Grid approximation of a singularly perturbed boundary value problem modelling heat transfer in the case of flow over a flat plate with suction of the boundary layer

AbstractIn the present paper we consider a boundary value problem on the semiaxis (0,∞) for a singularly perturbed parabolic equation with the two perturbation parameters ε1 and ε2 multiplying, respectively, the second and first derivatives with respect to the space variable. Depending on the relation between the parameters, the differential equation can be either of reaction–diffusion type or of convection–diffusion type. Correspondingly, the boundary layer can be either parabolic or regular. For this problem we consider the case when the boundary layer can be controlled by continuous suction of the fluid out of the boundary layer (model problems of this type appear in the mathematical modelling of heat transfer processes for flow past a flat plate). Errors in the approximations generated by standard numerical methods can be unsatisfactorily large for small values of the parameter ε1. We construct a monotone finite difference scheme on piecewise uniform meshes which generates numerical solutions converging ε-uniformly with order O(N−1lnN+N0−1), where N0 is the number of nodes in the time mesh and N is the number of meshpoints on a unit interval of the semiaxis in x. Although the solution of problem has a singularity only for ε1→0, the character of the boundary layer depends essentially on the vector-valued parameter ε=(ε1,ε2). This prevents us from constructing an ε-uniformly convergent scheme having a transition parameter which is independent of the parameter ε2

Ages of the Whitewater and Fairhaven tills in southwestern Ohio and southeastern Indiana

Alloisoleucine/isoleucine (aIle/Ile) ratios obtained from fossil mollusc shells collected at localities in southwestern Ohio and southeastern Indiana, where they occur in silt beds associated with the Whitewater and Fairhaven tills, indicate a pre-Wisconsinan age for these tills, which had previously been thought to be early or middle Wisconsinan. The aIle/Ile ratios in shells from beneath the buried soil (Sidney soil) and till exposed near Sidney, Ohio, are most similar to values in shells obtained from Illinoian sediments at Clough Creek in Hamilton County, Ohio; Mechanicsburg southwest, Illinois; and Trousdale Mine in Vermillion Co., Indiana. The first well-developed weathering profile in the sequence above the implied Illinoian age silt at the Sidney cut, therefore, probably represents Sangamonian, early and middle Wisconsinan weathering. Molluscs from an organic silt, exposed near the base of the Bantas Fork cutbank section, also have aIle/Ile ratios that are similar to those measured in shell recovered from the silt at the Sidney cut and from the silt inclusion in inferred Illinoian till at Clough Creek. These data indicate that the organic silt is pre-Wisconsinan. Therefore, the Fairhaven Till, which overlies the silt at the Bantas Fork locality, could be pre-Wisconsinan and the weathering profile developed in the Fairhaven Till may be correlative with the Sangamon Soil of Illinois. The New Paris Interstade silt overlies Whitewater Till at the American Aggregates quarry at Richmond, Indiana. Shells from the silt have aIle/Ile ratios that are intermediate between those obtained from inferred Illinoian age sediments at Bantas Fork, Sidney cut, and Clough Creek, and magnetically reversed sediments at Handley Farm, near Connersville, Fayette County, Indiana. These data suggest a pre-Illinoian age for the silt unit and the underlying Whitewater Till

The Origin of Late Pleistocene Deposits at Garfield Heights, Cuyahoga County, Ohio

