On the concept of optimality interval

The approximants to regular continued fractions constitute `best approximations' to the numbers they converge to in two ways known as of the first and the second kind.This property of continued fractions provides a solution to Gosper's problem of the batting average: if the batting average of a baseball player is 0.334, what is the minimum number of times he has been at bat? In this paper, we tackle somehow the inverse question: given a rational number P/Q, what is the set of all numbers for which P/Q is a `best approximation' of one or the other kind? We prove that inboth cases these `Optimality Sets' are intervals and we give aprecise description of their endpoints.

One-sided tolerance interval in a two-way balanced nested model with mixed effects

In many research areas (such as public health, environmental contamination, and others) one deals with the necessity of using data to infer whether some proportion (%) of a population of interest is (or one wants it to be) below and/or over some threshold, through the computation of tolerance interval. The idea is, once a threshold is given, one computes the tolerance interval or limit (which might be one or two - sided bounded) and then to check if it satisfies the given threshold. Since in this work we deal with the computation of one - sided tolerance interval, for the two-sided case we recomend, for instance, Krishnamoorthy and Mathew [5]. Krishnamoorthy and Mathew [4] performed the computation of upper tolerance limit in balanced and unbalanced one-way random effects models, whereas Fonseca et al [3] performed it based in a similar ideas but in a tow-way nested mixed or random effects model. In case of random effects model, Fonseca et al [3] performed the computation of such interval only for the balanced data, whereas in the mixed effects case they dit it only for the unbalanced data. For the computation of twosided tolerance interval in models with mixed and/or random effects we recomend, for instance, Sharma and Mathew [7]. The purpose of this paper is the computation of upper and lower tolerance interval in a two-way nested mixed effects models in balanced data. For the case of unbalanced data, as mentioned above, Fonseca et al [3] have already computed upper tolerance interval. Hence, using the notions persented in Fonseca et al [3] and Krishnamoorthy and Mathew [4], we present some results on the construction of one-sided tolerance interval for the balanced case. Thus, in order to do so at first instance we perform the construction for the upper case, and then the construction for the lower case.

Borcherds products and arithmetic intersection theory on Hilbert modular surfaces

We prove an arithmetic version of a theorem of Hirzebruch and Zagier saying that Hirzebruch-Zagier divisors on a Hilbert modular surface are the coefficients of an elliptic modular form of weight 2. Moreover, we determine the arithmetic selfintersection number of the line bundle of modular forms equipped with its Petersson metric on a regular model of a Hilbert modular surface, and we study Faltings heights of arithmetic Hirzebruch-Zagier divisors.

Audit report on the Honey Creek Resort Operations Account maintained by Central Group Management, LLC for the year ended June 30, 2010

Audit report on the Honey Creek Resort Operations Account maintained by Central Group Management, LLC for the year ended June 30, 2010

Assessment of the soil compaction of two ultisols caused by logging operations

The impact of wood loads on bulk density and preconsolidation pressure and of harvester and forwarder traffic on rut depth, bulk density and preconsolidation pressure of two Ultisols were examined in this study. Our objective was to quantify the threshold beyond which significant soil compaction and rutting would occur. This study was carried out in the county of Eunápolis, state of Bahia, Brazil, (16 º 23 ' 17 '' S and 39 º 10 ' 06 '' W; altitude 80 m asl) in two Ultisols (PAd2 and PAd3) with different texture classes, in experimental areas with eucalypt plantation. The study involved measurements at the wood load site and machine driving at specific locations in the forest during logging operations. The treatments consisted of one harvester pass and, 8, 16 and 40 passes of a fully loaded forwarder. Thresholds were established based on the rut depth and percentage of preconsolidation pressure values in the region of additional soil compaction defined in the bearing capacity model. The percentage of soil samples with values of preconsolidation pressure in the region of additional soil compaction indicated a greater susceptibility of PAd3 than of PAd2 to soil compaction. The threshold levels established here based on preconsolidation pressure and rut depth indicated that no more than eight forwarder passes should be allowed in loading operations in order to minimize soil compaction.

