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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]

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]

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]

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]

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]

Online ride-hailing services provide additional transportation capability by recruiting private vehicles to meet people's growing travel demand. To ensure the profitability of drivers and platforms, pick-up efficiency and frequency must be maintained at high levels. Therefore, consistency between the spatial distribution of drivers and that of travel demand becomes a key issue to address. This paper proposes a prediction-based iterative Kuhn-Munkres approach for service vehicle reallocation in the context of large-scale online ride-hailing. Firstly, preliminaries are formally defined and a novel mathematical model for the problem is proposed. Secondly, a deep spatio-temporal residual perception network is designed to accurately predict travel demand. Thirdly, an iterative Kuhn-Munkres approach combined with an improved A-Star algorithm is developed to reallocate service vehicles to spatial locations according to their distinct travel demand densities. Finally, extensive experiments are conducted to evaluate and verify the performance of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper reflects on the paradigmatic assumptions and ideologies that have shaped algorithmic management research. We identify two sets of assumptions: one about the "ontology of algorithms" (which holds that human resource management [HRM] algorithms are non‐human entities with material agency) and one about the "ontology of management" that HRM algorithms afford (which understands algorithmic management as a form of control for maximizing economic/shareholder value). We explain how these core assumptions underpin existing research of HRM algorithms, causing blind spots that hinder new ways of understanding and studying algorithmic management. After identifying and unpacking the assumptions and blind spots, we offer avenues to overcome these blind spots, allowing for future research based on new ideological assumption grounds that will help move algorithmic management scholarship further in significant ways. [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]

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]

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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]

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]

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]

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]

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]

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]

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]

Bin packing problem (BPP) is one of the fastest-growing research issues within the field of combinatorial optimization. Over the last years, several studies carried out various BPP variants, mathematical models, and proposed methods to the BPPs. The classical BPP consists of packing a set of rectangular items in a minimum number of rectangular bins while respecting some constraints.Throughout the years, an improved typology was introduced by Wäscher et al. (2007), providing an excellent instrument for the organization and categorization criteria that defined the problem categories different from those of Dyckhoff (1990). Several early literature reviews have been conducted on various aspects of related packing problem variants.The contribution of this paper is to provide a comprehensive and refined taxonomy intended for BPPs. In addition to that, it is an up-to-date review based on a chronological taxonomy of the literature and depicts further research horizons.This systematic review allowed us to identify other characteristics and constraints, based on Wäscher's original ideas, mainly distinguished according to real cases studies. The detailed analysis provides a valuable framework for understanding the research gaps for future studies that should be acknowledged while proposing and solving new extensions. Note: The addresses of second and third authors have been corrected online. [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]

Due to today's competitive environment and information boom, companies are concerned about production planning in uncertain conditions. This paper integrates decision-making method with production scheduling model by considering limited resources. In this paper, a new mathematical model is extended for production project scheduling with multiple execution modes. The main aim of the formulation is to plan and schedule real production projects in uncertain environments. A new mixed-integer linear formulation is presented by considering trade-off of cost, time, as well as quality. Cost–time-quality trade-off is extended with the interval information. In the presented model, activity quality could be enhanced by reworking. The interval forms of some parameters, including duration, quality of activities, cost, and total available resources, are obtained by determining weights of experts and aggregating them. The presented group decision-making method is based on a bi-directional projection measure to deal with interval information. Since the mathematical model is multi-objective and some data are interval, a new modified solution method is developed for solving the model. The presented method for both decision-making and mathematical models is investigated by a real-world production project and two datasets to ascertain the accuracy of the model. Finally, an appropriate sensitivity analysis is proposed. [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 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]

The three-phase imbalance in low-voltage distribution networks (LVDNs) seriously threatens the security and stability of the power system. At present, a standard solution is automatic phase commutation, but this method has limitations because it does not address the branch imbalance and premature convergence or instability of the commutation algorithm. Therefore, this paper proposes a novel refined regulation commutation system, combined with a modified optimized commutation algorithm, and designs a model and simulation for feasibility verification. The refined regulatory model incorporates branch control units into the traditional commutation system. This effectively disperses the main controller's functions to each branch and collaborates with intelligent fusion terminals for precise adjustment. The commutation algorithm designed in this paper, combined with the above model, adopts strategies such as symbol encoding, cubic chaotic mapping, and adaptive adjustment based on traditional genetic algorithms. In addition, in order to verify the effectiveness of the proposed method, this paper establishes a mathematical model with the minimum three-phase imbalance and commutation frequency as objectives and establishes a simulation model. The results of the simulation demonstrate that this method can successfully lower the three-phase imbalance of the low-voltage distribution network. It leads to a decrease of the main circuit's three-phase load imbalance rate from 27% to 6% and reduces each branch line's three-phase imbalance ratio to below 10%. After applying the method proposed in this paper, the main and branches circuit three-phase imbalance are both lower than the limit ratio of the LVDNs, which can improve the quality and safety of electricity consumption. Additionally, the results also prove that the commutation algorithm under this method has faster convergence speed, better application effect, and better stability, which has promotion and application value. [ABSTRACT FROM AUTHOR]

