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The article deals with the problem of calculating the volume calendar plan of a paper mill. The presented mathematical model and methods make it possible to schedule paper production orders between several paper machines (PM) to even their loading, devise cutting plans for each winder and arrange the order of their implementation. When forming cutting plans, orders are grouped in accordance with such parameters as grammage, roll diameter, core diameter, product type and number of layers. Deadlines and volumes in customer orders are taken into account. The cutting plans for each winder account for the allowable roll width limits and the maximum number of knives. To find the optimal schedule, a combination of the following criteria is used: minimal trim loss, minimal changes to the knives' setup and smooth transitions by product grades. Solution algorithms are presented that use a combination of the simplex method, the column generation, the branch and bound methods, the greedy algorithm and the local search procedure. We tested the solution approach on real production data from a paper mill in European Russia and obtained the production sequence that better matches deadlines in customer orders compared to the plan devised manually by production planners. [ABSTRACT FROM AUTHOR]

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]

In this article, we present a mathematical model and numerical simulation of the coffee-ring effect on porous papers. The numerical method is based on Monte Carlo simulation. The proposed model is simple but can capture the main mechanism of coffee stain formation on porous papers. Several numerical experiments are presented to demonstrate the performance of the proposed algorithm. We can obtain the coffee-ring effect on porous papers as the computer simulation results. [ABSTRACT FROM AUTHOR]

The quest for cost-effective and thermal efficient structural materials onto beating the high cost of construction is gaining more attention among researchers. This study focused on the blending of cement and sand with waste paper pulp into cost-effective structural materials. The composites were prepared in four mix groups with each containing a fixed amount of sand at 5, 10, 15, and 20 wt.% (by weight of pulp). Cement was varied at 10, 20, 30, and 40 wt.% in each group, and curing was done for 28 days. Properties evaluated are compressive, bending, and splitting strengths. It was observed that increasing cement and sand contents enhanced strengths; howbeit, the blend of 30 wt.% cement/15 wt.% sand resulted in a reduction in bending strength even as 30 wt.% cement/20 wt.% sand engendered a decrease in bending and splitting strength. The microstructural features showed that inherent fibers of the pulp were well bonded with hydration products and sand content yielding good performance in the composites. The optimization procedure carried out depicted a combination of 35.27% cement and 20% sand as the optimum composition. Experimental outcomes were modelled for the purpose of prediction of responses. The models were confirmed statistically fit showing how varying cement content affected strength responses at fixed sand proportion. ANOVA affirmed the significant contribution of cement and sand on the strength responses. Compliance reliability was observed to be dependent on the interactive pattern between cement and sand. Going by the standard prescription for the strength properties, cement and sand content of 35.27 and sand 20 wt.% satisfied all strength requirements for low-cost construction having a compliance reliability of 1.31. [ABSTRACT FROM AUTHOR]

This work examines the impact of multi pre-exponential factors on the lifetime modelling of the paper in oil-immersed transformers. First, the corresponding pre-exponential factor was determined based on the concentrations of the three parameters known as oxygen, moisture and acid. Next, the pre-exponential factor for each of the parameters at different concentrations was combined based on the summative approach to obtain the overall impact on the lifetime of the paper. It is found that the expected life of the paper for overall multi pre-exponential factors is higher than either single or double pre-exponential factors. For a single pre-exponential factor, the expected life of the paper decreases by a factor of 59.8 as the oxygen concentration increases from 15,000 ppm to 210,000 ppm. Moisture can decrease the expected life of the paper by a factor of 34 as it increases from 0.5% to 5%. Low molecular weight acid (LMA) has a higher impact than high molecular weight acid (HMA), whereby its impact is further enhanced through multi pre-exponential factor effect whereby the expected life of the paper decreases by a factor of 7.9 as the moisture content increases from 0.5% to 5% and oxygen increases from 300 ppm to 20,000 ppm. [ABSTRACT FROM AUTHOR]

