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Motivated by a practical problem, this paper investigates the integrated planning of maintenance operations and workload allocation on a set of machines in a workshop. Given quantities of products to be produced per period on a planning horizon must be processed on unrelated flexible machines. Moreover, each machine has to undergo one or more maintenance operations that must be planned within a given time window and impact products differently. The main goal is to find a feasible plan that satisfies the machine capacity by allocating the production quantities to machines and assigning maintenance operations as late as possible in their time windows. Various original mathematical models are presented. In particular, we propose models that allow maintenance operations and some production quantities to overlap two consecutive periods. Computational experiments based on industrial data show that allowing this overlapping helps the earliness of maintenance operations to be significantly reduced in the most difficult instances, going for example from a total of 14 periods to only 1 period, and by more than 35% on average. [ABSTRACT FROM AUTHOR]

This paper proposes a new bi-objective aircraft and crew recovery model. Unlike previous researches, the proposed model considers all individual flight legs in the recovery process. The objective functions minimize the recovery cost regarding crew swapping, flight cancellation, flight delay, and crew deadhead costs. Besides, the crew sit time is reduced considering the maximum legal working hours and the minimum essential rest time. Moreover, maintenance operations can be done during the ground time, not necessarily at the end of duty day. The model is never infeasible because flight cancelation is an alternative solution for recovering a schedule. A modified Tabu Search (TS) approach has been developed to solve the model. The performance of the model and solution approach is examined by several test problems in small, medium, and large scales. The results indicate that TS reaches optimal and close-optimal in a short computational time, especially in large scale problems. [ABSTRACT FROM AUTHOR]

AbstractThe submerged arc welding (SAW) process generates a large quantity of slag, which, when disposed-of, harms the environment and wastes valuable ingredients. A technology was developed to recycle the SAW slag generated in stainless steel cladding, enabling its reuse as flux. Bead geometry and dilution play crucial roles in weld cladding. Dilution determines the minimum number of layers needed to achieve the desired chemistry, while bead width dictates the fewest passes required to cover the entire surface area. Additionally, bead geometry influences the mechanical strength of the clad layers. The microstructure and solidification mode also significantly affect clad quality. Therefore, understanding the impact of recycled slag on bead geometry, dilution, and microstructure is essential. This paper presents a systematic investigation into the effects of process variables and recycled slag on bead geometry and dilution in clad welding. It includes a comparison of microstructures obtained using fresh flux versus recycled slag. The results indicate that increasing the welding current (I) by 37.5% enhances weld penetration (p), bead width (w), reinforcement (r), and dilution (d) by 50.9%, 14.4%, 69.5%, and 5.5%, respectively. Conversely, increasing the travel speed (V) by 90%, decreases p, w, and r by 19.29%, 11.9%, and 25.3%, respectively; however, dilution (d) increases by 17.6%. On the other hand, increasing the open-circuit voltage (V) by 26.7% increases bead width (w) and dilution (d) by 10.4% and 5.4%, respectively, while reinforcement (r) decreases by 7.5%. Both single and multilayer claddings prepared with fresh flux and recycled slag exhibit similar microstructures. [ABSTRACT FROM AUTHOR]

The purpose of the study is to investigate the changing mathematical connection and metacognitive skills of students in the process of applying mathematical modelling. The data used for the study were collected from modelling activities, students’ written responses to modelling activities, audio recordings, semi-structured interviews, and observation notes. The data obtained were analysed using content analysis. As a result of the data analysis, it was found that metacognitive skills were used in each activity in the mathematical modelling process and were developed in interaction with each other. Although inter-concept and real-world connection skills are most commonly used in mathematical connection skills, modelling activities were found to enhance connection skills by allowing students to use connection skills with different disciplines and between different representations of the concept. It was found that metacognitive skills and mathematical connection skills develop interdependently, and it was found that mathematical modelling activities can be used as a tool for developing both of these skills. [ABSTRACT FROM AUTHOR]

During the last years, mathematical modelling has been entering the field of engineering education because it is a bridge between mathematics and industry that also promotes the development of skills that require the engineer of the twenty-first century. Nevertheless, the modelling process is involved and requires the deployment of cognitive skills of superior level, particularly metacognitive skills. This contribution presents the results of a multiple qualitative case study on metacognitive strategies used by groups of engineering students associated with each transition of the mathematical modelling process. During the development of the course, observations and retrospective interviews were carried out, which evidenced the use of metacognitive planning strategies from simplification to interpretation; metacognitive monitoring strategies throughout the modelling process, metacognitive regulation strategies from mathematization to mathematical work and metacognitive evaluation strategies during simplification, mathematization and validation. The results expand the classification framework of metacognitive strategies for engineering students. [ABSTRACT FROM AUTHOR]

