The aim of the present paper is to discuss in some detail the Laguerre geometry (cf. [1], [6]) which arises from the 3-dimensional real algebra L := R(ε), where ε = 0. This algebra generalizes the algebra of real dual numbers D = R(ε), where ε = 0. The Laguerre geometry over D is the geometry on the so-called Blaschke cylinder (Figure 1); the non-degenerate conics on this cylinder are called ch...

0.1. Notations and Conventions. During this note, we will fix a base field k (e.g. the complex numbers C). The multiplicative group of the field k will be denoted by Gm. All the vector spaces considered will be finite dimensional vector spaces over the field k. For a given vector space V of dimension≥ 1, we will denote the dual vector space, the projective space parameterizing 1-dimensional sub...

Experimental results on the multiplicative orders of Gauss periods in finite fields are presented. These results indicate that Gauss periods have high order and are often primitive (self-dual) normal elements in finite fields. It is shown that Gauss periods can be exponentiated in quadratic time. An application is an efficient pseudorandom bit generator.

An affine invariant point on the class of convex bodies Kn in R, endowed with the Hausdorff metric, is a continuous map from Kn to R which is invariant under one-to-one affine transformations A on R, that is, p ` A(K) ́ = A ` p(K) ́ . We define here the new notion of dual affine point q of an affine invariant point p by the formula q(K) = p(K) for every K ∈ Kn, where K denotes the polar of K with...

We study the Ginzburg-Landau functional I (u) := 1 ln(1= ) Z U 1 2 jruj2 + 1 4 2 (1 juj2)2 dx ; for u 2 H(U ; IR), where U is a bounded, open subset of IR. We show that if a sequence of functions u satis es sup I (u ) < 1, then their Jacobians Ju are precompact in the dual of C c for every 2 (0; 1]. Moreover, any limiting measure is a sum of point masses. We also characterize the -limit I( ) of...

We present fully formalized proofs of some central theorems from combinatorics. These are Dilworth’s decomposition theorem, Mirsky’s theorem, Hall’s marriage theorem and the Erdős-Szekeres theorem. Dilworth’s decomposition theorem is the key result among these. It states that in any finite partially ordered set (poset), the size of a smallest chain cover and a largest antichain are the same. Mi...

HADWIGER INTEGRATION OF DEFINABLE FUNCTIONS Matthew L. Wright Robert Ghrist, Advisor This thesis defines and classifies valuations on definable functionals. The intrinsic volumes are valuations on “tame” subsets of R, and by easy extension, valuations on functionals on R with finitely many level sets, each a “tame” subset of R. We extend these valuations, which we call Hadwiger integrals, to de...

Several distinct mechanisms of confinement and dynamical symmetry breaking (DSB) are identified, in a class of supersymmetric SU(nc), USp(2nc) and SO(nc) gauge theories. In some of the vacua, the magnetic monopoles carrying nontrivial flavor quantum numbers condense, causing confinement and symmetry breaking simultaneously. In more general classes of vacua, however, the effective low-energy deg...

There are very close connections between the arithmetic of integer lattices, algebraic properties of the associated ideals, and the geometry and the combinatorics of corresponding polyhedra. In this paper we investigate the generating sets (\Grr obner bases") of integer lattices that correspond to the Grr obner bases of the associated binomial ideals. Extending results by Sturmfels & Thomas, we...

Kuhlau, F. 2013. Responsible Conduct in Dual Use Research: Towards an Ethic of Deliberation in the Life Sciences. Acta Universitatis Upsaliensis. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Medicine 866. 95 pp. Uppsala. ISBN 978-91-554-8593-1. Life scientists have increasingly been asked to incorporate a dual use responsibility in their research conduct. In this...