Average pace and horizontal chords

We are motivated by a problem about running: If a race was completed in an average pace of P minutes per mile, is there necessarily some mile of the race that was run in exactly P minutes? The answer is no. We explain why, and describe the history of this celebrated problem, known as the Universal Chord Theorem. We also clarify and streamline the proof of a more powerful result by Heinz Hopf from 1937.Comment: 16 pages including appendix, 6 figure

Water Quality Sampling, Analysis and Annual Load Determinations for TSS, Nitrogen and Phosphorus at the Washington County Road 195 Bridge on the West Fork of the White River

A water quality sampling station was installed at the Washington County road 195 bridge on the West Fork of the White River just above the confluence of the three main forks of the Upper White River in December 2001. The Quality Assurance Project Plan (QAPP) was approved by EPA Region six on March 2002 and sampling was begun at that time. This station is coordinated with a USGS gauging station at the same location. This station was instrumented to collect samples at sufficient intervals across the hydrograph to accurately estimate the flux of total suspended solids, nitrogen and phosphorus into the upper end of Beaver Lake from the West Fork of the White River. The West Fork is listed on Arkansas\u27 1998 303d list as impaired from sediment. The Upper White was designated as the states highest priority watershed in the 1999 Unified Watershed Assessment. Accurate determination of stream nutrients and sediment is critical for future determinations of TMDLs, effectiveness of best management practices and trends in water quality

Predatory Profiling: The Role of Race and Ethnicity in the Location of Payday Lenders in California

In California and elsewhere, African Americans and Latinos make up a disproportionate share of payday loan borrowers. CRL's analysis reveals that the racial and ethnic composition of a neighborhood is the primary predictor of payday lending locations, while playing a very minimal role in explaining the variation in the location of bank branches. As a result, payday lending storefronts are most heavily concentrated in African American and Latino communities. By contrast, the location of mainstream financial service providers such as banks can be largely explained by supply and demand factors such as the presenceof retail space

Remote sensing applications to hydrologic modeling in the southern Sierra Nevada and portions of the San Joaquin Valley, volume 1

The author has identified the following significant results. Characteristics of LANDSAT MSS imagery present problems in using satellite radiation measurements to estimate the shortwave albedo of an alpine snow cover. Every 15 minute USGS quadrangle contains over 100,000 pixels which poses a computation problem if each pixel is to be evaluated individually. The sampling interval may be sufficiently great to mask some effects of terrain and vegetation on reflectance. Three frames of LANDSAT imagery are needed for complete coverage of the study area, yet less than one third of the area coverage from each frame covers an area of interest. Because of distortions inherent in the imagery, information regarding spacecraft altitude, attitude, and position must be statistically derived with respect to ground control points in the image whose geodetic locations are known. An inspection of shade points indicates that up to one third of the most heavily snow covered areas may saturate in bands 4 through 6. LANDSAT's 9 day repeat cycle is not optimum for snow cover reflectance modeling because the most pronounced changes in albedo occur most nearly following a new snowfall. Such a snowfall, occurring between overpasses, is inadequately represented by extrapolation from the previous overpasses

The Extreme Spin of the Black Hole in Cygnus X-1

The compact primary in the X-ray binary Cygnus X-1 was the first black hole to be established via dynamical observations. We have recently determined accurate values for its mass and distance, and for the orbital inclination angle of the binary. Building on these results, which are based on our favored (asynchronous) dynamical model, we have measured the radius of the inner edge of the black hole's accretion disk by fitting its thermal continuum spectrum to a fully relativistic model of a thin accretion disk. Assuming that the spin axis of the black hole is aligned with the orbital angular momentum vector, we have determined that Cygnus X-1 contains a near-extreme Kerr black hole with a spin parameter a/M>0.95 (3\sigma). For a less probable (synchronous) dynamical model, we find a/M>0.92 (3\sigma). In our analysis, we include the uncertainties in black hole mass, orbital inclination angle and distance, and we also include the uncertainty in the calibration of the absolute flux via the Crab. These four sources of uncertainty totally dominate the error budget. The uncertainties introduced by the thin-disk model we employ are particularly small in this case given the extreme spin of the black hole and the disk's low luminosity.Comment: Paper III of three papers on Cygnus X-1; 21 pages including 5 figures and 12 tables, ApJ in press. The paper is significantly restructured; two further tests of the robustness of our spin measurement are presented, and our error analysis has been substantially improved; the conclusions are unchange

Anti-mycobacterial assessment and characterization of 5-O-caffeoylquinic acid methyl ester and rutin from Pavetta crassipes

