Normal origamis of Mumford curves

An origami (also known as square-tiled surface) is a Riemann surface covering a torus with at most one branch point. Lifting two generators of the fundamental group of the punctured torus decomposes the surface into finitely many unit squares. By varying the complex structure of the torus one obtains easily accessible examples of Teichm\"uller curves in the moduli space of Riemann surfaces. The p-adic analogues of Riemann surfaces are Mumford curves. A p-adic origami is defined as a covering of Mumford curves with at most one branch point, where the bottom curve has genus one. A classification of all normal non-trivial p-adic origamis is presented and used to calculate some invariants. These can be used to describe p-adic origamis in terms of glueing squares.Comment: 21 pages, to appear in manuscripta mathematica (Springer

Introduction to Categories and Categorical Logic

The aim of these notes is to provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The notes are based on a lecture course given at Oxford over the past few years. They contain numerous exercises, and hopefully will prove useful for self-study by those seeking a first introduction to the subject, with fairly minimal prerequisites. The coverage is by no means comprehensive, but should provide a good basis for further study; a guide to further reading is included. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions. An Appendix contains a summary of what we will need, and it may be useful to review this first. In addition, some prior exposure to abstract algebra - vector spaces and linear maps, or groups and group homomorphisms - would be helpful.Comment: 96 page

The Physics of K0−Kˉ0K^0 -\bar K^0 Mixing: B^K\widehat{B}_K and ΔMLS\Delta M_{LS} in the Chiral Quark Model

We compute the $\widehat B_K$ parameter and the mass difference $\Delta M_{LS}$ of the $K^0-\bar K^0$ system by means of the chiral quark model. The chiral coefficients of the relevant $\Delta S=2$ and $\Delta S=1$ chiral lagrangians are computed via quark-loop integration. We include the relevant effects of one-loop corrections in chiral perturbation theory. The final result is very sensitive to non-factorizable corrections of $O(\alpha_S N)$ coming from gluon condensation. The size of the gluon condensate is determined by fitting the experimental value of the amplitude $K^+ \to \pi^+\pi^0$. By varying all the relevant parameters we obtain $\widehat{B}_K= 0.87 \pm 0.33\ .$ We evaluate within the model the long-distance contributions to $\Delta M_{LS}$ induced by the double insertion of the $\Delta S = 1$ chiral lagrangian and study the interplay between short- and long-distance amplitudes. By varying all parameters we obtain $\Delta M_{LS}^{th}/\Delta M_{LS}^{exp} = 0.76 ^{+0.64}_{-0.34} .$ Finally, we investigate the phenomenological constraints on the Kobayashi-Maskawa parameter Im $\lambda _t$ entering the determination of $\epsilon'/\epsilon$.Comment: 31 pages, Latex file including 7 eps figures. Revised version to appear in Nucl. Phys.

Clinical Evaluation of a Telemedically Linked Intraoral Drug Delivery System

The miniaturized intraoral drug delivery system BuccalDose is composed of a replaceable cartridge which is worn in a removable prosthesis and an external base station for telemedical therapy monitoring. The system has now been tested for the first time with Parkinson\u2019s disease (PD) patients. The study evaluated the usability of the entire system, the functionality of the telemedical transmission path and the functionality of the cartridge, which uses an osmotic pumping principle to release a liquid drug formulation to the buccal mucosa. The BuccalDose system was generally considered to be easy to handle, even with movement disorders, up to a mild-moderate disease stage. In addition, the obtained in vivo release rates of the cartridges confirmed the previously achieved in vitro release behavior

A series of coverings of the regular n-gon

We define an infinite series of translation coverings of Veech's double-n-gon for odd n greater or equal to 5 which share the same Veech group. Additionally we give an infinite series of translation coverings with constant Veech group of a regular n-gon for even n greater or equal to 8. These families give rise to explicit examples of infinite translation surfaces with lattice Veech group.Comment: A missing case in step 1 in the proof of Thm. 1 b was added. (To appear in Geometriae Dedicata.

Non-factorizable contribution in nonleptonic weak interactions of K mesons

Two pion decays of K mesons, K_L-K_S mass difference, two photon and the Dalitz decays of K_L are studied systematically by assuming that their amplitude is given by a sum of factorizable and non-factorizable ones. The former is estimated by using a naive factorization while the latter is assumed to be dominated by dynamical contributions of various hadron states.Comment: 23 pages,1 figur

Completing NLO QCD Corrections for Tree Level Non-Leptonic Delta F = 1 Decays Beyond the Standard Model

In various extensions of the Standard Model (SM) tree level non-leptonic decays of hadrons receive contributions from new heavy gauge bosons and scalars. Prominent examples are the right-handed W' bosons in left-right symmetric models and charged Higgs (H^\pm) particles in models with extended scalar sector like two Higgs doublet models and supersymmetric models. Even in the case of decays with four different quark flavours involved, to which penguin operators cannot contribute, twenty linearly independent operators, instead of two in the SM, have to be considered. Anticipating the important role of such decays at the LHCb, KEKB and Super-B in Rome and having in mind future improved lattice computations, we complete the existing NLO QCD formulae for these processes by calculating O(alpha_s) corrections to matching conditions for the Wilson coefficients of all contributing operators in the NDR-\bar{MS} scheme. This allows to reduce certain unphysical scale and renormalization scheme dependences in the existing NLO calculations. Our results can also be applied to models with tree-level heavy neutral gauge boson and scalar exchanges in Delta F = 1 transitions and constitute an important part of NLO analyses of those non-leptonic decays to which also penguin operators contribute.Comment: 24 pages, 6 figure

Estimate of B(K -> pi nu nubar) from Standard Model fits to lambda_t

We estimate B(K -> pi nu nubar) in the context of the Standard Model by fitting for lambda_t = Vtd x V*ts of the `kaon unitarity triangle' relation. We fit data from epsilon_K, the CP-violating parameter describing K-mixing, and a_{psi K}, the CP-violating asymmetry in B -> J/psi K decays. Our estimate is independent of the CKM matrix element Vcb and of the ratio of Bs to Bd mixing frequencies. The measured value of B(K+ -> pi+ nu nubar) can be compared both to this estimate and to predictions made from the ratio of B mixing frequencies.Comment: 8 pages, including 6 figures. v3 includes an expanded discussion of correlations between SM inputs to the lambda_t fit, clarifies the discussion of the independence of this result from the ratio of B mixing frequencies, includes minor updates to the values of SM input parameters, and includes some new and some updated reference

Splittings of generalized Baumslag-Solitar groups

We study the structure of generalized Baumslag-Solitar groups from the point of view of their (usually non-unique) splittings as fundamental groups of graphs of infinite cyclic groups. We find and characterize certain decompositions of smallest complexity (`fully reduced' decompositions) and give a simplified proof of the existence of deformations. We also prove a finiteness theorem and solve the isomorphism problem for generalized Baumslag-Solitar groups with no non-trivial integral moduli.Comment: 20 pages; hyperlinked latex. Version 2: minor change