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We present a mathematical model for the slow combustion (smoldering) of a two-dimensional sheet of paper. We describe the evolution of the char region, and we investigate the effects of an orthogonal air flow on the shape of the combustion front. The mathematical formulation consists in a set of two nonlinear PDEs for the temperature and the oxygen concentrations coupled with one ODE for the cellulose concentration. The (dimensionless) problem is solved numerically by means of a spectral collocation scheme based on Chebyshev polynomials. Our results show that the Péclet and the Lewis number strongly influence the shape of the ignition front and that the advancement of the combustion front does not occur if advection and diffusion are neglected (zero Péclet and Lewis numbers). In particular we observe that the burning region and the ignition front are strongly influenced by the velocity of the airflow and by the mass and heat transport phenomena due to diffusion and advection. We shall see that the increasing of the ratio between the convective and diffusive characteristic times (Péclet number) and the decreasing of the ratio between the mass and heat diffusive characteristic times (Lewis number) have a "flattening effect" on the combustion front. [ABSTRACT FROM AUTHOR]

Mathematical modeling is a high-leverage topic; it is critical to students' participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary level has been underemphasized, particularly research on supports and challenges for teachers who engage in designing authentic modeling tasks. In this study, we employed qualitative case study methods to investigate how elementary teachers designed and implemented authentic mathematical modeling tasks, with an explicit focus on how their tasks evidenced different dimensions of authenticity. We analyzed three cases of teams of elementary teachers as they developed modeling tasks connected to school and community contexts. The three cases were: 1) a student-driven modeling task related to paper and plastic waste in a school cafeteria, 2) a modeling task based on authentic situations at a community-run resource center, and 3) a modeling task focused on designing and monitoring a school community-building art project. Our cases illustrate that elementary teachers can successfully design and implement modeling activities that utilize different entry points and evidence multiple dimensions of authenticity. Furthermore, we found that the specific dimensions of authenticity may vary depending on the design supports and curriculum challenges within each context. [ABSTRACT FROM AUTHOR]

In this paper, we continue describing the project and the experimentation of "Ricerca Operativa Applicazioni Reali" (ROAR; in English, Real Applications of Operations Research), a three-year project for higher secondary schools, introduced. ROAR is composed of three teaching units, addressed to Grades 10, 11, and 12, respectively, having the main aim to improve students' interest, motivation, and skills related to Science, Technology, Engineering, and Mathematics disciplines by integrating mathematics and computer science through operations research. In a previous paper, we reported on the design and implementation of the first unit, started in Spring 2021 at the scientific high school IIS Antonietti in Iseo (Brescia, Italy), in a Grade-10 class. Here, we focus on the second unit, carried out in Winter/Spring 2022 with the same students, now in a Grade-11 class. In particular, we describe objectives, prerequisites, topics and methods, the organization of the lectures, digital technologies used, and a challenging final project. Moreover, we analyze the feedback from students and teachers involved in the experimentation.

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.

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.

Operations Research (OR) is a branch of applied mathematics that deals with optimization problems arising from different real contexts. The solving process of its problems is based on the construction and resolution of mathematical models, showing the possible connections between mathematics and the real world. Nevertheless, OR is not typically included in most curricula of higher secondary schools (i.e. Grades 9-12), but it is usually presented mainly at university level. To show how OR could be significant for these school students' education, the authors of this paper developed an educational project consisting of three teaching units. In this paper, we share the result of the teaching experiment related to the first unit, addressed to Grade 10. Qualitative and quantitative analyses show how it is appropriate to include OR and its typology of problems in regular school mathematics lectures. Second, these data also show how modelling and problem-solving skills, developed working with OR, can be fostered by implementing a collaborative way of working, also by making use of digital technologies. Last but not least, we demonstrate the positive impact such activities have on students' appreciation of OR.

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.

Mathematical modeling (MM) -- a cyclical process that involves using mathematics to make-sense of and analyze relevant, real-world situations -- has the potential to advance equity and challenge spaces of marginalization in the elementary mathematics classroom. When informed by culturally responsive teaching practices, MM creates opportunities to center the knowledge and experiences that students from diverse racial, cultural, and linguistic backgrounds bring to the classroom as valuable resources to support learning and inform action. It can disrupt power and status hierarchies in the classroom that contribute to structural and ideological marginalization. This paper describes ways teachers connected their teaching of MM with key components of a culturally responsive mathematics teaching framework. Analysis synthesizes data from an innovative, research-based professional development for elementary teachers to support teacher learning of equity-centered, culturally responsive MM instruction. Data sources include end of year teacher interviews, and professional development discussions from 19 teachers at four geographically, racially, and culturally diverse sites. Findings focus on how teachers connected their teaching of MM with key dimensions of culturally responsive mathematics teaching, and affordances and challenges related to resisting ideological and structural forms of marginalization.

