Jenkins in 2003 showed that every odd perfect number is divisible by a prime exceeding 107. Using the properties of cyclotomic polynomials, we improve this result to show that every perfect number is divisible by a prime exceeding 108.

Scholars, educators, and media designers are increasingly interested in whether and how digital games might contribute to civic learning. However, there are three main barriers to advancing understanding of games’ potential for civic education: the current practices of formal schooling, a dearth of evidence about what kinds of games best inspire learning about public life, and divergent paradig...

The importance and mechanisms of dispersal have long been subjects of evolutionary and ecological research (e.g. Bilton et al., 2001; Bohonak & Jenkins, 2003). The often reported mismatch between potential (i.e. assumed or predicted dispersal ability based on traits) for widespread dispersal and realized (i.e. empirical) patterns of geographically restricted dispersal and gene flow by stream in...

سعت هذه الدراسة الى امكانية التنبؤ بالمخاطرة لاسهم المؤسسات المدرجة في الاسواق المالية، وقد اجريت عدد من السوق المالية السعودية وشملت عينة (5) مؤسسات مدرجة السعودية، وتم اخذ المشاهدات اليومية لأسعار اغلاق اسهم للمدة (2013-2021). وانطلقت مشكلة يعاني منها اغلب المستثمرين وهي حالة عدم التأكد او القدرة على بمخاطر الاوراق والتي مازالت محل جدل حيث النماذج المستخدمة واساليب التحليل الفني الكثيرة، فضلا...

Citation: Neuert S, Nair S, Day MR, Doumith M, Ashton PM, Mellor KC, Jenkins C, Hopkins KL, Woodford N, de Pinna E, Godbole G and Dallman TJ (2018) Prediction of Phenotypic Antimicrobial Resistance Profiles From Whole Genome Sequences of Non-typhoidal Salmonella enterica. Front. Microbiol. 9:592. doi: 10.3389/fmicb.2018.00592 Prediction of Phenotypic Antimicrobial Resistance Profiles From Whole...

In the last five decades, Box Jenkins methodology has been in existence to model univariate time series data but fails or limitations on modeling volatility. Most financial do exhibit heavy tail and thick distribution, this effect various parametric semi-parametric non –linear models have proposed two three decades ago capture However, research entails measuring volatility its forecasting using...

We thank Drs Jenkins and Beasley for their comments in the recent editorial regarding tiotropium (SPIRIVA). Preceding the Singh et al analysis cited by the authors, Boehringer Ingelheim (BI) had analysed both the tiotropium HandiHaler and Respimat pooled datasets using patient-level data on-treatment as well as including vital status. The results showed a nominally statistically significant red...

BACKGROUND Predicting the incidence of tuberculosis (TB) plays an important role in planning health control strategies for the future, developing intervention programs and allocating resources. OBJECTIVES The present longitudinal study estimated the incidence of tuberculosis in 2014 using Box-Jenkins methods. MATERIALS AND METHODS Monthly data of tuberculosis cases recorded in the surveilla...

In the relatively few years since empirical research into English as a Lingua Franca began being conducted more widely, the field has developed and expanded remarkably, and in myriad ways. In particular, researchers have explored ELF from the perspective of a range of linguistic levels and in an ever-increasing number of sociolinguistic contexts, as well as its synergies with the field of Inter...