05 November 2010, Volume 26 Issue 11

    

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  On Relations of Vector Optimization Results with C^1,1 Data

  Dusan BEDNARIK, Karel PASTOR

  Acta Mathematica Sinica. 2010, 26(11): 2031-2040. https://doi.org/10.1007/s10114-010-7356-8

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  In this article we prove that some of the su?cient and necessary optimality conditions ob-tained by Ginchev,Guerraggio,Luc[Appl.Math.,51,5–36(2006)]generalize(strictly)those presentedby Guerraggio,Luc[J.Optim.Theory Appl.,109,615–629(2001)].While the former paper showsexamples for which the conditions given there are e?ective but the ones from the latter paper fail,itdoes not prove that generally the conditions it proposes are stronger.In the present note we completethis comparison with the lacking proof.
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  Oriented Tree Diagram Lie Algebras and Their Abelian Ideals

  Li LUO

  Acta Mathematica Sinica. 2010, 26(11): 2041-2058. https://doi.org/10.1007/s10114-010-8455-2

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  We introduce oriented tree diagram Lie algebras which are generalized from Xu’s bothupward and downward tree diagram Lie algebras,and study certain numerical invariants of thesealgebras related to abelian ideals.
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  Proportionally Modular Diophantine Inequalities and Their Multiplicity

  Jose Carlos ROSALES, Manuel Batista BRANCO, Paulo VASCO

  Acta Mathematica Sinica. 2010, 26(11): 2059-2070. https://doi.org/10.1007/s10114-010-7573-1

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  Let I be an interval of positive rational numbers.Then the set S(I)=T∩N,where T isthe submonoid of( Q⁺₀,+)generated by T,is a numerical semigroup.These numerical semigroups arecalled proportionally modular and can be characterized as the set of integer solutions of a Diophantineinequality of the form ax mod b≤cx.In this paper we are interested in the study of the maximal in-tervals I subject to the condition that S(I)has a given multiplicity.We also characterize the numericalsemigroups associated with these maximal intervals.
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  Boundedness of an Oscillating Multiplier on Triebel–Lizorkin Spaces

  Wei CAO, Jie Cheng CHEN, Da Shan FAN

  Acta Mathematica Sinica. 2010, 26(11): 2071-2084. https://doi.org/10.1007/s10114-010-9573-6

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  In this paper,we study Triebel–Lizorkin space estimates for an oscillating multiplierm_Ω,α,β.This operator was initially studied by Wainger and by Fefferman–Stein in the Lebesgue spaces.We obtain the boundedness results on the Triebel–Lizorkin spaceF^α,q_p(Rⁿ)for different p,q.
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  Implicit Function Theorem and Its Application to a Ulam’s Problem for Exact Differential Equations

  Soon-Mo JUNG

  Acta Mathematica Sinica. 2010, 26(11): 2085-2092. https://doi.org/10.1007/s10114-010-7611-z

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  We prove a global version of the implicit function theorem under a special condition andapply this result to the proof of a modified Hyers–Ulam–Rassias stability of exact differential equationsof the form,g(x,y)+h(x,y)y=0.
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  λ-Central BMO Estimates for Multilinear Commutators of Fractional Integrals

  Zeng Yan SI

  Acta Mathematica Sinica. 2010, 26(11): 2093-2108. https://doi.org/10.1007/s10114-010-9363-1

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  The author establishesλ-central BMO estimates for commutators of multilinear fractionalintegral operators on central Morrey spaces.
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  On Operators Satisfying T^*|T²|T≥T^*|T^*|²T

  Jun Li SHEN, Fei ZUO, Chang Sen YANG

  Acta Mathematica Sinica. 2010, 26(11): 2109-2116. https://doi.org/10.1007/s10114-010-9093-4

