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Planar functions were introduced by Dembowski and Ostrom () to describe projective planes possessing a collineation group with particular properties. Several classes of planar functions over a finite field are described, including a class whose associated affine planes are not translation planes or dual translation planes. This resolves in the negative a… (More)
Strong conditions are derived for when two commutative presemi-fields are isotopic. It is then shown that any commutative presemifield of odd order can be described by a planar Dembowski-Ostrom polynomial and conversely , any planar Dembowski-Ostrom polynomial describes a commutative presemifield of odd order. These results allow a classification of all… (More)
We consider a class of Weil sums involving polynomials of a particular shape. In all cases, explicit evaluations are obtained.
BACKGROUND The purpose of this study was to fill a significant void in the ophthalmic literature by performing a large scale, comprehensive, prospective study of the prevalence of vision disorders and ocular pathology in a clinical pediatric population using well-defined diagnostic criteria. METHODS A prospective study was performed on 2,023 consecutive… (More)
Black men who have sex with men (MSM) in the United States are disproportionately impacted by HIV. To better understand this public health problem, we reviewed the literature to calculate an estimate of HIV incidence among Black MSM. We used this rate to model HIV prevalence over time within a simulated cohort, which we subsequently compared to prevalence… (More)
We determine the number of Fq-rational points of a class of Artin-Schreier curves by using recent results concerning evaluations of some exponential sums. In particular, we determine infinitely many new examples of maximal and minimal plane curves in the context of the Hasse-Weil bound.
OBJECTIVES Using data from a regional census of high school students, we have documented the prevalence of cyberbullying and school bullying victimization and their associations with psychological distress. METHODS In the fall of 2008, 20,406 ninth- through twelfth-grade students in MetroWest Massachusetts completed surveys assessing their bullying… (More)
1 Dembowski-Ostrom Polynomials and Linearised Polynomials Let p be a prime and q = p e. Let F q denote the finite field of order q and F * q represent the set of non-zero elements of F q. The ring of polynomials in the indeterminate X with coefficients from F q will be represented by F q [X]. A polynomial f ∈ F q [X] which permutes F q under evaluation is… (More)