A stress-concentration-formula generating equation for arbitrary shallow surfaces

Latus: A new accelerator for generating combined iterative methods in solving nonlinear equation

A Generating Function for Blattner’s Formula

Abstract. Let G be a connected, semisimple Lie group with finite center and let K be a maximal compact subgroup. We investigate a method to compute multiplicities of K-types in the discrete series using a rational expression for a generating function obtained from Blattner’s formula. This expression involves a product with a character of an irreducible finite dimensional representation of K and...

MacLane's theorem for arbitrary surfaces

Given a closed surface S, we characterise the graphs embeddable in S by an algebraic condition asserting the existence of a sparse generating set for their cycle space. When S is the sphere, the condition defaults to MacLane’s planarity criterion.

Generating Function Associated with the Hankel Determinant Formula for the Solutions of the Painlevé IV Equation

We consider a Hankel determinant formula for generic solutions of the Painlevé IV equation. We show that the generating functions for the entries of the Hankel determinants are related to the asymptotic solution at infinity of the isomonodromic problem. Summability of these generating functions is also discussed.

Generating Function Associated with the Determinant Formula for the Solutions of the Painlevé II Equation

In this paper we consider a Hankel determinant formula for generic solutions of the Painlevé II equation. We show that the generating functions for the entries of the Hankel determinants are related to the asymptotic solution at infinity of the linear problem of which the Painlevé II equation describes the isomonodromic deformations.