Using the Magma Computer Algebra System in Abstract Algebra Courses

Students meeting their first serious course in abstract algebra commonly experience difficulty understanding many of the basic concepts. This makes it very hard for them to interpret and generate proofs. The first step in reaching an understanding of such concepts is often best achieved by constructing and manipulating instances in particular algebraic structures. Computer algebra systems open up the possibility of students being able to experiment rapidly and conveniently with such concepts in a variety of structures having non-trivial size and complexity. The new Magma computer algebra system has a syntax and semantics based directly on fundamental algebraic notions, and consequently should provide an appropriate learning environment for those branches of mathematics that are heavily algebraic in nature. This paper describes the development of Magma-based exercises and a course methodology that utilizes Magma as a key learning tool in a Pass-level Rings and Fields course given at the University of Sydney.     

FROM ARTIFICIAL LIFE TO REAL LIFE: COMPUTER SIMULATION OF PLANT GROWTH∗

Artificial life is by itself an important area of scientific investigation. However, this scientific discipline will be more effective if it can also help one to understand how natural living systems really work. It is argued that plant growth is an area where the studies in artificial life lend themselves to computer modeling of what really happens in nature. An approach for such modeling is described, and the initial results of implementing this approach for a corn plant growth are presented.     

New class of control laws for robotic manipulators Part 1. Non–adaptive case

A new class of exponentially stabilizing control laws for joint level control of robot arms is introduced. It has recently been recognized that the non-linear dynamics associated with robotic manipulators have certain inherent passivity properties. More specifically, the derivation of the robotic dynamic equations from Hamilton's principle gives rise to natural Lyapunov functions for control design based on total energy considerations. Through a slight modification of the energy Lyapunov function and the use of a convenient lemma to handle third–order terms in the Lyapunov function derivatives, closed–loop exponential stability for both the set point and tracking control problem is demonstrated. In one new design, the nonlinear terms are decoupled from real-time measurements which completely removes the requirement for on–line computation of non–linear terms in the controller implementation. In general, the new class of control laws offers alternatives to the more conventional computed torque method, providing trade–offs between computation and convergence properties. Furthermore, these control laws have the unique feature that they can be adapted in a very simple fashion to achieve asymptotically stable adaptive control.     

GENTRIFICATION AND THE RIGHT TO THE CITY: COMMUNITY CONFLICT AND CASINOS

Henri Lefebvre's right to the city concept is increasingly used to challenge the development prerogatives associated with neoliberal development. These challenges are more common as gentrification becomes a global urban strategy. This article is an empirical investigation that examines competing claims to community legitimacy and authenticity in a conflict over gentrification in a Philadelphia neighborhood. This conflict emerged in Fishtown when long‐time established residents went head to head with upper‐income gentrifiers over the location of a casino in the neighborhood. Place‐based identities and the temporal connection individuals had to Fishtown contributed to the differences in perspectives on the costs and benefits of the casino and on the legitimacy of long‐time residents versus newcomers to be representative voices on behalf of Fishtown. The findings illuminate problems in applying the right to the city to neighborhood struggles when communities are divided over what constitutes a benefit to the community. The right to the city may not be a universal claim, particularly within a neoliberal urban context.     

AUTOMATIC GENERATION OF TECHNICAL DOCUMENTATION

Natural-language generation (NLG) techniques can be used to automatically produce technical documentation from a domain knowledge base and linguistic and contextual models. We discuss this application of NLG technology from both a technical and a usefulness (costs and benefits) perspective. This discussion is based largely on our experiences with the Intelligent Documentation Advisory System (IDAS) documentation-generation project, and the reactions that various interested people from industry have had to IDAS. We hope that this summary of our experiences with IDAS and the lessons we have learned from it will be beneficial for other researchers who wish to build technical documentation-generation systems.     

Inventory control with general demand and lead time distributions

This paper extends an earlier paper in this journal by Murphy (1975) by presenting practical approaches for determining the expected lost sales for a reorder level system of inventory control. First, a set of formulas are derived for computing the first four moments (f.f.m.) of the lead time demand, these formulas are applicable to any distribution forms of daily demand and lead time. By fitting the lead time demand's f.f.m. to either a beta or a Schmeiser-Deutsch distribution, this paper then demonstrates how the expected lost sales can be easily computed. The approaches presented provide accurate modelling for diversified situations and the computations can be easily performed manually.     

YTTRIUM ALUMINATE CERAMIC FIBERS VIA PRE-CERAMIC POLYMER AND SOL-GEL ROUTES

ABSTRACT

Yttrium aluminum garnet (YAG - Y₃Al₅O₁₂) fibers have been prepared by dry spinning solutions of yttrium and aluminum carboxylate polymers (precursor route) and by dry spinning aqueous oxide sols (sol-gel route). Fibers from aqueous diphasic gels are prepared by mixing a colloidal alumina sol containing 50-nm hydrous alumina with a colloidal yttria sol containing 10-nm yttrium oxide, using polyvinylpyrrolidone as a spinning aid. Fibers by the precursor route are made from spinnable THF solutions of yttrium isobutyrate and aluminum isobutyrate or from aqueous solutions of polymeric aluminum formate and yttrium acetate.

The isobutyrate materials decompose between 200-400^°C to an amorphous residue. Crystallization occurs abruptly between 875°C and 900^°C, forming the YAG phase directly. The formate-acetate also decomposes to amorphous residues, which form YAG at 900^°C. In the diphasic gel, YAG forms gradually between 1000 and 1200^°C, with intermediate products YAP (YalO₃ perovskite) and/or YAM (Y₄Al₂O₉ monoclinic). At 1500^°C, single phase YAG is obtained as pore-free fibers with 500 nm grains.     

Impact of International Lending on Metals Industries

The world metals industries entered a period of turbulent change in the mid 1970s. Many of those changes—in terms of demand structure, supply sources, industry concentration, trade patterns, price/cost relationships, and financial arrangements— are still in process. Our topic relates to the impact of international lending on the metals industries, both private and public. The paper gives a brief overview of the various sources of lending available for the metal industries, and then looks at the changing patterns of financing for metals projects and the implications for metals operations and for lending institutions.     

The paradox of observation and the observation of paradox

Abstract

Achilles cannot overtake a fleeing tortoise because in the interval of time that he takes to get to where the tortoise was, it can move away. But even if it should wait for him Achilles must first reach the half-way mark between them and he cannot do this unless he first reaches the half-way mark to that mark, and so on indefinitely. Against such an infinite conceptual regression he cannot even make a start, and so motion is impossible (Zeno, according to Zippin 1962, p. 10).