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  Let T be a bounded linear operator on a complex Hilbert space H.In this paper weintroduce a new class denoted by l-*-A,of operators satisfying T^*|T²|T≥T^*|T^*|²T,and we prove thebasic properties of these operators.Using these results,we also prove that if T or T^*∈l-*-A,thenw(f(T))=f(w(T)),σ_ea(f(T))=f(σ_ea(T))for every f∈H(σ(T)),where H(σ(T))denotes the set ofall analytic functions on an open neighborhood ofσ(T).
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  g-Besselian Frames in Hilbert Spaces

  Ming Ling DING, Yu Can ZHU

  Acta Mathematica Sinica. 2010, 26(11): 2117-2130. https://doi.org/10.1007/s10114-010-9081-8

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  In this paper,we introduce the concept of a g-Besselian frame in a Hilbert space and discussthe relations between a g-Besselian frame and a Besselian frame.We also give some characterizationsof g-Besselian frames.In the end of this paper,we discuss the stability of g-Besselian frames.Ourresults show that the relations and the characterizations between a g-Besselian frame and a Besselianframe are different from the corresponding results of g-frames and frames.
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  Generalized Statistical Convergence and Statistical Core of Double Sequences

  Mohammad MURSALEEN, Celal CAKAN, Syed Abdul MOHIUDDINE, Ekrem SAVAS

  Acta Mathematica Sinica. 2010, 26(11): 2131-2144. https://doi.org/10.1007/s10114-010-9050-2

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  In this paper we extend the notion ofλ-statistical convergence to the(λ,μ)statisticalconvergence for double sequences x=(x_jk).We also determine some matrix transformations andestablish some core theorems related to our new space of double sequences S_λ,μ.
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  A Generalized Vector-valued Variational Principle in Frechet Spaces

  Jing Hui QIU, Xin Qing YANG

  Acta Mathematica Sinica. 2010, 26(11): 2145-2156. https://doi.org/10.1007/s10114-010-8524-6

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  In the framework of Frechet spaces,we give a generalized vector-valued Ekeland’s vari-ational principle,where the perturbation involves the subadditive functions of countable generatingsemi-norms.By modifying and developing the method of Cammaroto and Chinni,we obtain a densitytheorem on extremal points of the vector-valued variational principle,which extends and improves therelated known results.
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  A Modified Tikhonov Regularization Method for an Axisymmetric Backward Heat Equation

  Wei CHENG, Chu Li FU

  Acta Mathematica Sinica. 2010, 26(11): 2157-2164. https://doi.org/10.1007/s10114-010-8509-5

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  This paper deals with the inverse time problem for an axisymmetric heat equation.Theproblem is ill-posed.A modified Tikhonov regularization method is applied to formulate regularizedsolution which is stably convergent to the exact one.Meanwhile,a logarithmic-Holder type errorestimate between the approximate solution and exact solution is obtained by introducing a rathertechnical inequality and improving a priori smoothness assumption.
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  Oscillation of Second Order Semilinear Elliptic Equations with Damping

  Zhi Ting XU

  Acta Mathematica Sinica. 2010, 26(11): 2165-2178. https://doi.org/10.1007/s10114-010-8331-0

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  We obtain some new Kamenev-type oscillation theorems for the second order semilinearelliptic differential equation with damping under quite general assumptions.These results are extensions of the recent results of Sun[Sun,Y.G.:New Kamenev-type oscillation criteria of second order nonlinear differential equations with damping.J.Math.Anal.Appl.,291,341–351(2004)]in a natural way.In particular,we do not impose anyadditional conditions on the damped functions b_i(x)except the continuity.Several examples are givento illustrate the main results.
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  Effcient Estimation of a Varying-coeffcient Partially Linear Binary Regression Model

  Tao HU, Heng Jian CUI

  Acta Mathematica Sinica. 2010, 26(11): 2179-2190. https://doi.org/10.1007/s10114-010-8043-5

