What is rate? Does context or representation matter?

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students’ conceptions of rate, focussing on the influence of representation and context on their expression of their understanding of rate. This analysis shows that different representations of functions provide varying levels of rate-related information for individual students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important, but commonly misunderstood, mathematical concept with many everyday applications (Swedosh, Dowsey, Caruso, Flynn, & Tynan, 2007). It is a complicated concept comprising many interwoven ideas such as the ratio of two numeric, measurable quantities but in a context where both quantities are changing. In mathematics classes, this is commonly expressed as change in the dependent variable resulting from a unit change in the independent variable, and variously described as constant or variable rate; average or instantaneous rate. In addition, rate may be seen as a purely abstract mathematical notion or embedded in the understanding of real-world applications. This paper explores the research question: Are students’ expressions of their conceptions of rate affected by either context or mathematical representation? This question was part of a larger study (Herbert, 2010) conducted with Grade 10 students from the Australian state of Victoria.

Analysis of work hardening and recrystallization during the hot working of steel using a statistically based internal variable model

A mathematical model has been developed which describes the hot deformation and recrystallization behavior of austenite using a single internal variable: dislocation density. The dislocation density is incorporated into equations describing the rate of recovery and recrystallization. In each case no distinction is made between static and dynamic events, and the model is able to simulate multideformation processes. The model is statistically based and tracks individual populations of the dislocation density during the work-hardening and softening phases. After tuning using available data the model gave an accurate prediction of the stress–strain behavior and the static recrystallization kinetics for C–Mn steels. The model correctly predicted the sensitivity of the post deformation recrystallization behavior to process variables such as strain, strain rate and temperature, even though data for this were not explicitly incorporated in the tuning data set. In particular, the post dynamic recrystallization (generally termed metadynamic recrystallization) was shown to be largely independent of strain and temperature, but a strong function of strain rate, as observed in published experimental work.

A model of the Australia-US exchange rate

This paper develops a model of exchange rate determination within an error correction framework. The intention is to identify both long and short term determinants that can be used to forecast the AUD/US exchange rate. The paper identifies a set of significant variables associated with exchange rate movements over a twenty year period from 1984 to 2004. Specifically, the overnight interest rate differential, Australia's foreign trade-weighted exposure to commodity prices as well as exchange rate volatility are variables identified that are able explain movements in the AUDIUS dollar relationship. An error correction model is subsequently constructed that incorporates an equilibrium correction term, a short-term interest rate differential variable, a commodity price variable and a proxy for exchange rate volatility. The model is then used to forecast out of sample and is found to dominate a naIve random walk model based on three different metrics.

A class of modified variable step-size NLMS algorithms for system identification

This paper proposes a class of modified variable step-size normalized least mean square (VS NLMS) algorithms. The class of schemes are obtained from estimating the optimum step-size of NLMS that minimizes the mean square deviation (MSD). During the estimation, we consider the properties of the additive noise and the input excitation together. The developed class of VS NLMS algorithms have simple forms and give improved tradeoff of fast convergence rate and low misadjustment in system identification.

Textural fractography of fatigue failures under variable cycle loading

A new concept of counting time at fatigue processes is proposed, aimed to reach fractographic compatibility in cases of different loading sequences. Values of cycle effectivity are summarized to give the new reference time. The improvement is shown in application - textural fractography of three specimens loaded by constant cycle, constant cycle with periodic overloading, and a random block, respectively. In contrast to the conventional crack growth rate, the reference crack growth rate is related to common morphologic features of all fracture surfaces.

Performance of the Giant Reed (Arundo donax) in experimental wetlands receiving variable loads of industrial stormwater

Two emergent macrophytes, Arundo donax and Phragmites australis, were established in experimental subsurface flow, gravel-based constructed wetlands (CWs) and challenged by untreated stormwater collected from the hard-pan and other surfaces of a dairy processing factory in south-west Victoria, Australia. The hydraulic loading rate was tested at two levels, sequentially, 3.75 and 7.5 cm day -1. Some of the monitored variables were removed more efficiently by the planted beds in comparison to unplanted CWs (biochemical oxygen demand (BOD), total nitrogen (TN) and total phosphorus (TP); p<0.007) but there was no significant difference between the A. donax and P. australis CWs in removal of BOD, suspended solids (SS) and TN (p>0.007) at 3.75 cm day -1 or SS and TN at 7.5 cm day -1. At 3.75 cm day -1, BOD, SS, TN and TP removal in the A. donax and P. australis CWs was 71%, 61%, 78% and 75% and 65%, 60%, 73% and 41%, respectively. Nutrient removal at 7.5 cm day -1 in the A. donax and P. australis beds was 87%, 91%, 84% and 71% and 96%, 94%, 87% and 55%, respectively. As expected, the A. donax CWs produced considerably more biomass (10±1.2 kg wet weight) than the P. australis CWs (2.7±1.2 kg wet weight). This equates to approximately 107 and 36 tonnes ha -1 year -1 biomass (dry weight) for A. donax and P. australis, respectively (assuming 250 days of growing season and singlecut harvest). The performance similarity of the A. donax- and P. australis-planted CWs indicates that either may be used in HSSF wetlands treating dairy factory stormwater, although the planting of A. donax provides additional opportunities for secondary income streams through utilisation of the biomass produced.

