On the accuracy of surface spline interpolation on the unit sphere

This paper considers a novel modification to the surface splines that have previously been used on the unit sphere. The surface splines considered are a natural analogue of surface splines in IRd and possess a unique Fourier expansion in terms of an orthonormal basis of spherical harmonics. Knowing the decay of the associated Fourier coefficients is important because they enable error estimates for spherical interpolation. In this paper we explicitly compute the Fourier coefficients of the surface splines and employ a recent theoretical result [8] to provide a useful error bound. We illuminate our theoretical findings by performing numerical experiments on the sphere and also on the hemisphere

A Duchon framework for the sphere

In his fundamental paper (RAIRO Anal. Numer. 12 (1978) 325) Duchon presented a strategy for analysing the accuracy of surface spline interpolants to sufficiently smooth target functions. In the mid-1990s Duchon's strategy was revisited by Light and Wayne (J. Approx. Theory 92 (1992) 245) and Wendland (in: A. Le Méhauté, C. Rabut, L.L. Schumaker (Eds.), Surface Fitting and Multiresolution Methods, Vanderbilt Univ. Press, Nashville, 1997, pp. 337–344), who successfully used it to provide useful error estimates for radial basis function interpolation in Euclidean space. A relatively new and closely related area of interest is to investigate how well radial basis functions interpolate data which are restricted to the surface of a unit sphere. In this paper we present a modified version Duchon's strategy for the sphere; this is used in our follow up paper (Lp-error estimates for radial basis function interpolation on the sphere, preprint, 2002) to provide new Lp error estimates (p[1,∞]) for radial basis function interpolation on the sphere

L_(p)-error estimates for radial basis function interpolation on the sphere

In this paper we review the variational approach to radial basis function interpolation on the sphere and establish new Lp-error bounds, for p[1,∞]. These bounds are given in terms of a measure of the density of the interpolation points, the dimension of the sphere and the smoothness of the underlying basis function

Polyharmonic approximation on the sphere

The purpose of this article is to provide new error estimates for a popular type of SBF approximation on the sphere: approximating by linear combinations of Green's functions of polyharmonic differential operators. We show that the $L_p$ approximation order for this kind of approximation is $\sigma$ for functions having $L_p$ smoothness $\sigma$ (for $\sigma$ up to the order of the underlying differential operator, just as in univariate spline theory). This is an improvement over previous error estimates, which penalized the approximation order when measuring error in $L_p$, p>2 and held only in a restrictive setting when measuring error in $L_p$, p<2.Comment: 16 pages; revised version; to appear in Constr. Appro

Differences in Efficacy Between Gamithromycin, Tilmicosin, and Tulathromycin as Metaphylactic Treatments in High Risk Calves for Bovine Respiratory Disease

The cost of Bovine Respiratory Disease to the beef industry due to death, poorer conversions, and therapy is estimated to cost more than $3 billion per year. Identifying and mitigating Bovine Respiratory Disease in cattle can be difficult due to the increased susceptibility for Bovine Respiratory Disease in high risk cattle. One management option to minimize an outbreak of respiratory disease is the use of metaphylaxis, the mass treatment of a group of calves to reduce the incidence and adverse effects of respiratory disease on high risk animals. Criteria used to determine the necessity of metaphylactic treatment against Bovine Respiratory Disease in feedlots can be based on several factors depending on feedlot preference; however, the primary criteria often considered are: a known history of no previous vaccinations, overall appearance of cattle, source of cattle, Bovine Respiratory Disease in calves received from same source previously, long shipping distance, season of the year, and light arrival weight. The objective of this study was to compare the efficacy of treating newly received, highrisk feedlot calves with gamithromycin, tulathromycin, and tilmicosin as metaphylactic treatments on health and performance characteristics

Flake Density, Roll Diameter, and Flake Moisture All Influence Starch Availability of Steam-Flaked Corn

Steam-flaked corn is commonly fed in feedlot finishing diets because steam-flaking improves starch availability and nutrient utilization, thus improving the overall feeding value of corn. In most operations which utilize steam-flaked corn, grain is processed to a pre-determined flake density by setting the rolls to a specific separation distance and using tension to hold rolls together. Flaked grain is most often produced to a bulk density between 24 and 32 lb/bu, with a common recommendation of 27 lb/bu for corn; however, flake density among steam-flakers within a single mill and among feedlots can vary greatly. Flaking to a similar density using 2 flakers does not ensure similar starch availability. The degree of starch gelatinization or starch availability of steam-flaked corn can be estimated using analytical procedures such as enzymatic hydrolysis, gas production, and steam-flaked corn gelatinization methods. Routinely evaluating starch availability is used as a quality control method to standardize the steam-flaking process to ensure within-day and day-to-day manufacturing consistency. The concentration of readily available starch in steam-flaked corn is indicative of the rate of starch fermentation in the rumen. When starch is too readily available and is fermented at an excessively rapid rate, acid can accumulate in the rumen, reducing ruminal pH, and ultimately resulting in increased prevalence of digestive disturbances. Factors that contribute to variation between feedlot operations with respect to steamflaked corn quality include type and dimensions of flaking equipment, grain type, grain variety and moisture content, roll wear, and steam-flaking procedures. Sampling and handling procedures contribute to precision of results; therefore, sampling procedures need special attention, and consistency must be evaluated when attempting to determine starch availability of steam-flaked corn. The objective of this study was to evaluate starch availability of steam-flaked corn comparing roll dimensions and steam-flaked corn flake densities among flaking systems and feedyards and to provide information on the equipment utilized, steam-flaked corn flaking procedures, and to define current manufacturing practices of steam-flaking in commercial feedlot operations

On the Dynamics of the Deployment of Renewable Energy Production Capacities

This chapter falls within the context of modeling the deployment of renewable en-ergy production capacities in the scope of the energy transition. This problem is addressed from an energy point of view, i.e. the deployment of technologies is seen as an energy investment under the constraint that an initial budget of non-renewable energy is provided. Using the Energy Return on Energy Investment (ERoEI) characteristics of technologies, we propose MODERN, a discrete-time formalization of the deployment of renewable energy production capacities. Be-sides showing the influence of the ERoEI parameter, the model also underlines the potential benefits of designing control strategies for optimizing the deployment of production capacities, and the necessity to increase energy efficiency.Peer reviewe

Evaluation of the transmitted exposure through lead equivalent aprons used in a radiology department, including the contribution from backscatter

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135071/1/mp3207.pd