Manufacturing plays a vital role in fostering economic growth, yet it is one of the major consumers of energy. Considering energy consumption when devising an Aggregate Production Plan (APP) is a determinant of a more energy-efficient production schedule at the operational level. Manufacturers in emerging economies envisage planning challenges when energy reforms are introduced. A guide for analysis and decision-making in the transitional phase of phasing out energy subsidies is essential. This work tackles this problem by developing two mixed-integer linear programming models for energy-aware production planning. The first model targets maximising profit while explicitly using the energy cost as one of the cost elements. The second is an energy-driven model to minimise energy consumption while including profit as a constraint. The proposed models were validated via a real-life dataset. The models provide the decision-makers with the flexibility to improve their production plans' energy efficiency by either developing plans that reduce energy consumption without sacrificing profit or developing production plans that increase profit without increasing energy consumption. The results imply that adopting Energy-Efficient Production Planning (EEPP) is substantial with high subsidy levels. For low subsidy levels, strategic decision-making entailing the deployment of technological solutions is more efficient. [ABSTRACT FROM AUTHOR]

Working with approximations is a common practice in physics. This paper presents an exploratory study of student understanding of some of the elementary aspects of approximations encountered in college physics. For this purpose, a questionnaire (a set of 14 multiple-choice questions) was developed to probe how students dealt with these aspects in a variety of contexts. The questionnaire was finalized after a trial of its pilot version on 7 students on the basis of their written scripts and interviews. After content validation by three external experts, the test was administered to a sample of 141 senior undergraduate physics students from a diverse set of colleges and national institutes. Data analysis reveals several significant student pitfalls in the topic related principally to (i) the identification of a dimensionless ratio to characterize an approximation, (ii) the notion of the order of approximation and consistent handling of a problem up to the required order, and (iii) the notion of the order of infinitesimal in calculus-based derivations. The findings are of direct pedagogic relevance. [ABSTRACT FROM AUTHOR]

A cloud manufacturing (CMfg) system is presented as a novel service- and customer-oriented manufacturing paradigm that integrates the distributed manufacturing enterprises to share their manufacturing capabilities or resources and collaborate as an interconnected system in a dynamic environment. Since the high performance of this system depends on the formation of a suitable group of manufacturing service providers, this paper develops an integrated c onfiguration design and capacity planning problem for the CMfg system by considering the dynamic environment of this system. In this regard, dynamic service providers and dynamic demand are considered as two aspects of the dynamic nature of this system. A multi-period multi-objective mathematical model is proposed by maximising the utilities of all three stakeholders of the system. Moreover, three extensions of a discrete multi-objective grey wolf optimiser (DMOGWO) algorithm are devised to solve the medium- and large-scale instances. A comprehensive computational experiment is conducted to assess the performance of the developed meta-heuristic algorithms. Furthermore, by carrying out a sensitivity analysis, some managerial insight is suggested for the managers. [ABSTRACT FROM AUTHOR]

This study aims to develop a sustainable freight transportation network considering capacitated cross-docks for minimising the overall supply chain costs, including carbon emission cost. The problem is inspired by a major retail company based in India, which would like to expand its product portfolio in the new region. A mathematical model is developed to minimise total costs encompassing transportation cost, pipeline and retailers inventory cost, fixed cost of cross-dock and carbon emission costs. The deterministic time dependant demand, multiple products and multiple sourcing and distribution are some of the challenges faced by the retail industry. A two-level self-adaptive variable neighbourhood search algorithm is applied to solve a computationally complex problem. The results based on a two-level self-adaptive variable neighbourhood search algorithm are compared with the variable neighbourhood search algorithm to test the robustness of the developed model. Results reveal that an increase in retailers over suppliers significantly influences the number of open cross-docks. A multiple-case scenario approach captures the implications of varying capacity on the number of open cross-docks; thus, supporting the freight distribution managers in making sustainability-driven decisions. [ABSTRACT FROM AUTHOR]

Communication is pivotal for the emergence of coordination and cooperation within teams. As a result, communication plays an important role in team dynamics as better communication between teammates can lead to more efficient and successful teams. To better understand communication dynamics and their impact on team performance, we develop a modelling framework of two-agent interaction dynamics in a discrete-time fashion. Our proposed model considers the communications between two agents based on each agent's personality and their individual impact on any received communication. Combined with data, we perform mathematical analysis and bifurcation diagrams to study how agents' personality and training may impact the quality of the team's communications and therefore their performance in task completion. The validations and parameter estimations of our model from data could potentially help us to select team members that could work together efficiently, and train members in the established team to collaborate better. [ABSTRACT FROM AUTHOR]

This research aims to investigate the relationships between the mathematical modelling process and the levels of covariational reasoning through a multiple instrumental case study with six college students solving a task in the context of science. We designed a modelling task based on a problem faced by Newton: obtaining higher temperature values than a thermometer could register; and analysed the participants’ modelling processes and covariational reasoning as they solved the task. The results show that the modelling task promoted covariational reasoning. The results also show that participants used covariational reasoning to solve the task, and the participants were unaware of nonlinear covariational reasoning which prevented them from making mathematical models closer to reality. Furthermore, participants required specific levels of covariational reasoning at specific steps in the mathematical modelling process, and as they advanced in the mathematical modelling process they exhibited more sophisticated levels of covariational reasoning. [ABSTRACT FROM AUTHOR]

