中国科学院数学与系统科学研究院期刊网

15 February 2014, Volume 30 Issue 2

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  • Oana LUPAŞCU
    Acta Mathematica Sinica. 2014, 30(2): 187-196. https://doi.org/10.1007/s10114-014-2751-1
    Abstract ( 888 ) Download PDF ( 890 )   Knowledge map   Save
    We show that the subordination induced by a convolution semigroup (subordination in the sense of Bochner) of a C0-semigroup of sub-Markovian operators on an Lp space is actually associated to the subordination of a right (Markov) process. As a consequence, we solve the martingale problem associate with the Lp-infinitesimal generator of the subordinate semigroup. We also prove quasi continuity properties for the elements of the domain of the Lp-generator of the subordinate semigroup. It turns out that an enlargement of the base space is necessary. A main step in the proof is the preservation under such a subordination of the property of a Markov process to be a Borel right process. We use several analytic and probabilistic potential theoretical tools.
  • José Manuel RODRÍGUEZ
    Acta Mathematica Sinica. 2014, 30(2): 197-212. https://doi.org/10.1007/s10114-013-2467-7
    Abstract ( 855 ) Download PDF ( 671 )   Knowledge map   Save
    To decide when a graph is Gromov hyperbolic is, in general, a very hard problem. In this paper, we solve this problem for the set of short graphs (in an informal way, a graph G is r-short if the shortcuts in the cycles of G have length less than r): an r-short graph G is hyperbolic if and only if S9r(G) is finite, where SR(G):=sup{L(C) : C is an R-isometric cycle in G} and we say that a cycle C is R-isometric if dC(x, y) ≤ dG(x, y)| + R for every x, yC.
  • Zhe Feng XU, Tian Ping ZHANG
    Acta Mathematica Sinica. 2014, 30(2): 213-228. https://doi.org/10.1007/s10114-014-3324-z
    Abstract ( 816 ) Download PDF ( 696 )   Knowledge map   Save
    Let k be a positive integer and n a nonnegative integer, 0 < λ1, . . . , λk+1 ≤ 1 be real numbers and w = (λ1, λ2, . . . , λk+1). Let q ≥ max{[ 1/λi] : 1 ≤ i ≤ k + 1} be a positive integer, and a an integer coprime to q. Denote by N(a, k,w, q, n) the 2n-th moment of (b1 . . . bk - c) with b1 . . . bkca (mod q), 1 ≤ bi ≤ λiq (i = 1, . . . , k), 1 ≤ c ≤ λk+1q and 2 |(b1 +. . . + bk + c). We first use the properties of trigonometric sum and the estimates of n-dimensional Kloosterman sum to give an interesting asymptotic formula for N(a, k,w, q, n), which generalized the result of Zhang. Then we use the properties of character sum and the estimates of Dirichlet L-function to sharpen the result of N(a, k,w, q, n) in the case of w = (1/2 , 1/2 , . . . , 1/2) and n = 0. In order to show our result is close to the best possible, the mean-square value of N(a, k, q) - φk(q)/2k+2 and the mean value weighted by the high-dimensional Cochrane sum are studied too.
  • Edcarlos Domingos DA SILVA, Francisco Odair DE PAIVA
    Acta Mathematica Sinica. 2014, 30(2): 229-250. https://doi.org/10.1007/s10114-014-2750-2
    Abstract ( 825 ) Download PDF ( 591 )   Knowledge map   Save
    We establish the existence and multiplicity of solutions for Steklov problems under nonresonance or resonance conditions using variational methods. In our main theorems, we consider a weighted eigenvalue problem of Steklov type.
  • Ji Chang YU, Yue Yong SHI, Qing Long YANG, Yan Yan LIU
    Acta Mathematica Sinica. 2014, 30(2): 251-260. https://doi.org/10.1007/s10114-014-3180-x
    Abstract ( 944 ) Download PDF ( 645 )   Knowledge map   Save
    Case-cohort design usually requires the disease rate to be low in large cohort study, although it has been extensively used in practice. However, the disease with high rate is frequently observed in many clinical studies. Under such circumstances, it is desirable to consider a generalized case-cohort design, where only a fraction of cases are sampled. In this article, we propose the inference procedure for the additive hazards regression under the generalized case-cohort sampling. Asymptotic properties of the proposed estimators for the regression coefficients are established. To demonstrate the effectiveness of the generalized case-cohort sampling, we compare it with simple random sampling in terms of asymptotic relative efficiency. Furthermore, we derive the optimal allocation of the subsamples for the proposed design. The finite sample performance of the proposed method is evaluated through simulation studies.