Final Report-Freeway Operations Analysis of I-80 to I-29 Interchange, January 1974

A t the request of the Iowa State Highway Commission, the Engineering Research Institute observed the traffic operations at the Interstate 29 (1-29) and Interstate 80 (1-80) interchange in the southwest part of Council Bluffs. The general location of the site is shown in Figure 1. Before limiting the analysis to the diverging area the project staff drove the entire Council Bluffs freeway system and consulted with M r . Philip Hassenstab (Iowa State Highway Commission, District 4, Resident Maintenance Engineer at Council Bluffs). The final study scope was delineated as encompassing only the operational characteristics of the diverge area where 1-29 South and 1-80 East divide and the ramp to merge area where 1-80 West joins 1-29 North (both areas being contained within the aforementioned interchange). Supplementing the traffic operations scope, was an effort to delineate and document the applicability of video-tape techniques to traffic engineering studies and analyses. Documentation was primarily in the form of a demonstration video-tape.

Backhoe loaders as base machines in logging operations

Summary

Audit report on the Honey Creek Resort Operations Account maintained by Central Group Management, LLC for the year ended June 30, 2011

Audit report on the Honey Creek Resort Operations Account maintained by Central Group Management, LLC for the year ended June 30, 2011

Pharmacokinetic variability of extended interval tobramycin in burn patients.

BACKGROUND: Aminoglycosides are mandatory in the treatment of severe infections in burns. However, their pharmacokinetics are difficult to predict in critically ill patients. Our objective was to describe the pharmacokinetic parameters of high doses of tobramycin administered at extended intervals in severely burned patients. METHODS: We prospectively enrolled 23 burned patients receiving tobramycin in combination therapy for Pseudomonas species infections in a burn ICU over 2 years in a therapeutic drug monitoring program. Trough and post peak tobramycin levels were measured to adjust drug dosage. Pharmacokinetic parameters were derived from two points first order kinetics. RESULTS: Tobramycin peak concentration was 7.4 (3.1-19.6)microg/ml and Cmax/MIC ratio 14.8 (2.8-39.2). Half-life was 6.9 (range 1.8-24.6)h with a distribution volume of 0.4 (0.2-1.0)l/kg. Clearance was 35 (14-121)ml/min and was weakly but significantly correlated with creatinine clearance. CONCLUSION: Tobramycin had a normal clearance, but an increased volume of distribution and a prolonged half-life in burned patients. However, the pharmacokinetic parameters of tobramycin are highly variable in burned patients. These data support extended interval administration and strongly suggest that aminoglycosides should only be used within a structured pharmacokinetic monitoring program.

U.S.-Norway Comparison of Interval Breast Cancers

Background: Publications from the International Breast Screening Network (IBSN) have shown that varying definitions create hurdles for comparison of screening performance. Interval breast cancer rates are particularly affected. Objective: to test whether variations in definition of interval cancer rates (ICR) affect comparisons of international ICR, specific to a comparison of ICR in Norway and North Carolina (NC). Methods: An interval cancer (IC) was defined as a cancer diagnosed following a negative screening mammogram in a defined follow-up period. ICR was calculated for women ages 50-69, at subsequent screening in Norway and NC, during the time period 1996 - 2002. ICR was defined using three different denominators (negative screens, negative final assessments and all screens) and three different numerators (DCIS, invasive cancer and all cancers). ICR was then calculated with two methods: 1) number of ICs divided by the number of screens, and ICs divided by the number of women-years at risk for IC. Results: There were no differences in ICR depending on the definition used. In the 1-12 month follow up period ICR (based on number of screens) were: 0.53, 0.54, and 0.54 for Norway; and 1.20, 1.25 and 1.17 for NC, for negative screens, negative final assessment and all screens, respectively: The same trend was seen for 13-24 and 1-24 months follow-up. Using women-years for the analysis did not change the trend. ICR was higher in NC compared to Norway under all definitions and in all follow-up time periods, regardless of calculation method. Conclusion: The ICR within or between Norway and NC did not differ by definition used. ICR were higher in NC than Norway. There are many potential explanations for the difference.