Constant Rate Of Change Research Articles

Developing (Pedagogical) content knowledge of constant rate of change: The case of Samantha

We present the results of a teaching experiment designed to foster a pre-service secondary teacher’s construction of a quantitative scheme for constant rate of change. Although the research participant developed a productive conception of constant rate of change as an interiorized ratio, images of chunky continuous covariation constrained her ability to reason efficiently across a variety of applied contexts. The participant constructed a scheme for constant rate of change at the reflected level of thought, which enabled her to become cognizant of its essential aspects and to appreciate its general applicability. Our results suggest that engaging in reflected abstraction is critical for supporting pre-service teachers’ construction of coherent and refined mathematical schemes.

Models for Estimating Intrinsic r and the Mean Age of a Population at Stability: Evaluations at the National and Sub-national Level

Using Canada’s provinces and territories in conjunction with the “Cohort Change Ratio” approach to generating a stable population, I test the accuracy of two regression models constructed from national-level data designed to estimate two factors of a population at stability from initial conditions at the sub-national levels: (1) its constant rate of change, denoted here by r'; and (2) mean population age. In a test of accuracy at the national level I find that these models provide reasonably accurate estimates. In the tests at the subnational level, the accuracy, as expected, is less, but the results indicate that the national level models provide estimates that are useful. The models are useful because they are tractable and provide information not available from the traditional analytical approaches. Evaluating these models also provides the opportunity to look at Canada’s provinces and territories from a stable population perspective. The findings support the use of: (1) The Cohort Change Ratio approach in examining stable population concepts; and (2) the two regression models for estimating r' and the mean age of a population at stability. They also show that there are connections between initial conditions and stability that have been overlooked. This knowledge gap may be due to the fact that widespread knowledge and acceptance of the ergodic nature of the “age structure factor,” have served to mask the possibility that ergodicity does not always apply to other factors. Further exploration of these potential linkages appears to be in order.

High DC-Bias Stability and Reliability in BaTiO3-Based Multilayer Ceramic Capacitors: The Role of the Core-Shell Structure and the Electrode.

With the miniaturization of multilayer ceramic capacitors (MLCCs) and the increase of the electric field on a single dielectric layer, dielectric constant DC-bias stability and reliability have gradually aroused attention in the advanced electronics industry. In this study, MLCCs with outstanding DC-bias stability and reliability were prepared by using dielectric ceramic optimization and electrode optimization strategies. The effect of the Dy-Y doping concentration on the microstructure, dielectric properties, and reliability of BaTiO3-based ceramics was investigated. The shell ratio and effective shell doping concentration of the core-shell structure in ceramic grains play important roles in defects and electrical performances. The ceramic with appropriate doping contents shows a dielectric constant of 1800 and a dielectric constant change rate of -17% under a DC field of 4 kV/mm, which was fabricated into prototype MLCCs with different Ni electrodes. MLCCs exhibit outstanding DC-bias stability with a -28% degradation in the dielectric constant under a DC field of 4 kV/mm while possessing a dielectric constant of 2300 and satisfying the EIA X7S specification. Additionally, it was discovered that MLCCs prepared by using fine-size Ni particle electrodes have low electrode roughness and high interfacial Schottky barriers, resulting in better reliability. This study provides promising candidate materials and theoretical references for high-end and high DC-bias stability MLCCs.

Energy budget diagnosis of changing climate feedback.

The climate feedback determines how Earth's climate responds to anthropogenic forcing. It is thought to have been more negative in recent decades due to a sea surface temperature "pattern effect," whereby warming is concentrated in the western tropical Pacific, where nonlocal radiative feedbacks are very negative. This phenomenon has however primarily been studied within climate models. We diagnose a pattern effect from historical records as an evolution of the climate feedback over the past five decades. Our analysis assumes a constant rate of change of the climate feedback, which is justified post hoc. We find a decrease in climate feedback by 0.8 ± 0.5 W m-2 K-1 over the past 50 years, corresponding to a reduction in climate sensitivity. Earth system models' climate feedbacks instead increase over this period. Understanding and simulating this historical trend and its future evolution are critical for reliable climate projections.

