The interpretation of the optical Appell transformation, as previously elaborated in relation to the free-space paraxial propagation under both a rectangular and a circular cylindrical symmetry, is reviewed. Then, the caloric Appell transformation, well known in the theory of heat equation, is shown to be amenable for a similar interpretation involving the Laplace transform rather than the Four...

It is widely held that a free, natural dialogue model is more efficient and less distracting than system-initiative, state based dialogue. This paper describes an evaluation of two systems one using system-directed dialogue and one using a more “free” dialogue focusing on distraction and efficiency. The level of distraction is measured using an automotive industry standard test (LCT), and the e...

Canonical transformation (CT) theory describes dynamic correlation in multireference systems with large active spaces. Here we discuss CT theory's intruder state problem and why our previous approach of overlap matrix truncation becomes infeasible for sufficiently large active spaces. We propose the use of strongly and weakly contracted excitation operators as alternatives for dealing with intr...

Let D, x be a free divisor germ in a complex manifold X of dimension n > 2. It is an open problem to find out which are the properties required for D, x to satisfy the so-called Logarithmic Comparison Theorem (LCT), that is, when the complex of logarithmic differential forms computes the cohomology of the complement of D, x. We give a family of Euler homogeneous free divisors which, somewhat un...