The notion of adequate subgroups was introduced by Jack Thorne [59]. It is a weakening of the notion of big subgroups used by Wiles and Taylor in proving automorphy lifting theorems for certain Galois representations. Using this idea, Thorne was able to strengthen many automorphy lifting theorems. It was shown in [22] and [23] that if the dimension is smaller than the characteristic then almost...

" Timely and reliable data are an essential component of public health assessment, policy development , and assurance at all levels of government. " — Institute of Medicine, The Future of the Public's Health Responsible decision making requires adequate data — and the Institute of Medicine (IOM) report is 1 of several reports and initiatives that look forward to a new era of timely, high-qualit...

Over one month 103 patients with acute abdominal pain were admitted to the Western Infirmary. Criteria for entry to the study were: (1) no contraindication to the use of potent analgesia or antacid treatment (which might mask important clinical signs); (2) a pain score ¢6 on a visual analogue scalexanging from 0 to 102; and (3) no medical contraindication to the use of potent analgesia. Fifty o...

When inspection is used to enforce a rule in a context such as arms control, auditing, or food and drug inspection, there is a conflict between inspector and inspectee that can be modeled as a non-zerosum strategic-form game. Suppose that the inspectee may violate at any subset of n non-identical “sites”, complying at the rest. The inspector chooses k < n sites at which to assess the inspectee’...