Literature screening is the process of identifying all relevant records from a pool of candidate paper records in systematic review, meta-analysis, and other research synthesis tasks. This process is time consuming, expensive, and prone to human error. Screening prioritization methods attempt to help reviewers identify most relevant records while only screening a proportion of candidate records with high priority. In previous studies, screening prioritization is often referred to as automatic literature screening or automatic literature identification. Numerous screening prioritization methods have been proposed in recent years. However, there is a lack of screening prioritization methods with reliable performance. Our objective is to develop a screening prioritization algorithm with reliable performance for practical use, for example, an algorithm that guarantees an 80% chance of identifying at least 80% of the relevant records. Based on a target-based method proposed in Cormack and Grossman, we propose a screening prioritization algorithm using sampling with replacement. The algorithm is a wrapper algorithm that can work with any current screening prioritization algorithm to guarantee the performance. We prove, with mathematics and probability theory, that the algorithm guarantees the performance. We also run numeric experiments to test the performance of our algorithm when applied in practice. The numeric experiment results show this algorithm achieve reliable performance under different circumstances. The proposed screening prioritization algorithm can be reliably used in real world research synthesis tasks.

Ultrasound hip screening is suitable for the early identification of developmental dysplasia of the hip (DDH). Newborn and infant home visits are good opportunities for hip screening in the community, but studies focusing on nurse-led screenings are lacking. Based on a pre–post design, this study aims to develop and evaluate an ultrasound training program to improve nurses' assessment skills in detecting DDH cases during newborn and infant home visits. Said educational program will include e-learning, hands-on seminars, and clinical training. The primary outcome will be the success rate of imaging standard planes (standardized images for hip assessment) in clinical training. The secondary outcomes will include knowledge test results, objective structured clinical examination scores, time required for imaging, and inter-rater reliability between nurses and physicians. The educational program will address the issue of missed and late detection of DDH cases in resource-limited communities. This study will demonstrate the feasibility of procedures and the effectiveness of the educational program in 2024. The protocol was registered in the University Hospital Medical Information Network Clinical Trial Registry before starting the study (no. UMIN000051929, 16 August 2023). [ABSTRACT FROM AUTHOR]

In this paper, we discuss how a professor could have students, using rational and exponential functions, develop models for several different density-dependent populations based on characteristics of the species. Students would then need to choose an appropriate method from among three different analytic methods (find a solution, phase-line analysis, graphing approximate solutions) to analyse their models. We then discuss how to use aspects of a species' behaviour to choose an appropriate model from among the ones developed. Finally, we show how a professor could apply what students have learned to develop general principles for sustainable harvesting of such species.

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.

Students exit calculus with understandings of change that want for conceptual depth and are disconnected from real-world contexts. In this paper, we present a problem that will develop their skills in using "change" concepts for learning differential equations through modelling. The problem comes from a qualitative study of how STEM majors approach and think about differential equations as models for real-world scenarios. Our purpose is to inform faculty who are using open, authentic, scenario-driven instructional materials about the ways their students think about what are often taken-for-granted concepts in advanced mathematics and to support faculty in ensuring their students get the most from their innovative instructional materials.

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.

Mathematical modeling is a high-leverage topic; it is critical to students' participation in STEM education and supports civic engagement. Until recently, research on modeling at the elementary level has been underemphasized, particularly research on supports and challenges for teachers who engage in designing authentic modeling tasks. In this study, we employed qualitative case study methods to investigate how elementary teachers designed and implemented authentic mathematical modeling tasks, with an explicit focus on how their tasks evidenced different dimensions of authenticity. We analyzed three cases of teams of elementary teachers as they developed modeling tasks connected to school and community contexts. The three cases were: 1) a student-driven modeling task related to paper and plastic waste in a school cafeteria, 2) a modeling task based on authentic situations at a community-run resource center, and 3) a modeling task focused on designing and monitoring a school community-building art project. Our cases illustrate that elementary teachers can successfully design and implement modeling activities that utilize different entry points and evidence multiple dimensions of authenticity. Furthermore, we found that the specific dimensions of authenticity may vary depending on the design supports and curriculum challenges within each context.

In this paper, we draw on recent research on so-called Fermi problems and situate the fundamental principles underlying this type of tasks and their use from a task design perspective. We use the models and modelling perspective on teaching and learning to elaborate on aspects related to the design of single-use, as well as sequences of, Fermi problems. In addition, we discuss a framework (called the Fermi problem activity template [FPAT] framework) for supporting the design and use of Fermi problems to facilitate students' learning within particular mathematics content areas and/or aimed at particular concepts or higher-order thinking skills. We also illustrate how the FPAT framework can be used to (i) facilitate interdisciplinary collaborations with other subjects such as the social sciences, but in particular with the other STEM subjects; and (ii) support teachers in adapting and implementing Fermi problems in their classrooms.

In this paper, we introduce novel instructional approaches to engage students in using modelling with data to motivate and teach differential equations. Specifically, we introduce a pedagogical framework that will execute instructional modules to teach different solution techniques for differential equations through repositories and notebook environments during real-time instruction. Each of these teaching modules employs a literate programming approach that uses the notebook environment to explain the concepts in anatural language, such as English, interspersed with snippets of macros and traditional source code on a web browser. The pedagogical approach employed is reproducible and leads to openaccess material for students to motivate and teach differential equations efficiently. We will share examples of this framework applied to teaching advanced concepts such as machine learning and neural network approaches for solving ordinary and partial differential equations as well as estimating parameters in these equations for given datasets. More details of the work can be accessed from https://aoguedao.github.io/teaching-ml-diffeq.