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]

One of the main problems to be addressed in a multi-robot system is the selection of the best robot, or group of them, to carry out a specific task. Among the large number of solutions provided to allocate tasks to a group of robots, this work focuses on swarm-like approaches, and more specifically on response-threshold algorithms, where each robot selects the next task to perform by following a Markov process. To the best of our knowledge, the current response-threshold algorithms do not provide any formal method to generate new transition functions between tasks. Thus, this paper provides, for the first time, a mathematical model, as based on the so-called fuzzy preorders, for the allocation of tasks to a collective of robots with communication capabilities. In our previous work, we proved that transitions in the aforementioned process can be modeled as fuzzy preorders, constructed through the aggregation of asymmetric distances, in such a way that each robot makes its decision without taking into account the decisions of its teammates. Now, we extend this model in such a way that each robot will take into account the number of robots previously allocated for each task. To implement this method, a very simple communication mechanism has been considered. Several simulations have been carried out in order to validate our approach. The results confirm that fuzzy preorders are able to model the evolution of the system when this type of communication is considered and show when and how the communication process improves the system's performance. Experimental results show the existence of a set of good values for the maximum communication distance between robots and that these values depend on the distribution of the tasks in the environment. Thus, in some cases, a better communication mechanism does not imply better results. [ABSTRACT FROM AUTHOR]

Drug-resistant tuberculosis (DR-TB) threatens progress in the control of TB. Mathematical models are increasingly being used to guide public health decisions on managing both antimicrobial resistance (AMR) and TB. It is important to consider bacterial heterogeneity in models as it can have consequences for predictions of resistance prevalence, which may affect decision-making. We conducted a systematic review of published mathematical models to determine the modelling landscape and to explore methods for including bacterial heterogeneity. Our first objective was to identify and analyse the general characteristics of mathematical models of DR-mycobacteria, including M. tuberculosis. The second objective was to analyse methods of including bacterial heterogeneity in these models. We had different definitions of heterogeneity depending on the model level. For between-host models of mycobacterium, heterogeneity was defined as any model where bacteria of the same resistance level were further differentiated. For bacterial population models, heterogeneity was defined as having multiple distinct resistant populations. The search was conducted following PRISMA guidelines in five databases, with studies included if they were mechanistic or simulation models of DR-mycobacteria. We identified 195 studies modelling DR-mycobacteria, with most being dynamic transmission models of non-treatment intervention impact in M. tuberculosis (n = 58). Studies were set in a limited number of specific countries, and 44% of models (n = 85) included only a single level of "multidrug-resistance (MDR)". Only 23 models (8 between-host) included any bacterial heterogeneity. Most of these also captured multiple antibiotic-resistant classes (n = 17), but six models included heterogeneity in bacterial populations resistant to a single antibiotic. Heterogeneity was usually represented by different fitness values for bacteria resistant to the same antibiotic (61%, n = 14). A large and growing body of mathematical models of DR-mycobacterium is being used to explore intervention impact to support policy as well as theoretical explorations of resistance dynamics. However, the majority lack bacterial heterogeneity, suggesting that important evolutionary effects may be missed. Author summary: The emergence of drug-resistant tuberculosis (DR-TB), where the causative bacterium Mycobacterium tuberculosis is resistant to key antibiotics such as rifampicin and isoniazid, poses a significant threat to TB control efforts. To gain a broader understanding of the challenges surrounding DR-TB, mathematical models are increasingly being employed to estimate the impact of interventions, effectiveness of treatment, and to predict the evolution of drug-resistance. However, pragmaticism surrounding model construction often means that important aspects, such as bacterial heterogeneity, are overlooked. We undertook a systematic review of the existing DR-mycobacterium modelling literature, with the specific aim of capturing methods for including bacterial heterogeneity. Our analysis revealed that most models of drug-resistance in mycobacteria primarily focus on intervention strategies and cost-effectiveness analyses, with minimal attention to bacterial heterogeneity. Where heterogeneity is included it mostly consisted of different fitness costs for resistance. [ABSTRACT FROM AUTHOR]

