15 December 2007, Volume 23 Issue 12

    

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  Classification of Flat Lagrangian Surfaces in Complex Lorentzian Plane

  Bang-Yen CHEN, Johan FASTENAKELS

  Acta Mathematica Sinica. 2007, 23(12): 2111-2144. https://doi.org/10.1007/s10114-007-0991-z

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  One of the most fundamental problems in the study of Lagrangian submanifolds from Riemannian geometric point of view is to classify Lagrangian immersions of real space forms into complex space forms.The main purpose of this paper is thus to classify flat Lagrangian surfaces in the Lorentzian complex plane C₁².Our main result states that there are thirty-eight families of flat Lagrangian surfaces in C₁².Conversely,every flat Lagrangian surface in C₁² is locally congruent to one of the thirty-eight families.
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  Group of Self-Equivalences of Sum Object

  Hao ZHAO, Wen Huai SHEN

  Acta Mathematica Sinica. 2007, 23(12): 2145-2154. https://doi.org/10.1007/s10114-007-0992-y

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  In general category,the group of self-equivalences of sum object can decompose as the product of its two subgroups under certain conditions and also several split short exact sequences are obtained.Subsequently,we apply the above results to the category of space under a space and get some results which are dual to those in fibrewise category.
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  Moment Maps and Equivariant Volumes

  Alberto DELLA VEDOVA, Roberto PAOLETTI

  Acta Mathematica Sinica. 2007, 23(12): 2155-2188. https://doi.org/10.1007/s10114-007-0994-9

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  The study of the volume of big line bundles on a complex projective manifold M has been one of the main veins in the recent interest in the asymptotic properties of linear series.In this article,we consider an equivariant version of this problem,in the presence of a linear action of a reductive group on M.
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  The Maximum Principle for One Kind of Stochastic Optimization Problem and Application in Dynamic Measure of Risk

  Shao Lin, JI Zhen WU

  Acta Mathematica Sinica. 2007, 23(12): 2189-2204. https://doi.org/10.1007/s10114-007-0989-6

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  The authors get a maximum principle for one kind of stochastic optimization problem motivated by dynamic measure of risk.The dynamic measure of risk to an investor in a financial market can be studied in our framework where the wealth equation may have nonlinear coefficients.
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  Existence and Uniqueness of Fixed Point in Partially Ordered Sets and Applications to Ordinary Differential Equations

  Juan J. NIETO, Rosana RODRÍGUEZ-LóPEZ

  Acta Mathematica Sinica. 2007, 23(12): 2205-2212. https://doi.org/10.1007/s10114-005-0769-0

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  We prove some fixed point theorems in partially ordered sets,providing an extension of the Banach contractive mapping theorem.Having studied previously the nondecreasing case,we consider in this paper nonincreasing mappings as well as non monotone mappings.We also present some applications to first-order ordinary differential equations with periodic boundary conditions,proving the existence of a unique solution admitting the existence of a lower solution.
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  Graphs of NMS Flows on S³with Knotted Saddle Orbits and No Heteroclinic Trajectories

  B. CAMPOS, P. VINDEL

  Acta Mathematica Sinica. 2007, 23(12): 2213-2224. https://doi.org/10.1007/s10114-007-0969-x

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  We consider NMS systems on S³ without heteroclinic trajectories connecting two saddles orbits and we build the dual graphs associated with this kind of.ows.We prove that flows coming from essential attachments of orientable round 1-handles can be reproduced from the corresponding dual graph.
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  L^q Interior Estimates of the Gradient for Weak Solutions of Quasilinear Elliptic Equations

  Feng Ping YAO, Yong Yong CAI

  Acta Mathematica Sinica. 2007, 23(12): 2225-2234. https://doi.org/10.1007/s10114-007-0988-7

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  The authors present a new proof of Lq interior estimates of the gradient for weak solutions of a quasilinear elliptic equation of p-Laplacian type.
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  A Note on the Left Essential Spectra of Operator Matrices

  Yuan LI, Xiu Hong SUN, Hong Ke DU

  Acta Mathematica Sinica. 2007, 23(12): 2235-2240. https://doi.org/10.1007/s10114-007-0966-0

