15 June 2015, Volume 31 Issue 6

    

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  Multiple Positive Solutions for a Nonlinear Elliptic Equation Involving Hardy-Sobolev-Maz'ya Term

  Shuang Jie PENG, Jing YANG

  Acta Mathematica Sinica. 2015, 31(6): 893-912. https://doi.org/10.1007/s10114-015-4230-8

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  In this paper, we study the existence and nonexistence of multiple positive solutions for the following problem involving Hardy-Sobolev-Maz'ya term:
  -Δu-λ u/|y|² = (|u|^pt-1u)/|y|^t + μf(x), x∈ Ω,
  where Ω is a bounded domain in R^N(N ≥ 2), 0 ∈ Ω, x = (y, z) ∈ R^k ×R^N-k and p_t = (N+2-2t)/(N-2) (0 ≤ t ≤ 2). For f(x) ∈ C¹(Ω)\{0}, we show that there exists a constant μ^* >0 such that the problem possesses at least two positive solutions if μ ∈ (0, μ^*) and at least one positive solution if μ = μ^*. Furthermore, there are no positive solutions if μ ∈ (μ^*,+∞).
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  Quasi Sure Large Deviation for Increments of Fractional Brownian Motion in Hölder Norm

  Jie XU, Yun Min ZHU, Ji Cheng LIU

  Acta Mathematica Sinica. 2015, 31(6): 913-920. https://doi.org/10.1007/s10114-015-3560-x

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  In this paper, we first prove Schilder's theorem in Hölder norm (0 ≤ α <1) with respect to Cr,p-capacity. Then, based on this result, we further prove a sharpening of large deviation principle for increments of fractional Brownian motion for C_r,p-capacity in the stronger topology.
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  Gelfand-Kirillov Dimensions of the Z²-graded Oscillator Representations of sl(n)

  Zhan Qiang BAI

  Acta Mathematica Sinica. 2015, 31(6): 921-937. https://doi.org/10.1007/s10114-015-4237-1

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  We find an exact formula of Gelfand-Kirillov dimensions for the infinite-dimensional explicit irreducible sl(n,F)-modules that appeared in the Z²-graded oscillator generalizations of the classical theorem on harmonic polynomials established by Luo and Xu. Three infinite subfamilies of these modules have the minimal Gelfand-Kirillov dimension. They contain weight modules with unbounded weight multiplicities and completely pointed modules.
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  On the Deformation of Lie-Yamaguti Algebras

  Jie LIN, Liang Yun CHEN, Yao MA

  Acta Mathematica Sinica. 2015, 31(6): 938-946. https://doi.org/10.1007/s10114-015-4106-y

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  The deformation theory of Lie-Yamaguti algebras is developed by choosing a suitable cohomology. The relationship between the deformation and the obstruction of Lie-Yamaguti algebras is obtained.
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  A Note on Weighted Composition Operators on the Weighted Bergman Space

  Lian Kuo ZHAO, Sheng Zhao HOU

  Acta Mathematica Sinica. 2015, 31(6): 947-952. https://doi.org/10.1007/s10114-015-4473-4

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  This paper gives a note on weighted composition operators on the weighted Bergman space, which shows that for a fixed composition symbol, the weighted composition operators are bounded on the weighted Bergman space only with bounded weighted symbols if and only if the composition symbol is a finite Blaschke product.
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  Maps Preserving Peripheral Spectrum of Generalized Jordan Products of Operators

  Wen ZHANG, Jin Chuan HOU, Xiao Fei QI

  Acta Mathematica Sinica. 2015, 31(6): 953-972. https://doi.org/10.1007/s10114-015-4367-5

