Oct 2011, Volume 6 Issue 5

    

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• SURVEY ARTICLE

  Some results and problems on commutators

  Shanzhen LU

  2011, 6(5): 821-833. https://doi.org/10.1007/s11464-011-0157-2

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  In this paper, the author introduces some late results and puts forward a few problems on commutators of many important operators in harmonic analysis, included the Bochner-Riesz operator below the critical index, the strongly singular integral operator, the pseudo-differential operator, a class of convolution operators with oscillatory kernel, the Marcinkiewicz integral operator, and the fractional integral operator with rough kernel.

• RESEARCH ARTICLE

  Nonexistence of block-transitive 6-designs

  Jing CHEN, Weijun LIU

  2011, 6(5): 835-845. https://doi.org/10.1007/s11464-011-0154-5

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  In this paper, we prove that there are no nontrivial block-transitive 6-designs for k≤100. This supports the long-standing conjecture of Cameron and Praeger that there are no nontrivial block-transitive 6-designs.

• RESEARCH ARTICLE

  On minimal non-MSN-groups

  Pengfei GUO, Xiuyun GUO

  2011, 6(5): 847-854. https://doi.org/10.1007/s11464-011-0115-z

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  A finite group G is called an MSN-group if all maximal subgroups of the Sylow subgroups of G are subnormal in G. In this paper, we determinate the structure of non-MSN-groups in which all of whose proper subgroups are MSN-groups.

• RESEARCH ARTICLE

  Transmutation theory of a coquasitriangular weak Hopf algebra

  Guohua LIU, Quanguo CHEN, Haixing ZHU

  2011, 6(5): 855-869. https://doi.org/10.1007/s11464-011-0149-2

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  Let H be a coquasitriangular quantum groupoid. In this paper, using a suitable idempotent element e in H, we prove that eH is a braided group (or a braided Hopf algebra in the category of right H-comodules), which generalizes Majid’s transmutation theory from a coquasitriangular Hopf algebra to a coquasitriangular weak Hopf algebra.

• RESEARCH ARTICLE

  F-Willmore submanifold in space forms

  Jin LIU, Huaiyu JIAN

  2011, 6(5): 871-886. https://doi.org/10.1007/s11464-011-0140-y

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  We introduce an F-Willmore functional of submanifold in space forms, which generalizes the well-known Willmore functional. Its critical point is called the F-Willmore submanifold, for which the variational equation and Simons’ type integral inequality are obtained.

• RESEARCH ARTICLE

  Ring of invariants of general linear group over local ring ?pm

  Jizhu NAN, Yin CHEN

  2011, 6(5): 887-899. https://doi.org/10.1007/s11464-011-0151-8

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  Let ?pm be the ring of integers modulo p^m, where p is a prime and m≥1. The general linear group GL_n(?pm) acts naturally on the polynomial algebra An:=?pm[x1,?,xn]. Denote by AnGLn(?pm) the corresponding ring of invariants. The purpose of the present paper is to calculate this invariant ring. Our results also generalize the classical Dickson’s theorem.

• RESEARCH ARTICLE

  Remarks on α-strongly irreducible ideals

  M. J. NIKMEHR, F. FATAHI

  2011, 6(5): 901-910. https://doi.org/10.1007/s11464-011-0156-3

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  In this article, we study α-irreducible and α-strongly irreducible ideals of a commutative ring. The relations between α-strongly irreducible ideals of a ring and α-strongly irreducible ideals of localization of the ring are also studied.

• RESEARCH ARTICLE

  Quadratic perturbations of a quadratic reversible center of genus one

  Linping PENG

  2011, 6(5): 911-930. https://doi.org/10.1007/s11464-011-0155-4

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  In this paper, we study a reversible and non-Hamitonian system with a period annulus bounded by a hemicycle in the Poincaré disk. It is proved that the cyclicity of the period annulus under quadratic perturbations is equal to two. This verifies some results of the conjecture given by Gautier et al.

