Coordination of aproximations in secondary school students’ understanding of limit concept

The aim of this research is to characterize the coordination of the processes of approximation related to the understanding of the limit of a function. We analyze the answers of 64 post-secondary school students to 7 problems considering the dynamic and metric conception of limit of a function. Results indicate that the metric understanding of the limit in terms of inequality supports that the student is capable of coordinating the approximations in the domain and in the range when lateral approximations coincide. However, the student is not capable of this coordination when lateral approximations do not coincide. This indicates that the metric understanding of the limit begins with the previous construction of the dynamic conception in case of coincidence of the lateral approximations in the range.

¿Cómo estudiantes para profesor de matemáticas comprenden el aprendizaje del límite de una función?

En este estudio presentamos una investigación que tiene como objetivo generar información sobre cómo estudiantes para profesor de educación secundaria (EPS) comprenden el proceso de aprendizaje de las matemáticas. El contexto que hemos utilizado es la actividad de anticipar respuestas de los estudiantes de Bachillerato que reflejen diferentes niveles de desarrollo conceptual de la comprensión del concepto de límite de una función, como una actividad relevante vinculada a la competencia docente. Los resultados muestran dos formas distintas de considerar la comprensión del concepto de límite por parte de los EPS que tienen implicación sobre cómo anticipan las respuestas de los estudiantes y sobre las características de los problemas que plantean para apoyar el aprendizaje de la concepción dinámica de límite de los estudiantes.

AITPM Email Newsletter Volume 0910, October 2009 : Presidents Message

President’s Message Hello fellow AITPM members, Well I can’t believe it’s already October! My office is already organising its end of year function and looking to plan for 2010. Our whole School is moving to a different building next year, with the lovely L block eventually making way for a new shiny one. Those of you who have entered the Brisbane CBD from the south side, across the Captain Cook Bridge, would know L block as the big 9 storey brick and concrete Lego block ode to 1970’s functional architecture, which greets you on the right hand side. Onto traffic matters: an issue that has been tossing around in my mind of late is that of speed. I know I am growing older and may be prematurely becoming a “grumpy old man”, but everyone around me locally seems to be accelerating off from the stop line much faster than I was taught to for economical driving, both here and in the United States (yes they made my wife and me resit our written and practical driving tests when we lived there). People here in Australia also seem to be driving right on top of the posted speed limit, on whichever part of the Road Hierarchy, whether urban or rural. I was also taught on both sides of the planet that the posted speed limit is a maximum legal speed, not the recommended driving speed. This message did seem to sink in to the American drivers around me when we lived in Oregon - where people did appear to drive more cautiously. Further, posted speed limits in Oregon were, and I presume still are, set more conservative by about 5mph or 10km/h than Australian limits, for any given part of the Road Hierarchy. Another excellent speed limit treatment used in Oregon was in school zones, where reduced speed limits applied “when children are present” rather than during prescribed hours on school days. This would be especially useful here in Australia, where a lot of extra-curricular activities take place around schools outside of the prescribed speed limit hours. Before and after hours school care is on the increase (with parents dropping and collecting children near dawn and dusk in the winter), and many childcentred land uses are located adjacent to schools, such as Scouts/Guides halls, swimming pools and parks. Consequentially, I believe there needs to be some consideration towards more public campaigning about economical driving and the real purpose of the speed limit = or perhaps even a rethink of the speed limit concept, if people really are driving on top of it and it’s not just me becoming grumpier (our industrial psychology friends at the research centres may be able to assist us here). The Queensland organising committee is now in full swing organising the 2010 AITPM National Conference, What’s New?, so please keep a lookout for related content. Best regards to all, Jon Bunker PS A Cartoonists view of traffic engineers I thought you might enjoy this. http://xkcd.com/277/

Some limit theorems for regenerative queues

We consider a single server queue with the interarrival times and the service times forming a regenerative sequence. This traffic class includes the standard models: lid, periodic, Markov modulated (e.g., BMAP model of Lucantoni [18]) and their superpositions. This class also includes the recently proposed traffic models in high speed networks, exhibiting long range dependence. Under minimal conditions we obtain the rates of convergence to stationary distributions, finiteness of stationary moments, various functional limit theorems and the continuity of stationary distributions and moments. We use the continuity results to obtain approximations for stationary distributions and moments of an MMPP/GI/1 queue where the modulating chain has a countable state space. We extend all our results to feedforward networks where the external arrivals to each queue can be regenerative. In the end we show that the output process of a leaky bucket is regenerative if the input process is and hence our results extend to a queue with arrivals controlled by a leaky bucket.

