Smooth Approximation of Lipschitz functions on Riemannian manifolds

We show that for every Lipschitz function $f$ defined on a separable Riemannian manifold $M$ (possibly of infinite dimension), for every continuous $\epsilon:M\to (0,+\infty)$, and for every positive number $r>0$, there exists a $C^\infty$ smooth Lipschitz function $g:M\to\mathbb{R}$ such that $|f(p)-g(p)|\leq\epsilon(p)$ for every $p\in M$ and $\textrm{Lip}(g)\leq\textrm{Lip}(f)+r$. Consequently, every separable Riemannian manifold is uniformly bumpable. We also present some applications of this result, such as a general version for separable Riemannian manifolds of Deville-Godefroy-Zizler's smooth variational principle.Comment: 10 page

High Resolution Near-Infrared Spectra of Protostars

We present new high resolution (R = 21,000) near-infrared (2 microns) spectroscopic observations of a sample of Class I and flat-spectrum protostellar objects in the rho Ophiuchi dark cloud. None of the five Class I spectra show CO v = 0 -- 2 absorption features, consistent with high K-band continuum veilings, 4 <= r_k <= 20 and fast stellar rotation, assuming that the underlying protostellar photospheres are of late spectral type, as is suggested by the low luminosities of most of these objects. Two of the flat-spectrum protostellar objects also show no absorption features and are likely to be highly veiled. The remaining two flat-spectrum sources show weak, broad absorptions which are consistent with an origin in quickly rotating (v sin i ~ 50 km / s) late-type stellar photospheres which are also strongly veiled, r_k = 3 - 4. These observations provide further evidence that: 1)-Class I sources are highly veiled at near-infrared wavelengths, confirming previous findings of lower resolution spectroscopic studies; and 2)- flat-spectrum protostars rotate more rapidly than classical T Tauri stars (Class II sources), supporting findings from a recent high resolution spectroscopic study of other flat-spectrum sources in this cloud. In addition our observations are consistent with the high rotation rates derived for two of the Class I protostellar objects in our sample from observations of variable hard X-ray emission obtained with the ASCA satellite. These observations suggest that certain Class I sources can rotate even more rapidly than flat-spectrum protostars, near breakup velocity.Comment: 16 pages including 2 tables and 2 figures (AASTeX 5.x) to be published in The Astronomical Journal July 200

The Concordiensis, Volume 1, Number 1

Literary: A Revery; Marshal Ney; Prof. Issac W. Jackson; English Literature in College Education; Prof. Taylor Lewis; Honor; To my Niece; Editorial: Salutatory; Military Drill; New Rule for Seniors; Football; Downtown Disturbances; To Our Alumni; Duty of the Seniors; Fall Athletics; Class Elections, Personals; Paragraphshttps://digitalworks.union.edu/concordiensis_1877/1000/thumbnail.jp

The Concordiensis, Volume 1, Number 2

Literary: Midnight; Public Opinion as the Theory of Practice; Teaching as a Profession; The Triumph of Ideas; The Scientific Course Editorial: Literary Societies; Reorganization of the Theological Society; Damage to College Property; Sabbath Service in Chapel; Protest against removal of cows from College pasture; Protest against singing College Songs at night, etc.; Gillespie Club; Resignation of Dr. Lowell; Receptions of President and Mrs. Potter; Scientific Association; Freaks of Students, Locals; Personals; Paragraphshttps://digitalworks.union.edu/concordiensis_1877/1001/thumbnail.jp

Ultrafast dynamics in the presence of antiferromagnetic correlations in electron-doped cuprate La2−x_{2-x}Cex_xCuO4±δ_{4\pm\delta}

We used femtosecond optical pump-probe spectroscopy to study the photoinduced change in reflectivity of thin films of the electron-doped cuprate La$_{2-x}$Ce$_x$CuO$_4$ (LCCO) with dopings of x$=$0.08 (underdoped) and x$=$0.11 (optimally doped). Above T$_c$, we observe fluence-dependent relaxation rates which onset at a similar temperature that transport measurements first see signatures of antiferromagnetic correlations. Upon suppressing superconductivity with a magnetic field, it is found that the fluence and temperature dependence of relaxation rates is consistent with bimolecular recombination of electrons and holes across a gap (2$\Delta_{AF}$) originating from antiferromagnetic correlations which comprise the pseudogap in electron-doped cuprates. This can be used to learn about coupling between electrons and high-energy ($\omega>2\Delta_{AF}$) excitations in these compounds and set limits on the timescales on which antiferromagnetic correlations are static

Andreev Reflection in Heavy-Fermion Superconductors and Order Parameter Symmetry in CeCoIn_5