Among the problems identified at Technical and Vocational Education and Training (TVET) colleges, low achievement in mathematical subjects is the most prominent one. This paper documents a qualitative case study undertaken at TVET College in Gauteng with the purpose of exploring the National Certificate Vocational (NC(V)) Level 4 students' errors and associated misconceptions when answering optimisation questions in differential calculus. The participants were 60 students who were registered for a course in mathematics. Data were generated from the written student responses to two non-routine test items followed by interviews. Using the Newman error hierarchical model to analyse the data, it was discovered that students errors were conceptual and procedural as well as systematic and non-systematic. The literature also alluded to instructional approaches as some of the causes of students' misconceptions and the errors and that interventions should target students as well as the instructors.

Problem solving in chemical kinetics poses substantial challenges for university students since it often involves significant use of mathematics as a tool and language, with challenging translations and transitions between chemical phenomena and mathematical representations. In this paper, we present key findings from a study investigating chemistry students solving tasks centred around the steady-state approximation. Building upon the mathematical modelling cycle (MMC), qualitative analysis of the data collected using a think-aloud protocol led to the development of the extended MMC. This empirically derived extended MMC offers a more detailed account of the processes involved in mathematical modelling of chemical phenomena, highlighting aspects such as the occurrence of deliberation and evaluation throughout the modelling cycle, as well as the varying characteristics, points of activation and roles of extra-mathematical resources during problem solving. We further introduce and use problem-solving trajectories as a tool for visualising and analysing the complex and diverse approaches used by students in their attempts at reaching a solution. Overall, the extended MMC provides a finer-grained model of the cognitive and metacognitive activities that students engage in, offering further insights for research and practice.

Background Following years of sustained pressure on the UK health service, there is recognition amongst health professionals and stakeholders that current models of healthcare are likely to be inadequate going forward. Therefore, a fundamental review of existing social models of healthcare is needed to ascertain current thinking in this area, and whether there is a need to change perspective on current thinking. Method Through a systematic research review, this paper seeks to address how previous literature has conceptualized a social model of healthcare and, how implementation of the models has been evaluated. Analysis and data were extracted from 222 publications and explored the country of origin, methodological approach, and the health and social care contexts which they were set. Results The publications predominantly drawn from the USA, UK, Australia, Canada and Europe identified five themes namely: the lack of a clear and unified definition of a social model of health and wellbeing; the need to understand context; the need for cultural change; improved integration and collaboration towards a holistic and person-centred approach; measuring and evaluating the performance of a social model of health. Conclusion The review identified a need for a clear definition of a social model of health and wellbeing. Furthermore, consideration is needed on how a model integrates with current models and whether it will act as a descriptive framework or, will be developed into an operational model. The review highlights the importance of engagement with users and partner organizations in the co-creation of a model of healthcare. [ABSTRACT FROM AUTHOR]

I will briefly discuss the history of research-related projects that Mark Burgin and I worked on together. I will then discuss our joint research related to the circle of sense and nonsense. One paper was entitled In a search for deeper meanings: navigating the circle of Sense and Nonsense and in turn articulating logical varieties as knowledge illuminators and the second was entitled In the Circle of Sense and Nonsense, Including A Mathematic Model of Meaning. This research represents a bridge between the media arts and sciences (my artwork) as a means of embodying ideas exploring a particular approach to meaning production and related computation, as well as Burgin's concepts related to logical varieties and mathematical models of meaning. I will refer to the full papers and links because they present a very robust and full articulation of the concepts discussed here. In this paper, I will briefly touch on the areas of research, supply short definitions, and refer to the relevant historical publications. [ABSTRACT FROM AUTHOR]

Back in 1974, DeGroot first introduced the concept of achieving consensus through iterative averaging processes using square stochastic matrices. A pivotal question arises regarding the feasibility of extending the classical DeGroot model from square stochastic matrices to higher-order stochastic hyper-matrices. In the paper, we introduce a novel mathematical model for opinion-sharing dynamics employing the Krause mean process that is generated by off-diagonally positive doubly stochastic hyper-matrices. The principal objective is to achieve consensus within the multi-agent system. [ABSTRACT FROM AUTHOR]

Alzheimer's disease is a complex, multi-factorial, and multi-parametric neurodegenerative etiology. Mathematical models can help understand such a complex problem by providing a way to explore and conceptualize principles, merging biological knowledge with experimental data into a model amenable to simulation and external validation, all without the need for extensive clinical trials. We performed a scoping review of mathematical models describing the onset and evolution of Alzheimer's disease as a result of biophysical factors following the PRISMA standard. Our search strategy applied to the PubMed database yielded 846 entries. After using our exclusion criteria, only 17 studies remained from which we extracted data, which focused on three aspects of mathematical modeling: how authors addressed continuous time (since even when the measurements are punctual, the biological processes underlying Alzheimer's disease evolve continuously), howmodels were solved, and how the high dimensionality and non-linearity of models were managed. Most articles modeled Alzheimer's disease at the cellular level, operating on a short time scale (e.g., minutes or hours), i.e., the micro view (12/17); the rest considered regional or brain-level processes with longer timescales (e.g., years or decades) (the macro view). Most papers were concerned primarily with amyloid beta (n = 8), few described both amyloid beta and tau proteins (n = 3), while some considered more than these two factors (n = 6). Models used partial differential equations (n = 3), ordinary differential equations (n = 7), and both partial differential equations and ordinary differential equations (n = 3). Some did not specify their mathematical formalism (n = 4). Sensitivity analyses were performed in only a small number of papers (4/17). Overall, we found that only two studies could be considered valid in terms of parameters and conclusions, and two more were partially valid. This puts the majority (n = 13) as being either invalid or with insufficient information to ascertain their status. This was themain finding of our paper, in that serious shortcomings make their results invalid or non-reproducible. These shortcomings come from insufficient methodological description, poor calibration, or the impossibility of experimentally validating or calibrating the model. Those shortcomings should be addressed by future authors to unlock the usefulness of mathematicalmodels in Alzheimer's disease. [ABSTRACT FROM AUTHOR]

