monopoles with continuous scattering data, and then the equation can be linearized by the scattering data,allowing one to use the inverse scattering method to solve the Cauchy problem with rapidly decaying small initial data.In this paper,we use the terminology of holomorphic bundle and transversality of certain maps,parametrized by initial data,to give more initial data,with which we can use scattering method to solve the Cauchy problem of the monopole equation up to gauge transformation.
  • Global Existence and Uniqueness of Weak Solution to Nonlinear Viscoelastic Full Marguerre–von Karman Shallow Shell Equations
    Fu Shan LI
    Acta Mathematica Sinica. 2009, 25(12): 2133-2156. https://doi.org/10.1007/s10114-009-7048-4
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    By Galerkin finite element method,we show the global existence and uniqueness of weak solution to the nonlinear viscoelastic full Marguerre–von Karman shallow shell equations.
  • On Cauchy Problem of the Benney–Lin Equation with Low Regularity Initial Data
    Xiang Qing ZHAO, Shang Bin CUI
    Acta Mathematica Sinica. 2009, 25(12): 2157-2168. https://doi.org/10.1007/s10114-009-7029-7
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    In this work we prove that the initial value problem of the Benney–Lin equation ut+uxxx+β(uxx+uxxxx)+ηuxxxxx+uux=0(x∈R,t≥0),whereβ>0 andη∈R,is locally well-posed in Sobolev spaces Hs(R)for s≥-7/5.The method we use to prove this result is the bilinear estimate method initiated by Bourgain.
  • A New Kernel Function Yielding the Best Known Iteration Bounds for Primal-Dual Interior-Point Algorithms
    Yan Qin BAI, Jin Li GUO, Cornelis ROOS
    Acta Mathematica Sinica. 2009, 25(12): 2169-2178. https://doi.org/10.1007/s10114-009-6457-8
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    Kernel functions play an important role in defining new search directions for primal-dual interior-point algorithm for solving linear optimization problems.In this paper we present a new kernel function which yields an algorithm with the best known complexity bound for both large-and small-update methods.
  • Selfinjective Koszul Algebras of Finite Complexity
    Jin Yun GUO, Ai Hua LI, Qiu Xian WU
    Acta Mathematica Sinica. 2009, 25(12): 2179-2198. https://doi.org/10.1007/s10114-009-6703-0
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    In this paper,we study selfinjective Koszul algebras of finite complexity.We prove that the complexity is a nonnegative integer when it is finite;and that the category Ct of modules with complexity less or equal to t,is resolving and coresolving.We show that for each 0≤l≤m there exist a family of modules of complexity l parameterized by G(l,m),the Grassmannian of l-dimensional subspaces of an m-dimensional vector space V,for the exterior algebra of V.Using complexity,we also give a new approach to the representation theory of a tame symmetric algebra with vanishing radical cube over an algebraically closed field of characteristic 0,via skew group algebra of a finite subgroup of SL(2,C)over the exterior algebra of a 2-dimensional vector space.
  • Erratum to:Existence of Positive Solutions for a Singularp-Laplacian Diffierential Equation
    Li XIA, Zheng An YAO, Wen Shu ZHOU
    Acta Mathematica Sinica. 2009, 25(12): 2199-2220. https://doi.org/10.1007/s10114-009-6238-4
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  • Erratum to:Spectral Gap and Logarithmic Sobolev Constant for Continuous Spin Systems
    Mu Fa CHEN
    Acta Mathematica Sinica. 2009, 25(12): 2201-2202. https://doi.org/10.1007/s10114-009-7293-6
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