15 October 2014, Volume 30 Issue 10

    

• Select all
  |

Articles
• Select
  On Double Vector Bundles

  Zhuo CHEN, Zhang Ju LIU, Yun He SHENG

  Acta Mathematica Sinica. 2014, 30(10): 1655-1673. https://doi.org/10.1007/s10114-014-2412-4

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we construct a category of short exact sequences of vector bundles and prove that it is equivalent to the category of double vector bundles. Moreover, operations on double vector bundles can be transferred to operations on the corresponding short exact sequences. In particular, we study the duality theory of double vector bundles in term of the corresponding short exact sequences. Examples including the jet bundle and the Atiyah algebroid are discussed.
• Select
  Matching Realization of U_q(sl_n+1) of Higher Rank in the Quantum Weyl Algebra W_q(2n)

  Nai Hong HU, Shen You WANG

  Acta Mathematica Sinica. 2014, 30(10): 1674-1688. https://doi.org/10.1007/s10114-014-3721-3

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In the paper, we further realize the higher rank quantized universal enveloping algebra U_q(sl_n+1) as certain quantum differential operators in the quantum Weyl algebra W_q(2n) defined over the quantum divided power algebra A_q(n) of rank n. We give the quantum differential operators realization for both the simple root vectors and the non-simple root vectors of U_q(sl_n+1). The nice behavior of the quantum root vectors formulas under the action of the Lusztig symmetries once again indicates that our realization model is naturally matched.
• Select
  A Weak^* Similarity Degree Characterization for Injective von Neumann Algebras

  Zhe DONG, Ya Fei ZHAO

  Acta Mathematica Sinica. 2014, 30(10): 1689-1697. https://doi.org/10.1007/s10114-014-3143-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this note, we show that a von Neumann algebra M is injective if and only if the weak^* similarity degree d_*(M) ≤ 2.
• Select
  On Commuting Tonelli Hamiltonians：Time-periodic Case

  Xiaojun CUI

  Acta Mathematica Sinica. 2014, 30(10): 1698-1718. https://doi.org/10.1007/s10114-014-3156-x

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  We show that the Aubry sets, the Mañé sets and the barrier functions are the same for two commuting time-periodic Tonelli Hamiltonians.
• Select
  Poincaré andWeak Poincaré Inequalities for the Mixed Poisson Measure

  Chang Song DENG

  Acta Mathematica Sinica. 2014, 30(10): 1719-1728. https://doi.org/10.1007/s10114-014-3310-5

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  By using the Mecke identity, we study a class of birth-death type Dirichlet forms associated with the mixed Poisson measure. Both Poincaré and weak Poincaré inequalities are established, while another Poincaré type inequality is disproved under some reasonable assumptions.
• Select
  Eigenvalue Estimates and L¹ Energy on Closed Manifolds

  Li MA

  Acta Mathematica Sinica. 2014, 30(10): 1729-1734. https://doi.org/10.1007/s10114-014-1726-6

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we study Lichnerowicz type estimate for eigenvalues of drifting Laplacian operator and the decay rates of L¹ and L² energy for drifting heat equation on closed Riemannian manifolds with weighted measure.
• Select
  Notes on Global Existence for the Nonlinear Schrödinger Equation Involves Derivative

  Shi Yang ZHENG

  Acta Mathematica Sinica. 2014, 30(10): 1735-1747. https://doi.org/10.1007/s10114-014-3534-4

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we consider the scattering for the nonlinear Schrödinger equation with small,smooth, and localized data. In particular, we prove that the solution of the quadratic nonlinearSchrödinger equation with nonlinear term |u|² involving some derivatives in two dimension exists globallyand scatters. It is worth to note that there exist blow-up solutions of these equations withoutderivatives. Moreover, for radial data, we prove that for the equation with p-order nonlinearity withderivatives, the similar results hold for p≥(2d+3)/(2d-1) and d≥ 2, which is lower than the Strauss exponents.Keywords Schrödinger equation, global well-posedness, scatter, small data, quadratic
• Select
  Dunkl's Theory and Best Approximation by Entire Functions of Exponential Type in L₂-metric with Power Weight