To enhance the quality and efficiency of computer-enabled generation of papers for Test for English Majors Band 8 (TEM-8), a paper generation model supported by sparrow search algorithm-genetic algorithm was studied. First, a simplified test paper generation mathematical model was set up after analyzing and studying types and characteristics of TEM-8 tasks. In the model, quantity, type, difficulty, discrimination degree, scores, exposure, and answering time of test questions were taken into consideration. To enhance the optimizing effect of the genetic algorithm for searching test questions, the traditional genetic algorithm was improved by introducing the sparrow search algorithm into the model to achieve a better crossover rate, variance rate, optimization precision, and speed of the genetic algorithm. A new sparrow search-genetic algorithm (SSA-GA) was designed, and the optimizing effect of SSA-GA was verified to be ideal through optimizing six standard test functions. Then, SSA-GA was applied to conduct experimentation with test paper generation, and comparison with traditional genetic algorithms was also made. The values of best and average fitness of SSA-GA were better than those of the traditional genetic algorithm (GA) in the paper generation. Exposure rate and success rate in TEM-8 paper generation of SSA-GA were higher than those of traditional GA in TEM-8 paper generation. Results showed that the studied SSA-GA could implement test paper generation with higher speed and better quality. [ABSTRACT FROM AUTHOR]

Industrial progress in papermaking in the early nineteenth century led to the technologies that resulted in more acidic papers, which was caused mainly by the exploitation of alum (KAl(SO4)2) and rosin as sizing agents. The papers prepared by such technologies have degraded more quickly. From the 1930s various deacidification and preservation processes with basic agents have been developed. The most widespread deacidification process is with the aerosol (spray system) consisting of microscale particles MgO and perfluoroheptane (PFH) as a carrier (the so-called Bookkeeper process). The shortcomings of this process are the low dissolution of solid MgO particles and the transport to the interior of acidic paper. We have developed a theoretical two-level model of the Bookkeeper process suitable for prediction of deacidification extent. The model involves both the dissolution/reaction of the solid particles and transport of solvated ions and solid particles inside the bulk of paper. The developed model coincides with the results of the performed deacidification experiment. The model is also in good agreement with the Lucas–Washburn equation, which is usually used for the description of the penetration of a deacidifying agent into the paper. [ABSTRACT FROM AUTHOR]

The generation and distribution of furfural are significantly affected by moisture content in the insulating paper. However, the diffusion mechanism of furfural under moisture effect is not clear, hence, this study investigates the effect of moisture on the diffusion characteristics of furfural by combining macro experiment and micro molecular dynamics simulation. The simulation results demonstrate that the increased moisture content in paper accelerates the diffusion of furfural from paper to oil, which is also proved by the experimental data. Then, the results of interaction energy analysis indicate that the increase of moisture enhances the van der Waals force between oil and furfural. The present findings are expected to improve the theoretical level of furfural analysis, which will facilitate the aging evaluation of the transformer insulating paper based on furfural. [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.

The space charge effect of transformer insulating paper will distort its internal electric field, and its space charge effect will be more prominent under extremely complex working conditions. At present, the micromechanism of charge transport and electric field distortion characteristics of paperboard are not clear under complex working conditions. So in this article, based on the bipolar carrier transport (BCT) model and the dynamic carrier balance model, the effects of high temperature, aging degree, moisture content, and bent degree on charges accumulation in paperboard are studied under dc high voltage by numerical simulation and the measured data needed for simulation. The results show that the higher temperature strengthens the carrier migration, deepens the injection depth of the charge, and aggravates the distortion of electric field intensity in paperboard. The more extended the aging time of paperboard, the greater the internal trap density and the deeper the trap depth, which lead to charges migration difficultly. Increasing water content in the paperboard will accelerate space charges to reach a steady state, while further increasing it will slow down this process, which is related to the shallow trap getting deeper. When the critical part of paperboard is extruded, many traps are introduced, resulting in charges accumulation seriously. The research results can reference the design of paperboard and the maintenance of transformer insulation system. [ABSTRACT FROM AUTHOR]

Howard Rachlin's widely influential behavioral economic approach to self‐control and related issues provides the model for this submission. The topic is overconsumption. Current human consumption levels are unsustainable. Explanations typically focus on societal factors, such as the seductive power of advertising and/or misguided tax policies. However, the effectiveness of these factors depends on the degree to which individuals are susceptible to the message: "consume more." Humans are not blank slates. This paper argues that how individuals frame their choices establishes the susceptibility to overconsume. According to economic theory, consumers frame their options as bundles, composed of different combinations of the available items and activities. This leads to maximizing. In experiments, participants tend to frame their options as "either‐or" choices. This leads to the matching law. Mathematical models of concurrent schedule choice procedures show that (1) the matching law implies overconsumption of the most preferred option and (2) that individuals will persist in preferring their favorite option even when doing so reduces overall reward rates. Given that the matching law better describes how individuals choose than does maximizing, the mathematical models of widely used choice procedures help explain why efforts to increase consumption have been more influential than efforts to control consumption. [ABSTRACT FROM AUTHOR]

