Cohen, Stephen D., Kapetanakis, Giorgos, and Reis, Lucas
Comptes Rendus. Mathématique, Vol 360, Iss G6, Pp 641-652 (2022)
Subjects
finite fields, character sums, elliptic curves, Mathematics, and QA1-939
Abstract
Let $\mathcal{C}_Q$ be the cyclic group of order $Q$, $n$ a divisor of $Q$ and $r$ a divisor of $Q/n$. We introduce the set of $(r,n)$-free elements of $\mathcal{C}_Q$ and derive a lower bound for the number of elements $\theta \in \mathbb{F}_q$ for which $f(\theta )$ is $(r,n)$-free and $F(\theta )$ is $(R,N)$-free, where $ f, F \in \mathbb{F}_q[x]$. As an application, we consider the existence of $\mathbb{F}_q$-primitive points on curves like $y^n=f(x)$ and find, in particular, all the odd prime powers $q$ for which the elliptic curves $y^2=x^3 \pm x$ contain an $\mathbb{F}_q$-primitive point.
Agnihotry, Anirudha, Gill, Karanjot Singh, Stevenson III, Richard G, Fedorowicz, Zbys, Kumar, Vijay, Sprakel, Julie, Cohen, Stephen, and Thompson, Wendy
Brazilian Dental Journal. July 2019 30(4)
Subjects
antibiotics, endodontics, survey, dentists, pain, and prescriptions
Abstract
Antibiotic resistance is a growing public health concern. Antibiotics continue to be prescribed by some clinicians to resolve dental pain even though research indicates that antibiotics are not effective for treating conditions such as irreversible pulpitis. The objective of this study was to determine the extent to which current research and evidence around irreversible pulpitis has been translated into dental practice and the gaps in dentists’ knowledge. An on-line clinical vignette format survey questionnaire about treatment of irreversible pulpitis was distributed to the members of the Academy of Operative Dentistry and Academy of General Dentistry (US based international dental bodies). Their responses were recorded and evaluated. A total of 403 dentists participated in the survey. Over a third (39.3%) indicated they would prescribe antibiotics for symptomatic irreversible pulpitis in a permanent tooth occurring without any signs of systemic infection. The rest indicated they would not prescribe antibiotics; most of them would prescribe an analgesic combined with pulpectomy. Those who had undertaken advanced education training achieved a significantly higher mean knowledge score compared to those with just a primary dental degree (p=0.011). Similarly, full or part time academicians had a higher mean knowledge score than the clinicians who work only in private practice (p=0.014). Some dentists continue to prescribe antibiotics inappropriately for alleviating pain due to irreversible pulpitis. Antibiotic prescribing practices of dentists with advanced education or academic engagement were better as compared to the other participants. There is clear evidence of antibiotic over-prescribing for irreversible pulpitis which needs to be addressed urgently.
