中国科学院数学与系统科学研究院期刊网

04 May 2011, Volume 54 Issue 3
    

  • Select all
    |
    Articles
  • Qing Ying XUE, Ju Yang ZHANG, Wen Juan LI
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 353-372. https://doi.org/10.12386/A2011sxxb0037
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let μ be a positive Radon measure μ on Rd which may be non-doubling. The only condition that μ is μ(B(x, 2r)) ≤ C0μ(B(x, r)) for all xRd, r > 0 and some fixed constant C0. In this paper, the authors define Littlewood–Paley’s gλ*,b,m function as follows: gλ*,b,m(x) = gλ*([b(x)-b(·)]mf)(x), x ∈ Rd, and mainly studied its endpoint estimates when they are related to non-doubling measure μ. These estimates can be considered as extensions of related classical results.  
  • Feng WANG, Yu Jun CUI, Fang ZHANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 373-380. https://doi.org/10.12386/A2011sxxb0038
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Existence results of positive solutions for semilinear operator equations without the assumption of normal cones are obtained by the help of the properties of a fixed point index for A-proper semilinear operators in this paper. As an application of our results, we prove the existence theorem concerning the existence of positive solutions for the second order m-point boundary value problems at resonance.  
  • Yong Min LIU, Hao LIU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 381-396. https://doi.org/10.12386/A2011sxxb0039
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, using the estimate of the higher order derivative of the function in mixed norm spaces, the properties of the analytic function and operator theory, the authors characterize the boundedness and compactness of the Volterra-type composition operator from mixed norm spaces H(p, q, Φ) to Zygmund spaces by means of constructing some test functions, and some necessary and sufficient conditions of the Volterra-type composition operators to be bounded and compact are obtained.  
  • Yan E WANG, Jian Hua WU, Hua NIE
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 397-408. https://doi.org/10.12386/A2011sxxb0040
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    An unstirred chemostat model with B-D functional response is discussed. First, we treat the growth rate of v as the bifurcation parameter to obtain the global structure of this system by the theorem of global bifurcation. Second, by the means of comparison principle, regularity theorem and Lyapunov function, the asymptotic behavior of solutions of the system is considered.  
  • Bin GUO, Wen Jie GAO
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 409-414. https://doi.org/10.12386/A2011sxxb0041
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The aim of this paper is to investigate the existence of generalized solutions to coupling evolution p-Laplacian systems with the first initial boundary value conditions. The authors applied the method of parabolic regularization to prove the existence of generalized solution to the problem. By making a sequence of estimates to the solutions, the authors proved the weak convergence of the approximation solution sequence and hence testified the existence of generalized solutions. Finally, the authors found some conditions under which the solutions exists globally.  
  • Xiao YU, Xiao Bao YAN
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 415-426. https://doi.org/10.12386/A2011sxxb0042
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We consider the commutators of multilinear potential operators defined by where satisfies some certain conditions.We prove that the operator is bounded from Lp1(v1p1 ×···× Lpm(vmpm) to Lq(uq) for all Lp1(v1p1)×···× Lpm(vmpm), provided that the weights v1,···,vm,u satisfiy some power and logarithmic bumps conditions.  
  • Dong Ming WANG, Zu Huan YU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 427-434. https://doi.org/10.12386/A2011sxxb0043
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We study Weingarten surfaces in Euclidean 3-space that satisfy a Weingarten relation of (1/κ1)-(1/κ2)=c, where c ∈ R and κ1, κ2 denote the principal curvature at each point of the surface. We have classified all the rotational Weingarten surfaces that satisfies the relationship of above, and we find that all these surfaces are parallel each other.  
  • Wen Yi HUANG, Shao Yong LAI, Jian ZHANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 435-442. https://doi.org/10.12386/A2011sxxb0044
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The nonlinear Klein–Gordon equation with damping term and nonnegative potentials is investigated. The potential well argument is used to study the Cauchy problem of the equation. A new existence theorem for the global solutions and the blowup solutions of the problem is established. The relation of the above two phenomena is derived as a sharp condition.  
