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Search Results: 1 - 10 of 19158 matches for " Yanli Song "
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Formal Verlinde Module
Yanli Song
Mathematics , 2014,
Abstract: Let G be a compact, simple and simply connected Lie group and $\A$ be an equivariant Dixmier-Douady bundle over G. For any fixed level k, we can define a G-C*-algebra $C_{\A^{k+h}}(G)$ as all the continuous sections of the tensor power $\A^{k+h}$ vanishing at infinity. A deep theorem by Freed-Hopkins-Teleman showed that the twisted K-homology $KK^{G}(C_{\A^{k+h}}(G), \C)$ is isomorphic to the level k Verlinde ring R_{k}(G). By the construction of crossed product, we define a C*-algebra $C^{*}(G,C_{\A^{k+h}}(G))$. We show that the K-homology KK(C^{*}(G,C_{\A^{k+h}}(G)),\C) is isomorphic to the formal Verlinde module $R^{-\infty}(G) \otimes_{R(G)} R_{k}(G)$, where $R^{-\infty}(G) = Hom_{\Z}(R(G),\Z)$ is the completion of the representation ring.
A K-homological approach to the quantization commutes with reduction problem
Yanli Song
Mathematics , 2014,
Abstract: Kasparov defined a distinguished K-homology fundamental class, so called the Dirac element. We prove a localization formula for the Dirac element in K-homology of crossed product of C^{*}-algebras. Then we define the quantization of Hamiltonian G-spaces as a push-forward of the Dirac element. With this, we develop a K-homological approach to the quantization commutes with reduction theorem.
Dirac operators on quasi-Hamiltonian G-spaces
Yanli Song
Mathematics , 2015,
Abstract: We develop notions of twisted spinor bundle and twisted pre-quantum bundle on quasi-Hamiltonian G-spaces. The main result of this paper is that we construct a Dirac operator with index given by positive energy representation of loop group. This generalizes the quantization of Hamiltonian $G$-spaces to quasi-Hamiltonian G-spaces.
Proper maps, bordism, and geometric quantization
Yanli Song
Mathematics , 2012,
Abstract: Let $G$ be a compact connected Lie group acting on a stable complex manifold $M$ with equivariant vector bundle $E$. Besides, suppose $\phi$ is an equivariant map from $M$ to the Lie algebra $\mathfrak{g}$. We can define some equivalence relation on the triples $(M, E, \phi)$ such that the set of equivalence classes form an abelian group. In this paper, we will show that this group is isomorphic to a completion of character ring $R(G)$. In this framework, we provide a geometric proof to the "Quantization Commutes with Reduction" conjecture in the non-compact setting.
On the Vergne conjecture
Peter Hochs,Yanli Song
Mathematics , 2015,
Abstract: Consider a Hamiltonian action by a compact Lie group on a possibly noncompact symplectic manifold. We give a short proof of a geometric formula for decomposition into irreducible representations of the equivariant index of a Spin$^c$-Dirac operator in this context. This formula was conjectured by Mich\`ele Vergne in 2006 and proved by Ma and Zhang in 2014.
An equivariant index for proper actions
Peter Hochs,Yanli Song
Mathematics , 2015,
Abstract: Equivariant indices have previously been defined in cases where either the group or the orbit space in question is compact. In this paper, we develop and apply an equivariant index without assuming the group or the orbit space to be compact. This allows us to generalise an index of deformed Dirac operators, defined for compact groups by Braverman. In the case of compact orbit spaces, we show how the index is related to the analytic assembly map from the Baum-Connes conjecture, Kasparov's generalisation of Atiyah's index of transversally elliptic operators, and an index used by Mathai and Zhang. We use the index to define a notion of $K$-homological Dirac induction, and show that, under conditions, it satisfies the quantisation commutes with reduction principle.
