中国科学院数学与系统科学研究院期刊网

15 March 2010, Volume 53 Issue 2
    

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  • Ye ZHANG, Huai Xin CAO
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 209-218. https://doi.org/10.12386/A2010sxxb0026
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    In this paper, the effective sequences in a Hilbert space are discussed and by introducing the adjoint sequence of a sequence, an equivalent characterization of an effective sequence is presented. Next, some properties of linear operators preserving the effectiveness of effective sequences are discussed. It is proved that a linear operator maps every effective sequence as an effective sequence if and only if it is a unitary. Finally, we give a necessary and sufficient condition for a sequence obtained by adding a unit vector into an orthonormal basis to be an effective sequence.

  • Lei DAI, Xiao Hong CAO, Chen Hui SUN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 219-226. https://doi.org/10.12386/A2010sxxb0027
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    In this note we study the generalized property (ω), a variant of generalized Weyl's theorem, by means of the new spectrum. We establish for a bounded linear operator defined on a Banach space a sufficient and necessary condition for which generalized property (ω) holds. As a consequence of the main result, the stability of generalized property (ω) is considered.

  • Li WANG, Chuang Yi ZHANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 227-232. https://doi.org/10.12386/A2010sxxb0028
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    In this paper, we investigate the existence of\ almost periodic solutions of second-order neutral delay-differential equations with piecewise constant argument of the form (x(t)+px(t-1))"=qx(2[(t+1)/2])+f(t), where [·] denotes the greatest integer function, p, q are nonzero real constants and |p|=1, q≠-4, f(t) is almost periodic.

     

  • Cai Di ZHAO, Sheng Fan ZHOU
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 233-242. https://doi.org/10.12386/A2010sxxb0029
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    We first recast some sufficient conditions for the existence of exponential attractors for general lattice dynamical systems. Then we apply the result to the following nonlinear Schrödinger equations on infinite lattices: Under some conditions on γ, κ,δ,σ and gm, the existence of exponential attractors is established.  
  • Can Qin TANG, Bo Lin MA
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 243-250. https://doi.org/10.12386/A2010sxxb0030
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    In this paper, the boundedness of commutators associated with singular integral operators T satisfying H(m) with Lipschitz functions from Lp(Rn) to some Lq(Rn) spaces is obtained. The boundedness on Hardy space is also considered. The results are applied to obtain the boundedness of commutators of Riesz transforms associated with Schrödinger operator and Lipschitz functions.

     

  • Xian Geng ZHOU, Min ZHAN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 251-256. https://doi.org/10.12386/A2010sxxb0031
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    In this paper proves some representation theorems of Δ(Δm)-statistical convergence and double sequence (double sequence double Lacunary) statistical convergence in Banach space X.

     

  • Li Ping LUO, Yuan Hong YU
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 257-262. https://doi.org/10.12386/A2010sxxb0032
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    The oscillation of a class of impulsive vector neutral parabolic partial differential equations is studied. To change the multi-dimensional oscillation problems into the problems of which one-dimensional impulsive delay differential inequalities haven't eventually positive solution by employing the concept of H-oscillation introduced by Domslak and the method of reducing dimension with the inner product, some sufficient criteria for H-oscillation of all solutions of the equations are established under Dirichlet boundary value condition, where H is a unit vector of RM.

     

  • Ding Xing ZHONG, Hong An SUN, Ting Fang ZHANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 263-278. https://doi.org/10.12386/A2010sxxb0033
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    Let x:MSn+1 be a hypersurface in the (n+1)-dimensional unit sphere Sn+1 without umbilics. Four basic invariants of x under the Moebius transformation group in Sn+1 are a Riemannian metric g called Moebius metric, a 1-form Φ called Moebius form, a symmetric (0,2) tensor A called Blaschke tensor and symmetric (0,2) tensor B called Moebius second fundamental form. Let D =AB, where λ is a constant. Then D is a symmetric (0,2) tensor and a Moebius invariant. D is called Para-Blaschke tensor of x. Li and Wang have studied the hypersurfaces x:MSn+1, which satisfy: (i) Φ=0, (ii) AB+μg=0 for some functions λ and μ on M; they have proved that λ and μ must be constants and have classified the hypersurfaces; in fact, they have classified the hypersurfaces which satisfy: (i) Φ=0, (ii) D has only one distinct constant eigenvalue. In this paper, We classify the hypersurfaces x:MS5, which satisfy: (i) Φ=0, (ii) D has constant eigenvalues for some constants λ.

