We show that the extensional collapse of the relational model of linear logic is the model of prime-algebraic complete lattices, a natural extension to linear logic of the well known Scott semantics of the lambda-calculus.

— Let x1, x2, . . . , xn be the zeroes of a polynomial P (x) of degree n and y1, y2, . . . , ym be the zeroes of another polynomial Q(y) of degree m. Our object of study is the permanent per(1/(xi − yj))1≤i≤n,1≤j≤m, here named “Scott-type” permanent, the case of P (x) = x − 1 and Q(y) = y + 1 having been considered by R. F. Scott. We present an efficient approach to determining explicit evaluat...

In this paper we give an outline of recent algebraic results concerning theories and models of the untyped lambda calculus.

In this work, from the category sight, we provide a generalization for the real interval theory. This generalization allows us to study generic properties of data which are “intervals” of another data, providing a categorical foundation of intervals as a parametric data type. In doing so we obtain some properties which holds for real intervals, complex intervals, interval vectors, interval matr...

Glass Capillary X-ray Waveguides Scott M. LaBrake December, \thisyear Dedication: To my wife Sandra and my daughter Alexandra. Acknowledgments: First and foremost I would like to thank my beautiful wife Sandra for all of her love and support over the last eight years. I could not have completed this without you. There are not enough words to express how I feel about you. You are my best friend ...

We show how two general notions of domain theory, the logic induced from the Scott topology on a domain, together with the Smyth powerdomain, interact with the theory of default reasoning introduced by Reiter 19]. We deene extensions, which are xed points of a certain non-monotonic operator on a Scott domain induced by a normal default set over that domain. We specialize this deenition to the S...