Bundles, Handcuffs, and Local Freedom

We answer a question of J. Anderson's by producing infinitely many commensurability classes of fibered hyperbolic 3-manifolds whose fundamental groups contain subgroups that are locally free and not free. These manifolds are obtained by performing 0–surgery on a collection of knots with the same properties.     

On Convergence Approach Spaces

The extension of two axioms due to Cook and Fischer to the category CAP of convergence approach spaces leads to the study of non-Archimedean approach spaces as well as two versions of regularity appropriate to CAP and related categories.     

Non-aqueous phase liquid drop formation within a water saturated fracture

This work focuses on the mechanisms of non-aqueous phase liquid (NAPL) drop formation within a single fracture fed from a NAPL reservoir by way of a circular orifice, such as a pore. The fracture is assumed to be fully saturated, the relative wettability of the system is assumed water-wet, and the water velocity profile within the fracture is described by a Poiseuille flow. The size of the NAPL drops is investigated for various water flow velocities and NAPL entrance diameters. A force balancing method was used to determine the radii of detached drops. The drop sizes calculated from the model developed here are shown to be in agreement with available experimental drop size data. It is shown that at low Reynolds numbers the buoyancy force is the dominant force acting on the drop during the formation process and at high Reynolds numbers the viscous forces dominate. A simplified expression relating the geometry of the fractured system to the drop radii is developed from the model equations, and it is shown to predict drop radii that match well with both the model simulations and the available experimental data.     

An investigation of dipeptides containing polar and nonpolar side groups by curie-point pyrolysis tandem mass spectrometry

Methionyl-leucine, leucyl-methionine, phenylalanyl-leucine, and leucyl-phenylalanine have been analyzed to determine dipeptide fragmentation mechanisms in Curie-point pyrolysis tandem mass spectrometry. Results show that fragmentations of dipeptides follow two general pathways, one involving direct cleavage of the dipeptide and the other involving cyclization of the dipeptide. Unique products and strong changes in relative mass spectral peak intensities arise, depending on constituent amino acid residues and their sequence. Also, the length and nature of the side groups strongly direct fragmentation. From these results, the major peaks in the spectra of eight other dipeptides could be readily explained; this suggests that a significant number of dipeptides follow the same general fragmentation mechanisms.     

Graphical unitary group approach to arbitrary spin representations

A graph theoretic approach to the representation of N particle systems involving arbitrary single-particle spin is presented. The method is a generalization of the Distinct Row Table (DRT ) technique employed by Shavitt in developing the graphical unitary group approach (GUGA ) to electronic spin-orbitals. A detailed analysis of the DRT and GUGA representations is presented based on several theoretical considerations and computer-tested implementations. The use of the representation to establish rules concerning the evaluation of the matrix elements of the group generators is also discussed.