     

  • You Fa LI, Shou Zhi YANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 279-290. https://doi.org/10.12386/A2010sxxb0034
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    Paraunitary matrices play a very important role in construction of wavelets, multiwavelets and frames. In this paper, we give an explicit algorithm for constructing paraunitary symmetric matrices (p.s.m. for short), whose components are symmetric or antisymmetric polynomials. Based on the constructed p.s.m. and the given orthogonal and symmetric multiwavelets (o.s.m. for short), parametrization of o.s.m. filter banks is given. Appropriately selecting some parameters, we can obtain o.s.m. with some additionally desirable properties such as Armlet. To embody our results, we construct a family of symmetric Chui--Lian Armlet filters.

  • Jun Feng XU, Hong Xun YI
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 291-296. https://doi.org/10.12386/A2010sxxb0035
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    In this paper, we use a new lemma to investigate the relation between solutions, their 1st, 2nd derivatives, differential polynomial of differential equations with function of small growth.

  • Yong Zhong HU, Ping Zhi YUAN
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 297-300. https://doi.org/10.12386/A2010sxxb0036
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    We show that when a=n+1, b=2n(n+1), c=2n(n+1)+1 with n positive integer, the equation ax+by=cz has only the positive integer solution (x,y,z)=(2,2,2). The proof is based on using the theorem about the existence of primitive divisors of Lucas numbers due to Bilu, Hanrot & Voutier and some fine results on the representation of the solutions of quadratic diophantine equations.

     

  • Tong Yi MA
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 301-314. https://doi.org/10.12386/A2010sxxb0037
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    In this paper, the three concepts of Lp-mixed centroid bodies Γp,iK and dual Lp-mixed centroid bodies Γ-p,iK and Lp-mixed harmonic Blaschke add of star bodies are introduced. The Shephard's question of Lp-mixed centroid bodies and dual Lp-mixed centroid bodies are solved succeed. In addition, the Brunn--Minkowski inequalities of the quermassintegrals and dual quermassintegrals of Lp-mixed centroid bodies associated with Lp-mixed harmonic Blaschke add are established, respectively. They extend some results of before document.  
  • Guo Xing JI, Fan Lian QU
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 315-322. https://doi.org/10.12386/A2010sxxb0038
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    Let B(H) be the algebra of all bounded linear operators on a complex Hilbert space H with dim H≥2. It is proved that a linear surjective map φ on B(H) preserves the nonzero projections of products of two operators if and only if there is a unitary operator U in B(H) such that φ(X)=λU*XU, ?XB(H) for some constants λ with λ2=1. Related results for linear surjective maps preserving Jordan triple products of two operators are also obtained.

     

  • Ying Qing XIAO, Wei Yuan QIU
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 323-328. https://doi.org/10.12386/A2010sxxb0039
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    Let P be a monic polynomial of degree d, and JP be the Julia set of P. We obtain the dn-th Chebyshev polynomials on the Julia set JP and on the equipotential curves ΓP(R) of JP, and give an example to show that they are not always equal.

     

  • Yong Hui FAN, Song Gui WANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 329-340. https://doi.org/10.12386/A2010sxxb0040
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    Inference on the mean vectors of several multivariate normal populations is an old and interesting problem. In this paper, by the distribution of the Bartlett's decomposition of sample covariance matrices, the concepts of an exact tests are proposed. Simulation shows these tests are more powerful than the existing tests. Also, by the Bartlett's decomposition of sample covariance matrices and the sample mean vectors, two generalized tests and a new traditional test are proposed to test the common mean of several multivariate normal populations. Simulation shows that the type I error probability of these tests is less than the nominal level and has more powers.

