Dots in rods as polarized single photon sources

We report the evidence of a polarized single photon flux from a colloidal nanoparticle. We analyze, by time and polarization resolved spectroscopy measurements, the polarization behavior of a single CdSe/CdS core/shell dot in rod, achieving a polarization ratio at room temperature of ∼75% and a lifetime of the excited state of ∼11 ns.     

Projective modules over noncommutative tori are multi-window Gabor frames for modulation spaces

In the present investigation we link noncommutative geometry over noncommutative tori with Gabor analysis, where the first has its roots in operator algebras and the second in time-frequency analysis. We are therefore in the position to invoke modern methods of operator algebras, e.g. topological stable rank of Banach algebras, to display the deeper properties of Gabor frames. Furthermore, we are able to extend results due to Connes and Rieffel on projective modules over noncommutative tori to Banach algebras, which arise in a natural manner in Gabor analysis. The main goal of this investigation is twofold: (i) an interpretation of projective modules over noncommutative tori in terms of Gabor analysis and (ii) to show that the Morita-Rieffel equivalence between noncommutative tori is the natural framework for the duality theory of Gabor frames. More concretely, we interpret generators of projective modules over noncommutative tori as the Gabor atoms of multi-window Gabor frames for modulation spaces. Moreover, we show that this implies the existence of good multi-window Gabor frames for modulation spaces with Gabor atoms in e.g. Feichtinger's algebra or in Schwartz space.     

Chern character for twisted K-theory of orbifolds

For an orbifold X and α∈H³(X,Z), we introduce the twisted cohomology and prove that the non-commutative Chern character of Connes-Karoubi establishes an isomorphism between the twisted K-groups and the twisted cohomology . This theorem, on the one hand, generalizes a classical result of Baum-Connes, Brylinski-Nistor, and others, that if X is an orbifold then the Chern character establishes an isomorphism between the K-groups of X tensored with C, and the compactly-supported cohomology of the inertia orbifold. On the other hand, it also generalizes a recent result of Adem-Ruan regarding the Chern character isomorphism of twisted orbifold K-theory when the orbifold is a global quotient by a finite group and the twist is a special torsion class, as well as Mathai-Stevenson's theorem regarding the Chern character isomorphism of twisted K-theory of a compact manifold.     

扭Heisenberg-Virasoro代数上Hom-李代数结构

Hom-李代数是一类满足反对称和Hom-Jacobi等式的非结合代数.扭Heisenberg-Virasoro代数是次数不超过1的微分算子代数的中心扩张,它是一类重要的无限维李代数,与一些曲线的模空间有关.文章主要研究扭Heisenberg-Virasoro代数上Hom-李代数结构,确定了扭Heisenberg-Virasoro代数上存在非平凡的Hom-李代数结构.     

交换Hopf代数扭余作用下的余代数的上同调

该文证明了若交换Hopf代数在余代数C上的扭余作用的coassociator是卷积可逆的,那么该扭余作用也是可逆的.在这种情形下,给出了余代数C的正则上同调的定义,并且证得每个可逆的扭余作用可以提升到H的系数属于C的一个三次正则上同调类,且扭余作用的obstruction是平凡的当且仅当该扭余作用对应着一个cleft余扩张.     

Twisted traces of singular values

Let p be a prime for which the congruence group Γ₀(p)^* is of genus zero, and j _p ^* be the corresponding Hauptmodul. We investigate the twisted traces of singular values of j _p ^* and construct infinite products related to them. This work was supported by the Korea Research Foundation Grant funded by the Korean Government (MOEHRD) (KRF-2006-331-C00006).     

Equivalence Bimodule between Spherical Noncommutative Tori

Let n _i ,m _j > 1. In [5], the sperical noncommutative torus was defined by twisting in by a totally skew multiplier p on for T ^pd a pd-homogeneous C*-algebra over . It is shown that is strongly Morita equivalent to . This work is supported by Grant No. 1999-2-102-001-3 from the interdisciplinary research program year of the KOSEF     

Counting SL2（F2^s） Representations of Torus Knot Groups

In this paper,we count the number of SL2(F2^s)-representations of torus knot groups up to a conjugacy.For the finite field F2^s with character 2,the counting method is similar to that in out previous work[1].Explicit formulae of the effective counting are given in this paper.Twisted Alexander polynomials related to those reprsentations are discussed.     

修饰β-环糊精／4-（N，N-二甲氨基）-苯甲酸-2′-乙基己基酯笼型包结物研究

用分子光谱法研究了甲基-β-环糊精(M-CD)和羟丙基-β-环糊精(HP-CD)与4-(N,N-二甲氨基)-苯甲酸-2′-乙基己基酯(EHDAB)分子间的包结作用.结果表明,柔性的2′-乙基己基和刚性的芳香端都包结在M-CD和HP-CD空腔中,形成了2∶1笼型主-客体包结物.疏水性2′-乙基己基在包结物的热力学稳定性中起重要作用,亲水性M-CD和HP-CD将EHDAB增溶在水中,提高了EHDAB分子的紫外吸收程度,M-CD和HP-CD空腔抑制了光诱导EHDAB分子内扭转电荷转移,显著提高了EHDAB的光化学稳定性,增强了其抗氧化性,降低了酸碱性水解程度,包结物的热稳定性与所用主体环糊精相当.