Continued fractions and S-units in function fields

The purpose of this article is two-fold: to present some results on continued fractions in function fields and show how continued fractions can be applied to find fundamental S-units in hyperelliptic fields

Continued fractions and -units in hyperelliptic fields

n function fields and to show how continued fractions can be used to find fundamental S-units in hyperelliptic fields

A new local-global principle for quadratic functional fields

A new local-global principle for existence of non-trivial units in quadratic functional fields is proved

On the Tits alternative for some generalized triangle goups

Rosenberger’s conjecture is proved for groups T(2,l,2,R) with l=6, 12, 30, 60 and some special groups T(3,4,2,R

Groups of -units in hyperelliptic fields and continued fractions

Abstract. New methods for calculating fundamental S-units in hyperelliptic fields are found. Continued fractions in function fields are investigated. As an application, it is proved that if a valuation is defined by a linear polynomial, then a fundamental S-unit in a hyperelliptic field can be found by expanding certain elements into continued fractions

Kallikrein‐related peptidase 4, matrix metalloproteinase 20, and the maturation of murine and porcine enamel

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90160/1/j.1600-0722.2011.00859.x.pd

On the Tits alternative for some generalized triangle groups

In the paper Rosenberger’s conjecture is proved for groups T(2, l, 2, R) with l = 6, 12, 30, 60 and some special groups T(3, 4, 2, R). Remove selecte

Regulation of calcium phosphate formation by amelogenins under physiological conditions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90115/1/EOS_911_sm_FigS1-S4.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/90115/2/j.1600-0722.2011.00911.x.pd

Effect of phosphorylation on the interaction of calcium with leucine‐rich amelogenin peptide

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/90185/1/j.1600-0722.2011.00900.x.pd

Crystal Initiation Structures in Developing Enamel: Possible Implications for Caries Dissolution of Enamel Crystals

Investigations of developing enamel crystals using Atomic and Chemical Force Microscopy (AFM, CFM) have revealed a subunit structure. Subunits were seen in height images as collinear swellings about 30 nM in diameter on crystal surfaces. In friction mode they were visible as positive regions. These were similar in size (30–50 nM) to collinear spherical structures, presumably mineral matrix complexes, seen in developing enamel using a freeze fracturing/freeze etching procedure. More detailed AFM studies on mature enamel suggested that the 30–50 nM structures were composed of smaller units, ~10–15 nM in diameter. These were clustered in hexagonal or perhaps a spiral arrangement. It was suggested that these could be the imprints of initiation sites for mineral precipitation. The investigation aimed at examining original freeze etched images at high resolution to see if the smaller subunits observed using AFM in mature enamel were also present in developing enamel i.e., before loss of the organic matrix. The method used was freeze etching. Briefly samples of developing rat enamel were rapidly frozen, fractured under vacuum, and ice sublimed from the fractured surface. The fractured surface was shadowed with platinum or gold and the metal replica subjected to high resolution TEM. For AFM studies high-resolution tapping mode imaging of human mature enamel sections was performed in air under ambient conditions at a point midway between the cusp and the cervical margin. Both AFM and freeze etch studies showed structures 30–50 nM in diameter. AFM indicated that these may be clusters of somewhat smaller structures ~10–15 nM maybe hexagonally or spirally arranged. High resolution freeze etching images of very early enamel showed ~30–50 nM spherical structures in a disordered arrangement. No smaller units at 10–15 nM were clearly seen. However, when linear arrangements of 30–50 nM units were visible the picture was more complex but also smaller units including ~10–15 nM units could be observed. Conclusions: Structures ~10–15 nM in diameter were detected in developing enamel. While the appearance was complex, these were most evident when the 30–5 nM structures were in linear arrays. Formation of linear arrays of subunits may be associated with the development of mineral initiation sites and attendant processing of matrix proteins