This study aims to characterise and understand the manifestation of critical mathematics consciousness (CMC) in the modelling process and the relationships that are established between mathematical modelling as a teaching methodology and the development of critical consciousness. Based on a contextualised topic of interest, the students produced mathematical models, and an improved analytical framework based on education for critical mathematical consciousness was used to analyse the interpretations and validations produced. In addition, a questionnaire was applied to ascertain consciousness at an individual level. The results show that the application of the analytical framework generated insights into the development of critical mathematics consciousness. Furthermore, it was noted that the use of questions seems to help in the development of mathematical modelling by deepening discussions and benefiting the development of CMC. This suggestion contributes to the evolution of CMC, through the reflection on social issues in the production of a model. It appears that mathematical modelling is favourable to the manifestation of CMC. [ABSTRACT FROM AUTHOR]

High-speed trains have to undergo special maintenance services. The maintenance service is highly specialized and can only run on specific platforms. Most of the optimization models proposed in the literature do not consider this problem integrated with the rolling-stock planning, although the two problems affect each other, and their separation leads to suboptimal solutions of the overall problem. This article presents an integrated approach based on a mixed integer mathematical formulation and computational results on a testbed of instances, derived from a real-world case study. This approach is compared with a two-stage one, commonly used in practice and in the literature. The results show that the rolling-stock planning problem can produce input parameters for the scheduling problem for which no feasible schedules exist. When a scheduling solution exists, the final percentage gap of the two-stage solution is much higher than the one provided by the integrated model. [ABSTRACT FROM AUTHOR]

Additive manufacturing (AM) has been recognised as a promising technology under the context of Industry 4.0, which is reshaping manufacturing paradigms. A prominent type of AM machine is the selective laser melting (SLM) machine, in which several parts may form a job and be produced concurrently. This paper aims to investigate a scheduling problem in an AM system with non-identical parallel SLM machines. Since, in this system, there might be differences in the material types of parts, the required setup time between two consecutive jobs on the relevant machine is dependent on their material types. Accordingly, a bi-objective mathematical model is extended for the problem, considering the makespan and the total tardiness penalty as two objective functions. Due to the high complexity of the problem, an efficient hybrid meta-heuristic algorithm is developed by combining the non-dominated sorting genetic algorithm (NSGA-II) with a novel learning-based local search founded on the k-means clustering algorithm and a regression neural network. The local search enhances the exploitation ability of the NSGA-II while intelligently being taught during the solving procedure. Finally, the superiority of the proposed hybrid algorithm is demonstrated through a computational experiment. [ABSTRACT FROM AUTHOR]

We adapt the Lanchester combat model to represent conflict between vampires and humans. It is assumed that vampires attack humans during the hours of darkness whilst humans attack vampires during the hours of light. The right-hand side of the differential equation model therefore depends upon the hour of the day. A key insight is that to answer the question ‘who wins’ it is not required to ‘stitch together’ the solutions to the differential equation over many days. Rather, the number of combatants surviving at the end of each day can be cast as a difference equation in terms of the numbers surviving at the end of the previous day. Two models are investigated and from the solutions the boundary delimiting the parameter regions of victory and defeat is found. Where appropriate we introduce discussion points, both mathematical and modelling. The mathematical techniques used include finding the eigenvalues and eigenvectors of a matrix, solving linear differential and discrete systems, and considering the physical meaning of the model and questioning its assumptions. Thus a variety of problem-solving skills are developed within the context of a model where students can question the underlying assumptions and propose, and investigate, models of their own. [ABSTRACT FROM AUTHOR]

The student experience with mathematical modelling has the potential to differ in nature to the experience of a typical mathematics student. The research reported in this paper forms part of a broader study looking into tertiary learning experiences for mathematical modelling. This paper reports on: What are the student experiences when learning to mathematically model? How might these experiences inform mathematics education? Data were collected across two different tertiary mathematical modelling courses in the form of student interviews. Student interviews were analysed, using reflective thematic analysis, to identify themes relating to the collective student learning experience. The results show that modelling provides an opportunity for students to be actively involved with their learning. Being open-minded was a key behaviour for a productive student experience. [ABSTRACT FROM AUTHOR]

Robotic Mobile Fulfillment Systems (RMFSs) are a recent type of automated warehouse deployed in e-commerce. In this parts-to-picker system, a fleet of small robots is tasked with retrieving and storing shelves of items in the warehouse. Due to the nature of the e-commerce market, and the high flexibility of RMFSs, there are many opportunities to improve the productivity of the warehouse by optimising operational decisions. Online retailers promise extremely fast deliveries, which requires that new orders be included in the set of requests to fulfil as soon as they are revealed. For this reason, and because of the very dynamic nature of the robots' cycles, decision-making needs to be done in real time, in an uncertain environment. Because such a problem often lacks a formal description, we propose a mathematical framework that models the operational decisions taking place in an RMFS as a stochastic dynamic program. Our objective is to formalise optimisation opportunities, to allow researchers to develop more advanced methods in a well-defined environment. Embedded in a discrete event simulator, this model is illustrated by simulations to compare against standard storage decision rules. [ABSTRACT FROM AUTHOR]

This research looks at the production planning of hollow-core slabs integrated to the optimisation problem of the use of moulds. Considering the production process of these structures, two mathematical models are proposed for the arising problem, which consists of a one-dimensional multi-period cutting stock problem with innovative aspects regarding the multiple manufacturing modes that can be used to produce the slabs. In addition, a theoretical analysis of the proposed models is presented. These models are solved using heuristic methods, both aiming to minimise production and inventory costs. Using data based on real information provided by a company, the computational results showed that the heuristic based on the compact model performed better than the one based on the extended model, due to some characteristics specific to the problem being studied. [ABSTRACT FROM AUTHOR]