  • Su Fang TANG, Jing Bo DOU
    Acta Mathematica Sinica. 2014, 30(2): 261-276. https://doi.org/10.1007/s10114-014-3071-1
    Abstract ( 838 ) Download PDF ( 579 )   Knowledge map   Save
    In this paper, we consider the following system of integral equations on upper half space 
    where R+n = {x = (x1, x2, . . . ,xn) ∈ Rn|xn > 0}, x = (x1, x2, . . . , xn-1,-xn) is the reflection of the point x about the hyperplane xn = 0, 0 < α < n, λi, μi, βi ≥ 0 (i = 1, 2) are constants, pi ≥ 0 and qi ≥ 0 (i = 1, 2, 3, 4). We prove the nonexistence of positive solutions to the above system with critical and subcritical exponents via moving sphere method.
  • Xiao Jun LIU, Shahar NEVO, Xue Cheng PANG
    Acta Mathematica Sinica. 2014, 30(2): 277-282. https://doi.org/10.1007/s10114-014-2542-8
    Abstract ( 948 ) Download PDF ( 851 )   Knowledge map   Save
    We prove that if D is a domain in C, α > 1 and C > 0, then the family F of functions f meromorphic in D such that |f'(z)|/(1+|f(z)|α) > C for every zD is normal in D. For α = 1, the same assumptions imply quasi-normality but not necessarily normality.
  • Subramanian ARUMUGAM, Mirka MILLER, Oudone PHANALASY, Joe RYAN
    Acta Mathematica Sinica. 2014, 30(2): 283-290. https://doi.org/10.1007/s10114-014-2381-7
    Abstract ( 960 ) Download PDF ( 914 )   Knowledge map   Save
    An antimagic labeling of a graph with q edges is a bijection from the set of edges to the set of positive integers {1, 2, . . . , q} such that all vertex weights are pairwise distinct, where the vertex weight of a vertex is the sum of the labels of all edges incident with that vertex. A graph is antimagic if it has an antimagic labeling.
    In this paper, we provide antimagic labelings for a family of generalized pyramid graphs.
  • Xiao Min LI, Lan LEI, Hong-Jian LAI, Meng ZHANG
    Acta Mathematica Sinica. 2014, 30(2): 291-304. https://doi.org/10.1007/s10114-014-2272-y
    Abstract ( 926 ) Download PDF ( 569 )   Knowledge map   Save
    A graph G is supereulerian if G has a spanning eulerian subgraph. Boesch et al. [J. Graph Theory, 1, 79-84 (1977)] proposed the problem of characterizing supereulerian graphs. In this paper, we prove that any 3-edge-connected graph with at most 11 edge-cuts of size 3 is supereulerian if and only if it cannot be contractible to the Petersen graph. This extends a former result of Catlin and Lai [J. Combin. Theory, Ser. B, 66, 123-139 (1996)].
  • Ramin KAZEMI
    Acta Mathematica Sinica. 2014, 30(2): 305-310. https://doi.org/10.1007/s10114-013-2115-2
    Abstract ( 906 ) Download PDF ( 672 )   Knowledge map   Save
    We consider bucket recursive trees of size n consisting of all buckets with variable capacities 1, 2, . . . , b and with a specific stochastic growth rule. This model can be considered as a generalization of random recursive trees like bucket recursive trees introduced by Mahmoud and Smythe where all buckets have the same capacities. In this work, we provide a combinatorial analysis of these trees where the generating function of the total weights satisfies an autonomous first order differential equation. We study the depth of the largest label (i.e., the number of edges from the root node to the node containing label n) and give a closed formula for the probability distribution. Also we prove a limit law for this quantity which is a direct application of quasi power theorem and compute its mean and variance. Our results for b = 1 reduce to the previous results for random recursive trees.