  • Huan Huan SHI, Cai Sheng CHEN, Hong Mei XU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 443-450. https://doi.org/10.12386/A2011sxxb0045
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We consider the global existence, uniqueness and L estimate of weak solution to the initial boundary value problem for the nonlocal degenerate parabolic equation ut-div(|▽u|m-2u)+k|u|μu=|u|β-1uΩ|u|αdx with zero boundary condition. The following results are established. If u0L1(Ω), then the global solution u(t) exists and satisfies ‖u(t)‖C(1+t-1/μ), t>0, and for any T > 0, ‖▽u(t)‖Ct-τ, t ∈ (0, T), where k, μ > 0, β ≥ 1, α ≥ 0, 2 < m< N, α+β < μ+1, τ is some positive constant depending on μ, N, m.  
  • Gang YANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 451-460. https://doi.org/10.12386/A2011sxxb0046
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    It is shown in the paper that for a general associative ring R, any complex C of R-modules is Gorenstein projective if and only if each R-module Cm is Gorenstein projective for all m∈Z, as immediate consequences of the result, Gorenstein projective dimensions of complexes are characterized. Furthermore, if C is an exact complex of R-modules such that this sequence remains exact when the functor Hom(-,Q) is applied to it for any projective R-module Q, then C is Gorenstein projective if and only if each Ker(δCm) is Gorenstein projective for all m∈Z. Similarly, Gorenstein injective and Gorenstein flat versions of all these results are given.  
  • Zeng Qiang LIN, Min Xiong WANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 461-466. https://doi.org/10.12386/A2011sxxb0047
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Koenig’s theorem describes a necessary and sufficient criterion for the existence of a recollement of derived categories of rings. This paper gives Koenig’s theorem for the version of a recollement of module categories of rings. As two applications, we give a new proof of Morita’s equivalent theorem and describe the close relation between a triangular matrix ring and a recollement of module categories of rings.  
  • Shu Xia FENG, Xiao Fei ZHAGN, Hui Yong CHEN
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 467-482. https://doi.org/10.12386/A2011sxxb0048
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We will give the definitions of parabolic starlike mappings, parabolic starlike mappings of order ρ, parabolic and spirallike mappings of type β, parabolic and spirallike mappings of type β and order ρ. Moreover we will prove that the generalized Rope–Suffridge extension operator can preserve these properties.  
  • Quan Zhi LUO, Qiang LI
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 483-494. https://doi.org/10.12386/A2011sxxb0049
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    The paper is concerned with the fundamental theorem of relative Hopf modules for relative Yetter–Drinfel’d Hopf algebras, which not only generalizes the fundamental theorem of Hopf modules for Yetter–Drinfel’d Hopf algebras, but also generalizes the fundamental theorem of relative Hopf modules. Moreover, Maschke Theorem for relative Yetter–Drinfel’d Hopf algebras is given.  
  • Yan Qing WANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 495-502. https://doi.org/10.12386/A2011sxxb0050
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    {β(s),s≥0} be the standard Brownian motion in R3 and let |Wr(t)| be the volume of the Wiener sausage associated with {β(s),s≥0} observed until time t. From the central limit theorem, we know that (|Wr(t)|- E|Wr(t)|)/√tlog t weakly converges to a normal distribution. In this paper, we study the corresponding moderate deviation.  
  • Lan Zhe LIU
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 503-512. https://doi.org/10.12386/A2011sxxb0051
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    In this paper, we establish a sharp maximal function estimate for the multilinear commutators generated by the strongly singular integral operators and weighted Lipschitz functions. As an application, we obtain the continuity for the multilinear commutators.  
  • Yue Xiang HE, Yue Shan WANG
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 513-520. https://doi.org/10.12386/A2011sxxb0052
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    Let 1<p<∞, α and β be Ap weight, ν=(αβ-1)(1/p) and b∈BMO(ν). We show that the commutator of Marcinkiewicz integral μb Ω is a bounded operator from Lp(α) into Lp(β). Here the kernel Ω is a homogeneous function of degree zero with cancellation property and satisfies the logarithmic type Lipschitz condition.  
  • Hai Bo YU, Wen Huai SHEN
    Acta Mathematica Sinica, Chinese Series. 2011, 54(3): 521-528. https://doi.org/10.12386/A2011sxxb0053
    Abstract ( ) Download PDF ( )   Knowledge map   Save
    We study the groups of self homotopy equivalences of topological pair in the category of topological pairs. For homotopy associative and inversive Co-H spaces X and Y , we obtain a split short exact sequence 1→E(X)→E(XY)→E(Y)→1 under certain conditions.