This paper reports a study of 10 post-secondary STEM (Science, Technology, Engineering, Mathematics) instructors’ beliefs about mathematical modelling and the role of mathematics in STEM coursework. The participants were selected from STEM disciplines that are atypical to the literature base (e.g. anthropology and geography), in order to extend what is known about STEM instructors’ beliefs to other disciplines. We conducted episodic narrative interviews to hypothesise the genesis of participants’ most salient beliefs. We then conducted a cross-case synthesis to reflect on the similarities between our participants’ beliefs and findings previously reported in STEM education literature. Our participants held many beliefs in common with typical STEM instructors with regards to how they define modelling, the role of modelling in STE (Science, Technology, Engineering) courses, and their views of students as learners of mathematics and modelling. Our analysis suggests participants’ commitments within these categories are interdependent and arise from lived experiences. Additionally, participants within the same field held competing beliefs about modelling, suggesting that constituting ‘major’ as an independent variable in future research may not be straightforward. [ABSTRACT FROM AUTHOR]

The emergence of COVID-19 favoured the development at Université de Montréal of an educational initiative aimed at promoting modelling and simulation in teaching and learning postsecondary mathematics. In our learning activities, modelling is not reduced to curve fitting; software is used and questions are asked to get a deeper understanding of the structure of a situation. In particular, compartmental epidemiological models were the topic of activities using digital tools (Insight Maker and Excel) that generated interest among teachers and students. With the possibilities offered by such tools of reflecting more adequately the complexity of the situation, we considered it relevant to model the perceptions related to significant effects of nonpharmaceutical interventions (NPIs) as well as the apparent social divide in behaviours regarding mandated measures and its effect on the epidemic. A study carried out on these aspects, based on data collected in Québec, led us to develop a new model which could form the basis for a new activity and be explored and further refined by students. This work leads to considering a social dimension to the teaching of modelling with differential equations and to include this teaching in the development of critical thinking. [ABSTRACT FROM AUTHOR]

We present an example of one of the modelling projects we assign to students in our differential equations classes. Students are asked to determine how to run a cost-efficient hot water heating system. We consider a cylindrical tank filled with water and heated by a heating element immersed in it. Together with students we discuss physical laws governing the process and make assumptions necessary to build a model. One of the goals of the modelling activity is to compute the time needed for water to reach the desired temperature given the power of the heating element and the size of the water tank. Several different scenarios can be discussed. Assuming the cost of heating the water is directly related to the time for which the power is ON, students can choose the most cost-efficient scenario. We provide the description of several modelling activities and obtained results. [ABSTRACT FROM AUTHOR]

This paper describes a teaching experiment in a Numerical Methods course for Master of Science students. The experiment uses scientific papers to develop modelling studies in the context of wine fermentation microbial interactions. The course involves theoretical and laboratory classes that focus on implementing numerical methods using Matlab for Initial Value Problems and Boundary Value Problems. The students are asked to formalise the mathematical model and build their own experiments using the information provided in the papers. Additionally, a parameter estimation experiment is organised, which involves generating synthetic data and computing noisy data to estimate the natural death rate of sensitive yeast. The results show that data noise significantly affects the parameter estimate and that scaling the data can help reduce the impact of measurement errors. The presented results can be used to investigate other possible assignments, such as how the evaluation of the Jacobian affects the estimation performance and compare different optimisation algorithms. [ABSTRACT FROM AUTHOR]

Mathematical modelling has great potential to motivate students towards studying mathematics. This article discusses several different approaches to integrating research work with a second-year undergraduate, mathematical modelling subject. I found sourcing papers from the areas of epidemiology and ecology to be a fruitful source area, particularly models involving only two or three coupled differential equations. These models were amenable to students as well as interesting and relevant to students because they came from real research papers. I will describe the use of scenarios and case studies in lectures, and group projects for assessment. The scenarios and case studies were published in a textbook that I wrote. Scenarios, case studies and projects provided an opportunity to expose students to some novel applications of differential equations. One example is developed here as a Classroom Note: modelling the dynastic cycles in Chinese history. [ABSTRACT FROM AUTHOR]

Gaining useful insight into real-world problems through mathematical modelling is a valued activity across several disciplines including mathematics, biology, computer science and engineering. Differential equations are a valuable tool used in modelling. Modelling provides a way for students to engage with differential equations within a contextual environment. Teaching mathematics in context has the potential of giving students something to anchor the mathematics to and hence act as cognitive roots With this in mind, in what ways can lecturers use mathematical modelling to provide students with contextual learning experiences of differential equations? A New Zealand study was carried out involving three case studies. Each case study comprised of a mathematical modelling course, lecturer participant and student participants. Modelling examples and activities that involved differential equations were part of all course content. In this paper, I will present information on each course, the main modelling activities each course used, and examples of students' use of differential equations for these activities. Insights discovered into the common practices of the three lecturers regarding using mathematical modelling to teach differential equations will also be presented. [ABSTRACT FROM AUTHOR]

We present an intriguing topic in a mathematical modelling course where Lanchester models are taught to our students. Lanchester models are some of the earliest and most important models used for combat modelling. We describe modelling activities and the use of technology that can be implemented in teaching this topic in this paper. [ABSTRACT FROM AUTHOR]

