### Akademisk avhandling för teknisk doktorsexamen vid

, 1994

"... 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 ..."

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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.

###
Nuclear Physics B *Proceedings* Supplement – preprint (2014) 1–42 Nuclear Physics B *Proceedings* Supplement Universal Aspects of QCD-like TheoriesI

"... In these lectures I review some basic examples of how the concepts of universality and scaling can be used to study aspects of the chiral and the deconfinement transition, if not in QCD directly but in QCD-like theories. As an example for flavor dynamics I discuss a quark-hadron model to describe th ..."

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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.### Disthbution IJnli~nited CONTRACT TITLE: THEORETICAL STUDIES OF HIGH-POWER ULTRAVIOLET AND INFRARED MATERIALS

, 1978

"... ~f d1400 Wilson Boulevard nc assi ie ..."

### AGR 05

"... Responses of soil biological processes to elevated atmospheric [CO2] and nitrogen addition in a poplar plantation ..."

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Responses of soil biological processes to elevated atmospheric [CO

*2*] and nitrogen addition in a poplar plantation### A Precise Error Bound for Quantum Phase Estimation

, 2011

"... Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be f ..."

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Quantum phase estimation is one of the key algorithms in the field of quantum computing, but up until now, only approximate expressions have been derived for the probability of error. We revisit these derivations, and find that by ensuring symmetry in the error definitions, an exact formula can be found. This new approach may also have value in solving other related problems in quantum computing, where an expected error is calculated. Expressions for two special cases of the formula are also developed, in the limit as the number of qubits in the quantum computer approaches infinity and in the limit as the extra added qubits to improve reliability goes to infinity. It is found that this formula is useful in validating computer simulations of the phase estimation procedure and in avoiding the overestimation of the number of qubits required in order to achieve a given reliability. This formula thus brings improved precision in the design of quantum computers.

### 3 USING D-OPERATORS TO CONSTRUCT ORTHOGONAL POLYNOMIALS SATISFYING HIGHER ORDER q-DIFFERENCE EQUATIONS

"... ar ..."

### and

, 2015

"... 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 adva ..."

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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### TO CODE OR NOT TO CODE

, 2002

"... de nationalité suisse et originaire de Zurich (ZH) et Lucerne (LU) acceptée sur proposition du jury: ..."

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de nationalité suisse et originaire de Zurich (ZH) et Lucerne (LU) acceptée sur proposition du jury: