15 May 2015, Volume 31 Issue 5

    

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  The Optimal Constant in Hardy-type Inequalities

  Mu-Fa CHEN

  Acta Mathematica Sinica. 2015, 31(5): 731-754. https://doi.org/10.1007/s10114-015-4731-5

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  To estimate the optimal constant in Hardy-type inequalities, some variational formulas and approximating procedures are introduced. The known basic estimates are improved considerably. The results are illustrated by typical examples. It is shown that the sharp factor is meaningful for each finite interval and a classical sharp model is re-examined.
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  Optimal D-RIP Bounds in Compressed Sensing

  Rui ZHANG, Song LI

  Acta Mathematica Sinica. 2015, 31(5): 755-766. https://doi.org/10.1007/s10114-015-4234-4

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  This paper establishes new bounds on the restricted isometry constants with coherent tight frames in compressed sensing. It is shown that if the sensing matrix A satisfies the D-RIP condition δ_k < 1/3 or δ_2k < √2/2, then all signals f with D^*f are k-sparse can be recovered exactly via the constrained l₁ minimization based on y = Af, where D^* is the conjugate transpose of a tight frame D. These bounds are sharp when D is an identity matrix, see Cai and Zhang's work. These bounds are greatly improved comparing to the condition δ_k < 0.307 or δ_2k < 0.4931. Besides, if δ_k < 1/3 or δ_2k < √2/2, the signals can also be stably reconstructed in the noisy cases.
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  Norming Subspaces Isomorphic to l₁

  Sofiya OSTROVSKA

  Acta Mathematica Sinica. 2015, 31(5): 767-771. https://doi.org/10.1007/s10114-015-4123-x

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  Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to l₁ provided that the following two conditions are satisfied: (1) X^* contains a subspace isomorphic to l₁; and (2) X^* contains a separable norming subspace.
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  On Edge Connectivity and Parity Factor

  Hong Liang, LU Wei WANG, Yuqing LIN

  Acta Mathematica Sinica. 2015, 31(5): 772-776. https://doi.org/10.1007/s10114-015-4104-0

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  By Petersen's Theorem, a bridgeless cubic graph has a 2-factor. Fleischner (Discrete Math., 101, 33-37 (1992)) has extended this result to bridgeless graphs of minimum degree at least three by showing that every such graph has an even factor without isolated vertices. Let m_e > 0 be even and m_o > 0 be odd. In this paper, we prove that every m_e-edge-connected graph with minimum degree at least m_e + 1 contains an even factor with minimum degree at least m_e and every (m_o + 1)- edge-connected graph contains an odd factor with minimum degree at least m_o, which further extends Fleischner's result. Moreover, we show that our results are best possible.
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  Busemann-Petty Problems for General L_p-Intersection Bodies

  Wei Dong WANG, Ya Nan LI

  Acta Mathematica Sinica. 2015, 31(5): 777-786. https://doi.org/10.1007/s10114-015-4273-x

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  For 0 < p < 1, Haberl and Ludwig defined the notions of symmetric L_p-intersection body and nonsymmetric L_p-intersection body. In this paper, we introduce the general L_p-intersection bodies. Furthermore, the Busemann-Petty problems for the general L_p-intersection bodies are shown.
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  Weakly Algebraic Ideal Topology of Effect Algebras

  Qing Jun LUO, Guo Jun WANG

  Acta Mathematica Sinica. 2015, 31(5): 787-796. https://doi.org/10.1007/s10114-015-3594-0

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  In this paper, we show that every weakly algebraic ideal of an effect algebra E induces a uniform topology (weakly algebraic ideal topology, for short) with which E is a first-countable, zero-dimensional, disconnected, locally compact and completely regular topological space, and the operation ⊕ of effect algebras is continuous with respect to these topologies. In addition, we prove that the operation  of effect algebras and the operations ∧ and ∨ of lattice effect algebras are continuous with respect to the weakly algebraic ideal topology generated by a Riesz ideal.
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  The Fixed Subgroups of Homeomorphisms of Seifert Manifolds

  Qiang ZHANG

  Acta Mathematica Sinica. 2015, 31(5): 797-810. https://doi.org/10.1007/s10114-015-3584-2

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  Let M be a compact connected orientable Seifert manifold with hyperbolic orbifold B_M, and f_π: π₁(M) → π₁(M) be an automorphism induced by an orientation-reversing homeomorphism f of M. We give a bound on the rank of the fixed subgroup of f_π, namely, rankFix(f_π) < 2rankπ₁(M), which is an analogue of inequalities on surface groups and hyperbolic 3-manifold groups.
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  The Growth Theorem and Distortion Theorem of Spirallike Mappings on B_p

  Hao LIU, Ke Ping LU, Fang Fang ZHANG

  Acta Mathematica Sinica. 2015, 31(5): 811-824. https://doi.org/10.1007/s10114-015-3549-5

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  In this paper, by using the parametric representation of spirallike mappings, we construct to obtain the growth theorem of spirallike mappings on Reinhardt domain B_p. Moreover, the distortion theorem of spirallike mappings is obtained.
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  Orbifold Gromov-Witten Invariants of Weighted Blow-up at Smooth Points

  Wei Qiang HE, Jian Xun HU

  Acta Mathematica Sinica. 2015, 31(5): 825-846. https://doi.org/10.1007/s10114-015-3479-2

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  In this paper, one considers the change of orbifold Gromov-Witten invariants under weighted blow-up at smooth points. Some blow-up formula for Gromov-Witten invariants of symplectic orbifolds is proved. These results extend the results of manifolds case to orbifold case.
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  Estimates for the Maximal Bilinear Singular Integral Operators

  Guo En HU

  Acta Mathematica Sinica. 2015, 31(5): 847-862. https://doi.org/10.1007/s10114-015-4112-0

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  In this paper, the behavior on the product of Lebesgue spaces is considered for the maximal operators associated with the bilinear singular integral operators whose kernels satisfy certain minimal regularity conditions.
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  Surfaces with Isotropic Blaschke Tensor in S³

  Feng Jiang LI, Jian Bo FANG, Lin LIANG

  Acta Mathematica Sinica. 2015, 31(5): 863-878. https://doi.org/10.1007/s10114-015-3706-x

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  Let M² be an umbilic-free surface in the unit sphere S³. Four basic invariants of M² under the Moebius transformation group of S³ are Moebius metric g, Blaschke tensor A, Moebius second fundamental form B and Moebius form Φ. We call the Blaschke tensor is isotropic if there exists a smooth function λ such that A = λg. In this paper, We classify all surfaces with isotropic Blaschke tensor in S³.
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  On Conformally Flat (α, β)-metrics with Special Curvature Properties

  Min Gao YUAN, Xin Yue CHENG

  Acta Mathematica Sinica. 2015, 31(5): 879-892. https://doi.org/10.1007/s10114-015-2584-6

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  In this paper, we study a significant non-Riemannian quantity Ξ-curvature, which is defined by S-curvature. Firstly, we obtain the formula of Ξ-curvature for (α, β)-metrics. Based on it, we show that the Ξ-curvature vanishes for a class of (α, β)-metrics. In the end, we get the relation of Ξ-curvature for conformally related Finsler metrics, and classify conformally flat (α, β)-metrics with almost vanishing Ξ-curvature.