Nonlinear dynamics of system with combined rolling–sliding contact and clearance

Rolling–sliding contacts are found in a variety of systems, such as gears, drum brakes, and tire pavements. Such systems inherently have multiple nonlinearities such as kinematic, contact, and friction nonlinearities. Further, most of these systems have clearance between components which causes excessive vibration and noise. The combination of clearance with other nonlinearities makes the system dynamically interesting. It is important to understand the dynamic behavior of such systems under various operating conditions. Hence, this article focuses on theoretically investigating the transient and steady-state responses of a cam–follower system with rolling–sliding contact and clearance as an exemplary case. A contact mechanics-based model for the same has been developed for this purpose. The transient behavior of the system is examined based on energy and time-varying frequency contents. The domain of attractors, frequency response plots, and phase portraits are deployed to analyze the effect of initial conditions and excitation speed on the steady-state behavior, quantitatively and qualitatively. The steady-state solutions were classified into various branches based on periodicity and phase portraits. In addition, parametric analyses of the effects of loading, damping, and friction on the response have been conducted. Finally, the system is examined for start-up and shut-down characteristics with a constant rate of change in excitation frequency.

Standardization of diagnostic indicators of gearbox teeth wear in aircraft gas-turbine engines

The gearboxes of aircraft gas turbine engines are their most stressed parts. One of the main gearbox defects is the tooth flank wear that causes resonant oscillations in engine structure elements. This defect is generally assessed using vibroacoustic diagnostics methods. It is noted that the currently existing recommendations on setting limit values for diagnostic indicators do not take into account the type of mathematical models that describe their dependence on the defect size. This can result in its uncontrolled development. We have shown that for the case under consideration, four kinds of mathematical models were earlier obtained to describe dependences of diagnostic indicators on the wear value: linear, power, exponential and combined (linear and exponential) models. The linear model is characterized by a constant rate of change in the level of a diagnostic indicator with the growth of wear. For power and exponential models the growth of wear leads to an increase of the rate of change in the diagnostic indicator value. The combined model is characterized by the presence of two zones of change in the diagnostic indicator intensity with the growth of wear: the constant rate zone and the zone of increasing rate. The use of diagnostic indicators with a continuous increase in their intensity depending on the growth of wear will require ensuring constant control of the gearbox vibration state, which is not always feasible. We give recommendations for setting standard values of the diagnostic indicator intensity for the considered models.

Trends in methamphetamine use, markets and harms in Australia, 2003-2019.

To describe trends in methamphetamine use, markets and harms in Australia from 2003 to 2019. Data comprised patterns of use and price from sentinel samples of people who inject drugs and who use MDMA/other illicit stimulants and population-level amphetamine-related police seizures, arrests, hospitalisations, treatment episodes and deaths from approximately 2003 to 2019. Bayesian autoregressive time-series models were analysed for: no change; constant rate of change; and change over time differing in rate after one to three changepoints. Related indicators were analysed post hoc with identical changepoints. The percentage of people who inject drugs reporting weekly use increased from 2010 to 2013 onwards, while use among samples of people who regularly use ecstasy and other illicit stimulants decreased. Seizures and arrests rose steeply from around 2009/10 to 2014/15 and subsequently plateaued. Price increased ($15.9 [95% credible interval, CrI $9.9, $28.9] per point of crystal per year) from around 2009 to 2011, plateauing and then declining from around 2017. Hospitalisation rates increased steeply from around 2009/10 until 2015/16, with a small subsequent decline. Treatment also increased (19.8 episodes [95% CrI 13.2, 27.6] with amphetamines as the principal drug of concern per 100 000 persons per year) from 2010/11 onwards. Deaths involving amphetamines increased (0.285 per 100 000 persons per year) from 2012 until 2016. These findings suggest that problematic methamphetamine use and harms escalated from 2010 to 2012 onwards in Australia, with continued demand and a sustained market for methamphetamine. [Correction added on 30 May 2022, after first online publication: In the Abstract under 'Discussion and Conclusions' 'onwards' has been added after … 2010 to 2012].