An all-in-one dry chemistry immunoassay for the screening of coccidiostat nicarbazin in poultry eggs and liver

An automated immunoassay for the detection of nicarbazin residues in poultry eggs and liver was developed. The assay was based on a novel all-in-one dry chemistry concept and time-resolved fluorometry. The analyte specific antibody was immobilized into a single microtiter well and covered with an insulation layer, on top of which the label was dried in a small volume. The extracted sample was added automatically to the dry microtiter well, and the result was available within 18 min. Due to the rapidity and simplicity, the quantitative immunoassay could also be used as a high throughput screening method. The analytical limit of detection for the assay was calculated as 0.1 ng mL(-1) (n = 12) and the functional limit of detection as 3.2 ng g(-1) for egg (n = 6) and 11.3 ng g(-1) for liver (n = 6) samples. The sample recovery varied from 97.3 to 115.6%. Typically, the intra-assay variations were less than 10%, and interassay variations ranged between 8.1 and 13.6%.

A specificity-enhanced time-resolved fluoroimmunoassay for zeranol employing the dry reagent all-in-one-well principle

A simple dry chemistry time-resolved fluorescence immunoassay (TR-FIA) method was developed for the measurement of zeranol in bovine urine samples. The samples were purified by immunoaffinity chromatography and a specificity-enhanced zeranol antibody was employed in the immunoassay. This resulted in a highly selective method, which had only negligible reactivity with Fusarium spp, toxins. The all-in-one-well dry chemistry concept made the assay very simple to use because all the assay-specific reagents were already present in the reaction wells in dry form. Only the addition of diluted sample extract was required to perform the competitive one-step TR-FIA and the results were available in less than 1 h. The analytical limit of detection (mean + 3s) for the immunoassay was 0.16 ng ml(-1) (n=12) and the functional limit of detection for the whole method, estimated by the analysis of zeranol-free samples, was 1.3 ng ml(-1) (n=20). The recovery of zeranol at the level of 2 ng ml(-1) was 99% (n=18) and the within-assay variation ranged between 4.5 and 9.0%.

Performance analysis of a slotted-ALOHA protocol on a capture channel with fading

We consider the slotted ALOHA protocol on a channel with a capture effect. There are M functional limit theorems. Our arrival streams contain all the traffic models suggested in the recent literature, including the ones which display long range dependence. We also obtain bounds on the stationary moments of waiting times which can be tight under realistic conditions. Finally, we obtain several results on the transient performance of the system, e.g., first time to overflow and the limits of the overflow process. We also extend the above results to the case of a capture channel exhibiting Markov modulated fading. Most of our results and proofs will be shown to hold also for the slotted ALOHA protocol without capture.

Laser conditioning of ZrO2 : Y2O3/SiO2 mirror coatings prepared by E-beam evaporation

Laser conditioning effects of the dielectric mirror coatings with different designs were investigated. Simple quarter-wave ZrO2:Y2O3/SiO2 mirrors and half-wave SiO2 over-coated ZrO2:Y2O3/SiO2 mirror coatings were fabricated by E-beam evaporation (EBE). The absorbance of the samples before and after laser conditioning was measured by surface thermal lensing (STL) technology and the defects density was detected under Nomarski microscope. The enhancement of the laser damage resistance was found after laser conditioning. The dependence of the laser conditioning on the coating design was also observed and the over-coated sample obtained greatest enhancement, whereas the absorbance of the samples did not change obviously. During the sub-threshold fluence raster scanning, the minor damage about defects size was found and the assumption of pre-damage mechanism, based on the functional damage concept, was put forward. The improvement of the laser induced damage threshold (LIDT) was attributed to the benign damage of the defects and the dependence on the coating design owed to the damage growth behavior of different coating designs. (C) 2004 Elsevier B.V. All rights reserved.

Trophic interactions in a changing world: modelling aboveground-belowground interactions

The rate and scale of human-driven changes can exert profound impacts on ecosystems, the species that make them up and the services they provide that sustain humanity. Given the speed at which these changes are occurring, one of society's major challenges is to coexist within ecosystems and to manage ecosystem services in a sustainable way. The effect of possible scenarios of global change on ecosystem services can be explored using ecosystem models. Such models should adequately represent ecosystem processes above and below the soil surface (aboveground and belowground) and the interactions between them. We explore possibilities to include such interactions into ecosystem models at scales that range from global to local. At the regional to global scale we suggest to expand the plant functional type concept (aggregating plants into groups according to their physiological attributes) to include functional types of aboveground-belowground interactions. At the scale of discrete plant communities, process-based and organism-oriented models could be combined into "hybrid approaches" that include organism-oriented mechanistic representation of a limited number of trophic interactions in an otherwise process - oriented approach. Under global change the density and activity of organisms determining the processes may change non-linearly and therefore explicit knowledge of the organisms and their responses should ideally be included. At the individual plant scale a common organism-based conceptual model of aboveground-belowground interactions has emerged. This conceptual model facilitates the formulation of research questions to guide experiments aiming to identify patterns that are common within, but differ between, ecosystem types and biomes. Such experiments inform modelling approaches at larger scales. Future ecosystem models should better include this evolving knowledge of common patterns of aboveground-belowground interactions. Improved ecosystem models are necessary toots to reduce the uncertainty in the information that assists us in the sustainable management of our environment in a changing world. (C) 2004 Elsevier GmbH. All rights reserved.