On the Margulis constant for Kleinian groups, I curvature

The Margulis constant for Kleinian groups is the smallest constant $c$ such that for each discrete group $G$ and each point $x$ in the upper half space ${\bold H}^3$, the group generated by the elements in $G$ which move $x$ less than distance c is elementary. We take a first step towards determining this constant by proving that if $\langle f,g \rangle$ is nonelementary and discrete with $f$ parabolic or elliptic of order $n \geq 3$, then every point $x$ in ${\bold H}^3$ is moved at least distance $c$ by $f$ or $g$ where $c=.1829\ldots$. This bound is sharp

Apparatus for purging systems handling toxic, corrosive, noxious and other fluids Patent

Fluid transferring system design for purging toxic, corrosive, or noxious fluids and fumes from materials handling equipment for cleansing and accident preventio

The Fatou Theorem for Functions Harmonic in a Half‐Space

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135177/1/plms0149.pd

Hausdorff Dimension and Quasiconformal Mappings

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135677/1/jlms0504.pd

Angles and Quasiconformal Mappings†

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135391/1/plms0001.pd

Equivalence between Poly\'a-Szeg\H{o} and relative capacity inequalities under rearrangement

The transformations of functions acting on sublevel sets that satisfy a P\'olya-Szeg\H{o} inequality are characterized as those being induced by transformations of sets that do not increase the associated capacity.Comment: 9 page

Advantageous use of metallic cobalt in the target for Pulsed Laser Deposition of cobalt-doped ZnO films

We investigate the magnetic properties of ZnCoO thin films grown by pulsed laser deposition (PLD) from targets made containing metallic Co or CoO precursors instead of the usual Co3O4. We find that the films grown from metallic Co precursors in an oxygen rich environment contain negligible amounts of Co metal, and have a large magnetization at room temperature. Structural analysis by X-ray diffraction and magneto-optical measurements indicate that the enhanced magnetism is due, in part, from Zn vacancies that partially compensate the naturally occurring n-type defects. We conclude that strongly magnetic films of Zn0.95Co0.05O that do not contain metallic cobalt can be grown by PLD from Co-metal-precursor targets if the films are grown in an oxygen atmosphere

Anomalous transverse acoustic phonon broadening in the relaxor ferroelectric Pb(Mg_1/3Nb_2/3)O_3

The intrinsic linewidth $\Gamma_{TA}$ of the transverse acoustic (TA) phonon observed in the relaxor ferroelectric compound Pb(Mg$_{1/3}$Nb$_{2/3})_{0.8}$Ti$_{0.2}$O$_3$ (PMN-20%PT) begins to broaden with decreasing temperature around 650 K, nearly 300 K above the ferroelectric transition temperature $T_c$ ($\sim 360$ K). We speculate that this anomalous behavior is directly related to the condensation of polarized, nanometer-sized, regions at the Burns temperature $T_d$. We also observe the ``waterfall'' anomaly previously seen in pure PMN, in which the transverse optic (TO) branch appears to drop precipitously into the TA branch at a finite momentum transfer $q_{wf} \sim 0.15$ \AA$^{-1}$. The waterfall feature is seen even at temperatures above $T_d$. This latter result suggests that the PNR exist as dynamic entities above $T_d$.Comment: 6 pages, 4 figure

Fractional Sobolev-Poincaré inequalities in irregular domains

This paper is devoted to the study of fractional (q, p)-Sobolev-Poincaré in- equalities in irregular domains. In particular, the author establishes (essentially) sharp fractional (q, p)-Sobolev-Poincaré inequalities in s-John domains and in domains satisfying the quasihyperbolic boundary conditions. When the order of the fractional derivative tends to 1, our results tend to the results for the usual derivatives. Furthermore, the author verifies that those domains which support the fractional (q, p)-Sobolev-Poincaré inequalities together with a separation property are s-diam John domains for certain s, depending only on the associated data. An inaccurate statement in [Buckley, S. and Koskela, P., Sobolev-Poincaré implies John, Math. Res. Lett., 2(5), 1995, 577–593] is also pointed out