  Yong Ping LIU, Chun Yuan SONG

  Acta Mathematica Sinica. 2014, 30(10): 1748-1762. https://doi.org/10.1007/s10114-014-2415-1

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we study the sharp Jackson inequality for the best approximation of f ∈L_2,κ(R^d) by a subspace E_κ²(σ) (SE_κ²(σ)), which is a subspace of entire functions of exponential type (spherical exponential type) at most σ. Here L_2,κ(R^d) denotes the space of all d-variate functions f endowed with the L₂-norm with the weight v_κ(x) = ∏_ξ∈R+ |(ξ, x)|^2κ(ξ), which is defined by a positive subsystem R₊ of a finite root system R ⊂ R^d and a function κ(ξ): R → R₊ invariant under the reflection group G(R) generated by R. In the case G(R) = Z₂^d, we get some exact results. Moreover, the deviation of best approximation by the subspace E_κ²(σ) (SE_κ²(σ)) of some class of the smooth functions in the space L_2,κ(R^d.) is obtained.
• Select
  On Invertible Nonnegative Hamiltonian Operator Matrices

  Guo Hai JIN, Guo Lin HOU, Alatancang CHEN, De Yu WU

  Acta Mathematica Sinica. 2014, 30(10): 1763-1774. https://doi.org/10.1007/s10114-014-3490-z

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  Some new characterizations of nonnegative Hamiltonian operator matrices are given. Several necessary and sufficient conditions for an unbounded nonnegative Hamiltonian operator to be invertible are obtained, so that the main results in the previously published papers are corollaries of the new theorems. Most of all we want to stress the method of proof. It is based on the connections between Pauli operator matrices and nonnegative Hamiltonian matrices.
• Select
  Composition Operators on Dirichlet Spaces and Bloch Space

  Yuan CHENG, Sanjay KUMAR, Ze Hua ZHOU

  Acta Mathematica Sinica. 2014, 30(10): 1775-1784. https://doi.org/10.1007/s10114-014-3171-y

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper we give a Carleson measure characterization for the compact composition operators between Dirichlet type spaces. We use this characterization to show that every compact composition operator on Dirichlet type spaces is compact on the Bloch space.
• Select
  C^∞-solutions for the Second Type of Generalized Feigenbaum's Functional Equations

  Min ZHANG

  Acta Mathematica Sinica. 2014, 30(10): 1785-1794. https://doi.org/10.1007/s10114-014-2289-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  This work focuses on the second type of generalized Feigenbaum's equation
  
  where φ(x) is C^∞-increasing function on [0, 1] and satisfies that φ(0) = 0, 0 < φ'(x) < 1 (x ∈ [0, 1]). Using constructive method, we discuss the existence of C^∞-single-valley solutions whose derivatives are not equal to 0 on origin of the above equation.
• Select
  On Value Distribution of Δⁿf

  Shuang Ting LAN, Zong Xuan CHEN

  Acta Mathematica Sinica. 2014, 30(10): 1795-1809. https://doi.org/10.1007/s10114-014-3382-2

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this paper, we mainly study zeros and poles of the forward differences Δⁿf(z), where f(z) is a finite order meromorphic function with two Borel exceptional values.
• Select
  A Filter Method for Nonlinear Semidefinite Programming with Global Convergence

  Zhi Bin ZHU, Hua Li ZHU

  Acta Mathematica Sinica. 2014, 30(10): 1810-1826. https://doi.org/10.1007/s10114-014-3241-1

  Abstract ( ) Download PDF ( )   Knowledge map   Save

  In this study, a new filter algorithm is presented for solving the nonlinear semidefinite programming. This algorithm is inspired by the classical sequential quadratic programming method. Unlike the traditional filter methods, the sufficient descent is ensured by changing the step size instead of the trust region radius. Under some suitable conditions, the global convergence is obtained. In the end, some numerical experiments are given to show that the algorithm is effective.