On the existence of infinitely many closed geodesics on orbifolds of revolution

Using the theory of geodesics on surfaces of revolution, we introduce the period function. We use this as our main tool in showing that any two-dimensional orbifold of revolution homeomorphic to S^2 must contain an infinite number of geometrically distinct closed geodesics. Since any such orbifold of revolution can be regarded as a topological two-sphere with metric singularities, we will have extended Bangert's theorem on the existence of infinitely many closed geodesics on any smooth Riemannian two-sphere. In addition, we give an example of a two-sphere cone-manifold of revolution which possesses a single closed geodesic, thus showing that Bangert's result does not hold in the wider class of closed surfaces with cone manifold structures.Comment: 21 pages, 4 figures; for a PDF version see http://www.calpoly.edu/~jborzell/Publications/publications.htm

Model networks of end‐linked polydimethylsiloxane chains. I. Comparisons between experimental and theoretical values of the elastic modulus and the equilibrium degree of swelling

Two samples of hydroxyl‐terminated polydimethylsiloxane having molecular weights the order of 2×104 and 1×103 g mol−1 were separated into a total of six fractions of relatively narrow molecular weight distribution. Portions of one of the unfractionated polymers and each of the fractions were cross‐linked by reacting the hydroxyl chain ends, in the undiluted state, with a tetrafunctional orthosilicate. The resulting networks of end‐linked chains were studied with regard to their stress–strain isotherms in elongation at 25°C and their equilibrium swelling in benzene at room temperature. Values of the elastic modulus obtained from the isotherms support theoretical arguments that fluctuations in the network chain vectors reduce the value of the modulus to approximately one‐half of the value predicted for affine deformations of chain vectors constrained in their fluctuations by cross‐links firmly embedded in the network medium. Values of the equilibrium degree of swelling of the networks calculated on this basis are also in good agreement with experiment. The networks formed by end‐linking relatively short chains have small values of the semiempirical constant 2C2 used as a measure of the departure of an observed stress–strain isotherm from the form predicted by theory. Although this observation is consistent with the suggestion that such end‐linked networks have a much smaller number of interchain entanglements than do randomly cross‐linked networks, other evidence and arguments unfortunately do not support this assumption.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71356/2/JCPSA6-66-3-1006-1.pd

The Military Divorce: An Overview

Your Court Review Editors asked Mark Sullivan, nationally known expert on the military divorce, to contribute an article to this journal. Mark recruited colleagues Joe DeWoskin of Kansas City, KS, a retired Army officer, and Kansas District Court Judge Dan Wiley, who presides over domestic relations cases, to assist him. What follows is their round table discussion of the key issues in a military divorce

Model networks of end‐linked polydimethylsiloxane chains. II. Viscoelastic losses

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/71107/2/JCPSA6-68-4-2010-1.pd

Constraining the Progenitor Companion of the Nearby Type Ia SN 2011fe with a Nebular Spectrum at +981 Days

We present an optical nebular spectrum of the nearby Type Ia supernova 2011fe, obtained 981 days after explosion. SN 2011fe exhibits little evolution since the +593 day optical spectrum, but there are several curious aspects in this new extremely late-time regime. We suggest that the persistence of the $\sim5800$~\AA\ feature is due to Na I D, and that a new emission feature at $\sim7300$~\AA\ may be [Ca II]. Also, we discuss whether the new emission feature at $\sim6400$~\AA\ might be [Fe I] or the high-velocity hydrogen predicted by Mazzali et al. The nebular feature at 5200~\AA\ exhibits a linear velocity evolution of $\sim350$ $\rm km\ s^{-1}$ per 100 days from at least +220 to +980 days, but the line's shape also changes in this time, suggesting that line blending contributes to the evolution. At $\sim 1000$ days after explosion, flux from the SN has declined to a point where contribution from a luminous secondary could be detected. In this work we make the first observational tests for a post-impact remnant star and constrain its temperature and luminosity to $T \gtrsim 10^4$ $\rm K$ and $L \lesssim 10^4$ $\rm L_{\odot}$. Additionally, we do not see any evidence for narrow H$\alpha$ emission in our spectrum. We conclude that observations continue to strongly exclude many single-degenerate scenarios for SN 2011fe.Comment: 11 pages, 10 figures, published by MNRA

Estimating forest structure in a tropical forest using field measurements, a synthetic model and discrete return lidar data