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  Let X₁ and X₂ be complex Banach spaces with dimension at least three, A₁ and A₂ be standard operator algebras on X₁ and X₂, respectively. For k ≥ 2, let (i₁, i₂, . . . , i_m) be a finite sequence such that {i₁, i₂, . . . , i_m} = {1, 2, . . . , k} and assume that at least one of the terms in (i₁, . . . , i_m) appears exactly once. Define the generalized Jordan productT₁ o T₂ o··· o T_k = T_i1T_i2··· T_im + T_im··· T_i2T_i1 on elements in Ai. This includes the usual Jordan product A₁A₂ + A₂A₁, and the Jordan triple A₁A₂A₃ + A₃A₂A₁. Let Φ : A₁ → A₂ be a map with range containing all operators of rank at most three. It is shown that Φ satisfies that σ_π(Φ(A₁) o··· o Φ(A_k)) = σ_π(A₁ o··· o A_k) for all A₁, . . . , A_k, where σ_π(A) stands for the peripheral spectrum of A, if and only if Φ is a Jordan isomorphism multiplied by an m-th root of unity.
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  Multiple Weighted Estimates for Commutators of Multilinear Maximal Function

  Pu ZHANG

  Acta Mathematica Sinica. 2015, 31(6): 973-994. https://doi.org/10.1007/s10114-015-4293-6

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  Let M be the multilinear maximal function and = (b₁, . . . , b_m) be a collection of locally integrable functions. Denote by M and [,M] the maximal commutator and the commutator of M with , respectively. In this paper, the multiple weighted strong and weak type estimates for operators M and [,M] are studied. Some characterizations of the class of functions b_j are given, for which these operators satisfy some strong or weak type estimates.
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  On the Adjoint of Operator Matrices with Unbounded Entries II

  De Yu WU, Alatancang CHEN

  Acta Mathematica Sinica. 2015, 31(6): 995-1002. https://doi.org/10.1007/s10114-015-4275-8

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  In this paper, the adjoint of a densely defined block operator matrix  in a Hilbert space X ×X is studied and the sufficient conditions under which the equality  holds are obtained through applying Frobenius-Schur factorization.
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  The Superiority of Bayes Estimators in a Multivariate Linear Model with Respect to Normal-Inverse Wishart Prior

  Kai XU, Dao Jiang HE

  Acta Mathematica Sinica. 2015, 31(6): 1003-1014. https://doi.org/10.1007/s10114-015-3649-2

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  In this paper, the multivariate linear model Y = XB+e, e ～ N_m×k(0, I_mΣ) is considered from the Bayes perspective. Under the normal-inverse Wishart prior for (BΣ), the Bayes estimators are derived. The superiority of the Bayes estimators of B and Σ over the least squares estimators under the criteria of Bayes mean squared error (BMSE) and Bayes mean squared error matrix (BMSEM) is shown. In addition, the Pitman Closeness (PC) criterion is also included to investigate the superiority of the Bayes estimator of B.
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  Local Phase Portraits through the Newton Diagram of a Vector Field

  Antonio ALGABA, Isabel CHECA, Cristóbal GARCÍA, Manuel REYES

  Acta Mathematica Sinica. 2015, 31(6): 1015-1034. https://doi.org/10.1007/s10114-015-3663-4

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  The Newton diagram and, in particular, the lowest-degree quasi-homogeneous terms of an analytic planar vector field allow us to determine the existence of characteristic orbits and separatrices of an isolated singular point. We give an easy algorithm for obtaining the local phase portrait near the origin of a bi-dimensional differential system and we provide several examples.
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  Circle Action with Prescribed Number of Fixed Points

  Ping LI

  Acta Mathematica Sinica. 2015, 31(6): 1035-1042. https://doi.org/10.1007/s10114-015-3630-0

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  Given any two positive integers k and n, this paper is concerned with the existence of a circle action on a closed, smooth orientable n-dimensional manifold with precisely k isolated fixed points. We first show that this existence problem can be reduced to that of an n-dimensional manifold with exactly three fixed points. Then by using a rigidity result, we determine possible weights on these three fixed points when n = 4.
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  Periodic Wave Solutions and Their Limits for the Modified KdV-KP Equations

  Ming SONG, Zheng Rong LIU, Chen Xi YANG

  Acta Mathematica Sinica. 2015, 31(6): 1043-1056. https://doi.org/10.1007/s10114-015-3362-1

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  In this paper, we use the bifurcation method of dynamical systems to study the periodic wave solutions and their limits for the modified KdV-KP equations. Some explicit periodic wave solutions are obtained. These solutions contain smooth periodic wave solutions and periodic blow-up solutions. Their limits contain solitary wave solutions, periodic wave solutions, kink wave solutions and unbounded solutions.