Adaptive personalized routing for vulnerable road users

This research presents an adaptive and personalized routing model that enables individuals with mobility impairments to save their route preferences to a mobility assistant platform. The proactive approach based on anticipated user need accommodates vulnerable road users' personalized optimum dynamic routing rather than a reactive approach passively awaiting input. Most currently available trip planners target the general public's use of simpler route options prioritized based on static road characteristics. These static normative approaches are only satisfactory when conditions of intermediate intersections in the network are consistent, a constant rate of change occurs per each change of the segment condition, and the same fixed routes are valid every day regardless of the user preference. In this study, the vulnerable road user mobility problem is modeled by accommodating personalized preferences changing by time, sidewalk segment traversability, and the interaction between sidewalk factors and weather conditions for each segment contributing to a path choice. The developed reinforcement learning solution presents a lower average cost of personalized, accessible, and optimal path choices in various trip scenarios and superior to traditional shortest path algorithms (e.g., Dijkstra) with static and dynamic extensions.

Abstract 86: Cancer Update in Rwanda (2009-2018)

Abstract Purpose: In Rwanda, cancer prevalence and death have not been accurately documented up to 2018. In response, Rwanda, through the Ministry of Health and supported by Albert Einstein College of Medicine with funding from the U.S. National Cancer Institute, established a National Cancer Registry (NCR) in July 2018 to collect national cancer data. We aimed to determine the number of cancers by type, the distribution of cancers in the Rwandan population, and cancer trends over the last ten years in Rwanda. Methods: Registry data were collected over a ten-year period (2009-2018) from public and private health institutions and the National Institute of Statistics. Cancers were coded using the third edition of the International Classification of Diseases for Oncology (ICD-O3). Data entry and analysis were performed using CanReg5 system and IARCcrg quality control. The National Institute of Statistics of Rwanda provided an estimate of the country's population census for 2012 by age and sex, and the annual population was estimated assuming constant rates of change within age-sex groups. Results: Over ten years (2009-2018), a total of 18,562 cancers were registered; 11,034 (59%) in women and 7,528 (41%) in men. Breast and cervical cancers were most common among women [n=2283 (21%) and n=2330 (21%), respectively] while prostate and stomach cancers were most common among men [n=976 (13%) and n=772 (10%), respectively]. Most cases were diagnosed in women aged 50-54 (n=1381) and 45-49 (n=1189) and men aged 60-64 (n=794) and 55-59 (n=756). Cancers diagnosed in Rwanda increased from 759 cases in 2009 to 2,862 cases in 2018. Conclusion: In Rwanda, Cancers are more common in women and are diagnosed at an earlier age in women than in men. There has been a significant increase in documented cancers over 10 years, potentially related to significant improvements in diagnostic capacity within the Rwandan health system. Citation Format: Lydia Businge, Francois Uwinkindi, Marc Hagenimana, Gad Murenzi, Gallican Kubwimana, Francoise Musabyimana, Charles Ingabire, Athanase Munyaneza, Cecile Ingabire, Thomas C Randall, Kathryn Anastos, Philip E Castle. Cancer Update in Rwanda (2009-2018) [abstract]. In: Proceedings of the 9th Annual Symposium on Global Cancer Research; Global Cancer Research and Control: Looking Back and Charting a Path Forward; 2021 Mar 10-11. Philadelphia (PA): AACR; Cancer Epidemiol Biomarkers Prev 2021;30(7 Suppl):Abstract nr 86.