     

  • Luo Zhong GONG, Wei Jun LIU, Shao Jun DAI
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 341-348. https://doi.org/10.12386/A2010sxxb0041
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    Line-transitively linear spaces are first divided into the point-imprimitive and the point-primitive, and the primitive ones are now subdivided into the socles which are elementary abelian or non-abelian simple. In this paper, the latter is considered. Namely, T is non-abelian simple, TG≤Aut(T) and G acts line-transitively on finite linear spaces. And we prove that when T is isomorphic to F4(q), if TL is not the subgroups of 2F4(q), B4(q), D4(qS3,3D4(q)·3, F4(q1/2) or of the parabolic subgroups of T, T is also line-transitive, where q is a power of the prime p.

     

  • Tie Feng MA, Ren Dao YE, Li Jie JIA
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 349-362. https://doi.org/10.12386/A2010sxxb0042
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    Multivariate linear mixed model with two variance components matrices is considered. For balanced model, based on spectral decomposition estimate (SDE), a class of nonnegative estimate of variance components matrices is proposed. For unbalanced model, a so-called generalized spectral decomposition estimate (GSDE) of variance components matrices is obtained. Our results show a sufficient and necessary condition for the GSDE to be equal to the analysis of variance estimate (ANOVAE). And then, based on GSDE, we also propose a class of nonnegative estimate and discuss the optimality. Furthermore, we extend the method proposed by Kelly and Mathew (1993) to multivariate model in this paper. Finally, some simulations and applications to illustrate the results are presented.

     

  • Ying LIU, Ke SU
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 363-374. https://doi.org/10.12386/A2010sxxb0043
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    We introduce an iterative sequence by the viscosity approximation method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of an asymptotically nonexpansive mapping in a Hilbert space and then obtain that the sequence converges strongly to a common element of two sets which solves some variational inequality. Using this result, we study three strong convergence problems and the optimization problem.

     

  • Jia Wei CHEN, Yun Zhi ZOU
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 375-384. https://doi.org/10.12386/A2010sxxb0044
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    In this paper, the authors investigate a class of F-implicit variational inequality problems in reflexive Banach spaces. By introducing a new concept of the generalized (F,g)-projection operator and a new definition of exceptional family and using Fan-KKM theorem and exceptional family under asymptotic h-g pseudomonotonicity and without monotonicity assumptions, respectively, the authors derive some existence theorems and some properties of the solutions.

     

  • Hong Bing QIU, Ji LUO
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 385-392. https://doi.org/10.12386/A2010sxxb0045
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    Robustness of F-test based on the general least squares estimate used in testing linear restrictions is discussed in general linear model. We mainly study robustness of the F-statistics in the cases of variance matrix of error including parameter and design matrix with reduced-rank columns. The maximal classes of variance matrix of error are derived, in which F(V(θ)) is F-statistics of the linear restriction. Also the robustness of F-statistics with respect to linear restrictions for partitioned parameters in partitioned linear model is considered.

     

  • Tian Liang TU, Ji En DENG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 393-408. https://doi.org/10.12386/A2010sxxb0046
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    For the convergence and order of approximation to by Hermite--Fejér interpolation at disturbed Fejér points on Γ, the open problem posed by Chui & Shen in Transactions of the AMS 1991 is solved completely. In the meantime, the boundary condition J2 is improved by in this paper.  
  • Ping Ping ZHANG, Quan Xin ZHANG
    Acta Mathematica Sinica, Chinese Series. 2010, 53(2): 409-416. https://doi.org/10.12386/A2010sxxb0047
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    This paper concerns the analytic solutions of iterative functional differential equation x'(z)=1/(x(az+(b/(x'(z))))), zC where a,b are complex numbers. First of all, we reduce the equation with the Schröder transformation to another functional differential equation without iteration. Then analytic solutions of auxiliary equation are discussed under the following conditions: the constant α given in Schröder transformation is on the unit circle, but not a root of the unity, the Brjuno condition is satisfied; α is not only on the unit circle, but also a root of the unity; α is inside of the unit circle. Following this, we prove the existence of local invertible analytic solution of primary function, and calculate its explicit form. Finally, our main result is illustrated with an example.