3 citations · 22 across the 56 of their papers we have counts for
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Projective Space: Harmonicity and Projectivity
P. L. Robinson
For an axiomatization of three-dimensional projective space based on points and planes, we discuss appropriate versions of the harmonicity axiom and the projectivity axiom, showing…
Projective Space: Tetrads and Harmonicity
P. L. Robinson
Within an axiomatic framework for three-dimensional projective space based on lines alone, we explore the Fano axiom of harmonicity according to which the diagonal lines of a compl…
Projective Space: Points and Planes
P. L. Robinson
We take points and planes as fundamental, lines as derived, in an axiomatic formulation of three-dimensional projective space, the self-dual nature of which formulation renders aut…
Painlevé IV and a third-order viewpoint
P. L. Robinson
We take a third-order approach to the fourth Painlevé equation and indicate the value of such an approach to other second-order ODEs in the Painlevé-Gambier list of 50.
Painlevé II transcendents and their squares
P. L. Robinson
We examine the relationship between the homogeneous second Painlevé equation and equation from the master list recorded by Ince.
Painlevé IV: roots and zeros
P. L. Robinson
We consider the (real) fourth Painlevé equation in which both parameters vanish, analyzing the square-roots of its solutions and paying special attention to their zeros.
Homogeneous Painlevé II transcendents
P. L. Robinson
We offer elementary proofs for fundamental properties of solutions to the homogeneous second Painlevé equation.
The triple-zero Painlevé I transcendent
P. L. Robinson
We offer elementary proofs for fundamental properties of the unique triple-zero solution to the first Painlevé equation.
Beyond Quartic Hamiltonians
P. L. Robinson
We investigate the Hamiltonian system generated by a homogeneous binary polynomial of order greater than four. In particular, we study the circumstances under which the associa…
Neville's primitive elliptic functions: the case
P. L. Robinson
The vanishing of the invariant attached to a lattice singles out a midpoint lattice and yields a square-root of the associated Weierstrass function .
Remarks on trigonometric functions after Eisenstein
P. L. Robinson
We modify the Whittaker-Watson account of the Eisenstein approach to the trigonometric functions, basing these functions independently on the Eisenstein function .
Classical theorems in the Implicational Propositional Calculus
P. L. Robinson
For formulas of the Implicational Propositional Calculus (IPC) that are theorems of the classical Propositional Calculus (PC) we show that PC proofs yield IPC proofs. As a conseque…
A Grätzer-Schmidt theorem for the Lindenbaum-Tarski algebra of IPC
P. L. Robinson
We prove a version of the Grätzer-Schmidt theorem for the Lindenbaum-Tarski algebra associated to the Implicational Propositional Calculus.