On elliptic curves with an isogeny of degree 7

We show that if $E$ is an elliptic curve over $\mathbf{Q}$ with a $\mathbf{Q}$-rational isogeny of degree 7, then the image of the 7-adic Galois representation attached to $E$ is as large as allowed by the isogeny, except for the curves with complex multiplication by $\mathbf{Q}(\sqrt{-7})$. The analogous result with 7 replaced by a prime $p > 7$ was proved by the first author in [7]. The present case $p = 7$ has additional interesting complications. We show that any exceptions correspond to the rational points on a certain curve of genus 12. We then use the method of Chabauty to show that the exceptions are exactly the curves with complex multiplication. As a by-product of one of the key steps in our proof, we determine exactly when there exist elliptic curves over an arbitrary field $k$ of characteristic not 7 with a $k$-rational isogeny of degree 7 and a specified Galois action on the kernel of the isogeny, and we give a parametric description of such curves.Comment: The revision gives a complete answer to the question considered in Version 1. Version 3 will appear in the American Journal of Mathematic

Directed Rh(I)-Catalyzed Asymmetric Hydroboration of Prochiral 1-Arylcycloprop-2-ene-1-carboxylic Acid Derivatives

This is the peer reviewed version of the following article: A. Edwards, M. Rubina, M. Rubin, Chem. Eur. J. 2018, 24, 1394., which has been published in final form at http://doi.org/10.1002/chem.201704443. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.A full account on rhodium-catalyzed asymmetric, directed hydroboration of functionalized prochiral cyclopropenes affording enantiomerically enriched cyclopropylboronates is reported. The scope and limitations of two alternate directing groups, ester and carboxamide, are evaluated. It was found that hydroboration of esters appeared to be more sensitive to substitution in the aromatic ring of the substrates. Specifically, ortho-halogens were detrimental for diastereo- and enantioselectivity, possibly because of additional coordination with rhodium. In contrast, more Lewis-basic amide directing groups allowed for stronger chelation to the transition metal, leading to consistently high diastereo- and enantioselectivity in hydroboration across a broader range of substrates

Space shuttle pogo studies

Topics covered include: (1) pogo suppression for main propulsion subsystem operation; (2) application of quarter-scale low pressure oxidizer turbopump transfer functions; (3) pogo stability during orbital maneuvering subsystem operation; and (4) errors in frequency response measurements

Acute pulmonary pathology and sudden death in rats following the intravenous administration of the plasticizer, DI (2-ethylhexyl) phthalate, solubilized with Tween surfactants

Intravenous administration of 200-300 mg/kg of di(2-ethylhexyl)phthalate (DEHP) solubilized in aqueous solutions of several Tween surfactants caused respiratory distress in rats. There was a dose-dependent lethality with death generally occurring within 90 minutes after injection. The lungs from DEHP:Tween treated animals were enlarged, generally darkened, and in some cases showed hemorrhagic congestion. Neither the overt symptoms nor the morphologic alterations resulting from DEHP:Tween administration could be reproduced by intravenous administration of aqueous Tween solutions alone. The absence of pulmonary abnormalities following the intravenous administration of DEHP as an aqueous emulsion given either alone or even as soon as 2 minutes after pretreatment with Tween 80, suggests that the specific in vivo interaction between DEHP and Tween surfactants depends on the prior formation of water-soluble micelles of DEHP

The ionization structure of the Orion nebula: Infrared line observations and models

Observations of the (O III) 52 and 88 micron lines and the (N III) 57 micron line have been made at 6 positions and the (Ne III) 36 micron line at 4 positions in the Orion Nebula to probe its ionization structure. The measurements, made with a -40" diameter beam, were spaced every 45" in a line south from and including the Trapezium. The wavelength of the (Ne III) line was measured to be 36.013 + or - 0.004 micron. Electron densities and abundance ratios of N(++)/O(++) have been calculated and compared to other radio and optical observations. Detailed one component and two component (bar plus halo) spherical models were calculated for exciting stars with effective temperatures of 37 to 40,000K and log g = 4.0 and 4.5. Both the new infrared observations and the visible line measurements of oxygen and nitrogen require T sub eff approx less than 37,000K. However, the double ionized neon requires a model with T sub eff more than or equal to 39,000K, which is more consistent with that inferred from the radio flux or spectral type. These differences in T sub eff are not due to effects of dust on the stellar radiation field, but are probably due to inaccuracies in the assumed stellar spectrum. The observed N(++)/O(++) ratio is almost twice the N(+)/O(+) ratio. The best fit models give N/H = 8.4 x 10 to the -5 power, O/H = 4.0 x 10 to the -4 power, and Ne/H = 1.3 x 10 to the -4 power. Thus neon and nitrogen are approximately solar, but oxygen is half solar in abundance. From the infrared O(++) lines it is concluded that the ionization bar results from an increase in column depth rather than from a local density enhancement

Unzipping an adsorbed polymer in a dirty or random environment

The phase diagram of unzipping of an adsorbed directed polymer in two dimensions in a random medium has been determined. Both the hard-wall and the soft-wall cases are considered. Exact solutions for the pure problem with different affinities on the two sides are given. The results obtained by the numerical procedure adopted here are shown to agree with the exact results for the pure case. The characteristic exponents for unzipping for the random problem are different from the pure case. The distribution functions for the unzipped length, first bubble, and the spacer are determined.Comment: Published version, uses revtex4, 14 page

Theory of spike timing based neural classifiers

We study the computational capacity of a model neuron, the Tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random classification tasks. In contrast to its static analog, the Perceptron, the Tempotron's solutions space consists of a large number of small clusters of weight vectors. The capacity of the system per synapse is finite in the large size limit and weakly diverges with the stimulus duration relative to the membrane and synaptic time constants.Comment: 4 page, 4 figures, Accepted to Physical Review Letters on 19th Oct. 201