Finite-dimensional hopf algebras are free over grouplike subalgebras

AbstractLet H be a finite-dimensional Hopf algebra over a field k, and let G be a subgroup of the group of grouplikes of H. Then every left (H,kG)-Hopf module is free as a left kG-module. If k is algebraically closed and C is a simple subcoalgebra of H with gC = C for all g ∈ G, then the exponent of G and (in characteristic p > 0) the p-part of |G| divide n, wheren2 is the dimension of C

Transcriptomics reveal an integrative role for maternal thyroid hormones during zebrafish embryogenesis

Thyroid hormones (THs) are essential for embryonic brain development but the genetic mechanisms involved in the action of maternal THs (MTHs) are still largely unknown. As the basis for understanding the underlying genetic mechanisms of MTHs regulation we used an established zebrafish monocarboxylic acid transporter 8 (MCT8) knock-down model and characterised the transcriptome in 25hpf zebrafish embryos. Subsequent mapping of differentially expressed genes using Reactome pathway analysis together with in situ expression analysis and immunohistochemistry revealed the genetic networks and cells under MTHs regulation during zebrafish embryogenesis. We found 4,343 differentially expressed genes and the Reactome pathway analysis revealed that TH is involved in 1681 of these pathways. MTHs regulated the expression of core developmental pathways, such as NOTCH and WNT in a cell specific context. The cellular distribution of neural MTH-target genes demonstrated their cell specific action on neural stem cells and differentiated neuron classes. Taken together our data show that MTHs have a role in zebrafish neurogenesis and suggest they may be involved in cross talk between key pathways in neural development. Given that the observed MCT8 zebrafish knockdown phenotype resembles the symptoms in human patients with Allan-Herndon-Dudley syndrome our data open a window into understanding the genetics of this human congenital condition.Portuguese Fundacao para Ciencia e Tecnologia (FCT) [PTDC/EXPL/MARBIO/0430/2013]; CCMAR FCT Plurianual financing [UID/Multi/04326/2013]; FCT [SFRH/BD/111226/2015, SFRH/BD/108842/2015, SFRH/BPD/89889/2012]; FCT-IF Starting Grant [IF/01274/2014]info:eu-repo/semantics/publishedVersio

Semileptonic Branching Fraction of Charged and Neutral B Mesons

An examination of leptons in ${\Upsilon (4S)}$ events tagged by reconstructed $B$ decays yields semileptonic branching fractions of $b_-=(10.1 \pm 1.8\pm 1.4)\%$ for charged and $b_0=(10.9 \pm 0.7\pm 1.1)\%$ for neutral $B$ mesons. This is the first measurement for charged $B$. Assuming equality of the charged and neutral semileptonic widths, the ratio $b_-/b_0=0.93 \pm 0.18 \pm 0.12$ is equivalent to the ratio of lifetimes. A postscript version is available through World-Wide-Web in http://w4.lns.cornell.edu/public/CLNS/1994Comment: 9 pages (in REVTEX format) Preprint CLNS94-1286, CLEO 94-1

Observation of the Isospin-Violating Decay Ds∗+→Ds+π0D_s^{*+}\to D_s^+\pi^0

Using data collected with the CLEO~II detector, we have observed the isospin-violating decay $D_s^{*+}\to D_s^+\pi^0$. The decay rate for this mode, relative to the dominant radiative decay, is found to be $\Gamma(D_s^{*+}\to D_s^+\pi^0)/\Gamma(D_s^{*+}\to D_s^+\gamma)= 0.062^{+0.020}_{-0.018}\pm0.022$.Comment: 8 page uuencoded postscript file, also available through http://w4.lns.cornell.edu/public/CLN

Precision Measurement of the Ds∗+−Ds+D_s^{*+}- D_s^+ Mass Difference

We have measured the vector-pseudoscalar mass splitting $M(D_s^{*+})-M(D_s^+) = 144.22\pm 0.47\pm 0.37 MeV$, significantly more precise than the previous world average. We minimize the systematic errors by also measuring the vector-pseudoscalar mass difference $M(D^{*0})-M(D^0)$ using the radiative decay $D^{*0}\rightarrow D^0\gamma$, obtaining $[M(D_s^{*+})-M(D_s^+)]-[M(D^{*0})-M(D^0)] = 2.09\pm 0.47\pm 0.37 MeV$. This is then combined with our previous high-precision measurement of $M(D^{*0})-M(D^0)$, which used the decay $D^{*0}\rightarrow D^0\pi^0$. We also measure the mass difference $M(D_s^+)-M(D^+)=99.5\pm 0.6\pm 0.3$ MeV, using the $\phi\pi^+$ decay modes of the $D_s^+$ and $D^+$ mesons.Comment: 18 pages uuencoded compressed postscript (process with uudecode then gunzip). hardcopies with figures can be obtained by sending mail to: [email protected]

