The Changing Contexts of Family Care in Canada

Over the past 20 to 30 years, the importance of families as providers of assistance to older Canadians has been well documented through research. However, over these decades, the contexts within which families exist and provide support have changed considerably. This paper examines changes over this time period which affect family support to older adults. Specific areas examined include: likelihood of having a parent alive; living arrangements; divorce and single-parenthood; women's labour force participation, and combining employment and care of older relatives. The paper concludes with an assessment of policy changes in health and long-term care as these affect older Canadians and their families.family care; older population; policy change

Natural Density of Rectangular Unimodular Integer Matrices

In this paper, we compute the natural density of the set of k x n integer matrices that can be extended to an invertible n x n matrix over the integers. As a corollary, we find the density of rectangular matrices with Hermite normal form [O Id]. Connections with Cesaro's Theorem on the density of coprime integers and Quillen-Suslin's Theorem are also presented.Comment: 8 page

Public Key Cryptography based on Semigroup Actions

A generalization of the original Diffie-Hellman key exchange in $(\Z/p\Z)^*$ found a new depth when Miller and Koblitz suggested that such a protocol could be used with the group over an elliptic curve. In this paper, we propose a further vast generalization where abelian semigroups act on finite sets. We define a Diffie-Hellman key exchange in this setting and we illustrate how to build interesting semigroup actions using finite (simple) semirings. The practicality of the proposed extensions rely on the orbit sizes of the semigroup actions and at this point it is an open question how to compute the sizes of these orbits in general and also if there exists a square root attack in general. In Section 2 a concrete practical semigroup action built from simple semirings is presented. It will require further research to analyse this system.Comment: 20 pages. To appear in Advances in Mathematics of Communication

Simple non-destructive tests for electroexplosive devices

Electrothermal behavior of bridgewire-explosive interface is defined by pulsing electroexplosive device with a safe level of current and examining the resistance variation of bridgewire. Bridgewire provides signal which describes average wire temperature and heat sinking to the explosive and enclosure

Degree of the generalized Pl\"ucker embedding of a Quot scheme and Quantum cohomology

We compute the degree of the generalized Pl\"ucker embedding $\kappa$ of a Quot scheme $X$ over \PP^1. The space $X$ can also be considered as a compactification of the space of algebraic maps of a fixed degree from \PP^1 to the Grassmanian $\rm{Grass}(m,n)$. Then the degree of the embedded variety $\kappa (X)$ can be interpreted as an intersection product of pullbacks of cohomology classes from $\rm{Grass}(m,n)$ through the map $\psi$ that evaluates a map from \PP^1 at a point x\in \PP^1. We show that our formula for the degree verifies the formula for these intersection products predicted by physicists through Quantum cohomology~\cite{va92}~\cite{in91}~\cite{wi94}. We arrive at the degree by proving a version of the classical Pieri's formula on the variety $X$, using a cell decomposition of a space that lies in between $X$ and $\kappa (X)$.Comment: 18 pages, Latex documen

Families as Care-Providers versus Care-Managers? Gender and Type of Care in a Sample of Employed Canadians

This article extends previous research by examining care management as a distinct type of informal care. Using data drawn from a large Canadian study of work and family, the research is based on a study of a sub-sample of women (1068) and men (805) who were employed full-time and who had provided help to an elderly relative during the six month period preceding the interview. Results indicate that managerial care is a meaningful construct that denotes a distinct type of care. Most commonly, individuals combine managerial care with other types of assistance. Managerial care is a very common activity among caregivers and usually involves aspects of care other than arranging for formal services. Managerial care has an adverse impact on job costs and personal costs, and, among women, is associated with greater stress.elderly; caregiving