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  This article considers a semiparametric varying-coeffcient partially linear binary regressionmodel.The semiparametric varying-coeffcient partially linear regression binary model which is ageneralization of binary regression model and varying-coeffcient regression model that allows one toexplore the possibly nonlinear effect of a certain covariate on the response variable.A Sieve maximumlikelihood estimation method is proposed and the asymptotic properties of the proposed estimatorsare discussed.One of our main objects is to estimate nonparametric component and the unknownparameters simultaneously.It is easier to compute,and the required computation burden is much lessthan that of the existing two-stage estimation method.Under some mild conditions,the estimatorsare shown to be strongly consistent.The convergence rate of the estimator for the unknown smoothfunction is obtained,and the estimator for the unknown parameter is shown to be asymptoticallyeffcient and normally distributed.Simulation studies are carried out to investigate the performance ofthe proposed method.
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  A Characterization of Some Weighted Inequalities for the Vector-valued Weighted Maximal Function

  Cui Lan WU

  Acta Mathematica Sinica. 2010, 26(11): 2191-2198. https://doi.org/10.1007/s10114-010-8009-7

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  We give in this paper a necessary and suffcient condition of weighted weak and strongtype norm inequalities for the vector-valued weighted maximal function.
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  A Generalized Version of Branner–Hubbard Conjecture for Rational Functions

  Yu ZHAI

  Acta Mathematica Sinica. 2010, 26(11): 2199-2208. https://doi.org/10.1007/s10114-010-7632-7

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  In 1992,Branner and Hubbard raised a conjecture that the Julia set of a polynomial is aCantor set if and only if each critical component of its filled-in Julia set is not periodic.This conjecturewas solved recently.In this paper,we generalize this result to a class of rational functions.
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  Typical Frobenius Coverings

  Yan WANG, Rong Quan FENG, Jaeun LEE

  Acta Mathematica Sinica. 2010, 26(11): 2209-2214. https://doi.org/10.1007/s10114-010-7630-9

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  A covering p from a Cayley graph Cay(G,X)onto another Cay(H,Y)is called typicalFrobenius if G is a Frobenius group with H as a Frobenius complement and the map p:G→H is agroup epimorphism.In this paper,we emphasize on the typical Frobenius coverings of Cay(H,Y).Weshow that any typical Frobenius covering Cay(G,X)of Cay(H,Y)can be derived from an epimorphismf from G to H which is determined by an automorphism f of H.If Cay(G,X₁)and Cay(G,X₂)aretwo isomorphic typical Frobenius coverings under a graph isomorphismφ,some properties satisfied byφare given.
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  On s-semipermutable Subgroups of Finite Groups

  Yang Ming LI, Xuan Li HE, Yan Ming WANG

  Acta Mathematica Sinica. 2010, 26(11): 2215-2222. https://doi.org/10.1007/s10114-010-7609-6

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  Suppose that G is a finite group and H is a subgroup of G.We say that H is s-semipermutable in G if HG_p=G_pH for any Sylow p-subgroup G_p of G with(p,|H|)=1.Weinvestigate the influence of s-semipermutable subgroups on the structure of finite groups.Some recentresults are generalized and unified.
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  Zeta-Functions of Curves of Genus 3 over Finite Fields

  Fei YU, Hong Xi TONG

  Acta Mathematica Sinica. 2010, 26(11): 2223-2230. https://doi.org/10.1007/s10114-010-7476-1

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  In this paper,we determine zeta-functions of some curves of genus 3 over finite fields bygluing three elliptic curves based on Xing’s research,and the examples show that there exists a maximalcurve of genus 3 over F₄₉.
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  Principal Quasi-Baerness of Formal Power Series Rings

  Zhong Kui LIU, Wen Hui ZHANG

  Acta Mathematica Sinica. 2010, 26(11): 2231-2238. https://doi.org/10.1007/s10114-010-7429-8

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  Let R be a ring.We consider left(or right)principal quasi-Baerness of the left skewformal power series ring R[[x;α]]over R whereαis a ring automorphism of R.We give a necessaryand su?cient condition under which the ring R[[x;α]]is left(or right)principally quasi-Baer.As anapplication we show that R[[x]]is left principally quasi-Baer if and only if R is left principally quasi-Baer and the left annihilator of the left ideal generated by any countable family of idempotents in R isgenerated by an idempotent.