Finite Bruck loops

Bruck loops are Bol loops satisfying the automorphic inverse property. We prove a structure theorem for finite Bruck loops X, showing that X is essentially the direct product of a Bruck loop of odd order with a 2-element Bruck loop. The former class of loops is well understood. We identify the minimal obstructions to the conjecture that all finite 2-element Bruck loops are 2-loops, leaving open the question of whether such obstructions actually exist

Two Case Examples of Reaching the Hard-to-Reach: Low Income Minority and LGBT Individuals

‘Hard-to-reach’ is a term primarily used by researchers to describe groups of people who have been historically difficult to find or contact. It is important for the public interest to include hard-to-reach groups in research because excluding certain sub-populations diminishes the ability to identify groups that potentially have the highest burden of illness and to develop an understanding of why group differences exist. Thus, the purposes of this paper are to: 1) describe the challenges in recruiting hard-to-reach population in two separate research studies; 2) discuss the strategies that were used to overcome those challenges; and 3) provide recommendations for researchers. This paper followed a case study research strategy, with the authors using two of their own research studies involving hard-to-reach populations as case studies. The research studies used in these case studies involved two different hard-to-reach groups—low-income ethnic minorities who were un- or under-insured and lesbian or bisexual women and transgender men. Two overarching themes were identified as barriers to reaching the population of interest: (1) gaining interest and (2) building trust. These themes add to the literature regarding the multi-prong approach that is needed to recruit members of hard-to-reach populations. Despite the authors having buy-in from stakeholders and a multi-prong recruiting approach, barriers to gaining the interest of potential participants included language in recruitment flyers, competing demands for time, and transportation to the data collection site. Building trust with interested study participants was also a large issue noted between both studies, especially concerning sensitive questions or cultural barriers regardless of the reliability and validity of the tools used in the study

Axioms for trimedial quasigroups

We give new equations that axiomatize the variety of trimedial quasigroups. We also improve a standard characterization by showing that right semimedial, left F-quasigroups are trimedial.Comment: 6 pages, AMS-LaTeX. To appear in Comment. Math. Univ. Carolinae. for a special issue: the Proceedings of Loops03. Version 3: the proof of the main result is collected together more formally; other stylistic change

U.S. International Trade: Trends and Forecasts

[Excerpt] This report provides an overview of the current status, trends, and forecasts for U.S. import and export flows as well as certain balances. The purpose of this report is to provide current data and brief explanations for the various types of trade flows along with a brief discussion of trends that may require attention or point to the need for policy changes. The use of trade policy as an economic or strategic tool is beyond the scope of this report but can be found in various other CRS reports. Further detail on trade in specific commodities, with particular countries or regions, or for different time periods, can be obtained from the Department of Commerce, U.S. International Trade Commission, or by contacting the authors of this report

Two-dimensional electron system in high magnetic fields: Wigner crystal vs. composite-fermion liquid

The two dimensional system of electrons in a high magnetic field offers an opportunity to investigate a phase transition from a quantum liquid into a Wigner solid. Recent experiments have revealed an incipient composite fermion liquid in a parameter range where theory and many experiments had previously suggested the Wigner crystal phase, thus calling into question our current understanding. This Letter shows how very small quantitative corrections (< 1%) in the energy due to the weak interaction between composite fermions can cause a fundamental change in the nature of the ground state, thus providing insight into the puzzling experimental results.Comment: 4 pages, 2 figure