When the converter transformer core is grounded at multi-points, a fault loop will be formed and a circulation will be generated, leading to local overheating of the magnetic core and decomposition of insulating oil. Therefore, the converter transformer core will be single point grounded. As a rare internal lead of converter transformer, the ground current on the core ground lead can often reflect the running state of converter transformer. In this paper, theoretical analysis, modeling simulation and experimental research are carried out on the ground current of converter transformer at one point. Firstly, according to the structure characteristics of converter transformer, the analytical modeling of ground current is carried out. Secondly, based on the structure characteristics of oil paper insulation, the equivalent capacitance of converter transformer is calculated. Then, the analytical and finite element simulation model of converter transformer is established, and the ground current of converter transformer is calculated. Finally, the correctness of the proposed scheme is verified by measuring the grounding current of converter transformer core. [ABSTRACT FROM AUTHOR]

This paper undertakes a revisit of the sunk cost fallacy, which refers to the tendency of people to persist investing resources into something, even if it is destined to have no good outcome. We emphasize that the utilities associated with different alternatives are not static for decision makers, which is exactly opposite to the traditional perspective. This paper argues that the utility of an option may change due to the choice of another option, suggesting that decisions considered irrational by the traditional analytical method, i.e., sunk cost fallacy, may be rational. We propose a novel analytical method for decision making with sunk cost when considering the utility change and validate the effectiveness of this method through mathematical modeling and computational experiments. This paper mathematically describes such decision-making problems, analyzing the impact of changes in the utilities across different alternatives on decision making with a real-world example. Furthermore, we develop a two-stage stochastic optimization model for such decision-making problems and employ the sample average approximation (SAA) method to solve them. The results from computational experiments indicate that some decisions traditionally considered irrational are, in fact, rational when the utility of an option changes as a result of choosing another option. This paper, therefore, highlights the significance of incorporating utility changes into the decision-making process and stands as a valuable addition to the literature, offering a refreshed and effective decision-making method for improved decision making. [ABSTRACT FROM AUTHOR]

As a knowledge-intensive financial enterprise, intellectual capital can play a significant driving role in enhancing the value of financial enterprises. Especially in the current unstable and complex international financial market, it is necessary for financial enterprises to actively consider the advantages of intellectual capital to shape their competitive edge and maximize profit value. However, it is also important to consider the issue of asymmetric information within the financial system, particularly the attitudes and behaviors in the strategic interactions between governments and financial enterprises. Therefore, this paper took the strict logical structure and analytical method of game theory as an effective analytical tool to solve the problem of asymmetric information in the economy and to use the asymmetric information game method to construct a mathematical model of intellectual capital in order to cope with the mistrust in the game process. Based on game theory, this paper systematically analyzed the factors influencing intellectual capital and constructed mathematical models of game theory for adverse selection ex-ante and moral hazard ex-post, analyzing strategic behavior. The research results indicated that, from the perspectives of market reactions and financing constraints, there is an issue of information asymmetry between the government and financial enterprises. The paper also presents viable strategic recommendations for alleviating information asymmetry and achieving coordinated allocation of information resources between government and enterprises. [ABSTRACT FROM AUTHOR]

This document is a preface to a special issue of the journal Mathematics titled "State-of-the-Art Mathematical Applications in Europe." The special issue features twelve original research papers and one review paper from European researchers and their collaborators in various fields of mathematics. The papers cover topics such as mathematical physics, applied mathematics, algebra, navigation algorithms, decision-making models, Lagrange interpolation polynomials, and nonlinear fractional differential equations. The preface provides a brief overview of each paper and expresses gratitude to the authors and reviewers. The special issue has received significant interest and demonstrates the importance of open access research in applied mathematics. [Extracted from the article]