Author Institution: Department of Geology, Kent State University, Kent, Ohio 44240Illinoian sand and gravel, Sangamonian paleosol, Altonian and Farmdalian loesses, and Woodfordian sediments (laminated sand, silt, clay, and till) occur in superposition at the George Rackle and Sons Gravel Pit, situated in the valley of Mill Creek, Garfield Heights, Ohio. A molluscan fauna consisting of 17 species of terrestrial snails was identified from three studied sections of the Farmdalian loess. Ten species, Deroceras laeve, Discus cronkhitei, Gastrocopta armifera, Helicodiscus parallelus, Nesovitrea electrina, Punctum minutissimum, Strobilops sp., Triodopsis algonquinensis, Vertigo elatior, and V. gouldi hannai, are new to the Farmdalian loess of this area. Ten of the loess species do not occur at all of the sampled sections. These variations in the composition of the molluscan fauna, together with a consideration of the color and the structure of the Farmdalian loess examined at four sections within this pit, suggest that the deposition may have been interrupted by erosion, or a period of non-deposition, or both, and that it is probably steeply time-transgressive. Colluviation toward the end of the Farmdalian Substage is suggested by a contorted two- to six-inch zone containing broken, angular clasts of clay, pebbles, sand, and terrestrial snails, all contained in a silt (loess) matrix, that occurs locally near the top of the Farmdalian loess. The lower 6 feet of the overlying Woodfordian laminated sequence consists of intercalated layers of sand, silt, and clay, with scattered rock, shell, and plant fragments. This unit contained 12 species of terrestrial snails, all of which also occur in the Farmdalian loess. The terrestrial nature of the fauna, the similarity of the Woodfordian and Farmdalian snail assemblages, the total absence of pollen or of any aquatic organisms, and the presence of scattered clay-blebs, sand-sized quartz grains, and pebbles all suggest that the lower part of the Woodfordian sediments may have been derived locally from older units (Farmdalian loess, Sangamonian paleosol, and Illinoian sand and gravel). These materials were probably transported by some mass-wasting process and redeposited subaerially in topographic lows as slopewash, or as colluvium, or both. Layered modern sediments now accumulating in small, shallow depressions on the floors of abandoned borrow-pits in the area appear to simulate on a small scale the features observed in the basal Woodfordian sediments

The 'Parekh Report' - national identities with nations and nationalism

‘Multiculturalists’ often advocate national identities. Yet few study the ways in which ‘multiculturalists’ do so and in this article I will help to fill this gap. I will show that the Commission for Multi-Ethnic Britain’s report reflects a previously unnoticed way of thinking about the nature and worth of national identities that the Commission’s chair, and prominent political theorist, Bhikhu Parekh, had been developing since the 1970s. This way of thinking will be shown to avoid the questionable ways in which conservative and liberal nationalists discuss the nature and worth of national identities while offering an alternative way to do so. I will thus show that a report that was once criticised for the way it discussed national identities reflects how ‘multiculturalists’ think about national identities in a distinct and valuable way that has gone unrecognised

Bimodal release ondansetron for acute gastroenteritis among adolescents and adults: A randomized clinical trial

Importance: Vomiting resulting from acute gastroenteritis is commonly treated with intravenous antiemetics in acute care settings. If oral treatment were beneficial, patients might not need intravenous administered hydration or medication. Furthermore, a long-acting treatment could provide sustained relief from nausea and vomiting. Objective: To determine whether an experimental long-acting bimodal release ondansetron tablet decreases gastroenteritis-related vomiting and eliminates the need for intravenous therapy for 24 hours after administration. Design, Setting, and Participants: This placebo-controlled, double-blind, randomized clinical trial included patients from 19 emergency departments and 2 urgent care centers in the United States from December 8, 2014, to February 17, 2017. Patients 12 years and older with at least 2 vomiting episodes from presumed gastroenteritis in the previous 4 hours and symptoms with less than 36 hours\u27 duration were randomized using a 3:2 active to placebo ratio. Analyses were performed on an intent-to-treat basis and conducted from June 1, 2017, to November 1, 2017. Intervention: Bimodal release ondansetron tablet containing 6 mg of immediate release ondansetron and 18 mg of a 24-hour release matrix for a total of 24 mg of ondansetron. Main Outcomes and Measures: Treatment success was defined as no further vomiting, no need for rescue medication, and no intravenous hydration for 24 hours after bimodal release ondansetron administration. Results: Analysis included 321 patients (mean [SD] age, 29.0 [11.1] years; 195 [60.7%] women), with 192 patients in the bimodal release ondansetron group and 129 patients in the placebo group. Treatment successes were observed in 126 patients in the bimodal release ondansetron group (65.6%) compared with 70 patients in the placebo group (54.3%), with an 11.4% (95% CI, 0.3%-22.4%) absolute probability difference. The proportion of treatment success was 21% higher among patients who received bimodal release ondansetron compared with those who received a placebo (relative risk, 1.21; 95% CI, 1.00-1.46; P = .04). In an analysis including only patients with a discharge diagnosis of acute gastroenteritis and no major protocol violations, there were 123 treatment successes (69.5%) in the bimodal release ondansetron group compared with 67 treatment successes (54.9%) in the placebo group (relative risk, 1.27; 95% CI, 1.05-1.53; P = .01). Adverse effects were infrequent and similar to the known safety profile of ondansetron. Conclusions and Relevance: This randomized clinical trial found that a long-acting bimodal release oral ondansetron tablet was an effective antiemetic among adolescents and adults with moderate to severe vomiting from acute gastroenteritis. The drug benefits extended to 24 hours after administration. Bimodal release ondansetron may decrease the need for intravenous access and emergency department care to manage acute gastroenteritis. Trial Registration: ClinicalTrials.gov identifier: NCT02246439

