It was proved in [1] that lower and upper powerdomain constructions commute on all domains. In that proof, domains were represented as information systems. In [2] a rather complicated algebraic proof was given which relied on universality properties of powerdomains proved in the previous works of the author of [2]. Here we give an elementary algebraic proof that upper and lower powerdomain cons...

In this note we introduce a notion of essentially-Euclidean normed spaces (and convex bodies). Roughly speaking, an n-dimensional space is λ-essentially-Euclidean (with 0 < λ < 1) if it has a [λn]dimensional subspace which has further proportionally dimensional Euclidean subspaces of any proportion. We consider a space X1 = (Rn, ‖ · ‖1) with the property that if a space X2 = (Rn, ‖ · ‖2) is “no...

For f in L∞, the space of essentially bounded Lebesgue measurable functions on the unit circle, ∂D, the Toeplitz operator with symbol f is the operator Tf on the Hardy space H2 of the unit circle defined by Tfh = P (fh). Here P denotes the orthogonal projection in L2 with range H2. There are many fascinating problems about Toeplitz operators ([3], [6], [7] and [20]). In this paper we shall conc...

The Lake: Alice, Bertha, and Claudia live around Forest Lake, at some distance from each other. The ecosystem is sensitive, in particular to the solvent they have been using when painting their boats, and the lake is faring badly. Until recently, they had no way of knowing that the solvent would have this effect, but they just learned that it is in fact killing the fish in the lake, and that th...

Network algebra is proposed as a uniform algebraic framework for the description and analysis of dataflow networks. An equational theory, called BNA (Basic Network Algebra), is presented. BNA, which is essentially a part of the algebra of flownomials, captures the basic algebraic properties of networks. For synchronous and asynchronous dataflow networks, additional constants and axioms for conn...

We give an overview on Paclib, a library for parallel algebraic computation on shared memory multiprocessors. Paclib is essentially a package of C functions that provide the basic objects and methods of computer algebra in a parallel context. The Paclib programming model supports concurrency, shared memory communication, non-determinism and speculative parallelism. The system is based on a heap...

The primary intent of the present paper is to adapt familiar notions of algebraic topology, such as the fundamental group, homology, and cohomology to the context of algebraic maps and their (ramified) covering projections. The notion of a principal derived map is already fairly well understood in terms of the defining voltages; however, once it is recognized that voltages are essentially cohom...

We previously defined collagories essentially as “distributive allegories without zero morphisms”. Collagories are sufficient for accommodating the relation-algebraic approach to graph transformation, and closely correspond to the adhesive categories important for the categorical DPO approach to graph transformation. Heindel and Sobociński have recently characterised the Van-Kampen colimits use...

The ability to orchestrate different transformations in a flexible and reliable manner is a major challenge in MDE. Most of the current work on model transformations seems essentially operational and executable in nature. Such incomplete view on the composition issue provides suitable answers to a wide range of practical needs. However it does not cover the entire problem’s spectrum. In this ar...