Carryless Arithmetic Mod 10

We investigate what arithmetic would look like if carry digits into other digit position were ignored, so that 9 + 4 = 3, 5 + 5 = 0, 9 X 4 = 6, 5 X 4 = 0, and so on. For example, the primes are now 21, 23, 25, 27, 29, 41, 43, 45, 47, ... .Comment: 7 pages. To the memory of Martin Gardner (October 21, 1914 -- May 22, 2010). Revised version (with a number of small improvements), July 7 201

On Asymmetric Coverings and Covering Numbers

An asymmetric covering D(n,R) is a collection of special subsets S of an n-set such that every subset T of the n-set is contained in at least one special S with |S| - |T| <= R. In this paper we compute the smallest size of any D(n,1) for n <= 8. We also investigate ``continuous'' and ``banded'' versions of the problem. The latter involves the classical covering numbers C(n,k,k-1), and we determine the following new values: C(10,5,4) = 51, C(11,7,6,) =84, C(12,8,7) = 126, C(13,9,8)= 185 and C(14,10,9) = 259. We also find the number of nonisomorphic minimal covering designs in several cases.Comment: 11 page

“Don’t Jobs Change?” Substitution of Professionals by Support Staff in Public Libraries, 1997-2007

poster abstractAmong MLS-level librarians, there is substantial anecdotal prevalence of the idea that administrators of public libraries seek to reduce costs by replacing MLS librarians with support staff. The migration of tasks such as copy and original cataloging and reference services to support staff has been well-documented. This study used national data from the Public Libraries Survey, from 1997 and 2007, to test this substitution hypothesis. Data indicates that for this time period, the utilization of MLS librarians as a percent of total library staffs did not diminish overall. Relative to population served, libraries did not reduce MLS positions but did increase support staffing. This has implications for understanding the 2008-2013 period of reduced public resources, and for the staffing of public libraries in the longer term

Providing True Opportunity for Opportunity Youth: Promising Practices and Principles for Helping Youth Facing Barriers to Employment

Many "opportunity youth" -- youth who are not working or in school -- would benefit substantially from gaining work experience but need help overcoming barriers to employment and accessing the labor market.Those opportunity youth facing the most significant challenges, such as extreme poverty, homelessness, and justice system involvement, often need even more intensive assistance in entering and keeping employment, and are at risk of being left behind even by employment programs that are specifically designed to serve opportunity youth.This paper builds on the research literature with extensive interviews with employment program providers who have had success in helping the most vulnerable opportunity youth succeed in the workforce. Six principles for effectively serving these youth are identified