Anharmonic effects in the A15 compounds induced by sublattice distortions

We demonstrate that elastic anomalies and lattice instabilities in the the A15 compounds are describable in terms of first-principles LDA electronic structure calculations. We show that at T=0 V_3Si, V_3Ge, and Nb_3Sn are intrinsically unstable against shears with elastic moduli C_11-C_12 and C_44, and that the zone center phonons, Gamma_2 and Gamma_12, are either unstable or extremely soft. We demonstrate that sublattice relaxation (internal strain) effects are key to understanding the behavior of the A15 materials.Comment: 5 pages, RevTex, 3 postscript figures, Submitted to Phys. Rev. Lett. Apr. 23, 1997 July 7, 1997: minor corrections, final accepted versio

Rural/Nonrural Differences in Colorectal Cancer Incidence in the United States, 1998--2001

BACKGROUND. Few studies of colorectal cancer incidence by rural, suburban, and metropolitan residence have been published. METHODS. The authors examined colorectal cancer incidence among men and women in U.S. counties classified as rural, suburban, and metropolitan for the period 1998–2001. They examined rural/suburban/metropolitan differences in incidence by age, race, Hispanic ethnicity, stage at diagnosis, histology, and percentage of the total county population below the poverty level, using data from the CDC’s National Program of Cancer Registries, the NCI’s Surveillance, Epidemiology, and End Results Program, and the 2000 U.S. Census. RESULTS. A total of 495,770 newly diagnosed or incident cases of colorectal cancer were included in this analysis (249,919 among men and 245,851 among women). Over the period 1998–2001, the colorectal cancer incidence rates among men tended to be lower among those who resided in rural areas, for each of the subgroups examined, with the exception of Asians and Pacific Islanders and those living in more affluent counties. Among women aged 75 years and older, the colorectal cancer incidence rates tended to be lower among rural than metropolitan or suburban residents, though the differences were slight. In multivariate analysis, the incidence of colorectal cancer was higher in metropolitan, suburban, and rural areas for blacks than that for whites (incidence rate ratios [RR] = 1.12, 1.07, and 1.06, respectively, all P \u3c 0.015). CONCLUSIONS. This study suggests that black men who reside in metropolitan areas have a higher risk of colorectal cancer than black men who reside in rural areas. This finding suggests the need for diverse approaches for reducing colorectal cancer when targeting rural compared with metropolitan areas

The Carnegie Supernova Project: Analysis of the First Sample of Low-Redshift Type-Ia Supernovae

We present the analysis of the first set of low-redshift Type Ia supernovae (SNe Ia) by the Carnegie Supernova Project. Well-sampled, high-precision optical (ugriBV) and near-infrared (NIR; YJHKs) light curves obtained in a well-understood photometric system are used to provide light-curve parameters, and ugriBVYJH template light curves. The intrinsic colors at maximum light are calibrated to compute optical--NIR color excesses for the full sample, thus allowing the properties of the reddening law in the host galaxies to be studied. A low value of Rv~1.7, is derived when using the entire sample of SNe. However, when the two highly reddened SNe in the sample are excluded, a value Galactic standard of Rv~3.2 is obtained. The colors of these two events are well matched by a reddening model due to circumstellar dust. The peak luminosities are calibrated using a two-parameter linear fit to the decline rates and the colors, or alternatively, the color excesses. In both cases, dispersions in absolute magnitude of 0.12--0.16 mag are obtained, depending on the filter-color combination. In contrast to the results obtained from color excesses, these fits give Rv~1--2, even when the two highly reddened SNe are excluded. This discrepancy suggests that, beyond the "normal" interstellar reddening produced in the host galaxies, there is an intrinsic dispersion in the colors of SNe Ia which is correlated with luminosity but independent of the decline rate. Finally, a Hubble diagram is produced by combining the results of the fits for each filter. The resulting scatter of 0.12 mag appears to be limited by peculiar velocities as evidenced by the strong correlation between the distance-modulus residuals among the different filters. The implication is that the actual precision of SN Ia distances is 3--4%.Comment: 76 pages, 20 figures, accepted for publication in A