We show that, if $q$ is a prime power at most 5, then every rank-$r$ matroid with no $U_{2,q+2}$-minor has no more lines than a rank-$r$ projective geometry over GF$(q)$. We also give examples showing that for every other prime power this bound does not hold.

Jim Geelen Peter Nelson

We show that a simple rank-$r$ matroid with no $(t+1)$-element independent flat has at least as many elements as the matroid $M_{r,t}$ defined as the direct sum of $t$ binary projective geometries whose ranks pairwise differ by at most $1$. We also show for $r \ge 2t$ that $M_{r,t}$ is the unique example for which equality holds.

Peter Nelson Sergey Norin

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder $R$, its rough set-based Nelson algebra can be obtained by applying the well-known construction by Sendlewski. We prove that if the set of all $R$-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by a quasiorder forms an effective lattice, that is, an algebraic model of the logic $E_0$, which is characterised by a modal operator grasping the notion of "to be classically valid". We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder.

Jouni Järvinen Piero Pagliani Sándor Radeleczki

Large-scale warps in the outer parts of spiral galaxy discs have been observed for almost forty years, but their origin remains obscure. We review the dynamics of warped galaxy discs. We identify several mechanisms that could excite warps, all involving the gravitational interaction between the disc and the dark-matter halo.

Robert W. Nelson Scott Tremaine

A simple generalization of the MHD model accounting for the fluctuations of the configurations due to kinetic effects in plasmas in short times small scales is considered. The velocity of conductive fluid and the magnetic field are considerd as the stochastic fields (or random trial trajectories) for which the classical MHD equations play the role of the mean field equations in the spirit of stochastic mechanics of E. Nelson.

D. Volchenkov R. Lima

A rack shadow is a set X with a rack action by a rack R, analogous to a vector space over a field. We use shadow colorings of classical link diagrams to define enhanced rack counting invariants and show that the enhanced invariants are stronger than unenhanced counting invariants.

Wesley Chang Sam Nelson

We review recent work on the strong CP problem in the context of realistic string-inspired models. We discuss the various solutions, review the conjecture that CP is generally a gauged discrete symmetry in string theory and then consider models of the Nelson-Barr type. We note that squark non-degeneracy spoils the Nelson-Barr structure at the one loop level. We stress that string theory expectations, as well as naturalness arguments, make it very difficult to avoid the constraints on non-degeneracy.

R. G. Leigh

In the context of (2+1)--dimensional gravity, we use holonomies of constant connections which generate a $q$--deformed representation of the fundamental group to derive signed area phases which relate the quantum matrices assigned to homotopic loops. We use these features to determine a quantum Goldman bracket (commutator) for intersecting loops on surfaces, and discuss the resulting quantum geometry.

J. E. Nelson R. F. Picken

This poster describes the timing system being designed for Spallation Neutron Source being built at Oak Ridge National lab.

B. oerter R. Nelson T. Shea C. Sibley

The growth-rate function for a minor-closed class $\mathcal{M}$ of matroids is the function $h$ where, for each non-negative integer $r$, $h(r)$ is the maximum number of elements of a simple matroid in $\mathcal{M}$ with rank at most $r$. The Growth-Rate Theorem of Geelen, Kabell, Kung, and Whittle shows, essentially, that the growth-rate function is always either linear, quadratic, exponential, or infinite. Morover, if the growth-rate function is quadratic, then $h(r)\ge \binom{r+1}{2}$, with the lower bound coming from the fact that such classes necessarily contain all graphic matroids. We characterise the classes that satisfy $h(r) = \binom{r+1}{2}$ for all sufficiently large $r$.

Jim Geelen Peter Nelson