Over the fast few years, the numerical success of the generalized alternating direction method of multipliers (GADMM) proposed by Eckstein and Bertsekas [Math. Progam. 1992] has inspired intensive attention in analyzing its theoretical convergence properties. This paper is devoted to the linear convergence rate of the semi-proximal GADMM (sPGADMM) for solving linearly constrained convex composite optimization problems. The semi-proximal terms contained in each subproblem possess the abilities of handling with multi-block problems efficiently. We initially present some important inequalities for the sequence generated by the sPGADMM, and then establish the local linear convergence rate under the assumption of calmness. As a by-product, the global convergence property is also discussed. [ABSTRACT FROM AUTHOR]

There is an urgent and unmet need for specialist palliative care services in residential aged care. The Specialist Palliative Care in Aged Care (SPACE) Project aimed to improve palliative and end-of-life care for older people living in residential aged care facilities in Queensland. A representative working group developed a series of service principles around palliative care practice in aged care (comprehensive resident-focused care, streamlined service, and capacity building). Funding was allocated by population to the health services in Queensland to adapt and implement models of care aligned with these principles. SPACE successfully implemented a variety of decentralised models of care across Queensland. The critical elements for the success of SPACE were the use of an expert working group to define the core innovation, networking and implementation support from the central project team and community of practice, and adaptable models of care led by local facilitators. Lessons learned from this real-world case study could be adopted to guide and ensure the successful implementation and sustainability of future complex interventions in healthcare settings, both nationally and internationally. What is known about the topic? There is limited palliative care support for the 36% of Australians who die in residential aged care. What does this paper add? This paper describes the development of the Specialist Palliative Care in Aged Care (SPACE) Project, using locally tailored models of care to improve palliative and end-of-life care in aged care facilities across Queensland. What are the implications for practitioners? Critical elements for improving residents' palliative and end-of-life care included creation of an expert working group to define the innovation state-wide, a central project team that supported implementation, a community of practice, and local facilitation. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model is formulated, suitable to explain the evolution of income distribution over a population in the presence of production. The model is conceived from the perspective of complexity. Indeed, the income distribution emerges as the result of a myriad of economic exchanges taking place between individuals. In fact, the aim of the paper is to provide a framework and mathematical tools for the construction and the investigation of models having an exploratory character. The framework is expressed in the form of a system of nonlinear ordinary differential equations, as many as the income classes are, involving transition probabilities. Numerical solutions of these systems are constructed under different assumptions on the law of production and in the presence of different fiscal systems, which provides an example of the versatility of the method. [ABSTRACT FROM AUTHOR]

Purpose. Development of a two-dimensional field mathematical model of a magnetic gearbox operating as part of a lowpower wind turbine for the purpose of evaluating its parameters and characteristics and optimizing geometric parameters from the point of view of electromagnetic torque pulsations. Methodology. To carry out the research, the methods of the general theory of electromechanical energy converters, numerical methods of mathematical modeling based on the finite element method, numerical solution of nonlinear differential equations, and methods of spectral analysis to estimate pulsations of the electromagnetic torque were used in the work. Findings. The paper developed a two-dimensional numerical field mathematical model of a magnetic gearbox for an autonomous wind turbine. The model was developed to evaluate the parameters and characteristics of the magnetic gear, as well as to evaluate the influence of the design parameters on the magnitude of the electromagnetic torque and the magnitude of the pulsations of the electromagnetic torque. The effect of the configuration of permanent magnets, the parameters of the ferromagnetic inserts of the magnetic flux modulator and the size of the air gap was investigated in the paper. The obtained results show that there is an optimal configuration of permanent magnets and ferromagnetic elements of the magnetic flux modulator in which the maximum electromagnetic torque and minimum pulsations are achieved. Changing the parameters of the magnetic system affects the dynamics of the magnetic gear, its reliability and efficiency, therefore configuration optimization is an important task in the design, development and implementation of such systems. Originality. A two-dimensional field mathematical model of the magnetic gear has been developed, which makes it possible to estimate the change in its parameters and characteristics when the geometric dimensions change. This allows investigating the influence of various parameters of the magnetic system, such as the height of the permanent magnets and the width of the ferromagnetic inserts, on the electromagnetic torque. This makes it possible to obtain the optimal configuration of the system to achieve the optimal value of the torque and minimal pulsations and to determine the regularity of the change of the electromagnetic torque and other parameters of the gearbox under different operating modes in the future. Practical value. The simulation results indicate the prospects of industrial implementation of magnetic gaers as part of a wind power plant, and the obtained research results indicate the possibility of optimizing the design of magnetic gears in order to increase their reliability and efficiency. [ABSTRACT FROM AUTHOR]

