Iterative algebras are defined by the property that every guarded system of recursive equations has a unique solution. We prove that they have a much stronger property: every system of recursive equations has a unique strict solution. And we characterize those systems that have a unique solution in every iterative algebra.

In this note, we use the method of [3] to give a simple proof of famous Witten conjecture. Combining the coefficients derived in our note and this method, we can derive more recursion formulas of Hodge integrals.

A formalism is developed to study certain five-term recursion relations by discrete phase integral (or Wentzel-Kramers-Brillouin) methods. Such recursion relations arise naturally in the study of the Schrödinger equation for certain spin Hamiltonians. The conditions for the validity of the phase integral approximation are derived. It is shown that in contrast to the three-term problem, it is no...

We show that the equations of the Coherent Potential Approximation (C.P.A.) can be

Abstract. The evaluation of matrix functions of the form f(A)v, where A is a large sparse or structured symmetric matrix, f is a nonlinear function, and v is a vector, is frequently subdivided into two steps: first an orthonormal basis of an extended Krylov subspace of fairly small dimension is determined, and then a projection onto this subspace is evaluated by a method designed for small prob...

In this paper we look back to work done in the late 1980s, and that looked at links between grammars, data types and recursion principles, and illustrating it with examples that include enumerations of types and developing a structure editor. The work is introduced by a historical foreword, and closes with an afterword that discusses some of the subsequent developments of these ideas.