Mathematical modelling is an interlinking process between mathematics and real-world problems that can be applied as a means to increase motivation, develop cognitive competencies, and enhance the ability to transfer mathematical knowledge to other areas of science, such as engineering disciplines. This study was designed to investigate the effect of applying the modelling approach on problem-solving and mathematical performance of engineering undergraduates during a differential equations (DEs) course and compare the results with those of conventional teaching. A quasi-experimental method comprising a pretest-posttest design with a control group was applied in this study. Since the antecedent knowledge of calculus directly influences the ability of students to learn DEs, a placement test was first applied to both groups. A combination of results derived from the placement test and the modelling pretest was used as the covariate in the Analysis of Covariance (ANCOVA), and the modelling and mathematical performances of both groups were eventually examined. The results of this study indicate that apart from the fact that teaching DEs based on the modelling approach can increase the ability to apply mathematical knowledge in the field of engineering, it also can significantly enhance their problem-solving and mathematical performances. [ABSTRACT FROM AUTHOR]

The Banister impulse-response (IR) model was designed to predict an athlete's performance ability from their past training. Despite its long history, the model's usefulness remains limited due to difficulties in obtaining precise parameter estimates and performance predictions. To help address these challenges, we developed a Bayesian implementation of the IR model, which formalises the combined use of prior knowledge and data. We report the following methodological contributions: 1) we reformulated the model to facilitate the specification of informative priors, 2) we derived the IR model in Bayesian terms, and 3) we developed a method that enabled the JAGS software to be used while enforcing parameter constraints. To demonstrate proof-of-principle, we applied the model to the data of a national-class middle-distance runner. We specified the priors from published values of IR model parameters, followed by estimating the posterior distributions from the priors and the athlete's data. The Bayesian approach led to more precise and plausible parameter estimates than nonlinear least squares. We conclude that the Bayesian implementation of the IR model shows promise in addressing a primary challenge to its usefulness for athlete monitoring. [ABSTRACT FROM AUTHOR]

Sustainable diets must consider health, economic, environmental, and social outcomes. The development and production of alternative protein foods should also make these considerations. We examined the nutritional role of these foods, with New Zealand (NZ) as a case study.We used the DELTA Model® to assess 2020 NZ nutrient supply. We then simulated the substitution of 50% of meat supply (by mass) with various plant protein sources (soy, peas, beans, and mushroom), and observed the impact on nutrient supply.NZ had an undersupply of calcium (38%), vitamin E (34% deficit), dietary fibre (20%), potassium (13%), and vitamin C (10%) compared to population requirements. Contrastingly, there was sufficient protein and amino acid supply for an additional 2.4 million people. Halving of meat supply resulted in decreased availability for potassium (21% deficit), zinc (17%), folate (10%), and iron (9%).Soy proved the best nutritional replacement for meat, with reduced deficits for all undersupplied nutrients compared to 2020. Replacement with other modelled protein sources resulted in greater nutrient deficits.The nutritional implications beyond protein must be considered when making dietary substitutions. There are clear public health reasons to fortify alternative proteins with both the nutrients lost in substitution and those already in deficit. [ABSTRACT FROM AUTHOR]

This study investigated the sources of difficulties experienced by prospective teachers in mathematical modelling in the context of a semester-long course on mathematical modelling for teachers. The data reported in this study were collected from six prospective teachers through in-depth semi-structured interviews supported by audio and videotaped classroom observations and prospective teachers' written solutions for the modelling tasks. The results showed that the sources of difficulties experienced by prospective teachers in mathematical modelling could be subsumed under individual and contextual factors. The individual factors included four issues: lack of conceptual understanding of mathematics, the difficulty of connecting the real world and the mathematical world, the disposition to focus solely on reaching a result, and disorganized and unsystematic work. The contextual factors included two issues: insufficient previous experience with modelling tasks and time limitations. Some implications of these results are discussed. [ABSTRACT FROM AUTHOR]

Discrete time models, one linear and one non-linear, are investigated, both with a herbivore species that consumes a basal food source species. Results are presented for coexistence of the species and to illustrate chaotic behaviour as parameters are varied in the non-linear model. The results indicate the benefit of fertilization in terms of the region of parameter space for which coexistence occurs. Possible extensions from these models for independent investigations are provided alongside classroom exercises. [ABSTRACT FROM AUTHOR]

One of the most recent innovations to promote a circular economy during wastewater treatment is the production of biopolymers. It has recently been demonstrated that it is possible to integrate the production of biopolymers in the form of polyhydroxyalkanoates (PHA) with nitrogen removal via nitrite during the treatment of sludge reject water. In the present study, simulation of a new process for bioresource recovery was conducted by an appropriate modification of the Activated Sludge Model 3. The process consists of the integrated nitrogen removal via nitrite from sludge reject water and the selection of PHA-storing biomass by inducing a feast and famine regime under aerobic and anoxic conditions. According to the results, it is anticipated that simulation data matched very satisfactorily with the experimental data and confirmed the main experimental observation, showing that during the famine period the PHA depletion was almost complete due to the availability of nitrite as the electron acceptor. Simulation results indicate that the selection of the volumetric organic loading rate and of the relative duration of the aerobic feast/anoxic famine duration is critical in order to allow for the effective denitritation of the internally stored PHA during the famine phase. [ABSTRACT FROM AUTHOR]

