15 November 2009, Volume 25 Issue 11

    

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  On Integrable Roots in Split Lie Triple Systems

  A.J.CALDERON MARTIN

  Acta Mathematica Sinica. 2009, 25(11): 1759-1774. https://doi.org/10.1007/s10114-009-8292-3

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  We focus on the notion of an integrable root in the framework of split Lie triple systems
  T with a coherent 0-root space.As a main result,it is shown that if T has all its nonzero roots
  integrable,then its standard embedding is a split Lie algebra having all its nonzero roots integrable.
  As a consequence,a local finiteness theorem for split Lie triple systems,saying that whenever all
  nonzero roots of T are integrable then T is locally finite,is stated.Finally,a classification theorem for
  split simple Lie triple systems having all its nonzero roots integrable is given.
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  A Note on Tropical Triangles in the Plane

  M.ANSOLA M.J.de la PUENTE

  Acta Mathematica Sinica. 2009, 25(11): 1775-1786. https://doi.org/10.1007/s10114-009-7345-y

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  We define transversal tropical triangles(affne and projective)and characterize them via six
  inequalities to be satisfied by the coordinates of the vertices.We prove that the vertices of a transversal
  tropical triangle are tropically independent and they tropically span a classical hexagon whose sides have
  slopes∞,0,1.Using this classical hexagon,we determine a parameter space for transversal tropical
  triangles.The coordinates of the vertices of a transversal tropical triangle determine a tropically regular
  matrix.Triangulations of the tropical plane are obtained.
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  New Characterizations of Inhomogeneous Besov and Triebel–Lizorkin Spaces over Spaces of Homogeneous Type

  Yan Chang HAN

  Acta Mathematica Sinica. 2009, 25(11): 1787-1804. https://doi.org/10.1007/s10114-009-8348-4

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  In this paper we use the T 1 theorem to prove a new characterization with minimum
  regularity and cancellation conditions for inhomogeneous Besov and Triebel–Lizorkin spaces over spaces
  of homogeneous type.These results are new even for Rⁿ.
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  Picard Dimension of Signed Radial Kato Measures

  Allami BENYAICHE, Aiad ELGOURARI

  Acta Mathematica Sinica. 2009, 25(11): 1805-1818. https://doi.org/10.1007/s10114-009-7243-3

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  The Picard dimension dimμof a signed local Kato measureμon the punctured unit ball
  in R^d,d≥2,is the cardinal number of the set of extremal rays of the convex cone of all continuous
  solutions u≥0 of the time-independent Schrodinger equationΔu-uμ=0 on the punctured ball
  0<‖x‖<1,with vanishing boundary values on the sphere ‖x‖=1.Using potential theory associated
  with the Schrodinger operator we prove,in this paper,that the dimμfor a signed radial Kato measure
  is 0,1 or+∞.In particular,we obtain the Picard dimension of locally Holder continuous functions P
  proved by Nakai and Tada by other methods.
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  Control of Cauchy System for an Elliptic Operator

  G.MASSENGO MOPHOU, O.NAKOULIMA

  Acta Mathematica Sinica. 2009, 25(11): 1819-1834. https://doi.org/10.1007/s10114-009-7066-2

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  The control of a Cauchy system for an elliptic operator seems to be globally an open
  problem.In this paper,we analyze this problem using a regularization method which consists in
  viewing a singular problem as a limit of a family of well-posed problems.Following this analysis and
  assuming that the interior of considered convex is non-empty,we obtain a singular optimality system
  (S.O.S.)for the considered control problem.
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  Orthonormal Bases Associated with Multi-knot Piecewise Linear Function Sequences on[0,1)ⁿ

  Yu Lan LI, Dun Yan YAN

  Acta Mathematica Sinica. 2009, 25(11): 1835-1848. https://doi.org/10.1007/s10114-009-7702-x

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  We investigate two classes of orthonormal bases for L²([0,1)ⁿ).The exponential parts of
  those bases are multi-knot piecewise linear functions which are called spectral sequences.We charac-
  terize the multi-knot piecewise linear spectral sequences and give an application of the first class of
  piecewise linear spectral sequences.
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  Weakly Strongly Singular Integral Operators on Anisotropic Hardy Spaces and Their Dual Operators

  Yong DING, Sen Hua LAN

  Acta Mathematica Sinica. 2009, 25(11): 1849-1864. https://doi.org/10.1007/s10114-009-7506-z