Branching Fractions of tau Leptons to Three Charged Hadrons

From electron-positron collision data collected with the CLEO detector operating at CESR near \sqrt{s}=10.6 GeV, improved measurements of the branching fractions for tau decays into three explicitly identified hadrons and a neutrino are presented as {\cal B}(\tau^-\to\pi^-\pi^+\pi^-\nu_\tau)=(9.13\pm0.05\pm0.46)%, {\cal B}(\tau^-\to K^-\pi^+\pi^-\nu_\tau)=(3.84\pm0.14\pm0.38)\times10^{-3}, {\cal B}(\tau^-\to K^-K^+\pi^-\nu_\tau)=(1.55\pm0.06\pm0.09)\times10^{-3}, and {\cal B}(\tau^-\to K^-K^+K^-\nu_\tau)<3.7\times10^{-5} at 90% C.L., where the uncertainties are statistical and systematic, respectively.Comment: 10 pages postscript, also available through http://w4.lns.cornell.edu/public/CLNS, to appear in Phys. Rev. Let

Measurements of the Ratios B(Ds+→ηℓ+ν)/B(Ds+→ϕℓ+ν){\cal B}(D_s^+\to \eta\ell^+\nu)/{\cal B}(D_s^+\to \phi\ell^+\nu) and B(Ds+→η′ℓ+ν)/B(Ds+→ϕℓ+ν){\cal B}(D_s^+\to \eta'\ell^+\nu)/{\cal B}(D_s^+\to \phi\ell^+\nu)

Using the CLEO~II detector we measure ${\cal B}(D_s^+\to \eta e^+\nu)/{\cal B}(D_s^+\to \phi e^+\nu) =1.24\pm0.12\pm0.15$, ${\cal B}(D_s^+\to \eta' e^+\nu)/{\cal B}(D_s^+\to \phi e^+\nu) =0.43\pm0.11\pm0.07$ and ${\cal B}(D_s^+\to \eta' e^+\nu)/{\cal B}(D_s^+\to \eta e^+\nu) =0.35\pm0.09\pm0.07$. We find the vector to pseudoscalar ratio, ${\cal B}(D_s^+\to \phi e^+\nu)/{\cal B}(D_s^+\to (\eta+\eta') e^+\nu) =0.60\pm0.06\pm0.06$, which is similar to the ratio found in non strange $D$ decays.Comment: 11 page uuencoded postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN

Observation of a New Charmed Strange Meson

Using the CLEO-II detector, we have obtained evidence for a new meson decaying to $D^0 K^+$. Its mass is $2573.2^{+1.7}_{-1.6}\pm 0.8\pm 0.5$ {}~MeV/$c^2$ and its width is $16^{+5}_{-4}\pm 3$~MeV/$c^2$. Although we do not establish its spin and parity, the new meson is consistent with predictions for an $L=1$, $S=1$, $J_P=2^+$ charmed strange state.Comment: 9 pages uuencoded compressed postscript (process with uudecode then gunzip). hardcopies with figures can be obtained by sending mail to: [email protected]

A Search for Charmless B→VVB\to VV Decays

We have studied two-body charmless decays of the $B$ meson into the final states $\rho^0 \rho^0$, $K^{*0} \rho^0$, $K^{*0} K^{*0}$, $K^{*0} \bar{K^{*0}}$, $K^{*+} \rho^0$, $K^{*+} \bar{K^{*0}}$, and $K^{*+} K^{*-}$ using only decay modes with charged daughter particles. Using 9.7 million $B \bar{B}$ pairs collected with the CLEO detector, we place 90% confidence level upper limits on the branching fractions, $(0.46-7.0)\times 10^{-5}$, depending on final state and polarization.Comment: 8 pages postscript, also available through http://w4.lns.cornell.edu/public/CLN

Search for the Decay τ−→4pi−3π+(π0)ντ\tau^{-}\to 4pi^{-}3\pi^{+}(\pi^{0})\nu_{\tau}

We have searched for the decay of the tau lepton into seven charged particles and zero or one pi0. The data used in the search were collected with the CLEO II detector at the Cornell Electron Storage Ring (CESR) and correspond to an integrated luminosity of 4.61 fb^(-1). No evidence for a signal is found. Assuming all the charged particles are pions, we set an upper limit on the branching fraction, B(tau- -> 4pi- 3pi+ (pi0) nu_tau) < 2.4 x 10^(-6) at the 90% confidence level. This limit represents a significant improvement over the previous limit.Comment: 9 page postscript file, postscript file also available through http://w4.lns.cornell.edu/public/CLN