Partially automated assessment is implemented via the ‘Printable worksheet’ mode in the Numbas e-assessment system to create a mathematical modelling worksheet which is individualised with random parameters but completed and marked as if it were a non-automated piece of coursework, preserving validity while reducing the risk of academic misconduct via copying and collusion. A simple modelling scenario is used for this demonstration. A cylindrical tank of water is draining through a small hole in its base, with the size of the tank, size of the hole and initial volume of water randomised so that the details are different for each student. Students are guided through deriving a model of the movement of water out of their version of the tank, asked to compute the expected time for it to empty and asked to discuss some aspects of the model and their findings in a discursive narrative report. [ABSTRACT FROM AUTHOR]

The Bernoulli equation is useful to assess the motility and recovery rate with respect to time in order to measure the COVID-19 outbreak. The homotopy perturbation method was applied in the current article to compute the Bernoulli equation. For the existence and uniqueness of solutions, we also used the Caputo-Fabrizio Integral and differential operators. Additionally, we conducted a corresponding investigation for derivatives of integer and fractional orders on the estimated motility and recovery rate. [ABSTRACT FROM AUTHOR]

The concept of the sparsest packing is introduced in this paper. The sparsest packing is aimed to place the objects in the container as distant as possible. More specifically, the minimal Euclidean distance between the objects, as well as, between the objects and the boundary of the container is maximised. This new problem statement is motivated by modern clean and energy-saving technologies such as ultrasonic hardening and finishing by detonating gas mixtures. The sparsest packing of two-dimensional objects in a circular container is considered subject to balancing conditions. The objects may have regular or irregular shapes bounded by arcs and line segments. Using the phi-function technique a mathematical model is formulated and a corresponding nonlinear programming problem is stated. A solution algorithm is proposed and computational results are presented to illustrate the approach. [ABSTRACT FROM AUTHOR]

This study examines whether experiences at industrial facilities help pre-service maths teachers to design authentic mathematical-modelling activities intended for their classroom teaching in high school and how they view the benefits of integrating research and development issues into their instruction. 36 pre-service maths teachers at college in Israel participated the study. The results revealed that the pre-service maths teachers successfully designed authentic activities based on project-based learning that took into account the two cycles of mathematical modelling. The pre-service maths teachers reported that the implementation of the designed activities developed with researchers could serve as a way for them to present their students with a real-life problem that shows them the relevance of mathematics, promotes positive attitudes towards maths, and exposes the students to potential future jobs in the industries. The current study emphasised the use of mathematical modelling as a pathway that links industry and engineering with mathematics education. [ABSTRACT FROM AUTHOR]

This study examined seventh-grade students’ emergent and progressive financial literacy in the context of risk and reward while working on two mathematical modelling tasks. The participants were six seventh-grade students identified as ‘good at mathematics’ by their teachers. The data sources comprised videotaped group discussions, group presentations, worksheets, and researchers’ field notes. The results revealed that students’ financial experience and mathematical knowledge influenced the mathematical modelling process in the context of risk and reward. Students with experience in financial contexts, similar to those in the modelling tasks, were more successful in making financial comments and linking mathematical knowledge. We conclude that mathematical modelling tasks would have encouraged students to discuss and adopt different approaches that facilitated more advanced financial thinking. How mathematical modelling activities might activate students’ financial knowledge in the context of risk and reward was discussed, and limitations and recommendations for further research are included. [ABSTRACT FROM AUTHOR]

This study examines prospective elementary teachers' growth and development of competencies, conceptions, and perceptions of mathematical modelling in a mathematics content course for elementary teachers. A series of lessons were implemented that engaged students in the modelling process through modelling tasks. The goal was to capture prospective teachers' thoughts and perceptions on the meaning of mathematical modelling and their conceptions of teaching and learning modelling at the elementary and middle school level. The research questions were: (1) How do prospective teachers translate the mathematical modelling cycle into their practice of doing modelling? and (2) How do prospective teachers' conceptions of modelling and teaching and learning modelling evolve throughout the implementation of a series of mathematical modelling lessons? Data sources included posters, modelling reports, responses to a pre- and post-intervention questionnaire, and semi-structured interview dialogue. Data analyses included mixed methods using provisional coding, open coding, and a categorical rubric. Findings from this study indicate that (1)Prospective elementary teachers translated the modelling cycle into their practice by developing their range of modelling competencies including multiple components of the modelling cycle, and (2) They developed a professionally appropriate conception of mathematical modelling along with productive perceptions of the benefits of teaching and learning modelling. [ABSTRACT FROM AUTHOR]