Due to rapid temperature rise and insulation moisture, bubbles can generate in the oil-paper insulation of oil-immersed power transformers, which can reduce the dielectric strength of oil-paper insulation and even bring about the risk of insulation breakdown. In order to accurately evaluate the conditions of bubble formation, the physical process of bubble formation in oil-paper insulation is studied in this article. Considering the effects of water vaporization, gas dissolution in oil, and moisture migration on bubble formation, a bubble formation prediction model is constructed. Based on Henry’s law, the dissolution equilibrium of gas in oil is taken into consideration and the upper boundary of the initial temperature of bubble effect (ITBE) envelope is obtained in this model. Based on the moisture equilibrium in oil-paper insulation, the bubble formation process caused by the emergence and rapid evaporation of free water is analyzed, and then, the lower boundary of the ITBE envelope is obtained in this model. The model results show that the moisture content of the pressboard and the presence of free water have a great impact on ITBE. Specifically, the higher the moisture content, the lower the ITBE value. In addition, with the further increase of moisture content, the upper and lower boundaries of the ITBE envelope gradually tend to be the same. However, once free water is present on the surface of cellulose, ITBE decreases rapidly to below 120 °C. The model built in this article is of great significance to study the temperature limit of the power transformer. Hence the ITBE envelope can provide an important theoretical reference for reducing the risk of bubble formation during power transformer operation. [ABSTRACT FROM AUTHOR]

The mathematics of budgeting and space can lead to a justice-oriented experience for elementary students as they design a proposal for an inclusive playground. The authors' work focused on creating the space for elementary children to see the interconnectedness between mathematics and a community social injustice, lack of inclusive playground access, through community-based mathematical modeling (CBMM). This article highlights how third- and fourth-grade teachers, a math coach, and a university professor (also authors of this paper) collaboratively and thoughtfully engaged in the CBMM cycle.

• Combined effects of extruded brick compositions with paper sludge and expanded perlite were characterized. • The use of additives in bricks has significantly affected their thermo-physical and mechanical properties. • The effects of process parameters on brick properties were investigated with a new mathematical modeling approach. • Fired brick samples showed good thermal insulation performance. • Produced exruded bricks have good potential for energy saving. Lightweight bricks produced with addition of different additive materials such as expanded perlite (EP) and recycling paper sludge (RPS) waste have been accomplished by a pug mill. Porous fired bricks were produced by using organic and inorganic additives such as paper waste and expanded perlite as pore-makers. In the experimental study, the seventeen mixture sets were prepared with Box-Behnken experimental design procedure of two additive ratios and firing temperatures. The brick samples were produced with shaping by extrusion method and firing at 850, 950 and 1050 °C for two hours after drying. Physical characteristics such as bulk density, apparent porosity and water absorption, and also, compressive strength, thermal conductivity and microstructural properties of brick samples were studied. Influences of process parameters on brick properties were investigated with a detailed neuro-regression analysis. In conclusion, the best brick composition (10 % EP + 10 %RPS by weight) in terms of thermal conductivity corresponding to acceptable mechanical properties was optimized. Accordingly, the compressive strength values of all samples are around 10 to 27 MPa. Also, the samples with high additive content (especially 10 %RPS + 5 %EP sample) exhibited the lowest thermal conductivity value (0.432 W/mK) due to the low firing temperature. [ABSTRACT FROM AUTHOR]

Methanol concentration as an aging indicator can assess cellulose aging and estimate cellulose degree of polymerization (DP). Despite the advantages of methanol (MeOH), its major disadvantage is that its concentration in the oil decreases after some time. This point is called the MeOH peak in this article. Therefore, using this indicator when MeOH concentration is reduced leads to incorrect results. When using methanol, the main problem is that whenever the methanol concentration in a transformer is measured, it cannot be identified that the measured concentration belongs to the left or right side of the MeOH peak. If the measured concentration belongs to the right side of the MeOH peak, the estimated DP is incorrect. In this article, an empirical equation is established to estimate the DP value as a function of methanol concentration when methanol concentration belongs to the left side of the MeOH peak. Then, a new index called methanol peak detector index (MPDI) composed of a 2-furfural/MeOH ratio and normalized DP is presented to ensure the validity of the calculated DP value. If it is found that the measured concentration belongs to the left side of the MeOH peak, then the estimated DP by the presented equation is valid. Finally, the application of this method is verified by applying it to measurement data samples indicating the validity of the method. [ABSTRACT FROM AUTHOR]