This paper reviews current numerical developments for atmospheric modelling. Numerical atmospheric modelling now looks back to a history of about 70 years after the first successful numerical prediction. Currently, we face new challenges, such as variable and adaptive resolution and ultra-highly resolving global models of 1 km grid length. Large eddy simulation (LES), special applications like the numerical prediction of pollution and atmospheric contaminants belong to the current challenges of numerical developments. While pollution prediction is a standard part of numerical modelling in case of accidents, models currently being developed aim at modelling pollution at all scales from the global to the micro scale. The methods discussed in this paper are spectral elements and other versions of Local-Galerkin (L-Galerkin) methods. Classic numerical methods are also included in the presentation. For example, the rather popular second-order Arakawa C-grid method can be shown to result as a special case of an L-Galerkin method using low-order basis functions. Therefore, developments for Galerkin methods also apply to this classic C-grid method, and this is included in this paper. The new generation of highly parallel computers requires new numerical methods, as some of the classic methods are not well suited for a high degree of parallel computing. It will be shown that some numerical inaccuracies need to be resolved and this indicates a potential for improved results by going to a new generation of numerical methods. The methods considered here are mostly derived from basis functions. Such methods are known under the names of Galerkin, spectral, spectral element, finite element or L-Galerkin methods. Some of these new methods are already used in realistic models. The spectral method, though highly used in the 1990s, is currently replaced by the mentioned local L-Galerkin methods. All methods presented in this review have been tested in idealized numerical situations, the so-called toy models. Waypoints on the way to realistic models and their mathematical problems will be pointed out. Practical problems of informatics will be highlighted. Numerical error traps of some current numerical approaches will be pointed out. These are errors not occurring with highly idealized toy models. Such errors appear when the test situation becomes more realistic. For example, many tests are for regular resolution and results can become worse when the grid becomes irregular. On the sphere no regular grids exist, except for the five derived from Platonic solids. Practical problems beyond mathematics on the way to realistic applications will also be considered. A rather interesting and convenient development is the general availability of computer power. For example, the computational power available on a normal personal computer is comparable to that of a supercomputer in 2005. This means that interesting developments, such as the small sphere atmosphere with a resolution of 1 km and a spherical circumference between 180 and 360 km are available to the normal owner of a personal computer (PC). Besides the mathematical problems of new approaches, we will also consider the informatics challenges of using the new generation of models on mainframe computers and PCs. [ABSTRACT FROM AUTHOR]

In spite of the IMO's efforts to improve the safety of intact stability on ships, synchronous rolling still causes large rolling angles, resulting in a very dangerous situation on board. The implementation of automatic tools to predict this undesirable situation has not been widely implemented. Furthermore, the safety of ship stability is not the only responsibility of people involved in the design process, so ship operators must have enough knowledge to predict and avoid these dangerous situations well in advance. Therefore, from a theoretical point of view, in the first part, this paper aims to present a valuable guiding tool for ship operators in order to predict synchronous rolling and avoid undesirable situations on board by making use of only empirical observations of the wave profile and moments. With this purpose, mathematical models are first proposed, with the ship sailing in the worst condition, i.e., with and without considering the damping factor, at zero speed and considering the influence of any pure beam and trochoidal waves. Relevant results shown provide the exact time and wave profile at which the maximum rolling angles are reached. In the second part of the paper, a new control system making use of AI tools is proposed in order to be used by ship operators on board, avoiding dangerous situations. Finally, the results are validated using a set of ship rolling simulations for the most common and representative ship loading conditions and wave periods. [ABSTRACT FROM AUTHOR]

In this paper, we obtain the existence of at least two standing waves (and homoclinic solutions) for a class of time-dependent (and time-independent) discrete nonlinear Schrödinger systems or equations. The novelties of the paper are as follows. (1) Our nonlinearities are composed of three mixed growth terms, i.e., the nonlinearities are composed of sub-linear, asymptotically-linear and super-linear terms. (2) Our nonlinearities may be sign-changing. (3) Our results can also be applied to the cases of concave-convex nonlinear terms. (4) Our results can be applied to a wide range of mathematical models. [ABSTRACT FROM AUTHOR]

In the achromatic White's grid, the grey patches between the grey lines are perceived as darker while the same elements inserted between white lines are perceived lighter than their true measured values. A number of authors attempted to calculate the magnitude and direction of this effect using mathematical models based on multiple spatial filters. This paper uses different mathematical model, based on regression analysis, which has shown itself as an excellent tool for prediction of direction and magnitude of White's effect. The psychophysical visual experiment was conducted on 38 subjects of both genders. The differences in lightness perception ∆L00 were calculated in CIE ∆E_2000 system. This paper determined the functional dependence of White's effect magnitude ∆L00 to the lightness L of rectangular elements in White's achromatic grid. The results gave the square polynomial of very high quality (R² = 0,974). Regression polynomials were also found. The gave numerical values ∆L00 of difference in perception of left and right elements in comparison to their physical values (left R² = 0,943, right R² = 0,938) in dependence to variation of lightness parameter L. Results of the research clearly show the mathematical pattern of White's effect based on the lightness of rectangular elements. [ABSTRACT FROM AUTHOR]

This paper presents the numerical solution of the heat conduction model with a fractional derivative of the Riemann–Liouville type with respect to the spatial variable. The considered mathematical model assumes the dependence on temperature of the material parameters (such as specific heat, density, and thermal conductivity) of the model. In the paper, the boundary conditions of the first and second types are considered. If the heat flux equal to zero is assumed on the left boundary, then the thermal symmetry is obtained, which results in a simplification of the problem and the possibility of considering only half the area. The numerical examples presented in the paper illustrate the effectiveness and convergence of the discussed computational method. [ABSTRACT FROM AUTHOR]