  • György GÁT
    Acta Mathematica Sinica. 2014, 30(2): 311-322. https://doi.org/10.1007/s10114-013-1766-3
    Abstract ( 889 ) Download PDF ( 578 )   Knowledge map   Save
    The aim of this paper is to prove the a.e. convergence of sequences of the Cesàro and Riesz means of the Walsh-Fourier series of d variable integrable functions. That is, let a= (a1, . . . ,ad) : N → Nd (i>d ∈ P) such that aj(n + 1) ≥ δ supkn aj(k) (j = 1, . . . , d, n ∈ N) for some δ > 0 and a1(+∞) = . . . = ad(+∞) = +∞. Then, for each integrable function fL1(Id), we have the a.e. relation for the Cesàro means limn→∞ σa(n)αf = f and for the Riesz means limn→∞ σa(n)α,γf = f for any 0 < αj ≤ 1 ≤ γj (j = 1, . . . , d). A straightforward consequence of our result is the so-called cone restricted a.e. convergence of the multidimensional Cesàro and Riesz means of integrable functions, which was proved earlier by Weisz.
  • Chao ZHANG, Guang Fu CAO
    Acta Mathematica Sinica. 2014, 30(2): 323-330. https://doi.org/10.1007/s10114-013-1742-y
    Abstract ( 835 ) Download PDF ( 709 )   Knowledge map   Save
    We study the weighted composition operators Wh,ø on Hardy space H2(B) whenever H ∈ BMOA (resp. H ∈ VMOA). Analogous results are given for Hp(B) spaces and the scale of weighted Bergman spaces. In the latter case, BMOA is replaced by the Bloch space (resp. VMOA by the little Bloch space).
  • Jia ZHOU, Liang Wen LIAO
    Acta Mathematica Sinica. 2014, 30(2): 331-342. https://doi.org/10.1007/s10114-013-1640-3
    Abstract ( 849 ) Download PDF ( 610 )   Knowledge map   Save
    Suppose a quadratic rational map has a Siegel disk and a parabolic fixed point. If the rotation number of the Siegel disk is an irrational of bounded type, then the Julia set of the map is shallow. This implies that its Hausdorff dimension is strictly less than two.
  • Jian Feng HOU, Gui Zhen LIU
    Acta Mathematica Sinica. 2014, 30(2): 343-352. https://doi.org/10.1007/s10114-013-1497-5
    Abstract ( 852 ) Download PDF ( 572 )   Knowledge map   Save
    A proper coloring of a graph G is acyclic if G contains no 2-colored cycle. A graph G is acyclically L-list colorable if for a given list assignment L = {L(v) : vV (G)}, there exists a proper acyclic coloring φ of G such that φ(v) ∈ L(v) for all vV (G). If G is acyclically L-list colorable for any list assignment L with |L(v)| ≥ k for all vV (G), then G is acyclically k-choosable. In this article, we prove that every toroidal graph is acyclically 8-choosable.
  • Abdalla M. MANSUR, Daniel C. OFFIN
    Acta Mathematica Sinica. 2014, 30(2): 353-360. https://doi.org/10.1007/s10114-013-1299-9
    Abstract ( 869 ) Download PDF ( 789 )   Knowledge map   Save
    In this paper, we prove that the homographic solutions to the rhombus four body problem are the variational minimizers of the Lagrangian action restricted on a holonomically constrained rhombus loop space.
  • Qing Liu YAO
    Acta Mathematica Sinica. 2014, 30(2): 361-370. https://doi.org/10.1007/s10114-013-1291-4
    Abstract ( 867 ) Download PDF ( 601 )   Knowledge map   Save
    This paper studies the positive solutions of the nonlinear second-order periodic boundary value problem u''(t) + λ(t)u(t)=f(t, u(t)), a.e. t ∈ [0, 2π], u(0) = u(2π), u' (0) = u' (2π), where f(t, u) is a local Carathéodory function. This shows that the problem is singular with respect to both the time variable t and space variable u. By applying the Leggett-Williams and Krasnosel'skii fixed point theorems on cones, an existence theorem of triple positive solutions is established. In order to use these theorems, the exact a priori estimations for the bound of solution are given, and some proper height functions are introduced by the estimations.