Formulae relating the Bernstein and Iwahori-Matsumoto presentations of an affine Hecke algebra

We give explicit formulae for certain elements occurring in the Bernstein presentation of an affine Hecke algebra, in terms of the usual Iwahori- Matsumoto generators. We utilize certain minimal expressions for said elements and we give a sheaf-theoretic interpretation for the existence of these minimal expressions.Comment: To appear, J. of Algebr

Active regulation of the epidermal calcium profile

A distinct calcium profile is strongly implicated in regulating the multi-layered structure of the epidermis. However, the mechanisms that govern the regulation of this calcium profile are currently unclear. It clearly depends on the relatively impermeable barrier of the stratum corneum (passive regulation) but may also depend on calcium exchanges between keratinocytes and extracellular fluid (active regulation). Using a mathematical model that treats the viable sublayers of unwounded human and murine epidermis as porous media and assumes that their calcium profiles are passively regulated, we demonstrate that these profiles are also actively regulated. To obtain this result, we found that diffusion governs extracellular calcium motion in the viable epidermis and hence intracellular calcium is the main source of the epidermal calcium profile. Then, by comparison with experimental calcium profiles and combination with a hypothesised cell velocity distribution in the viable epidermis, we found that the net influx of calcium ions into keratinocytes from extracellular fluid may be constant and positive throughout the stratum basale and stratum spinosum, and that there is a net outflux of these ions in the stratum granulosum. Hence the calcium exchange between keratinocytes and extracellular fluid differs distinctly between the stratum granulosum and the underlying sublayers, and these differences actively regulate the epidermal calcium profile. Our results also indicate that plasma membrane dysfunction may be an early event during keratinocyte disintegration in the stratum granulosum

On the Andreadakis-Johnson filtration of the automorphism group of a free group

The Johnson filtration of the automorphism group of a free group is composed of those automorphisms which act trivially on nilpotent quotients of the free group. We compute cohomology classes as follows: (i) we analyze analogous classes for a subgroup of the pure symmetric automorphism group of a free group, and (ii) we analyze features of these classes which are preserved by the Johnson homomorphism. One consequence is that the ranks of the cohomology groups in any fixed dimension between 1 and n-1 increase without bound for terms deep in the Johnson filtraton.Comment: Corrections; revisions to proof of main theore

Airflow and precipitation structure of two leading stratiform mesoscale convective systems

Fall 2001.Also issued as author's thesis (M.S.) -- Colorado State University, 2001.Includes bibliographical references.An analysis of the airflow and precipitation structure of two leading stratiform (LS) mesoscale convective systems is presented. LS systems are defined as linear MCSs that consist of a convective line with leading stratiform rain. Case studies of LS systems on 30 April 2000 and 7 May 1997 were conducted using the available operational datasets. Several of the features observed, though not all, appear as a mirror image of those seen in trailing stratiform (TS) mesoscale convective systems. Their horizontal reflectivity structure has similar aspects, with convective cells which are sometimes elongated and canted with respect to the convective line, a transition zone of lower reflectivity, and an area of enhanced stratiform rain. Cold pools are situated beneath the convective line. The 30 April case shows a leading mesolow that resembles a TS wake low, but its propagation characteristics (and presumably dynamics) differ. A descending leading inflow jet, the counterpart of a rear inflow jet in a TS system, can be detected in both cases underneath a layer of strong ascending rear-to-front flow aloft. A few features of these LS systems are distinctive from TSs. Cells in the convective line appear to be more discontinuous and are elongated more than those of a TS. Rear­ feeding from an elevated Be maximum behind the system is an exclusive feature of these LSs, since TSs are typically fed from the boundary layer. Unlike the rear inflow jet in TS systems, neither case shows a reversal in the leading inflow jet as it descends to low levels near the convective line. Both cases exhibit front-to-rear surface flow throughout the LS systems. Finally, a schematic diagram is presented that illustrates the structure observed in the two cases, based heavily on a Doppler radar analysis of 7 May 1997.Sponsored by NSF under grant ATM-0071371, and a graduate fellowship from the American Meteorological Society