There is a lack of study on fault detection methods of medical equipment at home and abroad. The main reason is that the research of fault features is diverse and not systematic. This paper aims to propose a fault recognition method for medical equipment combining the electrical performance parameter features with fault events. First, it treats the equipment as a whole system, setting up the analysis model. Then, we are going to analyze the signal for indicator. This paper chooses the multi-index electrical performance parameters (MEPP) method for the fault identification an indicator. It is proved that the electrical performance signal can evaluate the status of equipment. Thus, it can also be used to recognize the fault or other working statuses. Then, the features of current, voltage, and power are studied exhaustively using a mathematical model. After that, the weight of each parameter feature in any specific event will be determined according to the influence of each parameter feature on fault events. At that time, the recognition method basically realizes the correlation between multi-index features and fault events through weight. Next, the above method needs to be verified in the experiment. This paper chooses six monitors for setting the rules of normal status. The normal status is the baseline for fault identification. Then, feature intervals of other faults are established around this reference. Finally, each feature interval will be constantly adjusted to meet the preset recognition rate and updated to the rules in the subsequent measurement. In this paper, 10 monitors are selected as samples to update a set of basic fault judgment rules based on MEPP, and by adjusting the overlapping interval, the fault recognition rate reaches more than 90% in this study. To sum up, this paper uses the MEPP method to find out the relationship of features of current, voltage, and power with fault events. It will become a new direction for fault recognition studies on electrical medical equipment and other device. [ABSTRACT FROM AUTHOR]

Reliability analysis is crucial for understanding the performance and failure characteristics of lifetime systems. This paper presents a comprehensive study on the reliability analysis of lifetime systems using the Weibull distribution. The Weibull distribution, known for its flexibility in modeling failure times, provides a versatile framework for capturing diverse failure behaviors. A useful model for redundancy systems is proposed in this paper. The model consists of (n+1) components, where n components serve as spare parts for the main component. The failure rate of the working component is time-dependent, denoted as λ(t), while the failure rates of the non-working components are assumed to be zero. Whenever a component fails, one of the spare parts immediately takes over its role. The failed components in this model are considered non-repairable. To analyze this model, we establish the differential equations that describe the system states. By solving these equations, we calculate important parameters such as system reliability and mean time to failure (MTTF) in real-time scenarios. These parameters provide valuable insights into the performance and behavior of the system under study. By employing the Weibull distribution and the proposed model, this paper contributes to enhancing the understanding of reliability analysis in lifetime systems and enables the estimation of important reliability parameters for practical applications. [ABSTRACT FROM AUTHOR]

The object of research is the reliability of information in information-control systems. The work considers a solution to an important scientific and practical problem – increasing the reliability of information in real-time control systems, in particular in positioning systems on road transport. To solve this task, the use of information redundancy, in particular, parallel information redundancy, is proposed. The paper studies the influence of the probability of occurrence of a controlled event, the majority coefficient, as well as the number and quality of information sensors on the reliability of information in an information control system with parallel information redundancy. For these dependences, the corresponding plots were constructed. The paper shows that a change in the quality of information sensors by 20 % can lead to an increase in the reliability of information by more than 0.5. Also, the paper shows that an increase in the majority index by 1 can lead to a change in the reliability of information by more than 0.3. The paper investigates parallel information redundancy systems with different structures and defines formulas for calculating the probabilistic characteristics of their operation. The mathematical modeling was carried out taking into account the probability of occurrence of the controlled event, which made it possible to determine the tendencies to build information-control systems with parallel information redundancy to control events with variable probability of occurrence. The results obtained are based on the theory of probability. The results reported in this work can be used in the construction of an information and control system with a programmatically variable structure to control the occurrence of an event with a variable probability of occurrence, in particular in positioning systems on road transport. [ABSTRACT FROM AUTHOR]

This document discusses the challenges faced in mathematical modeling and controlling COVID-19 epidemics. It highlights the global impact of the pandemic on the economy and health, as well as the uneven effects on different age groups. The availability of vaccines led to mass vaccination campaigns, prompting researchers to implement new strategies and innovative approaches. The document also mentions various journals that have published special issues on COVID-19, covering topics such as forecasting, vaccination strategies, and control measures. The special issue presented in this document consists of eleven papers that analyze clinical characteristics, variant spread, economic recovery, mortality rates, non-pharmaceutical interventions, and coordinated actions. The papers propose mathematical models and control strategies to minimize disease spread and prioritize vaccination. The document emphasizes the multidisciplinary nature of the research, involving fields such as applied mathematics, data science, engineering, biology, and economics. Overall, this special issue provides valuable insights into the mathematical modeling and control of COVID-19 epidemics. [Extracted from the article]

Articulating the complexities of relational wellbeing can be challenging at the best of times, and even more complex during periods of heightened stress and uncertainty. Taking inspiration from feminist materialisms and recent writings on material methods, we explore the potential of object interviews to reveal the material-discursive dimensions of women's experiences of wellbeing during the pandemic. In this paper we describe our research process conducting object interviews with 38 women living in Aotearoa New Zealand from a range of socio-economic, cultural, and ethnic backgrounds. We explore the potential and challenges of object interviews for surfacing new ways of knowing (theoretically, methodologically, and cross-culturally) wellbeing beyond human-oriented health, medical and social-constructionist models, and towards more multidimensional and relational understandings. This paper offers our reflections and learnings about the process of re-turning object interviews and the potential of such approaches for evoking complex ways of knowing wellbeing during and beyond pandemic times. [ABSTRACT FROM AUTHOR]

