7 papers
The Integral of Secant and Stereographic Projections of Conic Sections
George Jennings, David Ni, Wai Yan Pong +1
We show that the four best-known substitutions used to integrate secant rely on different rational parametrizations of conic sections, coming from stereographic projections. We als…
Arithmetic properties of -cycles of quadratic maps over
Patrick Morton, Serban Raianu
It is shown that is the unique rational number of smallest denominator, and the unique rational number of smallest numerator, for which the map has a ra…
Partition Problems and a Pattern of Vertical Sums
Eunice Krinsky, Serban Raianu, Alexander Wittmond
We give a possible explanation for the mystery of a missing number in the statement of a problem that asks for the non-negative integers to be partitioned into three subsets. We in…
Differences of Harmonic Numbers and the -Conjecture
Natalia da Silva, Serban Raianu, Hector Salgado
Our main source of inspiration was a talk by Hendrik Lenstra on harmonic numbers, which are numbers whose only prime factors are two or three. Gersonides proved 675 years ago that…
The Bijectivity of the Antipode Revisited
Miodrag C. Iovanov, Serban Raianu
We provide a very short approach to several fundamental results for Hopf algebras with nonzero integrals. Besides being short, our approach is the first to prove the bijectivity of…
The antipode of a dual quasi-Hopf algebra with nonzero integrals is bijective
Margaret Beattie, Miodrag Cristian Iovanov, Serban Raianu
For a Hopf algebra of arbitrary dimension over a field , it is well-known that if has nonzero integrals, or, in other words, if the coalgebra is co-Frobenius, then t…