Basal metabolic rate of canidae from hot deserts to cold arctic climates

Canids form the most widely distributed family within the order Carnivora, with members present in a multitude of different environments from cold arctic to hot, dry deserts. We reviewed the literature and compared 24 data sets available on the basal metabolic rate (BMR) of 12 canid species, accounting for body mass and climate, to examine inter- and intraspecific variations in mass-adjusted BMR between 2 extreme climates (arctic and hot desert). Using both conventional and phylogenetically independent analysis of covariance, we found that canids from the arctic climate zone had significantly higher mass-adjusted BMR than species from hot deserts. Canids not associated with either arctic or desert climates had an intermediate and more variable mass-adjusted BMR. The climate effect also was significant at the intraspecific level in species for which we had data in 2 different climates. Arctic and desert climates represent contrasting combinations of ambient temperatures and water accessibility that require opposite physiological adaptations in terms of metabolism. The fact that BMR varies within species when individuals are subjected to different climate regimes further suggests that climate is an important determinant of BMR.

A case study on effect of feed rate on machinability of austempered ductile iron

Austempered Ductile Iron (ADI) is a type of nodular, ductile cast iron subjected to heat treatments - austenitising and austempering. Whilst machining is conducted prior to heat treatment and offers no significant difficulty, machining post heat treatment is demanding and often avoided. Phase transformation of retained austenite to martensite leading to poor machinability characteristics is a common problem experienced during machining. This case study explains the effect of feed rate on machinability of ADI using cutting force analysis and tool failure analysis. The experimental design consists of conducting drilling trials on grade 1200 and 1400 at constant depth of cut, 25mm; constant speed, 45m/min; no coolant and variable feed rates from 0.2 to 0.35 mm/rev (increment of 0.025mm/rev). Metallography and X-ray diffraction technique was carried out in order to identify and quantify the microstructural phases before and after drilling. The results from the trial infer that the best way to machine ADI efficiently without tool failure is using low feeds and high speeds and without coolant.

N-dimensional animal energetic niches clarify behavioural options in a variable marine environment

Animals respond to environmental variation by exhibiting a number of different behaviours and/or rates of activity, which result in corresponding variation in energy expenditure. Successful animals generally maximize efficiency or rate of energy gain through foraging. Quantification of all features that modulate energy expenditure can theoretically be modelled as an animal energetic niche or power envelope; with total power being represented by the vertical axis and n-dimensional horizontal axes representing extents of processes that affect energy expenditure. Such an energetic niche could be used to assess the energetic consequences of animals adopting particular behaviours under various environmental conditions. This value of this approach was tested by constructing a simple mechanistic energetics model based on data collected from recording devices deployed on 41 free-living Magellanic penguins (Spheniscus magellanicus), foraging from four different colonies in Argentina and consequently catching four different types of prey. Energy expenditure was calculated as a function of total distance swum underwater (horizontal axis 1) and maximum depth reached (horizontal axis 2). The resultant power envelope was invariant, irrespective of colony location, but penguins from the different colonies tended to use different areas of the envelope. The different colony solutions appeared to represent particular behavioural options for exploiting the available prey and demonstrate how penguins respond to environmental circumstance (prey distribution), the energetic consequences that this has for them, and how this affects the balance of energy acquisition through foraging and expenditure strategy.

Behavioral inference of diving metabolic rate in free-ranging leatherback turtles

