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 there exists a continuous compactly supported function ' de ned on the reals satsifying '(x) = c0'(2x) + c1'(2x 1) + c2'(2x 2) if and only if c1 = 1, c0 + c2 = 1, and jc0j; jc2j < 1. The functions ' are examples of scaling functions from the theory of wavelets. x