Low fertility willingness has become a major practical reality in China. From the perspective of family gender equality, this paper analyzes the impact of division of housework on women's fertility willingness by using the data of China Family Panel Studies (CFPS). The results of propensity score matching method and instrumental variable method show that husbands' participation in housework can effectively improve wives' fertility willingness. Mechanism analysis shows that husbands' active participation in housework can effectively reduce wives' work–family conflict, increase wives' satisfaction with husbands' housework contribution, and help improve wives' happiness and fertility willingness. Further discussion on whether families have had children or not shows that women who have had children are more sensitive to their husbands' participation in housework. This study provides empirical evidence for the applicability of family gender equality theory in China and the factors affecting women's fertility willingness. [ABSTRACT FROM AUTHOR]

Mathematical models within the Ross–Macdonald framework increasingly play a role in our understanding of vector-borne disease dynamics and as tools for assessing scenarios to respond to emerging threats. These threats are typically characterized by a high degree of heterogeneity, introducing a range of possible complexities in models and challenges to maintain the link with empirical evidence. We systematically identified and analysed a total of 77 published papers presenting compartmental West Nile virus (WNV) models that use parameter values derived from empirical studies. Using a set of 15 criteria, we measured the dissimilarity compared with the Ross–Macdonald framework. We also retrieved the purpose and type of models and traced the empirical sources of their parameters. Our review highlights the increasing refinements in WNV models. Models for prediction included the highest number of refinements. We found uneven distributions of refinements and of evidence for parameter values. We identified several challenges in parametrizing such increasingly complex models. For parameters common to most models, we also synthesize the empirical evidence for their values and ranges. The study highlights the potential to improve the quality of WNV models and their applicability for policy by establishing closer collaboration between mathematical modelling and empirical work. [ABSTRACT FROM AUTHOR]

It is common in financial markets for market makers to offer prices on derivative instruments even though they are uncertain about the underlying asset's value. This paper studies the mathematical problem that arises as a result. Derivatives are priced in the risk-neutral framework, so as the market maker acquires more information about the underlying asset, the change of measure for transition to the risk-neutral framework (the pricing kernel) evolves. This evolution takes a precise form when the market maker is Bayesian. It is shown that Bayesian updates can be characterized as additional informational drift in the underlying asset's stochastic process. With Bayesian updates, the change of measure needed for pricing derivatives is two-fold: the first change is from the prior probability measure to the posterior probability measure, and the second change is from the posterior probability measure to the risk-neutral measure. The relation between the regular pricing kernel and the pricing kernel under this two-fold change of measure is characterized. [ABSTRACT FROM AUTHOR]

Chemical mechanical planarization (CMP) is vital for ensuring chip fabrication uniformity at nanometer scales. The emergence of a series of phenomenological CMP process models (Stine et al., 1997; Gbondo-Tugbawa, 2002; Xie, 2007; Vasilev, 2011) suggests that the existing model upgrade approach is largely based on a change in phenomenological model assumptions, demanding deep insights into complex process mechanisms and protracted period for accuracy improvements. To tackle this issue, this paper proposes a decoupling regression strategy for model upgrades. This strategy employs a data-driven approach to enhance the coupling relationships within the model, facilitating continuous improvement of simulation accuracy based on the existing model. It is capable of achieving improvements in model accuracy even in scenarios where modelers lack insight into complex process mechanisms. We validate our method by upgrading the Density Step Height (DSH) model to the Extend-DSH model to address poor erosion predictions at the 28nm node. Comparing model predictions with silicon data reveals that the Extend-DSH model aligns better with the measured data, reducing the root mean square error from 159.31Å to 6.89Å and increasing the coefficient of determination from -0.83561 to 0.6058, showcasing the effectiveness of the proposed chip-level CMP model upgrade method grounded in the decoupling regression strategy. [ABSTRACT FROM AUTHOR]

Edge computing networks are critical infrastructures for processing massive data and providing instantaneous services. However, how to efficiently allocate resources in edge computing networks to meet the embedding requirements of service function chains has become an urgent problem. In this paper, we model the resource allocation problem in edge computing networks as a service function chain embedding problem model, aiming to optimize the resource allocation through reinforcement learning algorithms to achieve the goals of low cost, high revenue, and high embedding rate. In this paper, the basic concepts of edge computing network and service function chain are elaborated, and the resource allocation problem is transformed into a service function chain embedding problem by establishing a mathematical model, which provides a foundation for the subsequent algorithm design. In this paper, a service function chain embedding algorithm based on reinforcement learning is designed to gradually optimize the resource allocation decision by simulating the learning process. In order to verify the effectiveness of the algorithm, a series of simulation experiments are conducted in this paper and compared with other algorithms. The experimental results show that the service function chain embedding algorithm based on reinforcement learning proposed in this paper exhibits superior performance in resource allocation. Compared with traditional resource allocation methods, the algorithm achieves significant improvement in terms of low cost, high revenue, and high embedding rate. [ABSTRACT FROM AUTHOR]