Differential conductance spectra are obtained from nanoscale junctions on the heavy-fermion superconductor CeCoIn$_5$ along three major crystallographic orientations. Consistency and reproducibility of characteristic features among the junctions ensure their spectroscopic nature. All junctions show a similar conductance asymmetry and Andreev reflection-like conductance with reduced signal (~ 10%-13%), both commonly observed in heavy-fermion superconductor junctions. Analysis using the extended Blonder-Tinkham-Klapwijk model indicates that our data provide the first spectroscopic evidence for $d_{x^2-y^2}$ symmetry. To quantify our conductance spectra, we propose a model by considering the general phenomenology in heavy fermions, the two-fluid behavior, and an energy-dependent density of states. Our model fits to the experimental data remarkably well and should invigorate further investigations.Comment: 4 pages, 4 figures; Phys. Rev. Lett., published versio

Spectroscopic Detection of a Stellar-like Photosphere in an Accreting Protostar

We present the first spectrum of a highly veiled, strongly accreting protostar which shows photospheric absorption features and demonstrates the stellar nature of its central core. We find the spectrum of the luminous (L_bol = 10 L_sun) protostellar source, YLW 15, to be stellar-like with numerous atomic and molecular absorption features, indicative of a K5 IV/V spectral type and a continuum veiling r_k = 3.0. Its derived stellar luminosity (3 L_sun) and stellar radius (3.1 R_sun) are consistent with those of a 0.5 M_sun pre-main-sequence star. However, 70% of its bolometric luminosity is due to mass accretion, whose rate we estimate to be 1.6 E-6 M_sun / yr onto the protostellar core. We determine that excess infrared emission produced by the circumstellar accretion disk, the inner infalling envelope, and accretion shocks at the surface of the stellar core of YLW 15 all contribute signifi- cantly to its near-IR continuum veiling. Its projected rotation velocity v sin i = 50 km / s is comparable to those of flat-spectrum protostars but considerably higher than those of classical T Tauri stars in the rho Oph cloud. The protostar may be magnetically coupled to its circumstellar disk at a radius of 2 R_*. It is also plausible that this protostar can shed over half its angular momentum and evolve into a more slowly rotating classical T Tauri star by remaining coupled to its circumstellar disk (at increasing radius) as its accretion rate drops by an order of magnitude during the rapid transition between the Class I and Class II phases of evolution. The spectrum of WL 6 does not show any photospheric absorption features, and we estimate that its continuum veiling is r_k >= 4.6. Together with its low bolometric luminosity (2 L_sun), this dictates that its central core is very low mass, ~0.1 M_sun.Comment: 14 pages including 9 figures (3 figures of 3 panels each, all as separate files). AASTeX LaTex macros version 5.0. To be published in The Astronomical Journal (tentatively Oct 2002

Productivity and the Determinants of Efficiency in Irish Agriculture (1996-2006)

The competitiveness and productivity of Irish agriculture has been at the forefront of debate in recent times given successive and impending changes to agricultural policy. This paper examines the trend in total factor productivity in Irish agriculture over the recent past and explores the effects of specific variables on relative efficiency levels. The findings of this research have shown that productivity growth was highest in the Cattle Rearing sector followed by the Dairy, Cattle Finishing, Sheep and Cereals sectors during the period 1996 to 2006. The research has also shown that efficiency levels are, in general, positively correlated with extension use soil quality, the overall size of the farm, the level of intensification and the level of specialisation. The use of artificial insemination was also positively correlated with efficiency in the Dairy sectorProduction Economics,

Aeroheating Measurements of BOLT Aerodynamic Fairings and Transition Module

The Air Force Office of Scientific Research (AFOSR) has sponsored the Boundary Layer Transition (BOLT) Experiments to investigate hypersonic boundary layer transition on a low-curvature, concave surface with swept leading edges. This paper presents aeroheating measurements on a subscale model of the BOLT Flight Geometry, aerodynamic fairings, and Transition Module (TSM) in the NASA Langley 20-Inch Mach 6 Air Tunnel. The purpose of the test was to investigate and identify any areas of localized heating on the TSM for inclusion in the BOLT Critical Design Review (CDR). Surface heating distributions were measured using global phosphor thermography, and data were obtained for a range of model attitudes and free stream Reynolds numbers. Measurements showed low heating on the fairings and TSM. Additional analysis was completed after the CDR to compare heating on the TSM for the nominal BOLT vehicle reentry angle-of-attack with heating on the TSM for possible reentry angle-of-attack excursions. The results of this analysis were used in conjunction with thermal analyses from Johns Hopkins Applied Physics Lab (JHU/APL) and the Air Force Research Laboratory (AFRL) to assess the need for thermal protection on the flight vehicle TSM

Fields of definition of finite hypergeometric functions

Finite hypergeometric functions are functions of a finite field ${\bf F}_q$ to ${\bf C}$. They arise as Fourier expansions of certain twisted exponential sums and were introduced independently by John Greene and Nick Katz in the 1980's. They have many properties in common with their analytic counterparts, the hypergeometric functions. One restriction in the definition of finite hypergeometric functions is that the hypergeometric parameters must be rational numbers whose denominators divide $q-1$. In this note we use the symmetry in the hypergeometric parameters and an extension of the exponential sums to circumvent this problem as much as posssible.Comment: 8 page