PENGEMBANGAN WELCOME DRINK BERBAHAN DASAR TEMULAWAK (Curcuma xanthorrhiza roxb) BERBASIS PEMODELAN MATEMATIKA DAN EKSPERIMEN

Welcome drink is an added value that enhances the Indonesian hospitality in the hotel industry, especially if it is made with spices such as curcuma, cinnamon, lemon, and brown sugar however industries that make typical curcuma beverage are often found to use excessive sugar and tend to turn off the distinctive taste of curcuma, besides that it also has an adverse effect on health.This research is an applied research which aims to make a beverage from curcuma and cinnamon with a mathematical approach at the end of the making process, a mathematical model can be simulated by numerical computation so that information on sugar levels are normal and reasonable for consumption in the welcome drink that has been made. Result of the research obtained 1st order homogeneous linear differential equation and simulation results using 40-80 gram sugar obtained a constant rate of change in sugar substances of or equivalent to 9-120 brix

Trends in cocaine use, markets and harms in Australia, 2003-2019.

This paper aims to describe cocaine use, markets and harms in Australia from 2003 to 2019. Outcome indicators comprised prevalence of use from triennial household surveys; patterns of use from annual surveys of sentinel samples who use stimulants; and cocaine-related seizures, arrests, hospitalisations, deaths and treatment episodes. Bayesian autoregressive time-series analyses were conducted to estimate trend over time: Model 1, no change; Model 2, constant rate of change; and Model 3, change over time differing in rate after one change point. Past-year population prevalence of use increased over time. The percentage reporting recent use in sentinel samples increased by 6.1% (95% credible interval [CrI95% ] 1.2%,16.9%; Model 3) per year from around 2017 (48%) until the end of the series (2019: 67%). There was a constant annual increase in number of seizures (count ratio: 1.1, CrI95% 1.1,1.2) and arrests (1.2, CrI95% 1.1,1.2), and percentage reporting cocaine as easy to obtain in the sentinel samples (percent increase 1.2%, CrI95% 0.5%,1.8%; Model 2). Cocaine-related hospitalisation rate increased from 5.1 to 15.6 per 100 000 people from around 2011-2012 to 2017-2018: an annual increase of 1.3 per 100 000 people (CrI95% 0.8,1.8; Model 3). While the death rate was low (0.23 cocaine-related deaths per 100 000 people in 2018; Model 2), treatment episodes increased from 3.2 to 5.9 per 100 000 people from around 2016-2017 to 2017-2018: an annual increase of 2.9 per 100 000 people (CrI95% 1.6,3.7; Model 3). Cocaine use, availability and harm have increased, concentrated in recent years, and accompanied by increased treatment engagement.

Kinetics analysis of the effect of types and concentrations of ripening agents on the physical quality changes of banana fruit (Musa acuminata Colla)

Nowadays there are many fruit ripening agents available in the market, thus, it is important to know the performance of those ripening agents in applications. This research determined the effect of the type of ripening agents and applied concentrations on the physical changed of banana during ripening process. Ethylene, acetylene, and ethephon in three different concentrations of 0, 250, and 500 ppm were investigated in a 3×3 factorial with three replications. Green mature bananas were treated with those ripening agents in closed boxes, after being treated then stored in the open ambient room until they were ripened. Weight loss, soluble solid content, and firmness of the samples were monitored every 12 hours until the samples were ripened. Results indicated that in the three ripening agents, the changes of weight loss, soluble solid content, and firmness followed zero, first, and second order kinetics equations, respectively. In general, the values of constant rate of change for weight loss and firmness increased with the concentration but not for soluble solid content. Statistical analysis indicated that the type of ripening agent significantly affected the k values of weight loss, soluble solid content, and firmness.

Time-lapse visualization of spatial and temporal patterns of stream network dynamics.

Time-lapse visualization of spatial and temporal patterns of stream network dynamics.