Pavetta crassipes leaf (Fam. Rubiaceae) is used as part of a combination herbal remedy for the treatment of tuberculosis (TB) and other respiratory infections in Nigerian ethno medicine. However, little scientific data is available to support the use in ethnomedical therapy so the objective of the study was to assess the antitubercular property and to identify the bioactive components. The dried powdered leaf was sequentially extracted with solvents to obtain hexane, dichloromethane, methanol and water extracts. Following which, the extracts were then screened against Mycobacterium aurum, a rapidly growing saprophytic mycobacterium species for activity. The methanol extract exhibited inhibitory activity at an MIC value of 250 µg/mL against M. aurum and two known polyphenolic compounds were isolated as 5-O-caffeoylquinic acid methyl ester and quercetin-3-rutinoside (rutin). Reversed phase semi-preparative HPLC, mass spectrometry and 1H and 13C NMR techniques were utilized in isolating and characterizing the two components. The assignments of the structures were consistent with data from the literature. The study has shown that the methanol extract has some activity and hyphenation of LC-MS can be used for the isolation of polyphenols from the methanol fraction without a rigorous purification process

Ares I-X Flight Test--The Future Begins Here

In less than two years, the National Aeronautics and Space Administration (NASA) will launch the Ares I-X mission. This will be the first flight of the Ares I crew launch vehicle, which, together with the Ares V cargo launch vehicle, will eventually send humans to the Moon, Mars, and beyond. As the countdown to this first Ares mission continues, personnel from across the Ares I-X Mission Management Office (MMO) are finalizing designs and fabricating vehicle hardware for a 2009 launch. This paper will discuss the hardware and programmatic progress of the Ares I-X mission

Association between daily antiretroviral pill burden and treatment adherence, hospitalisation risk, and other healthcare utilisation and costs in a US medicaid population with HIV

Objectives: Lower pill burden leads to improved antiretroviral therapy (ART) adherence among HIV patients. Simpler dosing regimens have not been widely explored in real-world populations. We retrospectively assessed ART adherence, all-cause hospitalisation risk and costs, and other healthcare utilisation and costs in Medicaid enrollees with HIV treated with ART as a once-daily single-tablet regimen (STR) or two or more pills per day (2+PPD). Design: Patients with an HIV diagnosis from 2005 to 2009 receiving complete ART (ie, two nucleoside/nucleotide reverse transcriptase inhibitors plus a third agent) for ≥60 days as STR or 2+PPD were selected and followed until the first of (1) discontinuation of the complete ART, (2) loss of enrolment or (3) end of database. Adherence was measured using the medication possession ratio. Monthly all-cause healthcare utilisation and costs were observed from regimen initiation until follow-up end. Results: Of the 7381 patients who met inclusion criteria, 1797 were treated with STR and 5584 with 2+PPD. STR patients were significantly more likely to reach 95% adherence and had fewer hospitalisations than 2+PPD patients (both p<0.01). STR patients had mean (SD) total monthly costs of $2959 ($4962); 2+PPD patients had $3544 ($5811; p<0.001). Hospital costs accounted for 53.8% and pharmacy costs accounted for 32.5% of this difference. Multivariate analyses found that STR led to a 23% reduction in hospitalisations and a 17% reduction in overall healthcare costs. ART adherence appears to be a key mechanism mediating hospitalisation risk, as patients with ≥95% adherence (regardless of regimen type) had a lower hospitalisation rate compared with <95% adherence. Conclusions: While it was expected that STR patients would have lower pharmacy costs, we also found that STR patients had fewer hospitalisations and lower hospital costs than 2+PPD patients, resulting in significantly lower total healthcare costs for STR patients

Observed Binary Fraction Sets Limits on the Extent of Collisional Grinding in the Kuiper Belt

The size distribution in the cold classical Kuiper belt can be approximated by two idealized power laws: one with steep slope for radii R>R* and one with shallow slope for R<R*, where R*~25-50 km. Previous works suggested that the SFD roll-over at R* can be the result of extensive collisional grinding in the Kuiper belt that led to the catastrophic disruption of most bodies with R<R*. Here we use a new code to test the effect of collisions in the Kuiper belt. We find that the observed roll-over could indeed be explained by collisional grinding provided that the initial mass in large bodies was much larger than the one in the present Kuiper belt, and was dynamically depleted. In addition to the size distribution changes, our code also tracks the effects of collisions on binary systems. We find that it is generally easier to dissolve wide binary systems, such as the ones existing in the cold Kuiper belt today, than to catastrophically disrupt objects with R~R*. Thus, the binary survival sets important limits on the extent of collisional grinding in the Kuiper belt. We find that the extensive collisional grinding required to produce the SFD roll-over at R* would imply a strong gradient of the binary fraction with R and separation, because it is generally easier to dissolve binaries with small components and/or those with wide orbits. The expected binary fraction for R<R* is <0.1. The present observational data do not show such a gradient. Instead, they suggest a large binary fraction of ~0.4 for R=30-40 km. This may indicate that the roll-over was not produced by disruptive collisions, but is instead a fossil remnant of the KBO formation process.Comment: The Astronomical Journal, in pres