Independence and Alpern Multitowers

Let $T$ be any invertible, ergodic, aperiodic measure-preserving transformation of a Lebesgue probability space (X, \calB, \mu), and \P\, any finite measurable partition of $X$. We show that a (finite) Alpern multitower may always be constructed whose base is independent of \P

The Effectiveness of Blended Instruction in Core Postsecondary Mathematics Courses

Most students in U.S. universities are required to take a collection of core courses regardless of their degree or major. These courses are known as general education courses. The general education requirements typically include at least one mathematics course. Unfortunately each year hundreds of thousands of students in the US do not succeed in these general education mathematics courses causing them to act as a barrier to degree completion. Low student success rates in these courses are pervasive, and it is well documented that the U.S. needs to improve student success and retention in general education mathematics courses. In this paper, we compare the impact of a new instructional style on student retention and success in three general education mathematics courses. The new instructional style, that we have dubbed the Memphis Mathematics Method (MMM), is a blended learning instructional model, developed in conjunction with the National Center for Academic Transformation (NCAT). Our control consists of conventional lectures using identical syllabuses. The data contains 12,261 enrollments in College Algebra, Foundations of Mathematics, anq Elementary Calculus over the Fall 2007 to Spring 2010 terms at the University of Memphis. Our results show the MMM was positive and significant for raising success rates particularly in Elementary Calculus. In addition, the results show the MMM as a potential vehicle for closing the achievement gap between black and white students in such courses

Increasing Retention in STEM: Results from a STEM Talent Expansion Program at the University of Memphis

MemphiSTEP is a five-year STEM Talent Expansion Program at the University of Memphis sponsored by the National Science Foundation. The project focuses on retention and persistence to graduation to increase the number of STEM majors and graduates. The project includes a range of student retention programs, including a Summer Mathematics Bridge Bootcamp, Networking Program, Research Award Program, Travel Award program and STEM Learning Communities; Results from the first four years of the project suggest that MemphiSTEP is making a positive impact on student retention and performance in STEM fields. Our data indicate that even after controlling for gender, race, and prior performance, STEM students taking part in MemphiSTEP activities are retained at higher rates and perform better than University of Memphis STEM students who have not participated in MemphiSTEP activities

Gender in the time of COVID-19: Evaluating national leadership and COVID-19 fatalities

In this paper we explore whether countries led by women have fared better during the COVID-19 pandemic than those led by men. Media and public health officials have lauded the perceived gender-related influence on policies and strategies for reducing the deleterious effects of the pandemic. We examine this proposition by analyzing COVID-19-related deaths globally across countries led by men and women. While we find some limited support for lower reported fatality rates in countries led by women, they are not statistically significant. Country cultural values offer more substantive explanation for COVID-19 outcomes. We offer several potential explanations for the pervasive perception that countries led by women have fared better during the pandemic, including data selection bias and Western media bias that amplified the successes of women leaders in OECD countries

Reducing the environmental impact of surgery on a global scale: systematic review and co-prioritization with healthcare workers in 132 countries

Abstract Background Healthcare cannot achieve net-zero carbon without addressing operating theatres. The aim of this study was to prioritize feasible interventions to reduce the environmental impact of operating theatres. Methods This study adopted a four-phase Delphi consensus co-prioritization methodology. In phase 1, a systematic review of published interventions and global consultation of perioperative healthcare professionals were used to longlist interventions. In phase 2, iterative thematic analysis consolidated comparable interventions into a shortlist. In phase 3, the shortlist was co-prioritized based on patient and clinician views on acceptability, feasibility, and safety. In phase 4, ranked lists of interventions were presented by their relevance to high-income countries and low–middle-income countries. Results In phase 1, 43 interventions were identified, which had low uptake in practice according to 3042 professionals globally. In phase 2, a shortlist of 15 intervention domains was generated. In phase 3, interventions were deemed acceptable for more than 90 per cent of patients except for reducing general anaesthesia (84 per cent) and re-sterilization of ‘single-use’ consumables (86 per cent). In phase 4, the top three shortlisted interventions for high-income countries were: introducing recycling; reducing use of anaesthetic gases; and appropriate clinical waste processing. In phase 4, the top three shortlisted interventions for low–middle-income countries were: introducing reusable surgical devices; reducing use of consumables; and reducing the use of general anaesthesia. Conclusion This is a step toward environmentally sustainable operating environments with actionable interventions applicable to both high– and low–middle–income countries

A contraction mapping proof of the smooth dependence on parameters of solutions to Volterra integral equations

We consider the linear Volterra equation x (t) = a (t) - ∫0t K (t, s) x (s) d s and suppose that the kernel K and forcing function a depend on some parameters ε{lunate} ∈ Rd. We prove that, under suitable conditions, the solutions depend on ε{lunate} as smoothly the functions a and K. The proof is based on the contraction mapping principle and the variational equation. Though our conditions are not the most generally possible, they nonetheless include many important examples. © 2010 Elsevier Ltd. All rights reserved