The increasing trend of retirement age in Europe represents a critical phenomenon for manufacturing and material handling activities, where repetitive activities, involving the handling of different loads at various frequencies, are usually required. These tasks can lead to occupational diseases and work-related musculoskeletal disorders, which can affect more heavily older workers, due to their decreased functional and physical capacities. On the other side, older workers positively contribute to the manufacturing processes through their expertise and their skills developed over time. This paper introduces a bi-objective mathematical model useful to assign different workers exposed to the risk of repetitive work to various workstations. A person-job fit approach is proposed, which analyses the workers' physical capacities, competencies and mental and relational skills together with the requirements of each workstation in terms of capabilities and ergonomic load. The aim is to define the activities scheduling through two objectives: the first one considering the matches among workers abilities and workstations activities, the second one reducing the ergonomic risk of repetitive work by varying the assignments during the work shift. The method is also applied to an industrial case, whose results show its applicability and potential benefits, in terms of ergonomics and overall efficiency improvement. [ABSTRACT FROM AUTHOR]

Motivated by important chemical engineering applications, we study probabilistic mechanisms of stochastic effects in a randomly forced model of the continuous stirred tank reactor. The bifurcation analysis of the deterministic model reveals the parameter zone of bistability with coexistence of the equilibrium and oscillatory regimes. It is shown that the boundary between basins of these regimes is moving as the bifurcation parameter changes. We study noise-induced transitions across this boundary leading to the stochastic generation of spiking oscillations and backward effect of the noise-induced suppression of large-amplitude spiking. In the study of these stochastic effects, we use statistics extracted from the direct numerical simulation, and an analytical approach using confidence ellipses method. An important probabilistic phenomenon of coherence resonance is revealed and discussed. [ABSTRACT FROM AUTHOR]

A novel simplified method is presented for the estimation of the metabolism of plasma proteins (albumin, fibrinogen, α, β and γ-globulin, glycoprotein) with regard to the whole body protein metabolism in a young male volunteer (22 years, 81 kg body mass). This method is based on multiple oral administration of [15N]glycine followed by measurement of 15N in plasma proteins, total free amino acids, urea and excreted urinary N. The fractional synthesis rate of albumin was estimated to 6.8 % d−1 based on amino acids and 3.3 % d−1 based on urea, respectively. The fractional synthesis rate of the other plasma proteins ranged from 4.3 % d−1 (γ-globulin) to 26.4 % d−1 (α-globulin, fibrinogen). We conclude that the simplified approach using [15N]glycine provides results which are similar to results based on the simultaneously applied 131I-human serum albumin technique as 'gold standard' and to those reported in literature. The compartmental analysis considering comprehensive tracer kinetic data ensures reliable data treatment and enables statistical evaluation. The analytical effort is minimal because the 15N enrichment of plasma protein after chemical digestion may be directly used. Therefore, the novel stable isotope 15N method is suitable for studies in clinical and nutritional research and practice. [ABSTRACT FROM AUTHOR]

A new framework for the parametric reconstruction of curved fibres from glass fibre-reinforced composite X-ray computed tomography data is proposed. It allows us to detect fibres in a fibre-reinforced polymer sample from a low-dose, low resolution computed tomography scan. An efficient curve representation is then used for each detected fibre, of which the parameters are estimated directly from few 2D high-resolution projection images. The framework is validated on both simulated and real data of glass fibre-reinforced polymers. The generated results demonstrate that it is robust to noise and requires less than 10 high-resolution projections to obtain reasonable fibre estimates. The method can also improve upon existing estimation frameworks relying on full 3D scans. [ABSTRACT FROM AUTHOR]

This study aims to provide a framework to analyse future flood scenarios considering the effects of three main drivers of flood aggravation: climate change (rainfall intensification and sea level rise); unplanned urbanization; and poor maintenance of urban drainage systems. These stressors were chosen because they represent the aggravation of a natural phenomenon, the urban sprawl effects and the degradation of the drainage system. This analysis intends to make it clear what the main drivers of increasing risks are. Subsequently, a uchronic scenario is developed to analyse how adequate urban planning and infrastructure provision can contribute to a sustainable and resilient city regarding flood alleviation. The method is supported by hydrodynamic simulation. Results demonstrate that precarious urban growth without providing adequate infrastructure coverage can be even more dramatic than climate change. Otherwise, the uchronic scenario demonstrates the benefits of adequately planning cities in a sustainable way, giving lessons to this process. [ABSTRACT FROM AUTHOR]

In this study, using construction activities as an example, a proposal is made for the time-dependent prediction of the thermal sensation and the performance loss using a cooling vest, under transient conditions. The approach presented here can, mutatis mutandis, be used for any work activity and the use of a cooling vest, whether or not in a building. [ABSTRACT FROM AUTHOR]

This paper has the objective to initiate a discussion on potential improvements or extension of the validity of the original equation of the Predicted Percentage of Dissatisfied (PPD), according to (NEN-)EN-ISO 7730. This paper is to be regarded as a supplement to a paper on a re-derivation of the PMV equation in the Fanger model (Roelofsen, Jansen, and Vink 2021). In practice, in scientific research it regularly appears that the PMV (Predicted Mean Vote), and by extension the PPD, are applied outside the range based on which the PMV and the PPD equation are derived. In practice, this can occur, for example, in the evaluation of the measurement or calculation of temperature exceedances in a room, for sedentary activities. As it turns out, a PMV equation with an application of −3 to 3, for at least sedentary activities, would be useful in the different fields of study. For that reason, Roelofsen has adapted the PMV equation in the (NEN-)EN-ISO model. But to what extent should the PPD equation also be adjusted? After all, the PPD is also derived from and limited to a PMV of −2 to 2, according to (NEN-)EN-ISO 7730. [ABSTRACT FROM AUTHOR]