Purpose: Reducing aircraft fuel consumption has become a paramount research area, focusing on optimizing operational parameters like speed and altitude during the cruise phase. However, the existing methods for fuel reduction often rely on complex experimental calculations and data extraction from embedded systems, making practical implementation challenging. To address this, this study aims to devise a simple and accessible approach using available information. Design/methodology/approach: In this paper, a novel analytic method to estimate and optimize fuel consumption for aircraft equipped with jet engines is proposed, with a particular emphasis on speed and altitude parameters. The dynamic variations in weight caused by fuel consumption during flight are also accounted for. The derived fuel consumption equation was rigorously validated by applying it to the Boeing 737–700 and comparing the results against the fuel consumption reference tables provided in the Boeing manual. Remarkably, the equation yielded closely aligned outcomes across various altitudes studied. In the second part of this paper, a pioneering approach is introduced by leveraging the particle swarm optimization algorithm (PSO). This novel application of PSO allows us to explore the equation's potential in finding the optimal altitude and speed for an actual flight from Algiers to Brussels. Findings: The results demonstrate that using the main findings of this study, including the innovative equation and the application of PSO, significantly simplifies and expedites the process of determining the ideal parameters, showcasing the practical applicability of the approach. Research limitations/implications: The suggested methodology stands out for its simplicity and practicality, particularly when compared to alternative approaches, owing to the ready availability of data for utilization. Nevertheless, its applicability is limited in scenarios where zero wind effects are a prevailing factor. Originality/value: The research opens up new possibilities for fuel-efficient aviation, with a particular focus on the development of a unique fuel consumption equation and the pioneering use of the PSO algorithm for optimizing flight parameters. This study's accessible approach can pave the way for more environmentally conscious and economical flight operations. [ABSTRACT FROM AUTHOR]

The purpose of the present paper is to further investigate the mathematical structure of sentences—proposed in a recent paper—and its connections with human short–term memory. This structure is defined by two independent variables which apparently engage two short–term memory buffers in a series. The first buffer is modelled according to the number of words between two consecutive interpunctions—variable referred to as the word interval, I P —which follows Miller's 7 ± 2 law; the second buffer is modelled by the number of word intervals contained in a sentence, M F , ranging approximately for one to seven. These values result from studying a large number of literary texts belonging to ancient and modern alphabetical languages. After studying the numerical patterns (combinations of I P and M F ) that determine the number of sentences that theoretically can be recorded in the two memory buffers—which increases with the use of I P and M F —we compare the theoretical results with those that are actually found in novels from Italian and English literature. We have found that most writers, in both languages, write for readers with small memory buffers and, consequently, are forced to reuse sentence patterns to convey multiple meanings. [ABSTRACT FROM AUTHOR]

In this paper, a fault recovery strategy for a distribution network based on a pigeon-inspired optimization (PIO) algorithm is proposed to improve the recoverability of the network considering the increased proportion of distributed energy resources. First, an improved Kruskal algorithm-based island partitioning scheme is proposed considering the electrical distance and important load level during the island partitioning process. Secondly, a mathematical model of fault recovery is established with the objectives of reducing active power losses and minimizing the number of switching actions. The conventional PIO algorithm is improved using chaos, reverse strategy, and Cauchy perturbation strategy, and the improved pigeon-inspired optimization (IPIO) algorithm is applied to solve the problem of fault recovery of the distribution network. Finally, simulation analysis is carried out to verify the effectiveness of the proposed PIO algorithm considering a network restauration problem after fault. The results show that compared with traditional algorithms, the proposed PIO algorithm has stronger global search capability, effectively improving the node voltage after restauration and reducing circuit loss. [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]

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]

