中国科学院数学与系统科学研究院期刊网

05 December 2010, Volume 26 Issue 12
    

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  • Zohra BENDOUAD, Isabelle CHALENDAR, Jean ESTERLE, Jonathan R.PARTINGTON
    Acta Mathematica Sinica. 2010, 26(12): 2239-2254. https://doi.org/10.1007/s10114-010-8569-6
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    This paper is concerned first with the behaviour of differences T(t)-T(s)near the origin,where(T(t))is a semigroup of operators on a Banach space,defined either on the positive real line ora sector in the right half-plane(in which case it is assumed analytic).For the non-quasinilpotent caseextensions of results in the published literature are provided,with best possible constants;in the case ofquasinilpotent semigroups on the half-plane,it is shown that,in general,di?erences such as T(t)?T(2t)have norm approaching 2 near the origin.The techniques given enable one to derive estimates of otherfunctions of the generator of the semigroup;in particular,conditions are given on the derivatives nearthe origin to guarantee that the semigroup generates a unital algebra and has bounded generator.
  • Jia Yi JIANG, Di Sheng XU
    Acta Mathematica Sinica. 2010, 26(12): 2255-2258. https://doi.org/10.1007/s10114-010-0116-y
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    In this paper,we characterize the commutant of Toeplitz operators on weighted Bergmanspace with symbol polynomial by using algebraic curves theory.
  • Maria D.ACOSTA, Jeronimo ALAMINOS, Domingo GARCIA, Manuel MAESTRE
    Acta Mathematica Sinica. 2010, 26(12): 2259-2268. https://doi.org/10.1007/s10114-010-8638-x
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    If X is an Asplund space,then every uniformly continuous function on BX*which isholomorphic on the open unit ball,can be perturbed by a w*continuous and homogeneous polynomialon X*to obtain a norm attaining function on the dual unit ball.This is a consequence of a versionof Bourgain–Stegall’s variational principle.We also show that the set of N-homogeneous polynomialsbetween two Banach spaces X and Y whose transposes attain their norms is dense in the correspondingspace of N-homogeneous polynomials.In the case when Y is the space of Radon measures on a compactK,this result can be strengthened.
  • Qun CHEN, Cai Rong XIANG
    Acta Mathematica Sinica. 2010, 26(12): 2269-2282. https://doi.org/10.1007/s10114-010-0061-9
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    This paper concerns the submanifold geometry in the ambient space of warped productmanifolds Fn×σR,this is a large family of manifolds including the usual space forms Rm,Sm andHm.We give the fundamental theorem for isometric immersions of hypersurfaces into warped productspace Rn×σR,which extends this kind of results from the space forms and several spaces recentlyconsidered by Daniel to the cases of infinitely many ambient spaces.
  • Martin BACA, Mirka MILLER, Oudone PHANALASY
    Acta Mathematica Sinica. 2010, 26(12): 2283-2294. https://doi.org/10.1007/s10114-010-9502-8
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    This paper deals with the problem of labeling the vertices,edges and faces of a plane graphin such a way that the label of a face and the labels of the vertices and edges surrounding that face addup to a weight of that face,and the weights of all s-sided faces constitute an arithmetic progression ofdifference d,for each s that appears in the graph.The paper examines the existence of such labelings for disjoint union of plane graphs.
  • Gyorgy GAT, Karoly NAGY
    Acta Mathematica Sinica. 2010, 26(12): 2295-2304. https://doi.org/10.1007/s10114-010-9340-8
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    For the two-dimensional Walsh system,Gat and Weisz proved the a.e.convergence of Fejermeansσnf of integrable functions,where the set of indices is inside a positive cone around the identicalfunction,that is,β-1≤n1/n2≤βis provided with some fixed parameterβ≥1.In this paper wegeneralize the result of Gat and Weisz.We not only generalize this theorem,but give a necessary andSuffcient condition for cone-like sets in order to preserve this convergence property.
  • Hong Bing FAN, Gui Zhen LIU, Ji Ping LIU, He Ping LONG
    Acta Mathematica Sinica. 2010, 26(12): 2305-2312. https://doi.org/10.1007/s10114-010-9006-6
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    For any even integer k and any integer i,we prove that a(kr+i)-regular multigraphcontains a k-factor if it contains no more than kr-3k/2+i+2 cut edges,and this result is the bestpossible to guarantee the existence of k-factor in terms of the number of cut edges.We further give acharacterization for k-factor free regular graphs.
  • Ali GHAFFARI
    Acta Mathematica Sinica. 2010, 26(12): 2313-2324. https://doi.org/10.1007/s10114-010-9498-0
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    Let G be a locally compact group and let Γbe a closed subgroup of G×G.Pier introducedthe notion of Γ-amenability which gives a new classification of groups.This concept generalizes theconcept of amenability and inner amenability for locally compact groups.In this paper,among otherthings,we extend some standard results for amenable groups toΓ-amenable groups and give variouscharacterizations forΓ-amenable groups.A sequence of characterizations of Γ-amenable groups is givenhere by developing the well-known FΦlner’s conditions for amenable locally compact groups.Severalcharacterizations of inner amenability are also given.
  • Yong Seung CHO
    Acta Mathematica Sinica. 2010, 26(12): 2325-2334. https://doi.org/10.1007/s10114-010-8132-5
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    Let a finite group act semi-freely on a closed symplectic four-manifold with a 2-dimensionalfixed point set.Then we show that the relative Gromov–Witten invariants are the same as the invariantson the quotient set-up with respect to the fixed point set.
