Projective quantum spaces

Associated to the standard $SU_{q}(n)$ R-matrices, we introduce quantum spheres $S_{q}^{2n-1}$, projective quantum spaces $CP_{q}^{n-1}$, and quantum Grassmann manifolds $G_{k}(C_{q}^{n})$. These algebras are shown to be homogeneous quantum spaces of standard quantum groups and are also quantum principle bundles in the sense of T Brzezinski and S. Majid (Comm. Math. Phys. 157,591 (1993)).Comment: 8 page

Classification of All Poisson-Lie Structures on an Infinite-Dimensional Jet Group

A local classification of all Poisson-Lie structures on an infinite-dimensional group $G_{\infty}$ of formal power series is given. All Lie bialgebra structures on the Lie algebra {\Cal G}_{\infty} of $G_{\infty}$ are also classified.Comment: 11 pages, AmSTeX fil

The relationship between transcription initiation RNAs and CCCTC-binding factor (CTCF) localization

Background: Transcription initiation RNAs (tiRNAs) are nuclear localized 18 nucleotide RNAs derived from sequences immediately downstream of RNA polymerase II (RNAPII) transcription start sites. Previous reports have shown that tiRNAs are intimately correlated with gene expression, RNA polymerase II binding and behaviors, and epigenetic marks associated with transcription initiation, but not elongation. Results: In the present work, we show that tiRNAs are commonly found at genomic CCCTC-binding factor (CTCF) binding sites in human and mouse, and that CTCF sites that colocalize with RNAPII are highly enriched for tiRNAs. To directly investigate the relationship between tiRNAs and CTCF we examined tiRNAs originating near the intronic CTCF binding site in the human tumor suppressor gene, p21 (cyclin-dependent kinase inhibitor 1A gene, also known as CDKN1A). Inhibition of CTCF-proximal tiRNAs resulted in increased CTCF localization and increased p21 expression, while overexpression of CTCF-proximal tiRNA mimics decreased CTCF localization and p21 expression. We also found that tiRNA-regulated CTCF binding influences the levels of trimethylated H3K27 at the alternate upstream p21 promoter, and affects the levels of alternate p21 (p21) transcripts. Extending these studies to another randomly selected locus with conserved CTCF binding we found that depletion of tiRNA alters nucleosome density proximal to sites of tiRNA biogenesis. Conclusions: Taken together, these data suggest that tiRNAs modulate local epigenetic structure, which in turn regulates CTCF localization

Hamiltonian type Lie bialgebras

We first prove that, for any generalized Hamiltonian type Lie algebra $L$, the first cohomology group $H^1(L,L \otimes L)$ is trivial. We then show that all Lie bialgebra structures on $L$ are triangular.Comment: LaTeX, 16 page

The Dwarf Spheroidal Companions to M31: Variable Stars in Andromeda VI

We have surveyed Andromeda VI, a dwarf spheroidal galaxy companion to M31, for variable stars using F450W and F555W observations obtained with the Hubble Space Telescope. A total of 118 variables were found, with 111 being RR Lyrae, 6 anomalous Cepheids, and 1 variable we were unable to classify. We find that the Andromeda VI anomalous Cepheids have properties consistent with those of anomalous Cepheids in other dwarf spheroidal galaxies. We revise the existing period-luminosity relations for these variables. Further, using these and other available data, we show that there is no clear difference between fundamental and first-overtone anomalous Cepheids in a period-amplitude diagram at shorter periods, unlike the RR Lyrae. For the Andromeda VI RR Lyrae, we find that they lie close to the Oosterhoff type I Galactic globular clusters in the period-amplitude diagram, although the mean period of the RRab stars, = 0.588 d, is slightly longer than the typical Oosterhoff type I cluster. The mean V magnitude of the RR Lyrae in Andromeda VI is 25.29+/-0.03, resulting in a distance 815+/-25 kpc on the Lee, Demarque, & Zinn distance scale. This is consistent with the distance derived from the I magnitude of the tip of the red giant branch. Similarly, the properties of the RR Lyrae indicate a mean abundance for Andromeda VI which is consistent with that derived from the mean red giant branch color.Comment: 23 pages, including 13 figures and 6 tables, emulateapj5/apjfonts style. Accepted by the Astronomical Journal. We recommend the interested reader to download the preprint with full-resolution figures, which can be found at http://www.noao.edu/noao/staff/pritzl/M31dwarfs.htm

Lie bialgebras of generalized Witt type

In a paper by Michaelis a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In this paper, all Lie bialgebra structures on the Lie algebras of generalized Witt type are classified. It is proved that, for any Lie algebra $W$ of generalized Witt type, all Lie bialgebras on $W$ are coboundary triangular Lie bialgebras. As a by-product, it is also proved that the first cohomology group $H^1(W,W \otimes W)$ is trivial.Comment: 14 page

Heisenberg realization for U_q(sln) on the flag manifold

We give the Heisenberg realization for the quantum algebra $U_q(sl_n)$, which is written by the $q$-difference operator on the flag manifold. We construct it from the action of $U_q(sl_n)$ on the $q$-symmetric algebra $A_q(Mat_n)$ by the Borel-Weil like approach. Our realization is applicable to the construction of the free field realization for the $U_q(\widehat{sl_n})$ [AOS].Comment: 10 pages, YITP/K-1016, plain TEX (some mistakes corrected and a reference added

Anisotropy of graphite optical conductivity

The graphite conductivity is evaluated for frequencies between 0.1 eV, the energy of the order of the electron-hole overlap, and 1.5 eV, the electron nearest hopping energy. The in-plane conductivity per single atomic sheet is close to the universal graphene conductivity $e^2/4\hbar$ and, however, contains a singularity conditioned by peculiarities of the electron dispersion. The conductivity is less in the $c-$direction by the factor of the order of 0.01 governed by electron hopping in this direction.Comment: 3 pages, 3 figure

Development of lung tissue phantoms for bioluminescent imaging

White nylon material was chosen to make cylindrical tissue phantoms for development of bioluminescence tomography techniques. A low-level light source, delivered through an optic fiber of core diameter 200 μm, was placed at different locations on one phantom surface. The light travels through the phantom, reaches the external surface, and is captured by a liquid nitrogen-cooled CCD camera. The scattering, absorption, and anisotropy parameters of the phantom are obtained by matching the measured light transmission profiles to the profiles generated by the TracePro software. The perturbation analysis, with the homogeneous phantoms, demonstrated that the imaging system is sufficiently sensitive to capture intensity change of higher than 0.5nW/cm2 or a location shift of the light source of more than 200 microns. It is observed that the system can distinguish two point light sources with separation of about 2 mm. The perturbation analysis is also performed with the heterogeneous phantom. Based on our data, we conclude that there is inherent tomographic information in bioluminescent measures taken on the external surface of the mouse, which suggests the feasibility of bioluminescence tomography for biomedical research using the small animals, especially the mice

The Wicked Machinery of Government: Malta and the Problems of Continuity under the New Model Administration

This is a study focused on the early years of British rule in Malta (1800-1813). It explores the application to the island of the “new model” of colonial government, one based on direct rule from London mediated by the continuation of existing laws and institutions. Systemic deficiencies are identified. These tended to undermine the effectiveness of direct British rule. This study also reveals, in the context of legal and constitutional continuity, unresolved tensions between modernity and tradition. The political stability of the island was damaged and the possibility of continued British possession was threatened