On the Topology and Geometry of Spaces of Affine Shapes

We define the space of affine shapes of k points in R ⁿ to be the topological quotient of (R ⁿ ) ^k modulo the natural action of the affine group of R ⁿ . These spaces arise naturally in many image-processing applications, and despite having poor separation properties, have some topological and geometric properties reminiscent of the more familiar Procrustes shape spaces Σ _n ^k in which one identifies configurations related by an orientation-preserving Euclidean similarity transformation. We examine the topology of the connected, non-Hausdorff spaces Sh _n ^k in detail. Each Sh _n ^k is a disjoint union of naturally ordered strata, each of which is homeomorphic in the relative topology to a Grassmannian, and we show how the strata are attached to each other. The top stratum carries a natural Riemannian metric, which we compute explicitly for k>n, expressing the metric purely in terms of “pre-shape” data, i.e. configurations of k points in R ⁿ .     

Concurrency in Ada and multicomputers

Implementation of Ada's parallel tasks on a multicomputer architecture requires additional communication and naming overhead because tasks can operate on shared data via global variables and pointers. This increases the complexity of implementing Ada and has a negative impact on program understandability.     

Concurrency in programming languages: A survey

This paper surveys concurrency issues of programming languages. The evolution of these issues is analyzed in the context of the evolution of other language concepts, such as data and control abstraction.Specific concurrency concepts discussed in the paper include: granularity of parallelism, degree of parallelism, synchronization and communication, and physical distribution. The review of the problems of synchronization and communication includes semaphores, messages and mailboxes, and monitors.Concurrency aspects of ADA are also presented as a case study of a state-of-the-art programming language.     

Oval Domes: History,Geometry and Mechanics

An oval dome may be defined as a dome whose plan or profile (or both) has an oval form. The word “oval” comes from the Latin ovum, egg. The present paper contains an outline of the origin and application of the oval in historical architecture; a discussion of the spatial geometry of oval domes, that is, the different methods employed to lay them out; a brief exposition of the mechanics of oval arches and domes; and a final discussion of the role of geometry in oval arch and dome design.     

Determinacy and Concurrency Issues in Process Engineering

The goal of creating high-quality process systems for real-world applications leads to the need for an engineering approach to process system development. The development of process engineering as a distinct discipline can be greatly facilitated through the development of an engineering framework that supports the rigorous engineering of process systems.Reliability, cost and timeliness are key attributes of quality for engineering artifacts, independent of the specific engineering discipline. As a result, attention to these and other related issues of process system quality during process system design is viewed as necessary if order to achieve desired levels of quality in the resulting process systems.The task system model, a task-based process formalism that can serve as the basis for a process engineering framework, is described. Extensions to this model that are specifically intended to address process system reliability and parallelism are introduced. Process system reliability is addressed through the introduction of methods to ensure determinacy among concurrently executing tasks of a process system that share resources.Process system operating costs and execution timeliness are addressed by maximizing parallelism to the extent that reliability is not compromised.