Bayesian phylolinguistics infers the internal structure and the time-depth of the Turkic language family

Abstract Despite more than 200 years of research, the internal structure of the Turkic language family remains subject to debate. Classifications of Turkic so far are based on both classical historical–comparative linguistic and distance-based quantitative approaches. Although these studies yield an internal structure of the Turkic family, they cannot give us an understanding of the statistical robustness of the proposed branches, nor are they capable of reliably inferring absolute divergence dates, without assuming constant rates of change. Here we use computational Bayesian phylogenetic methods to build a phylogeny of the Turkic languages, express the reliability of the proposed branches in terms of probability, and estimate the time-depth of the family within credibility intervals. To this end, we collect a new dataset of 254 basic vocabulary items for thirty-two Turkic language varieties based on the recently introduced Leipzig–Jakarta list. Our application of Bayesian phylogenetic inference on lexical data of the Turkic languages is unprecedented. The resulting phylogenetic tree supports a binary structure for Turkic and replicates most of the conventional sub-branches in the Common Turkic branch. We calculate the robustness of the inferences for subgroups and individual languages whose position in the tree seems to be debatable. We infer the time-depth of the Turkic family at around 2100 years before present, thus providing a reliable quantitative basis for previous estimates based on classical historical linguistics and lexicostatistics.

두 중학생 간의 ‘변화율의 일정함’과 ‘변화율의 일정한 변화’에 대한 이해의 차이 비교 및 분석

The purpose of this case study is to analyze students’ understanding of ‘constant rate of change’ and ‘constant rate of change of rate of change’ in a functional situation. Two students participated in a class six times (April to June, 2018). Neither student had ever learned linear functions at school. Analysis of the class revealed marked differences between student A and student B in graphically expressing and interpreting situations involving varying rates of change. This study focuses on their actions to express and to interpret analyzed the two students’ meaning of ‘constant rate of change’ and ‘constant rate of change of rate of change’. These results indicate the importance of understanding ‘constant rate of change' when learning graphs and functions.

Time-dependent saddle–node bifurcation: Breaking time and the point of no return in a non-autonomous model of critical transitions

There is a growing awareness that catastrophic phenomena in biology and medicine can be mathematically represented in terms of saddle–node bifurcations. In particular, the term “tipping”, or critical transition has in recent years entered the discourse of the general public in relation to ecology, medicine, and public health. The saddle–node bifurcation and its associated theory of catastrophe as put forth by Thom and Zeeman has seen applications in a wide range of fields including molecular biophysics, mesoscopic physics, and climate science. In this paper, we investigate a simple model of a non-autonomous system with a time-dependent parameter p(τ) and its corresponding “dynamic” (time-dependent) saddle–node bifurcation by the modern theory of non-autonomous dynamical systems. We show that the actual point of no return for a system undergoing tipping can be significantly delayed in comparison to the breaking timeτˆ at which the corresponding autonomous system with a time-independent parameter pa=p(τˆ) undergoes a bifurcation. A dimensionless parameter α=λp03V−2 is introduced, in which λ is the curvature of the autonomous saddle–node bifurcation according to parameter p(τ), which has an initial value of p0 and a constant rate of change V. We find that the breaking time τˆ is always less than the actual point of no return τ∗ after which the critical transition is irreversible; specifically, the relation τ∗−τˆ≃2.338(λV)−13 is analytically obtained. For a system with a small λV, there exists a significant window of opportunity (τˆ,τ∗) during which rapid reversal of the environment can save the system from catastrophe.

