Our aim is to study how the interpretive approach — inserting an interpreter between a source program and a program specializer — can be used to improve the transformation of programs and to automatically generate program transformers by self-application of a program specializer. We show that a few semantics-preserving transformations applied to a straightforward interpretive definition of a fi...

A split diabatic representation is proposed as a technique for generating diabatic potential curves with the maximal physical content and favorable computational characteristics. This method is a mixed adiabaticdiabatic representation, in which smoothly varying couplings appear in both the kineticand potential-energy matrices. It requires the solution of the first-order differential equation fo...

In this paper we propose a general recipe for calculating the automorphism groups of semigroups consisting of partial endomorphisms of relational structures with a single m-ary relation for any m ∈ N over a finite set. We use this recipe to determine the automorphism groups of the following semigroups: the full transformation semigroup, the partial transformation semigroup, and the symmetric in...

With the objective of generating “shape-preserving” smooth interpolating curves that represent data with abrupt changes in magnitude and/or knot spacing, we study a class of first-derivative-based C1-smooth univariate cubic L1 splines. An L1 spline minimizes the L1 norm of the difference between the first-order derivative of the spline and the local divided difference of the data. Calculating t...

1. General statement. Soph us Lie studied transformations from lineal-elements into lineal-elements, and also transformations from surface-elements into surface-elements of space. The contact group is obtained by requiring all unions to be converted into unions. Lie's fundamental theorems may be stated as follows. All the contact linealelement transformations form the group of extended point tr...

We show that a certain type of conservative, ergodic, measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also consider distribution asymptotics of information; e.g. for Boole’s transformation, information is asymptotically mod-normal, a property shared by certain ergodic, probability preserving transformations with zero entropy. §0 Intr...

We show that a certain type of quasi finite, conservative, ergodic , measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic , measure preserving transformation which is not quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole’s transformation, information is as...

We show that a certain type of quasi finite, conservative, ergodic , measure preserving transformation always has a maximal zero entropy factor, generated by predictable sets. We also construct a conservative, ergodic , measure preserving transformation which is not quasi finite; and consider distribution asymptotics of information showing that e.g. for Boole’s transformation, information is as...