Equivariant indices of Spin$^c$-Dirac operators for proper moment maps
Peter Hochs,Yanli Song
Mathematics , 2015,
Abstract: We define an equivariant index of Spin$^c$-Dirac operators on possibly noncompact manifolds, acted on by compact, connected Lie groups. The main result in this paper is that the index decomposes into irreducible representations according to the quantisation commutes with reduction principle.
A Cultural Examination of Shapiro’s Translation of the Marsh Heroes’ Nicknames  [PDF]
Yanli Bai
Advances in Literary Study (ALS) , 2016, DOI: 10.4236/als.2016.43006
Abstract: What roles the culture plays in translating has been a focus in the translating circle. The stratifica-tional relation of language to cultural context in Systemic Functional Linguistics (SFL) makes it necessary that the process of translation should take the cultural factors into consideration. The present paper aims to discuss the parts that culture plays in translating by analyzing some prob-lems in Shapiro’s translation of the nicknames in the Outlaws of the Marsh. The paper starts off from the relation of language to culture context in translation in an SFL angle, followed with a brief introduction to the connotation and the artistic magic of the Marsh Heroes’ Nicknames and some examples of Shapiro’s translations of the nicknames, in order to demonstrate the importance of culture factors in translating.
Relationship of Post-Stroke Aphasic Types with Sex, Age and Stroke Types  [PDF]
Jingfan Yao, Zaizhu Han, Yanli Song, Lei Li, Yun Zhou, Weikang Chen, Chunxue Wang, Yongjun Wang, Yumei Zhang
World Journal of Neuroscience (WJNS) , 2015, DOI: 10.4236/wjns.2015.51004
Abstract: Aim:To explore what is the relationship of the types of post-stroke aphasia with sex, age andstroke types.Methods:Retrospective analysis was administrated on data of 421 patients with acutestroke. Western battery aphasia was used to measure aphasiac type and aphasia quotient (AQ)score. The patients were divided into three age groups: young, middle-aged and elderly. The stroketypes were classified into cerebral infraction (CI) and intracerebral hemorrhage (ICH). Results: All subjects were right-handed, which males and females accounted for 69.60% and 30.40%, respectively. There were 116 cases of Broca’s aphasia (85 males), 35 cases of Wernicke’s aphasia (20 males),15 cases of conductive aphasia (10 males), 63 cases of transcortical motor aphasia (50 males), 11 cases of transcortical sensory aphasia (8 males), 27 cases of transcortical combined aphasia (13 males), 73 cases of anomic aphasia (47 males) and 81 cases of global aphasia (60 males). Male patients (69.60%) have a significantly higher morbidity of aphasia than that of females (30.40%) after stroke (χ2
Relationship of Post-Stroke Aphasic Types with Sex, Age and Stroke Types  [PDF]
Jingfan Yao, Zaizhu Han, Yanli Song, Lei Li, Yun Zhou, Weikang Chen, Yongmei Deng, Yongjun Wang, Yumei Zhang
World Journal of Neuroscience (WJNS) , 2015, DOI: 10.4236/wjns.2015.51004
Abstract: Aim: To explore what is the relationship of the types of post-stroke aphasia with sex, age and stroke types. Methods: Retrospective analysis was administrated on data of 421 patients with acute stroke. Western battery aphasia was used to measure aphasiac type and aphasia quotient (AQ) score. The patients were divided into three age groups: young, middle-aged and elderly. The stroke types were classified into cerebral infraction (CI) and intracerebral hemorrhage (ICH). Results: All subjects were right-handed, which males and females accounted for 69.60% and 30.40%, respectively. There were 116 cases of Broca’s aphasia (85 males), 35 cases of Wernicke’s aphasia (20 males), 15 cases of conductive aphasia (10 males), 63 cases of transcortical motor aphasia (50 males), 11 cases of transcortical sensory aphasia (8 males), 27 cases of transcortical combined aphasia (13 males), 73 cases of anomic aphasia (47 males) and 81 cases of global aphasia (60 males). Male patients (69.60%) have a significantly higher morbidity of aphasia than that of females (30.40%) after stroke (χ2 = 11.57
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