Tropical forests are huge reservoirs of terrestrial carbon and are experiencing rapid degradation and deforestation. Understanding forest structure proves vital in accurately estimating both forest biomass and also the natural disturbances and remote sensing is an essential method for quantification of forest properties and structure in the tropics. Our objective is to examine canopy vegetation profiles formulated from discrete return LIght Detection And Ranging (lidar) data and examine their usefulness in estimating forest structural parameters measured during a field campaign. We developed a modeling procedure that utilized hypothetical stand characteristics to examine lidar profiles. In essence, this is a simple method to further enhance shape characteristics from the lidar profile. In this paper we report the results comparing field data collected at La Selva, Costa Rica (10° 26′ N, 83° 59′ W) and forest structure and parameters calculated from vegetation height profiles and forest structural modeling. We developed multiple regression models for each measured forest biometric property using forward stepwise variable selection that used Bayesian information criteria (BIC) as selection criteria. Among measures of forest structure, ranging from tree lateral density, diameter at breast height, and crown geometry, we found strong relationships with lidar canopy vegetation profile parameters. Metrics developed from lidar that were indicators of height of canopy were not significant in estimating plot biomass (p-value = 0.31, r2 = 0.17), but parameters from our synthetic forest model were found to be significant for estimating many of the forest structural properties, such as mean trunk diameter (p-value = 0.004, r2 = 0.51) and tree density (p-value = 0.002, r2 = 0.43). We were also able to develop a significant model relating lidar profiles to basal area (p-value = 0.003, r2 = 0.43). Use of the full lidar profile provided additional avenues for the prediction of field based forest measure parameters. Our synthetic canopy model provides a novel method for examining lidar metrics by developing a look-up table of profiles that determine profile shape, depth, and height. We suggest that the use of metrics indicating canopy height derived from lidar are limited in understanding biomass in a forest with little variation across the landscape and that there are many parameters that may be gleaned by lidar data that inform on forest biometric properties

Cuba Sanctions: Legislative Restrictions Limiting the Normalization of Relations

This report provides background information Trade Promotion Authority (TPA), and discusses U.S. trade negotiating objectives, procedures for congressional-executive notification and consultation, and expedited legislative procedures

U.S. Economic Sanctions Through 1996

Since the early 1960s, the United States has imposed a range of economic sanctions on Cuba, the most prominent of which is a comprehensive embargo prohibiting trade with Cuba. This Congressional Research Service report first provides an overview of U.S.-Cuba relations and U.S. policy toward Cuba. It then examines the history and current legislative and executive authorities of the various components of U.S. sanctions against Cuba, including aid, trade, and other restrictions

Late-Time Spectral Observations of the Strongly Interacting Type Ia Supernova PTF11kx

PTF11kx was a Type Ia supernova (SN Ia) that showed time-variable absorption features, including saturated Ca II H&K lines that weakened and eventually went into emission. The strength of the emission component of H{\alpha} increased, implying that the SN was undergoing significant interaction with its circumstellar medium (CSM). These features were blueshifted slightly and showed a P-Cygni profile, likely indicating that the CSM was directly related to, and probably previously ejected by, the progenitor system itself. These and other observations led Dilday et al. (2012) to conclude that PTF11kx came from a symbiotic nova progenitor like RS Oph. In this work we extend the spectral coverage of PTF11kx to 124-680 rest-frame days past maximum brightness. These spectra of PTF11kx are dominated by H{\alpha} emission (with widths of ~2000 km/s), strong Ca II emission features (~10,000 km/s wide), and a blue "quasi-continuum" due to many overlapping narrow lines of Fe II. Emission from oxygen, He I, and Balmer lines higher than H{\alpha} is weak or completely absent at all epochs, leading to large observed H{\alpha}/H{\beta} intensity ratios. The broader (~2000 km/s) H{\alpha} emission appears to increase in strength with time for ~1 yr, but it subsequently decreases significantly along with the Ca II emission. Our latest spectrum also indicates the possibility of newly formed dust in the system as evidenced by a slight decrease in the red wing of H{\alpha}. During the same epochs, multiple narrow emission features from the CSM temporally vary in strength. The weakening of the H{\alpha} and Ca II emission at late times is possible evidence that the SN ejecta have overtaken the majority of the CSM and agrees with models of other strongly interacting SNe Ia. The varying narrow emission features, on the other hand, may indicate that the CSM is clumpy or consists of multiple thin shells.Comment: 12 pages, 7 figures, 1 table, re-submitted to Ap