We investigate 3-permutability, in the sense of universal algebra, in an abstract categorical setting which unifies the pointed and the non-pointed contexts in categorical algebra. This leads to a unified treatment of regular subtractive categories and of regular Goursat categories, as well as of E-subtractive varieties (where E is the set of constants in a variety) recently introduced by the f...

The solution to the biharmonic equation in a simply connected region in the plane is computed in terms of the Goursat functions. The boundary conditions are conformally transplanted to the disk with a numerical conformal map. A linear system is obtained for the Taylor coeecients of the Goursat functions. The coeecient matrix of the linear system can be put in the form I + K where K is the discr...

In Book 1, Proposition 7, Problem 2 of his 1687 Philosophiae Naturalis Principia Mathematica, Isaac Newton poses and answers the following question: Let orbit a particle moving in central force field be an off-center circle. How does magnitude depend on position onthat circle? this article, we identify potential that can produce such force, only at zero energy. We further map zero-energy orbits...

In this paper, the method of transmutation operators is used to construct an exact solution Goursat problem for a fourth-order hyperbolic equation with singular Bessel operator. We emphasise that in many other papers and monographs fractional Erdélyi-Kober are as integral operators, but our approach them additional new properties important applications. Specifically, it extends its applications...