Following the experimental lead, we construct a general mathematical model which, depending on whether the uniaxial scalar order parameter is constant or not, can predict either the classical shear striping instability or the molecular auxetic response and mechanical Fréedericksz transition observed in different liquid crystal elastomers. Our theoretical model can shed some light on the role of nematic order in these stretch-induced mechanical instabilities not observed in conventional rubber-like solids. [ABSTRACT FROM AUTHOR]

The aim of this study is to develop a descriptive framework for teacher educators to assist teachers to plan and realize modelling implementations in their classrooms and for researchers to describe and analyse how modelling is implemented. The planning process and implementations of 12 middle and high school mathematics teachers who conducted modelling implementations were analysed by the researchers to achieve this aim. The data used in the study were lesson plans regarding each modelling implementation, the transcripts of the voice recordings of pre-implementation interviews with the teachers, transcriptions of the video recording of each implementation, and the observation notes of the researchers. The data were analysed within the framework of the grounded theory approach. All modelling implementations consisted of three main sections: planning, implementation, and assessment. The planning section includes identifying the goals, deciding the modelling task and making preparations. The implementation section consists of conducting warm up activities, sharing norms, sharing assessment criteria, presenting the modelling task and tracking students’ work. The assessment section involves presenting solutions, discussing solutions and necessary revisions, assessing competencies, and sharing assessment results and arriving at decisions. [ABSTRACT FROM AUTHOR]

Mathematical modelling has garnered national and international interest due to its importance. Mathematical modelling can develop students' mathematical understandings, teamwork and communication practices. The ability for teachers to select appropriate mathematical modelling tasks is important to ensure the benefits listed for students are realized. The purpose of this study was to investigate the alignment to mathematical modelling of teacher-created curricular resources available through the Teachers Pay Teachers (TPT) website. The TPT website, where teachers can buy and sell resources, is used by millions of teachers each year. Through this research, we sought to investigate if the curricula that resulted in searches for mathematical modelling are aligned to mathematical modelling. We found that about 6% of the curricula resources in our searches could be considered mathematical modelling. These curricular resources are described. We also categorized the curricular resources from the searches, that were not coded as mathematical modelling. This provides insights into teachers' misconceptions of mathematical modelling. Implications for teachers and researchers for issues to be considered as the prevalence of online resources increases are discussed. [ABSTRACT FROM AUTHOR]

Industrial processes are typically multi-input-multi-output (MIMO) in nature. The main challenge to control such processes is the interaction among the loops. In this study, primarily, the mathematical model of a practical quad-coupled tank process, i.e. MIMO by nature, consisting of two upper and two lower tanks, is identified. Subsequently, a fuzzy knowledge-based decoupler is designed for the identified model. Maintaining the water levels at desired heights for upper tanks in the presence of interactions and disturbances is the prime goal for this two-input-two-output (TITO) process. The proposed fuzzy decoupler combined with IMC-PID controllers is used to test the closed loop performance of the interacting coupled tank system. Real-time experimental results substantiate the effectiveness of the proposed scheme by providing enhanced performance toward maintaining the desired levels of the individual tanks, even in the presence of measurement noise. [ABSTRACT FROM AUTHOR]

Simulation and emulation of electric motor faults are particularly useful to study, test, and evaluate the motor condition monitoring products based on the motor current signature and vibration analysis. Many researchers have proposed and developed several DAQ & computer-based simulation tools. This paper aims to develop a system to simulate and emulate the maximum types of faults which can occur in a three-phase induction motor. In this paper, an embedded system based induction motor fault simulator and the emulator is proposed and developed. The focus of this paper is to model the induction motor faults mathematically based on the motor current signature and vibration frequency spectrum, which are theoretically derived and proved by the early generation researchers and engineers. The novelty of the proposed approach is a cost-effective, portable, and handy tool for field evaluation of the motor condition monitoring products. This paper presents the hardware and software development for making a stand-alone motor faults simulator and emulator. The system employs a powerful high-end and powerful embedded system INTEL ATOM Minnow Board, which is built around E3826, Dual Core, and 1.46 GHz processor. A dedicated 4-channel Direct Digital Synthesizer (DDS) with 12-bit resolution along with software generates all three-phase induction motor faults for both MCSA and vibration analysis. The simulated and emulated faults signals are compared and evaluated against the Standards with the help of a digital storage oscilloscope. [ABSTRACT FROM AUTHOR]

Lack of homogeneity in the product (LHP) appears in some production processes that confer heterogeneity in the characteristics of the products obtained. Supply chains with this issue have to classify the product in different homogeneous subsets, whose quantity is uncertain during the production planning process. This paper proposes a generic framework for reviewing in a unified way the literature about production planning models dealing with LHP uncertainty. This analysis allows the identification of similarities among sectors to transfer solutions between them and gaps existing in the literature for further research. The results of the review show: (1) sectors affected by LHP inherent uncertainty, (2) the inherent LHP uncertainty types modelled, and (3) the approaches for modelling LHP uncertainty most widely employed. Finally, we suggest a conceptual model reflecting the aspects to be considered when modelling the production planning in sectors with LHP in an uncertain environment. [ABSTRACT FROM AUTHOR]