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Search Results: 1 - 10 of 37422 matches for " Fang Xin "
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Conceptual Metaphor and Vocabulary Teaching in the EFL Context  [PDF]
Xin Fang
Open Journal of Modern Linguistics (OJML) , 2014, DOI: 10.4236/ojml.2014.42030
Abstract: Metaphor, as a matter of thought, a way of cognition, is pervasive in our everyday life and language. As human beings’ important cognitive way, metaphor also serves as one of the important ways for language to develop, including vocabulary. Traditionally, most students memorize vocabulary mechanically with unpleasant results. They don’t realize most words come from metaphorical way, and metaphor is an important process of word meanings expanding and evolution. This paper will give a brief discussion about conceptual metaphor theory and analyze how to apply this theory into vocabulary teaching in the EFL context, in order to help learners to learn vocabulary thoroughly, systematically, and efficiently.
Quantum groups, q-Boson algebras and quantized Weyl algebras
Xin Fang
Mathematics , 2010,
Abstract: We give a unified construction of quantum groups, q-Boson algebras and quantized Weyl algebras and an action of quantum groups on quantized Weyl algebras. This enables us to give a conceptual proof of the semi-simplicity of the category $\mathcal{O}(B_q)$ introduced by T.Nakashima and the classification of all simple objects in it.
A Borel-Weil-Bott type theorem of quantum shuffle algebras
Xin Fang
Mathematics , 2012,
Abstract: We prove in this paper a Borel-Weil-Bott type theorem for the coHochschild homology of a quantum shuffle algebra associated with quantum group datum taking coefficients in some well-chosen bicomodules, which can be looked as an analogue of equivariant line bundles over flag varieties in the non-commutative case.
Non-symmetrizable quantum groups: defining ideals and specialization
Xin Fang
Mathematics , 2013,
Abstract: Two generating sets of the defining ideal of a Nichols algebra of diagonal type are proposed, which are then applied to study the bar involution and the specialization problem of quantum groups associated to non-symmetrizable generalized Cartan matrices.
Generalized virtual braid groups, quasi-shuffle product and quantum groups
Xin Fang
Mathematics , 2013,
Abstract: We introduce in this paper the generalized virtual braid group on n strands GVB_n, generalizing simultaneously the braid groups and their virtual versions. A Mastumoto-Tits type section lifting shuffles in a symmetric group S_n to the monoid associated to GVB_n is constructed, which is then applied to characterize the quantum quasi-shuffle product. A family of representations of GVB_n is constructed using quantum groups.
Dedekind η-function and quantum groups
Xin Fang
Mathematics , 2012,
Abstract: We realize some powers of Dedekind $\eta$-function as traces on quantum coordinate algebras.
On defining ideals and differential algebras of Nichols algebras
Xin Fang
Mathematics , 2011,
Abstract: This paper is devoted to understanding the defining ideal of a Nichols algebra from the decomposition of specific elements in the group algebra of braid groups. A family of primitive elements are found and algorithms are proposed. To prove the main result, the differential algebra of a Nichols algebra is constructed. Moreover, another point of view on Serre relations is provided.
Multi-brace cotensor Hopf algebras and quantum groups
Xin Fang,Marc Rosso
Mathematics , 2012,
Abstract: We construct multi-brace cotensor Hopf algebras with bosonizations of quantum multi-brace algebras as examples. Quantum quasi-symmetric algebras are then obtained by taking particular initial data; this allows us to realize the whole quantum group associated to a symmetrizable Kac-Moody Lie algebra as a quantum quasi-symmetric algebra and all highest weight irreducible representations can be constructed using this machinery. It also provides a systematic way to construct simple modules over the quantum double of a quantum group.
Torus fixed points in Schubert varieties and Genocchi numbers
Xin Fang,Ghislain Fourier
Mathematics , 2015,
Abstract: We give a new proof for the fact that the number of torus fixed points for the degenerated flag variety is equal to the normalized median Genocchi number, using the identification with a certain Schubert variety. We further study the torus fixed points for the symplectic degenerated flag variety and develop a combinatorial model, symplectic Dellac configurations, so parametrize them. The number of these symplectic fixed points is conjectured to be the median Euler number.
Marked chain-order polytopes and string polytopes
Xin Fang,Ghislain Fourier
Mathematics , 2015,
Abstract: We introduce in this paper the marked chain-order polytopes associated to a marked poset, generalizing the marked chain polytopes and marked order polytopes by putting them as extremal cases in an Ehrhart equivalent family. Some combinatorial properties of these polytopes are studied. As an application, we related these marked chain-order polytopes to string polytopes arising from representation theory of Lie algebras and to toric degenerations of linearly degenerate flag varieties.
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