mcmxciv This thesis deals with combinatorics in connection with Coxeter groups, finitely generated but not necessarily finite. The representation theory of groups as nonsingular matrices over a field is of immense theoretical importance, but also basic for computational group theory, where the group elements are data structures in a computer. Matrices are unnecessarily large structures, and part of this thesis is concerned with small and efficient representations of a large class of Coxeter groups (including most Coxeter groups that anyone ever payed any attention to.) The main contents of the thesis can be summarized as follows. • We prove that for all Coxeter graphs constructed from an n-path of unlabelled edges by adding a new labelled edge and a new vertex (sometimes two new edges and vertices), there is a permutational representation of the corresponding group. Group elements correspond to integer n-sequences and the nodes in the path generate all n! permutations. The extra node has a more complicated action, adding a certain quantity to some of the numbers.

the phase diagram of two-color QCD with the functional renormalization group. Universal aspects of deconfinement are illustrated mainly in the 2 + 1 dimensional SU(N) gauge theories with second order transition where many exact results from spin models can be exploited.

Abstract not found

Effective support for custom proof automation is essential for large-scale interactive proof develop-ment. However, existing languages for automation via tactics either (a) provide no way to specify the behavior of tactics within the base logic of the accompanying theorem prover, or (b) rely on advanced type-theoretic machinery that is not easily integrated into established theorem provers. We present Mtac, a lightweight but powerful extension to Coq that supports dependently typed tactic programming. Mtac tactics have access to all the features of ordinary Coq programming, as well as a new set of typed tactical primitives. We avoid the need to touch the trusted kernel type-checker of Coq by encapsulating uses of these new tactical primitives in a monad, and instrumenting Coq so that it executes monadic tactics during type inference. 1

I first thank my thesis advisors Thiemo Voigt and Adam Dunkels for being my excellent advisors, and also for being the great colleagues you still are. Thiemo and Adam have complemented each other superbly, giving me feedback, perspectives, insights, and having made every single new venture truly fun. My deepest thanks also go to my professor Per Gunningberg, Uppsala University. Per has in a seemingly easy way spotted erroneous assumptions, has valued my research contributions, and has connected my own work with another broader world of research. I want to thank all colleagues in the Networked Embedded Systems group:

and methotrexate were 1000, 100 and 10 nmol/L per reaction. P60 was used at final concentrations of 1428 .57, 142.86, and 14.29 µg/L and, thus, contained 1060 , 106, and 10.6 nmol/L EGCG and 1427.3 nmol/L of the gallated catechins (EGCG, ECG and gallocatechin gallate), respectively. Rat study Fifty male Wistar