• RESEARCH ARTICLE

  Growth and distortion theorems on subclasses of quasi-convex mappings in several complex variables

  Jianfei WANG, Taishun LIU, Jin LU

  2011, 6(5): 931-944. https://doi.org/10.1007/s11464-011-0158-1

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  In this paper, the refining growth and covering theorems for f are established, where f is a quasi-convex mapping of order α and x = 0 is a zero of order k + 1 of f(x) - x. As an application, we obtain the upper and lower bounds on the distortion theorem of f(x) defined on the unit polydisc of ?n. The upper bound of the distortion theorem for f(x) defined on the unit ball of a complex Banach space is also given. Our results extend the growth and distortion theorems for convex functions of one complex variable to quasi-convexmappings of several complex variables.

• RESEARCH ARTICLE

  Essential closed surfaces in surface sum of product I-bundle of closed surfaces

  Shuxin WANG

  2011, 6(5): 945-956. https://doi.org/10.1007/s11464-011-0150-9

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  In this paper, we will give some results on the classification of essential closed surfaces in the surface sum of product I-bundle of closed surfaces and some applications of these results.

• RESEARCH ARTICLE

  A primal-dual approximation algorithm for stochastic facility location problem with service installation costs

  Xing WANG, Dachuan XU, Xinyuan ZHAO

  2011, 6(5): 957-964. https://doi.org/10.1007/s11464-011-0153-6

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  We consider the stochastic version of the facility location problem with service installation costs. Using the primal-dual technique, we obtain a 7-approximation algorithm.

• RESEARCH ARTICLE

  von Neumann’s mean ergodic theorem on complete random inner product modules

  Xia ZHANG, Tiexin GUO

  2011, 6(5): 965-985. https://doi.org/10.1007/s11464-011-0139-4

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  We first prove two forms of von Neumann’s mean ergodic theorems under the framework of complete random inner product modules. As applications, we obtain two conditional mean ergodic convergence theorems for random isometric operators which are defined on L?p(?,H) and generated by measure-preserving transformations on Ω, where H is a Hilbert space, Lp(?,H) (1≤p<∞) the Banach space of equivalence classes of H-valued p-integrable random variables defined on a probability space (Ω, ?, P), ? a sub σ-algebra of ?, and L?p(?,H) the complete random normed module generated by Lp(?,H).

• RESEARCH ARTICLE

  Strongly irreducible operators and Cowen-Douglas operators on c₀, l_p (1≤p<∞)

  Yunnan ZHANG, Huaijie ZHONG

  2011, 6(5): 987-1001. https://doi.org/10.1007/s11464-011-0141-x

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  This paper gives some sufficient conditions for the strongly irreducibility of operators which have the forms of upper triangular operator matrices on Banach spaces. Based on these results, strongly irreducible Cowen-Douglas operators of index n are constructed on c₀, l_p (1≤p<∞) for all 1≤n≤∞.

• RESEARCH ARTICLE

  On Lefschetz series

  Xu’an ZHAO, Hongzhu GAO

  2011, 6(5): 1003-1008. https://doi.org/10.1007/s11464-011-0142-9

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  Let R=⊕i=0∞Ri be a connected graded commutative algebra over the field ? of rational numbers, and let f be a graded endomorphism of R. In this paper, we show that the Lefschetz series of f can be computed directly from the induced linear map Q(f) on the ? vector space of indecomposables of R. We give an explicit algorithm to compute the Lefschetz series of f from Q(f). The main tool we used is the graded algebra version of Gr?bner basis theory. At the end of this paper, some examples and applications are given.

• RESEARCH ARTICLE

  Coquasitriangular Hopf group coalgebras and braided monoidal categories

  Meiling ZHU, Huixiang CHEN, Libin LI

  2011, 6(5): 1009-1020. https://doi.org/10.1007/s11464-011-0152-7

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  Let π be a group, and let H be a Hopf π-coalgebra. We first show that the category ?H of right π-comodules over H is a monoidal category and there is a monoidal endofunctor (F_α, id, id) of ?H for any α∈π. Then we give the definition of coquasitriangular Hopf π-coalgebras. Finally, we show that H is a coquasitriangular Hopf π-coalgebra if and only if ?H is a braided monoidal category and (F_α, id, id) is a braided monoidal endofunctor of ?H for any α∈π.