The universal character ring of some families of one-relator groups

We study the universal character ring of some families of one-relator groups. As an application, we calculate the universal character ring of two-generator one-relator groups whose relators are palindrome, and, in particular, of the (-2,2m+1,2n+1)-pretzel knot for all integers m and n. For the (-2,3,2n+1)-pretzel knot, we give a less technical proof of a result in [LT1] on its universal character ring, and an elementary proof of a result in [Ma] on the number of irreducible components of its character variety.Comment: Minor changes. To appear in Algebraic and Geometric Topolog

Characteristics of total suspended matter and associated hydrocarbon concentration adjacent to the Chesapeake Bay entrance

Methodologies used to determine concentrations of hydrocarbons and associated suspended particulates at stations in and adjacent to the entrance to the Chesapeake Bay are described and the results are presented. Passive and active remote sensing data were acquired in conjunction with sea truth data collection

How to preserve symmetries with cut-off regularized integrals?

We present a prescription to calculate the quadratic and logarithmic divergent parts of several integrals employing a cutoff in a coherent way, i.e. in total agreement with symmetry requirements. As examples we consider one-loop Ward identities for QED and a phenomenological chiral model.Comment: 11 pages, 3 graph

The relationship among sea surface roughness variations, oceanographic analyses, and airborne remote sensing analyses

The synthetic aperture radar (SAR) was studied to determine whether it could image large scale estuaries and oceanic features such as fronts and to explain the electromagnetic interaction between SAR and the individual surface front features. Fronts were observed to occur at the entrance to the Chesapeake Bay. The airborne measurements consisted of data collection by SAR onboard an F-4 aircraft and real aperture side looking radar (SLAR) in Mohawk aircraft. A total of 89 transects were flown. Surface roughness and color as well as temperature and salinity were evaluated. Cross-frontal surveys were made. Frontal shear and convergence flow were obtained. Surface active organic materials, it was indicated, are present at the air-sea interface. In all, 2000 analyses were conducted to characterize the spatial and temporal variabilities associated with water mass boundaries

Two regularizations - two different models of Nambu-Jona-Lasinio

Two variants of the Nambu--Jona-Lasinio model -- the model with 4-dimensional cutoff and the model with dimensionally-analytical regularization -- are systematically compared. It is shown that they are, in essence, two different models of light-quark interaction. In the mean-field approximation the distinction becomes apparent in a behavior of scalar amplitude near the threshold. For 4-dimensional cutoff the pole term can be extracted, which corresponds to sigma-meson. For dimensionally-analytical regularization the singularity of the scalar amplitude is not pole, and this singularity is quite disappeared at some value of the regularization parameter. Still more essential distinction of these models exists in the next-to-leading order of mean-field expansion. The calculations of meson contributions in the quark chiral condensate and in the dynamical quark mass demonstrate, that these contributions though their relatively smallness can destabilize the Nambu--Jona-Lasinio model with 4-dimensional cutoff. On the contrary, the Nambu--Jona-Lasinio model with dimensionally-analytical regularization is stabilized with the next-to-leading order, i.e. the value of the regularization parameter shifts to the stability region, where these contributions decrease.Comment: 14 pages; Journal version; parameter fixing procedure is modifie