Comparing Heegaard and JSJ structures of orientable 3-manifolds

The Heegaard genus g of an irreducible closed orientable 3-manifold puts a limit on the number and complexity of the pieces that arise in the Jaco-Shalen-Johannson decomposition of the manifold by its canonical tori. For example, if p of the complementary components are not Seifert fibered, then p < g. This result generalizes work of Kobayashi. The Heegaard genus g also puts explicit bounds on the complexity of the Seifert pieces. For example, if the union of the base spaces of the Seifert pieces has Euler characteristic X and there are a total of f exceptional fibers in the Seifert pieces, then f - X is no greater than 3g - 3 - p.Comment: 30 pages, 10 figure

The tunnel number of the sum of n knots is at least n

We prove that the tunnel number of the sum of n knots is at least n.Comment: 8 pages. To appear in Topolog

The Duration of Spells on Welfare and Off-welfare among Lone Mothers in Ontario

This paper provides a first look at the dynamics of social assistance use among lone mothers in Ontario. We use an administrative caseload data set to analyse the relationship between the duration of spells, both on welfare and off welfare, and a series of factors including the clients’ personal characteristics, their history of welfare use, the duration of current spells, labour market conditions and social assistance benefit levels. We find mixed evidence concerning the key policy question of the scarring or stigmatizing effects of welfare, that is, a “welfare trap”. There is evidence that the likelihood of exiting welfare declines during the first year of a spell. The support is weakest, however, in our preferred specification. There is more consistent evidence that the likelihood of returning to welfare declines during the first year after an exit, that is, staying off the rolls has the beneficial effect of making recidivism less likely. Clients who have spent more months on welfare in the past (controlling for age) do appear to have somewhat longer future spells on welfare and to return more quickly to the rolls once they leave, but the magnitude of this effect is very small. The length of both welfare and off-welfare spells is very sensitive to the levels of welfare benefits. Most of the other coefficients have significant effects of the expected sign. Welfare spells tend to be longer for those lone mothers who are younger, poorly educated, never married, not employable and for those who have more and younger children. Spell lengths also increase with the level of the unemployment rate and decrease with the level of the minimum wage. Off-welfare spells tend to be shorter (the return to welfare more rapid) for those lone mothers who are older, never married, not employable and who have very young children. Off- welfare spells are longer when the minimum wage is higher.

Using Your Library’s Objectives as the Organizational Framework for Library Documentation in Planning, Assessment, and Accreditation

The San Diego Christian/Southern California Seminary Library1 uses its objectives as the organizational framework for its strategic plan, annual report, assessment plan, and policies and procedures manual. This article describes how the library’s objectives compare to the Association of College and Research Libraries’ Standards (to ensure best practices), relate to the areas covered in the library strategic plan, annual report, and operations manual, and correspond to the standards and criteria from their respective accrediting agencies, showing how easy it is to identify supporting evidence for a program review or self-study when using this organizing method