Self-duality and associated parallel or cocalibrated G2{\mathrm{G}}_2 structures

We find a remarkable family of $\mathrm{G}_2$ structures defined on certain principal $\mathrm{SO}(3)$-bundles $P_\pm\longrightarrow M$ associated with any given oriented Riemannian 4-manifold $M$. Such structures are always cocalibrated. The study starts with a recast of the Singer-Thorpe equations of 4-dimensional geometry. These are applied to the Bryant-Salamon cons\-truction of complete $\mathrm{G}_2$-holonomy metrics on the vector bundle of self- or anti-self-dual 2-forms on $M$. We then discover new examples of that special holonomy on disk bundles over ${\cal H}^4$ and ${\cal H}^2_{\mathbb{C}}$, respectively, the real and complex hyperbolic space. Only in the end we present the new $\mathrm{G}_2$ structures on principal bundles.Comment: 20 pages; final version, to appear in Annales Academi{\ae} Scientiarum Fennic{\ae

Production and spectroscopy of hadrons containing a b quark at ATLAS

We present studies of the production and spectroscopy of some members of the B-hadron family. We reconstruct B ground states in their hadronic decay modes with a J/{\psi} or {\Upsilon} in the final state. These studies are based on the 2011 7 TeV dataset collected by the ATLAS detector.Comment: Presentation at the DPF 2013 Meeting of the American Physical Society Division of Particles and Fields, Santa Cruz, California, August 13-17, 2013. 11 pages, 12 figure

On the Stability of Randall-Sundrum Braneworlds with Conformal Bulk Fields

In the Randall-Sundrum scenario we consider exact 5-dimensional solutions with localized gravity which are associated with a well defined class of conformal bulk fields. We analyze their behaviour under radion field perturbations. We show that if the Randall-Sundrum exponential warp is the localizing metric function and the equation of state of the conformal fields is not changed by the radion perturbation then the 5-dimensional solutions are unstable. We present new stable solutions which describe on the brane the dynamics of inhomogeneous dust, generalized dark radiation and homogeneous polytopic matter.Comment: 10 pages, latex, no figures. Contribution to the special issue of Vestnik of Tomsk State Pedagogical University in the field QFT/Cosmology/Gravity/Strings, edited by Sergei D. Odintso

On Shrinking and Boundedly Complete Schauder Frames of Banach spaces

This paper studies Schauder frames in Banach spaces, a concept which is a natural generalization of frames in Hilbert spaces and Schauder bases in Banach spaces. The associated minimal and maximal spaces are introduced, as are shrinking and boundedly complete Schauder frames. Our main results extend the classical duality theorems on bases to the situation of Schauder frames. In particular, we will generalize James' results on shrinking and boundedly complete bases to frames. Secondly we will extend his characterization of the reflexivity of spaces with unconditional bases to spaces with unconditional frames