To achieve an accurate measurement of tread size after fixed-length cutting, this paper proposes a point-cloud-based tread size measurement method. Firstly, a mathematical model of corner points and a reprojection error is established, and the optimal solution of the number of corner points is determined by the non-dominated sorting genetic algorithm II (NSGA-II), which reduces the reprojection error of the RGB-D camera. Secondly, to address the problem of the low accuracy of the traditional pixel metric ratio measurement method, the random sampling consensus point cloud segmentation algorithm (RANSAC) and the oriented bounding box (OBB) collision detection algorithm are introduced to complete the accurate detection of the tread size. By comparing the absolute error and relative error data of several groups of experiments, the accuracy of the detection method in this paper reaches 1 mm, and the measurement deviation is between 0.14% and 2.67%, which is in line with the highest accuracy standard of the national standard. In summary, the RGB-D visual inspection method constructed in this paper has the characteristics of low cost and high inspection accuracy, which is a potential solution to enhance the pickup guidance of tread size measurement. [ABSTRACT FROM AUTHOR]

This research paper explores the realm of fault detection in distributed motors through the vision of the Internet of electrical drives. This paper aims at employing artificial neural networks supported by the data collected by the Internet of distributed devices. Cross-verification of results offers reliable diagnosis of industrial motor faults. The proposed methodology involves the development of a cyber–physical system architecture and mathematical modeling framework for efficient fault detection. The mathematical model is designed to capture the intricate relationships within the cyber–physical system, incorporating the dynamic interactions between distributed motors and their edge controllers. Fast Fourier transform is employed for signal processing, enabling the extraction of meaningful frequency features that serve as indicators of potential faults. The artificial neural network based fault detection system is integrated with the solution, utilizing its ability to learn complex patterns and adapt to varying motor conditions. The effectiveness of the proposed framework and model is demonstrated through experimental results. The experimental setup involves diverse fault scenarios, and the system's performance is evaluated in terms of accuracy, sensitivity, and false positive rates. [ABSTRACT FROM AUTHOR]

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Hydraulic power take-off (PTO) is increasingly favored as energy regulation and transmission system in wave energy converters (WEC), significantly smoothing the inherent randomness and fluctuation of wave energy. This paper designed a novel hydraulic PTO system composition of a double-acting hydraulic cylinder pump and accumulators. The dynamic process sub-division principle in an operating period of the hydraulic cylinder pump and accumulator and the mathematical model for explaining the fluctuations of pressure and flow rate in the hydraulic pump and accumulator circuit by means of the sub-division principle are put forward. The MATLAB/Simulink simulation model used to analyze pressure fluctuation in the hydraulic PTO system is established based on the mathematical model. The numerical results and MATLAB simulation results are mutually verified about the fine analysis of the accumulator smoothing fluctuation in the hydraulic PTO system. The results show that the pressure fluctuation amplitude of a hydraulic circuit is negatively correlated with the accumulator pre-charge pressure and the accumulator volume, and is positively correlated with the operating period of a hydraulic pump. The energy transfer efficiency of the hydraulic PTO system with accumulator fine compensation can be above 90%. The theory and model in this paper will serve as a valuable reference for designing fluctuation compensation parameters in hydraulic systems. [ABSTRACT FROM AUTHOR]

Tooth profile errors are the internal excitations that cause gear meshing errors, which are critical error factors affecting gear transmission accuracy. In existing studies, it is usually regarded as a constant or random distribution function. However, the actual machined tooth profile error is not a constant, so this estimation is inconsistent with the actual situation, resulting in an inaccurate evaluation of transmission accuracy. This paper proposes a method for representing tooth profile errors using distribution errors (including systematic and random errors), and a mathematical model of distributed tooth profile errors is presented. The contact stresses of the complex transmission system were compared with those obtained by formulas, proving that tooth profile errors increase contact stress. A method for calculating gear meshing error is proposed to evaluate the actual output accuracy of the complex transmission system. Compared with the test, the output accuracy is reduced by 13.8% under the temperature environment and distributed tooth profile errors. The proposed methods can accurately predict the transmission accuracy of precision transmission systems at the design stage and provide theoretical support for reducing systematic and random errors at the gear machining stage. [ABSTRACT FROM AUTHOR]

The role and potential impact of digital screen technology in the lives of children is heavily debated. Current evidence is limited by the weakness of measures typically used to characterise screen use, predominantly proxy- or self-reports with known inaccuracy and bias. However, robust and detailed evidence is needed to provide practical trustworthy guidance to families and professionals working with families. The purpose of this paper is to support researchers to select measurement method(s) that will provide robust and detailed evidence. The paper outlines the challenges in measuring contemporary screen use by children, using a child–technology interaction model to organise considerations. A range of different methods used to measure digital screen technology use in children and adolescents (i.e., questionnaires, diaries, electronically prompted sampling, direct observation, fixed room cameras, wearable/portable cameras, audio recorders, screen-device onboard logging, remote digital trace logging and proximity logging) are described along with examples of their use and constructs typically measured as well as a summary of the advantages and disadvantages of each method. A checklist and worked examples are provided to support researchers determining the best methods or combination of methods for a research project. [ABSTRACT FROM AUTHOR]