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

Investigation of the reaction of the lunar surface to the impact of a lunar probe final report

Flash phenomena associated with hypervelocity impact for estimating flash from impact of lunar prob

New Perspectives on Eye Development and the Evolution of Eyes and Photoreceptors

Recent experiments on the genetic control of eye development have opened up a completely new perspective on eye evolution. The demonstration that targeted expression of one and the same master control gene, that is, Pax6 can induce the formation of ectopic eyes in both insects and vertebrates, necessitates a reconsideration of the dogma of a polyphyletic origin of the various eye types in all the animal phyla. The involvement of Pax6 and six1 and six3 genes, which encode highly conserved transcription factors, in the genetic control of eye development in organisms ranging from planarians to humans argues strongly for a monophyletic origin of the eye. Because transcription factors can control the expression of any target gene provided it contains the appropriate gene regulatory elements, the conservation of the genetic control of eye development by Pax6 among all bilaterian animals is not due to functional constraints but a consequence of its evolutionary history. The prototypic eyes postulated by Darwin to consist of two cells only, a photoreceptor and a pigment cell, were accidentally controlled by Pax6 and the subsequent evolution of the various eye types occurred by building onto this original genetic program. A hypothesis of intercalary evolution is proposed that assumes that the eye morphogenetic pathway is progressively modified by intercalation of genes between the master control genes on the top of the hierarchy and the structural genes like rhodopsin at the bottom. The recruitment of novel genes into the eye morphogenetic pathway can be due to at least two different genetic mechanisms, gene duplication and enhancer fusion. In tracing back the evolution of eyes beyond bilaterians, we find highly developed eyes in some box-jellyfish as well as in some Hydrozoans. In Hydrozoans the same orthologous six genes (six1 and six3) are required for eye regeneration as in planarians, and in the box jellyfish Tripedalia a pax B gene, which may be a precursor of Pax6, was found to be expressed in the eyes. In contrast to the adults, which have highly evolved eyes, the Planula larva of Tripedalia has single- celled photoreceptors similar to some unicellular protists. For the origin of photoreceptor cells in metazoa, I propose two hypotheses, one based on cellular differentiation and a more speculative one based on symbiosis. The former assumes that photoreceptor cells originated from a colonial protist in which all the cells were photosensitive and subsequent cellular differentiation to give rise to photoreceptor cells. The symbiont hypothesis, which I call the Russian doll model, assumes that photosensitivity arose first in photosynthetic cyanobacteria that were subsequently taken up into red algae as primary chloroplasts. The red algae in turn were taken up by dinoflagellates as secondary chloroplasts and in some species evolved into the most sophisticated eye organelles, as found, for example, in some dinoflagellates like Erythropsis and Warnovia, which lack chloroplasts. Because dinoflagellates are commonly found as symbionts in cnidarians, the dinoflagellates may have transferred their photoreceptor genes to cnidarians. In cnidarians such as Tripedalia the step from photoreceptor organelles to multicellular eyes has occurred. These two hypotheses, the cellular differentiation and the symbiont hypothesis, are not mutually exclusive and are the subject of further investigation

Hausdorff Dimension and Quasiconformal Mappings

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

Quantum Impurities in the Two-Dimensional Spin One-Half Heisenberg Antiferromagnet

The study of randomness in low-dimensional quantum antiferromagnets is at the forefront of research in the field of strongly correlated electron systems, yet there have been relatively few experimental model systems. Complementary neutron scattering and numerical experiments demonstrate that the spin-diluted Heisenberg antiferromagnet La2Cu(1-z)(Zn,Mg)zO4 is an excellent model material for square-lattice site percolation in the extreme quantum limit of spin one-half. Measurements of the ordered moment and spin correlations provide important quantitative information for tests of theories for this complex quantum-impurity problem.Comment: 11 pages, 3 figures. NOTE: possible errors in PDF version of Fig. 1. View postscript version of figure if possibl

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

Experimental investigations of simulated meteoroid damage to various spacecraft structures progress report no. 1, period ending 30 sep. 1964

Space simulation experimental studies of penetration mechanics of meteoroids into typical spacecraft structure