Layers of generality and types of generalization in pattern activities

Pattern generalization is considered one of the prominent routes for in-troducing students to algebra. However, not all generalizations are al-gebraic. In the use of pattern generalization as a route to algebra, we —teachers and educators— thus have to remain vigilant in order not to confound algebraic generalizations with other forms of dealing with the general. But how to distinguish between algebraic and non-algebraic generalizations? On epistemological and semiotic grounds, in this arti-cle I suggest a characterization of algebraic generalizations. This char-acterization helps to bring about a typology of algebraic and arithmetic generalizations. The typology is illustrated with classroom examples.

Computational modelling of freeze layers in smelting processes

The use of computational modelling in examining process engineering issues is very powerful. It has been used in the development of the HIsmelt process from its concept. It is desirable to further water-cool the HIsmelt vessel to reduce downtime for replacing refractory. Water-cooled elements close to a metal bath run the risk of failure. This generally occurs when a process perturbation causes the freeze and refractory layers to come away from the water-cooled element, which is then exposed to liquid metal. The element fails as they are unable to remove all the heat. Modelling of the water-cooled element involves modelling the heat transfer, fluid flow, stress and solidification for a localised section of the reaction vessel. The complex interaction between the liquid slag and the refractory applied to the outside of thewater-cooled element is also being examined to model the wear of this layer. The model is being constructed in Physica, a CFD code developed at the University of Greenwich. Modelling of this system has commenced with modelling solidification test cases. These test cases have been used to validate the CFD code’s capability to model the solidification in this system. A model to track the penetration of slag into refractory has also been developed and tested.

Wind mixing, food availability and mortality of anchovy larvae Engraulis encrasicolus in the northern Adriatic Sea

A study was carried out in June/July 1996 in the River Po outflow in the northern Adriatic to investigate spawning of anchovy Engraulis encrasicolus and survival of larvae in relation to food availability and wind mixing. Hydrographic- and bongo net sampling was carried out on 2 grid surveys; one after a period of low winds and settled weather, and the other after an intervening period of strong winds, which resulted in a decrease in water column stratification. The spawning areas of anchovy and the larval distributions were associated with the river outflow plume (most clearly on the second survey grid, after the period of higher winds). Potential food particles for anchovy larvae, primarily copepod nauplii and copepodite stages, were also concentrated in the area influenced by the river outflow. Although there was a nearly 50% reduction in the mean water column abundance of potential food particles between the 2 survey grids, mostly due to a decline in abundance outside the immediate river plume area, there was no significant change in mortality of anchovy larvae between the 2 grids; the exponential decline in numbers of eggs and larvae to 10 mm in length being equivalent to overall mortality rates of 43.2%/d on the first survey and 44.7%/d on the second. The resilience of larval survival under potentially less favourable feeding conditions, following the period of wind mixing, was ascribed, in part, to the maintenance of local water column stratification by the superficial low salinity input from the River Po. This stratification in the immediate outflow area was associated with the presence of concentrated layers of potential food particles (typically >50 particles/L and 1.5 to 2.8 times the mean water column abundance) in the upper 10 m of the water column, coincident with peak numbers of anchovy larvae. However, since there was no evidence for lower larval survival in areas, less influenced by the immediate river outflow plume, a simple direct relationship between enhanced water column stability, improved feeding conditions and larval survival was not supported.

Improved Equivalent Frame Analysis Method for Flat Plate Structures in Vicinity of Edge Columns

This paper proposes a modification to the ACI 318-02 equivalent frame method of analysis of reinforced concrete flat plate exterior panels. Two existing code methods were examined: ACI 318 and BS 8110. The derivation of the torsional stiffness of the edge strip as proposed by ACI 318 is examined and a more accurate estimate of this value is proposed, based on both theoretical analysis and experimental results. A series of 1/3-scale models of flat plate exterior panels have been tested. Unique experimental results were obtained by measuring strains in reinforcing bars at approximately 200 selected locations in the plate panel throughout the entire loading history. The measured strains were used to calculate curvature and, hence, bending moments; these were used along with moments in the columns to assess the accuracy of the equivalent frame methods. The proposed method leads to a more accurate prediction of the moments in the plate at the column front face, at the panel midspan, and in the edge column. Registered Subscribers: View the full article. This document is available as a free download to qualified members. An electronic (PDF) version is available for purchase and download. Click on the Order Now button to continue with the download.

SiGe HBTs on Bonded SOI Incorporating Buried Silicide Layers

The performance of silicon bipolar transistors has been significantly improved by the use of ultra narrow base layers of SiGe. To further improve device performance by minimising parasitic resistance and capacitance the authors produced an unique silicon-on-insulator (SOI) substrate incorporating a buried tungsten disilicide layer. This structure forms the basis of a recent submission by Zarlink Semiconductors ( Silvaco, DeMontfort & Queen�s) to DTI for high voltage devices for automotive applications. The Queen�s part of the original EPSRC project was rated as tending to outstanding.

Effect of Rapid Thermal Annealing on the Structure and Magnetic Properties of Chemical Vapour Deposition Cobalt Layers

Future read heads in hard disc storage require high conformal coatings of metal magnetic layers over high aspect ratio profiles. This paper describes pioneering work on the use of MOCVD for the deposition of cobalt layers. While pure cobalt layers could be deposited at 400C their magnetic properties are poor. It was found that the magnetic properties of the layers could be significantly enhanced with an optimised rapid thermal anneal. This work was sponsored by Seagate Technology and led to a follow up PhD studentship on the co-deposition of cobalt and iron by MOCVD.