Counting-Based Effective Dimension and Discrete Regularizations.

Fractal-like structures of varying complexity are common in nature, and measure-based dimensions (Minkowski, Hausdorff) supply their basic geometric characterization. However, at the level of fundamental dynamics, which is quantum, structure does not enter via geometric features of fixed sets but is encoded in probability distributions on associated spaces. The question then arises whether a robust notion of the fractal measure-based dimension exists for structures represented in this way.

Effective Number Theory: Counting the Identities of a Quantum State.

Quantum physics frequently involves a need to count the states, subspaces, measurement outcomes, and other elements of quantum dynamics. However, with quantum mechanics assigning probabilities to such objects, it is often desirable to work with the notion of a "total" that takes into account their varied relevance. For example, such an effective count of position states available to a lattice electron could characterize its localization properties.

Conceptual designs of conduction cooled MgB2 magnets for 1.5 and 3.0T full body MRI systems.

Conceptual designs of 1.5 and 3.0 T full-body magnetic resonance imaging (MRI) magnets using conduction cooled MgB superconductor are presented.