Identifying the early 2000s hiatus associated with internal climate variability

This study focuses on re-examining the early 2000s hiatus and the associated key components of the global mean surface temperature (GMST) using multiscale statistics for five well-known gridded surface temperature and two reanalysis datasets. The hiatus is characterized as a near-zero trend on the decadal scale corresponding to the maximum P-value via an F-test in statistics. The results reveal that the hiatus exists in both the GMST and global mean air temperature (GMAT) time series, rather than in global warming component, which has maintained an approximately constant rate of change of approximately 0.08 °C/decade over the past three decades. The hiatus’s duration is different from that of time series such as 2002–2012/2001–2013/2002–2014 in HadCRUT4, NOAA-old, ERA-Interim and NCEP-R2. The newly gridded datasets with data infilling or bias correction for interpreting the sea surface temperature (SST) measurement from the old versions show a slightly higher trend from 2002–2012 than the hiatus, which is thus regarded as a slowdown. Comparison suggests that the hiatus should be during the period 2002–2012. Orthogonal wavelet decomposition of the temperature time series shows that the hiatus was merely a decadal balance between cooling from interannual variability and global warming, in addition to weak warming from interdecadal and multidecadal climate oscillations. In addition, the evolutions of the GMST’s interannual composites are well coincided with Niño3.4 SST anomalies, which is consistent with the numerical simulation performed by Kosaka and Xie in 2013. Hence, it is the anomalous El Niño Southern Oscillation (ENSO) events in the early 2000s that caused the hiatus despite a constant rate of global warming and the maximum magnitude of the multidecadal composite that led to the limited contribution to the trend during this period. The multidecadal composite follows a downward path, which implies that future climate conditions will likely rely on competition between multidecadal cooling and global warming if the multidecadal climate cycle repeats, as was experienced during the second half of the twentieth century.

ScottyActivity: Mixed Discrete-Continuous Planning with Convex Optimization


 
 
 The state of the art practice in robotics planning is to script behaviors manually, where each behavior is typically generated using trajectory optimization. However, in order for robots to be able to act robustly and adapt to novel situations, they need to plan these activity sequences autonomously. Since the conditions and effects of these behaviors are tightly coupled through time, state and control variables, many problems require that the tasks of activity planning and trajectory optimization are considered together. There are two key issues underlying effective hybrid activity and trajectory planning: the sufficiently accurate modeling of robot dynamics and the capability of planning over long horizons. Hybrid activity and trajectory planners that employ mixed integer programming within a discrete time formulation are able to accurately model complex dynamics for robot vehicles, but are often restricted to relatively short horizons. On the other hand, current hybrid activity planners that employ continuous time formulations can handle longer horizons but they only allow actions to have continuous effects with constant rate of change, and restrict the allowed state constraints to linear inequalities. This is insufficient for many robotic applications and it greatly limits the expressivity of the problems that these approaches can solve. In this work we present the ScottyActivity planner, that is able to generate practical hybrid activity and motion plans over long horizons by employing recent methods in convex optimization combined with methods for planning with relaxed plan graphs and heuristic forward search. Unlike other continuous time planners, ScottyActivity can solve a broad class of robotic planning problems by supporting convex quadratic constraints on state variables and control variables that are jointly constrained and that affect multiple state variables simultaneously. In order to support planning over long horizons, ScottyActivity does not resort to time, state or control variable discretization. While straightforward formulations of consistency checks are not convex and do not scale, we present an efficient convex formulation, in the form of a Second Order Cone Program (SOCP), that is very fast to solve. We also introduce several new realistic domains that demonstrate the capabilities and scalability of our approach, and their simplified linear versions, that we use to compare with other state of the art planners. This work demonstrates the power of integrating advanced convex optimization techniques with discrete search methods and paves the way for extensions dealing with non-convex disjoint constraints, such as obstacle avoidance.
 
 

Two Middle School Students' Understanding of Constant Rate of Change Emerging through the Process of Expressing and Interpreting the Function Graphs

Two Middle School Students' Understanding of Constant Rate of Change Emerging through the Process of Expressing and Interpreting the Function Graphs

Combined linear and non‐linear controller design for motor position regulation

A composite robust controller is proposed for typical motor servo systems subject to control saturation and unknown disturbance. The controller contains a linear servo control law which achieves a fast response, and a non-linear control part to suppress the overshoot. The unknown disturbance is assumed to have a constant rate of change, and is treated as an extended state of the system. A reduced-order observer is then designed to estimate the unmeasurable state and disturbance for control and compensation. The controller is applied to a permanent magnet synchronous motor for position regulation, and digital simulation and experimental test are conducted to verify the superior performance and robustness of the design.