  • Li Guang WANG, Bo LIU
    Acta Mathematica Sinica. 2010, 26(12): 2335-2348. https://doi.org/10.1007/s10114-010-9330-x
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    In this paper,we investigate the Hyers–Ulam stability of the following function equation2f(2x+y)+2f(2x-y)=4f(x+y)+4f(x-y)+4f(2x)+f(2y)-8f(x)-8f(y)in quasi-β-normed spaces.
  • Hai Feng MA, Henryk HUDZIK, Yu Wen WANG, Zhao Feng MA
    Acta Mathematica Sinica. 2010, 26(12): 2349-2354. https://doi.org/10.1007/s10114-010-9329-3
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    In this paper,we introduce the concepts of generalized regular points and narrow spectrumpoints of bounded linear operators on Hilbert spaces.The concept of generalized regular points is anextension of the concept regular points,and so,the set of all spectrum points is reduced to the narrowspectrum.We present not only the same and di?erent properties of spectrum and of narrow spectrumbut also show the relationship between them.Finally,the well known problem about the invariantsubspaces of bounded linear operators on separable Hilbert spaces is simplified to the problem of theoperator with narrow spectrum only.
  • Li Qiong LIN, Huai Jie ZHONG, Yun Nan ZHANG
    Acta Mathematica Sinica. 2010, 26(12): 2355-2368. https://doi.org/10.1007/s10114-010-9263-4
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    We obtain the K-groups of the operator ideals contained in the class of Riesz operators.And based on the results,we calculate the K-groups of the operator algebras on H Dn spaces and QDnspaces.
  • Yu Can ZHU, Si Yuan WANG
    Acta Mathematica Sinica. 2010, 26(12): 2369-2376. https://doi.org/10.1007/s10114-010-9219-8
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    In this paper,we give some equivalent conditions on a Banach frame for a Banach spaceby using the pseudoinverse operator.We also consider the stability of a Banach frame for a Banachspace X with respect to Xd or an Xd-frame for a Banach space X under perturbation.These resultsgeneralize and improve the related works of Balan,Casazza,Christensen,Stoeva and Jian et al.
  • Qi LU
    Acta Mathematica Sinica. 2010, 26(12): 2377-2386. https://doi.org/10.1007/s10114-010-9051-1
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    In this paper,we establish a bang-bang principle of time optimal controls for a controlledparabolic equation of fractional order evolved in a bounded domainΩof Rn,with a controllerωtobe any given nonempty open subset ofΩ.The problem is reduced to a new controllability propertyfor this equation,i.e.the null controllability of the system at any given time T>0 when the controlis restricted to be active inω×E,where E is any given subset of[0,T]with positive(Legesgue)measure.The desired controllability result is established by means of a sharp observability estimateon the eigenfunctions of the Dirichlet Laplacian due to Lebeau and Robbiano,and a delicate result inthe measure theory due to Lions.
  • Zhi Guo WANG, Yi Qian WANG
    Acta Mathematica Sinica. 2010, 26(12): 2387-2398. https://doi.org/10.1007/s10114-010-9133-0
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    In this paper,we prove that the second order differential equationd2x/dt2+x2n+1f(x)+p(t)=0with p(t+1)=p(t),f(x+T)=f(x)smooth and f(x)>0,possesses Lagrangian stability despite ofthe fact that the monotone twist condition is violated.
  • Jin Bao JIAN, Dao Lan HAN, Qing Juan XU
    Acta Mathematica Sinica. 2010, 26(12): 2399-2420. https://doi.org/10.1007/s10114-010-7432-0
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    Based on a new e?cient identification technique of active constraints introduced in thispaper,a new sequential systems of linear equations(SSLE)algorithm generating feasible iterates isproposed for solving nonlinear optimization problems with inequality constraints.In this paper,we in-troduce a new technique for constructing the system of linear equations,which recurs to a perturbationfor the gradients of the constraint functions.At each iteration of the new algorithm,a feasible descentdirection is obtained by solving only one system of linear equations without doing convex combination.To ensure the global convergence and avoid the Maratos e?ect,the algorithm needs to solve two addi-tional reduced systems of linear equations with the same coe?cient matrix after finite iterations.Theproposed algorithm is proved to be globally and superlinearly convergent under some mild conditions.What distinguishes this algorithm from the previous feasible SSLE algorithms is that an improvingdirection is obtained easily and the computation cost of generating a new iterate is reduced.Finally,apreliminary implementation has been tested.
  • Ru Ying XUE
    Acta Mathematica Sinica. 2010, 26(12): 2421-2442. https://doi.org/10.1007/s10114-010-7321-6
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    we study an initial-boundary-value problem for the“good”Boussinesq equation on thehalf line The existence and uniqueness of low reguality solution to the initial-boundary-value problem is provedwhen the initial-boundary data(f,h,h1,h2)belong to the product spaceHs(R+)×Hs-1(R+)×Hs/2+1/4(R+s/2+1/4(R+)with 0≤s<1/2.The analyticity of the solution mapping between the initial-boundary-data and thesolution space is also considered.
  • Yun Xia LI, Jian Jun XU, Li Xin ZHANG
    Acta Mathematica Sinica. 2010, 26(12): 2443-2460. https://doi.org/10.1007/s10114-010-7193-9
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    In this paper,we study the asymptotic CUSUM tests for detecting changes in the meanor variance of a moving-average process with long memory.When there is no change over[0,T],theasymptotic distribution of the test statistic is derived,which allows us to find asymptotic critical values.When there is a change,the behavior of the test statistic is discussed.Conditions for the consistencyof these tests are also discussed.Based on the asymptotic results,simulation studies of testing forchanges in the mean show that the CUSUM test proposed performs well.