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Using matching and regression analyses, we measure the difference in citations between articles posted to Academia.edu and other articles from similar journals, controlling for field, impact factor, and other variables. Based on a sample size of 31,216 papers, we find that a paper in a median impact factor journal uploaded to Academia.edu receives 16% more(More)
We show that, for a finite set A of real numbers, the size of the set A + A A + A = { a + b c + d : a, b, c, d ∈ A, c + d 6= 0 } is bounded from below by ∣∣∣∣A + A A + A ∣∣∣∣ |A|2+1/4 |A/A|1/8 log |A| . This improves a result of Roche-Newton (2016).
We prove three theorems giving extremal bounds on the incidence structures determined by subsets of the points and blocks of a balanced incomplete block design (BIBD). These results generalize and strengthen known bounds on the number of incidences between points and m-flats in affine geometries over finite fields. First, we show an upper bound on the(More)
We introduce the bisector energy of an n-point set P in R2, defined as E(P) = ∣∣{(a, b, c, d) ∈ P | a, b have the same perpendicular bisector as c, d}∣∣ . If no line or circle contains M(n) points of P, then we prove that for any ε > 0 E(P) = O ( M(n) 2 5n 12 5 +ε +M(n)n ) . We also derive the lower bound E(P) = Ω(M(n)n2), which matches our upper bound when(More)
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