Difference equation approach to two-thermocouple sensor characterisation in constant velocity flow environments

Thermocouples are one of the most popular devices for temperature measurement due to their robustness, ease of manufacture and installation, and low cost. However, when used in certain harsh environments, for example, in combustion systems and engine exhausts, large wire diameters are required, and consequently the measurement bandwidth is reduced. This article discusses a software compensation technique to address the loss of high frequency fluctuations based on measurements from two thermocouples. In particular, a difference equation sDEd approach is proposed and compared with existing methods both in simulation and on experimental test rig data with constant flow velocity. It is found that the DE algorithm, combined with the use of generalized total least squares for parameter identification, provides better performance in terms of time constant estimation without any a priori assumption on the time constant ratios of the thermocouples.

Math-Towers: Promoting and supporting online collaborative mathematical exploration

Math-Towers (www.math-towers.ca) is a collaborative mathematics environment for pupils in grades 7 to 9. Using a fantasy adventure game context students are presented with a mathematical challenge, given online tools for working on the problem,and provided with a messaging system by which they may exchange ideas and partial solutions. This paper presents the philosophy behind the design of Math-Towers and work with students that indicates the extent to which we have been successful in meeting our aims. The technical and social problems encountered and revisions made to address these are also described.

Math-Towers: Online Interactive Collaborative Mathematics Explorations & Problem-Solving for Students Ages 11 to 15 years (Grades 6 to 10)

Math-Towers (www.math-towers.ca) is an online resource for students in grades 6 to 10 that supports collaborative problem-solving and investigations. This paper presents the philosophical position motivating the development of Math-Towers and describes how the site presents and motivates the mathematical challenges and supports participants' exploration and collaboration.