Good estimates of metabolic rate in free‐ranging animals are essential for understanding behavior, distribution, and abundance. For the critically endangered leatherback turtle (Dermochelys coriacea), one of the world’s largest reptiles, there has been a long‐standing debate over whether this species demonstrates any metabolic endothermy. In short, do leatherbacks have a purely ectothermic reptilian metabolic rate or one that is elevated as a result of regional endothermy? Recent measurements have provided the first estimates of field metabolic rate (FMR) in leatherback turtles using doubly labeled water; however, the technique is prohibitively expensive and logistically difficult and produces estimates that are highly variable across individuals in this species. We therefore examined dive duration and depth data collected for nine free‐swimming leatherback turtles over long periods (up to 431 d) to infer aerobic dive limits (ADLs) based on the asymptotic increase in maximum dive duration with depth. From this index of ADL and the known mass‐specific oxygen storage capacity (To2) of leatherbacks, we inferred diving metabolic rate (DMR) as . We predicted that if leatherbacks conform to the purely ectothermic reptilian model of oxygen consumption, these inferred estimates of DMR should fall between predicted and measured values of reptilian resting and field metabolic rates, as well as being substantially lower than the FMR predicted for an endotherm of equivalent mass. Indeed, our behaviorally derived DMR estimates ( mL O2 min−1 kg−1) were times the resting metabolic rate measured in unrestrained leatherbacks and times the average FMR for a reptile of equivalent mass. These DMRs were also nearly one order of magnitude lower than the FMR predicted for an endotherm of equivalent mass. Thus, our findings lend support to the notion that diving leatherback turtles are indeed ectothermic and do not demonstrate elevated metabolic rates that might be expected due to regional endothermy. Their capacity to have a warm body core even in cold water therefore seems to derive from their large size, heat exchangers, thermal inertia, and insulating fat layers and not from an elevated metabolic rate.

An organic ionic plastic crystal electrolyte for rate capability and stability of ambient temperature lithium batteries

Reliable, safe and high performance solid electrolytes are a critical step in the advancement of high energy density secondary batteries. In the present work we demonstrate a novel solid electrolyte based on the organic ionic plastic crystal (OIPC) triisobutyl(methyl)phosphonium bis(fluorosulfonyl)imide (P1444FSI). With the addition of 4 mol% LiFSI, the OIPC shows a high conductivity of 0.26 mS cm-1 at 22 °C. The ion transport mechanisms have been rationalized by compiling thermal phase behaviour and crystal structure information obtained by variable temperature synchrotron X-ray diffraction. With a large electrochemical window (ca. 6 V) and importantly, the formation of a stable and highly conductive solid electrolyte interphase (SEI), we were able to cycle lithium cells (LiLiFePO4) at 30 °C and 20 °C at rates of up to 1 C with good capacity retention. At the 0.1 C rate, about 160 mA h g-1 discharge capacity was achieved at 20 °C, which is the highest for OIPC based cells to date. It is anticipated that these small phosphonium cation and [FSI] anion based OIPCs will show increasing significance in the field of solid electrolytes.

Effects of Mitochondrial DNA Rate Variation on Reconstruction of Pleistocene Demographic History in a Social Avian Species, Pomatostomus superciliosus

Mitochondrial sequence data is often used to reconstruct the demographic history of Pleistocene populations in an effort to understand how species have responded to past climate change events. However, departures from neutral equilibrium conditions can confound evolutionary inference in species with structured populations or those that have experienced periods of population expansion or decline. Selection can affect patterns of mitochondrial DNA variation and variable mutation rates among mitochondrial genes can compromise inferences drawn from single markers. We investigated the contribution of these factors to patterns of mitochondrial variation and estimates of time to most recent common ancestor (TMRCA) for two clades in a co-operatively breeding avian species, the white-browed babbler Pomatostomus superciliosus. Both the protein-coding ND3 gene and hypervariable domain I control region sequences showed departures from neutral expectations within the superciliosus clade, and a two-fold difference in TMRCA estimates. Bayesian phylogenetic analysis provided evidence of departure from a strict clock model of molecular evolution in domain I, leading to an over-estimation of TMRCA for the superciliosus clade at this marker. Our results suggest mitochondrial studies that attempt to reconstruct Pleistocene demographic histories should rigorously evaluate data for departures from neutral equilibrium expectations, including variation in evolutionary rates across multiple markers. Failure to do so can lead to serious errors in the estimation of evolutionary parameters and subsequent demographic inferences concerning the role of climate as a driver of evolutionary change. These effects may be especially pronounced in species with complex social structures occupying heterogeneous environments. We propose that environmentally driven differences in social structure may explain observed differences in evolutionary rate of domain I sequences, resulting from longer than expected retention times for matriarchal lineages in the superciliosus clade.

New variable step-sizes minimizing mean-square deviation for the lms-type algorithms

The least-mean-square-type (LMS-type) algorithms are known as simple and effective adaptation algorithms. However, the LMS-type algorithms have a trade-off between the convergence rate and steady-state performance. In this paper, we investigate a new variable step-size approach to achieve fast convergence rate and low steady-state misadjustment. By approximating the optimal step-size that minimizes the mean-square deviation, we derive variable step-sizes for both the time-domain normalized LMS (NLMS) algorithm and the transform-domain LMS (TDLMS) algorithm. The proposed variable step-sizes are simple quotient forms of the filtered versions of the quadratic error and very effective for the NLMS and TDLMS algorithms. The computer simulations are demonstrated in the framework of adaptive system modeling. Superior performance is obtained compared to the existing popular variable step-size approaches of the NLMS and TDLMS algorithms. © 2014 Springer Science+Business Media New York.