Principal Bundles and the Dixmier Douady Class

A systematic consideration of the problem of the reduction and extension of the structure group of a principal bundle is made and a variety of techniques in each case are explored and related to one another. We apply these to the study of the Dixmier-Douady class in various contexts including string structures, U-res bundles and other examples motivated by considerations from quantum field theory.Comment: 28 pages, latex, no figures, uses amsmath, amsthm, amsfonts. Revised version - only change a lot of irritating typos remove

Timing of Deformation along the Iron Springs Thrust, Southern Sevier Fold-and-Thrust Belt, Utah: Evidence for an Extensive Thrusting Event in the mid-Cretaceous

The temporal and spatial distribution of strain associated with the Sevier orogeny in western North America is significantly different in the southern end of the belt, at the latitude of Las Vegas, Nevada, than farther to the north at the latitude of Salt Lake City, Utah. Reasons for these differences have been speculative as a lack of temporal constraints on thrusting in the intervening region hindered along-strike correlation across the belt. We determined a crystallization age of 100.18 ± 0.04 Ma for zircons extracted from a recently recognized dacite lapilli ash-fall tuff near the base of the synorogenic Iron Springs Formation. We propose the name “Three Peaks Tuff Member” for this unit, and identify a type stratigraphic section on the western flank of the “Three Peaks,” a topographic landmark in Iron County, Utah. Field relationships and this age constrain movement on the Iron Springs thrust and the end of the sub-Cretaceous unconformity in the critical intervening area to latest Albian/earliest Cenomanian. Movement on the Iron Springs thrust was synchronous with movement on multiple Sevier thrusts at ~100 Ma, indicating that the mid-Cretaceous was a period of extensive thrust-fault movement. This mid-Cretaceous thrusting event coincided with a period of global plate reorganization and increased convergence, and hence an increased subduction rate for the Farallon Plate beneath North America. The accelerated subduction contributed to a Cordilleran arc flare-up event and steepening of the orogenic wedge, which triggered widespread thrusting across the retroarc Sevier deformation belts. Additionally, based on temporal constraints and the strong spatial connection of mid-Cretaceous thrusts to lineaments interpreted as pre-orogenic transform faults, we suggest that temporal and spatial variations along the strike of the orogenic belt reflect tectonic inheritance of basement structures associated with the edge of the rifted Precambrian craton

Observing a Dynamical Skeleton of Turbulence in Taylor-Couette Flow Experiments

Recent work suggests unstable recurrent solutions of the equations governing fluid flow can play an important role in structuring the dynamics of turbulence. Here we present a method for detecting intervals of time where turbulence "shadows" (spatially and temporally mimics) recurrent solutions. We find that shadowing occurs frequently and repeatedly in both numerical and experimental observations of counter-rotating Taylor-Couette flow, despite the relatively small number of known recurrent solutions in this system. Our results set the stage for experimentally-grounded dynamical descriptions of turbulence in a variety of wall-bounded shear flows, enabling applications to forecasting and control

Targeting the folate receptor: Improving efficacy in inorganic medicinal chemistry

The discovery of the high-affinity, high-specificity folate receptor in mamalian kidney cells, coupled with the ability of folate to enter cells by folate receptor-mediated endocytosis and the subsequent elucidation of the folate receptor’s overexpression in specific cancer cell types; heralded the arrival of the area of chemotherapeutic folate targeting. The application of purely organic folate-based small-molecule drug conjugates that selectively target the folate receptor, which is over expressed in several diseases such as cancer, is well established. The application of inorganic folate-targeted drugs offers significant potential to expand and enhance this therapeutic approach. From the data made available to date, it is apparent that this aspect of inorganic medicinal chemistry is in its youth but has the capability to contribute greatly to cancer research, both in therapy and diagnosis. The union of folate-receptor targeting and inorganic medicine may also lead to the development of treatments for disorders such as chronic-inflammation, tuberculosis, neurodegenerative disease and leishmaniasis. In this review, we summarize what is known about the coordination chemistry of folic acid and the therapeutic potential of such complexes. We also describe approaches adopted to conjugate platinum drugs to folate- or folate-carrier- systems and their prospective ability to overcome problems associated with unwanted side-effects and resistance by improving their delivery and/or selectivity. The literature pertaining to non-platinum metal complex conjugates with folic acid is also reviewed revealing that this is an area that offers significant potential to develop targeted therapeutic approaches in areas such as chemotherapy and molecular imaging for diagnostics

Phaselocked patterns and amplitude death in a ring of delay coupled limit cycle oscillators

We study the existence and stability of phaselocked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical Hopf bifurcation. The coupling is limited to nearest neighbors and is linear. We analyze a model set of discrete dynamical equations using the method of plane waves. The resultant dispersion relation, which is valid for any arbitrary number of oscillators, displays important differences from similar relations obtained from continuum models. We discuss the general characteristics of the equilibrium states including their dependencies on various system parameters. We next carry out a detailed linear stability investigation of these states in order to delineate their actual existence regions and to determine their parametric dependence on time delay. Time delay is found to expand the range of possible phaselocked patterns and to contribute favorably toward their stability. The amplitude death state is studied in the parameter space of time delay and coupling strength. It is shown that death island regions can exist for any number of oscillators N in the presence of finite time delay. A particularly interesting result is that the size of an island is independent of N when N is even but is a decreasing function of N when N is odd.Comment: 23 pages, 12 figures (3 of the figures in PNG format, separately from TeX); minor additions; typos correcte