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  Let A be an expansive dilation.We define weakly strongly singular integral kernels and
  study the action of the operators induced by these kernels on anisotropic Hardy spaces associated
  with A.
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  Improved Hormander’s Theorem and New Methods for Oscillatory Integral Operators

  Sheng-Ming MA

  Acta Mathematica Sinica. 2009, 25(11): 1865-1874. https://doi.org/10.1007/s10114-009-7515-y

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  This paper proves a theorem on the decay rate of the oscillatory integral operator with a
  degenerate C^∞phase function,thus improving a classical theorem of Hormander.The proof invokes
  two new methods to resolve the singularity of such kind of operators:a delicate method to decompose
  the operator and balance the L² norm estimates;and a method for resolution of singularity of the
  convolution type.The operator is decomposed into four major pieces instead of infinite dyadic pieces,
  which reveals that Cotlar’s Lemma is not essential for the L² estimate of the operator.In the end
  the conclusion is further improved from the degenerate C^∞phase function to the degenerate C⁴ phase
  function.
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  A Criterion for the Generalized Riemann Hypothesis

  Jin Hong LI

  Acta Mathematica Sinica. 2009, 25(11): 1875-1880. https://doi.org/10.1007/s10114-009-7502-3

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  In this paper,we study the automorphic L-functions attached to the classical automorphic
  forms on GL(2),i.e.holomorphic cusp form.And we also give a criterion for the Generalized Riemann
  Hypothesis(GRH)for the above L-functions.
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  Carleson Measures on Planar Sets

  Zhijian QIU

  Acta Mathematica Sinica. 2009, 25(11): 1881-1892. https://doi.org/10.1007/s10114-009-7079-x

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  In this paper,we investigate what are Carleson measures on open subsets in the complex
  plane.A circular domain is a connected open subset whose boundary consists of finitely many disjoint
  circles.We call a domain G multi-nicely connected if there exists a circular domain W and a conformal
  mapψfrom W onto G such thatψis almost univalent with respect the arclength on∂W.We
  characterize all Carleson measures for those open subsets so that each of their components is multi-
  nicely connected and harmonic measures of the components are mutually singular.Our results suggest
  the extension of Carleson measures probably is up to this class of open subsets
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  An Information-Theoretic Approach to Effective Inference for Z-functionals

  Chang Chun WU, Run Chu ZHANG

  Acta Mathematica Sinica. 2009, 25(11): 1893-1960. https://doi.org/10.1007/s10114-009-6571-7

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  In this paper,through an information-theoretic approach,we construct estimations and
  confidence intervals of Z-functionals involving finite population and with the presence of auxiliary
  information.In particular,we give a method of estimating the variance of finite population with
  known mean.The modified estimates and confidence intervals for Z-functionals can adequately use
  the auxiliary information,at least not worse than what the standard ones do.A simulation study is
  presented to assess the performance of the modified estimates for the finite sample case.
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  On Equalities for BLUEs under Misspecified Gauss–Markov Models

  Yong Ge TIAN

  Acta Mathematica Sinica. 2009, 25(11): 1907-1920. https://doi.org/10.1007/s10114-009-6375-9

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  This paper studies relationships between the best linear unbiased estimators(BLUEs)of an
  estimable parametric functions Kβunder the Gauss–Markov model{y,Xβ,σ²Σ}and its misspecified
  model{y,X₀β,σ²Σ₀}.In addition,relationships between BLUEs under a restricted Gauss–Markov
  model and its misspecified model are also investigated.
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  Globally Proper Saddle Point in Ic-Cone-Convexlike Set-Valued Optimization Problems

  Guo Lin YU, San Yang LIU

  Acta Mathematica Sinica. 2009, 25(11): 1921-1928. https://doi.org/10.1007/s10114-009-6144-9

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  The existence conditions of globally proper e?cient points and a useful property of ic-
  cone-convexlike set-valued maps are obtained.Under the assumption of the ic-cone-convexlikeness,
  the optimality conditions for globally proper effcient solutions are established in terms of Lagrange
  multipliers.The new concept of globally proper saddle-point for an appropriate set-valued Lagrange
  map is introduced and used to characterize the globally proper e?cient solutions.The results which
  are obtained in this paper are proven under the conditions that the ordering cone need not to have a
  nonempty interior.