Critical sets in the elementary abelian 2- and 3- groups

In 1998, Khodkar showed that the minimal critical set in the Latin square corresponding to the elementary abelian 2-group of order 16 is of size at most 124. Since the paper was published, improved methods for solving integer programming problems have been developed. Here we give an example of a critical set of size 121 in this Latin square, found through such methods. We also give a new upper bound on the size of critical sets of minimal size for the elementary abelian 2-group of order $2^n$: $4^{n}-3^{n}+4-2^{n}-2^{n-2}$. We speculate about possible lower bounds for this value, given some other results for the elementary abelian 2-groups of orders 32 and 64. An example of a critical set of size 29 in the Latin square corresponding to the elementary abelian 3-group of order 9 is given, and it is shown that any such critical set must be of size at least 24, improving the bound of 21 given by Donovan, Cooper, Nott and Seberry.Comment: 9 page

Impact of globalization on monetary policy : commentary

Monetary policy ; Globalization ; Banks and banking, Central ; Inflation (Finance)

Household reports of energy assistance receipt increased 48 percent during recession: Proposed cuts threaten vulnerable families

This brief examines heating assistance usage and the implications of President Obama\u27s 2012 budget proposal to cut $2.5 billion from the$5.1 billion energy assistance fund for low-income families at a time when families are struggling with higher energy costs amid a difficult economy. The federal Low-Income Home Energy Assistance Program (LIHEAP) assists vulnerable families in paying their home heating and cooling bills. Nationwide, from the winter of 2006/2007 to the winter of 2009/2010, there was a 48 percent increase in households receiving energy assistance. This growth appears to have accelerated with the recession, particularly in the rural Northeast and Midwest. Many more families are eligible than receive assistance. Brief author Jessica Bean discusses how proposed cuts would have a concrete and immediate impact on families, particularly those in rural areas and in harsh winter climates