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  When A∈B(H) and B∈B(H) are given,we denote by M_C the operator matrix acting on the in.nite dimensional separable Hilbert space H⊕H of the form In this paper,a necessary and sufficient condition for M_c to be left Fredholm for some C∈F(H,H)(C∈Inv(H,H) is given,where F(H,H) and Inv(H,H) denote respectively,the set of Fredholm operators and the set of invertible operators of B(H,H) In addition,we give a necessary and sufficient condition for M_C to be left Fredholm for all C∈Inv(H,H.
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  A New Inequality for Weakly(K₁,K₂)-Quasiregular Mappings

  Hong Ya GAO, Shu Qing ZHOU, Yu Qin MENG

  Acta Mathematica Sinica. 2007, 23(12): 2241-2246. https://doi.org/10.1007/s10114-007-0972-2

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  We obtain a new inequality for weakly(K₁,K₂)-quasiregular mappings by using the McShane extension method.This inequality can be used to derive the self-improving regularity of(K₁,K₂)-Quasiregular Mappings.
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  Complex Polynomial Vector Fields Having a Finitely Curved Orbit

  B. SCÁRDUA

  Acta Mathematica Sinica. 2007, 23(12): 2247-2252. https://doi.org/10.1007/s10114-007-0987-8

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  The author proves that a non-singular polynomial vector field without invariant lines and having an entire finitely curved transcendent orbit on C2 must be equivalent to a trivial vector field by a holomorphic change of coordinates.Other classification results are obtained for polynomial vector fields having a finitely curved orbit on C2.
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  Wavelet Estimation in Heteroscedastic Model Under Censored Samples

  Han Ying LIANG, Jong IL BAEK

  Acta Mathematica Sinica. 2007, 23(12): 2253-2268. https://doi.org/10.1007/s10114-007-0996-7

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  Consider the heteroscedastic regression model Y#em/em#=g(x#em/em#)+σ#em/em#e#em/em#,1≤#em/em#≤n,where σ_i²=f(u_i),here(x#em/em#,u#em/em#) being fixed design points,g and f being unknown functions defined on [0,1],e#em/em# being independent random errors with mean zero.Assuming that Y#em/em# are censored randomly and the censored distribution function is known or unknown,we discuss the rates of strong uniformly convergence for wavelet estimators of g and f,respectively.Also,the asymptotic normality for the wavelet estimators of g is investigated.
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  Almost Everywhere Convergence of Fejér Means of L¹ Functions on Rarely Unbounded Vilenkin Groups

  György GÁT

  Acta Mathematica Sinica. 2007, 23(12): 2269-2294. https://doi.org/10.1007/s10114-007-0961-5

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  A highly celebrated problem in dyadic harmonic analysis is the pointwise convergence of the Fejér(or(C,1)) means of functions on unbounded Vilenkin groups.There are several papers of the author of this paper concerning this.That is,we know the a.e.convergence σ_nf→f(n→∞) for functions f∈L^p,where p>1(Journal of Approximation Theory,101(1),1-36,(1999)) and also the a.e.convergence σM_nf→f(n→∞) for functions f∈L¹(Journal of Approximation Theory,124(1),25-43,(2003).The aim of this paper is to prove the a.e.relation lim_n→σ_nf=f for each integrable function f on any rarely unbounded Vilenkin group.The concept of the rarely unbounded Vilenkin group is discussed in the paper.Basically,it means that the generating sequence m may be an unbounded one,but its "big elements" are not "too dense".
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  Strong Minkowski Separation and Co-Drop Property

  Jing Hui QIU

  Acta Mathematica Sinica. 2007, 23(12): 2295-2302. https://doi.org/10.1007/s10114-007-0980-2

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  In the framework of topological vector spaces,we give a characterization of strong Minkowski separation,introduced by Cheng,et al.,in terms of convex body separation.From this,several results on strong Minkowski separation are deduced.Using the results,we prove a drop theorem involving weakly countably compact sets in locally convex spaces.Moreover,we introduce the notion of the co-drop property and show that every weakly countably compact set has the co-drop property.If the underlying locally convex space is quasi-complete,then a bounded weakly closed set has the co-drop property if and only if it is weakly countably compact.