Employee mental health is a central issue in today's global workplace. This paper analyzes the effect of high performance work systems (HPWSs) on employee mental health. We integrate HPWS concepts with job demands‐resources (JD‐R) theory to examine competing theoretical perspectives—a positive HPWS influence and a negative HPWS influence on employee mental health. We examine employees' perceptions of psychological empowerment as an indicator of the motivational pathway of the JD‐R and work‐role overload as an indicator of the strain pathway to explain the differential effect of HPWSs on mental health. We also incorporate organizational identification theory to demonstrate how one's identification with the organization can either accentuate or attenuate feelings of both psychological empowerment and work‐role overload. Findings from a study of 999 employees in 174 South Korean organizations indicate that HPWSs are positively associated with employee mental health via employee perceptions of empowerment and that HPWSs are negatively associated with employee mental health through perceptions of work‐role overload. Furthermore, the study finds that organizational identification attenuates the relationship between HPWS and both empowerment and overload. Practice‐level post hoc analyses also reveal that the job design characteristics, pay level, and participative decision‐making are linked to empowerment. In addition, participative decision‐making is most strongly associated with work overload. [ABSTRACT FROM AUTHOR]

Artificial immune detection can be used to detect network intrusions in an adaptive approach and proper matching methods can improve the accuracy of immune detection methods. This paper proposes an artificial immune detection model for network intrusion data based on a quantitative matching method. The proposed model defines the detection process by using network data and decimal values to express features and artificial immune mechanisms are simulated to define immune elements. Then, to improve the accuracy of similarity calculation, a quantitative matching method is proposed. The model uses mathematical methods to train and evolve immune elements, increasing the diversity of immune recognition and allowing for the successful detection of unknown intrusions. The proposed model's objective is to accurately identify known intrusions and expand the identification of unknown intrusions through signature detection and immune detection, overcoming the disadvantages of traditional methods. The experiment results show that the proposed model can detect intrusions effectively. It has a detection rate of more than 99.6% on average and a false alarm rate of 0.0264%. It outperforms existing immune intrusion detection methods in terms of comprehensive detection performance. [ABSTRACT FROM AUTHOR]

Truck hoisting detection constitutes a key focus in port security, for which no optimal resolution has been identified. To address the issues of high costs, susceptibility to weather conditions, and low accuracy in conventional methods for truck hoisting detection, a non-intrusive detection approach is proposed in this paper. The proposed approach utilizes a mathematical model and an extreme gradient boosting (XGBoost) model. Electrical signals, including voltage and current, collected by Hall sensors are processed by the mathematical model, which augments their physical information. Subsequently, the dataset filtered by the mathematical model is used to train the XGBoost model, enabling the XGBoost model to effectively identify abnormal hoists. Improvements were observed in the performance of the XGBoost model as utilized in this paper. Finally, experiments were conducted at several stations. The overall false positive rate did not exceed 0.7% and no false negatives occurred in the experiments. The experimental results demonstrated the excellent performance of the proposed approach, which can reduce the costs and improve the accuracy of detection in container hoisting. [ABSTRACT FROM AUTHOR]

Recently Vasuki and Veeresha were able to prove Dedekind η-function identities of level 14 conjectured by Somos. In this paper, we show how these Somos's identities are the consequence of Ramanujan's modular equations of degree 7. Also, in their paper authors are using a known multiplier to prove Somos's identities and we explained the method of obtaining that multiplier in this paper. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to present a procedure for automating the scanning process based on a mathematical model for a handheld 3D scanner for shoes used in some indoor sports. The study aims to use inverse kinematics to automate 3d footwear scanning used for indoor sport (handball) using a robotic arm with three joints. A modeling of the robotic arm and final effector was performed, to simulate the minimum and maximum trajectory of the robot arm according to the angles shown based on the mathematical model and inverse kinematics. With an easy-to-use interface and ergonomic design, this 3D scanning solution offers the versatility to scan various objects (such as scanning two shoe models used in indoor sports) and complex surface types. This scanning manner represents the state of the art of 3D scanning solutions as well as a benchmark in the 3D measurement equipment industry. The data obtained as a result of this research provide new directions and solutions for sports shoe scanning for indoor sports based on scanning trajectories preset by inverse kinematics in order to automate the scanning process using a handheld 3D scanner. Based on the mathematical model presented in the paper, automation of the scanning process can be achieved by maintaining the proposed trajectory using an automated arm operating through a control program that can be run on a simple controller. [ABSTRACT FROM AUTHOR]

Inverse data envelopment analysis (InvDEA) is a remarkable and popular management tool. This paper deals with one application of this tool. In fact, the problem of the merging of units is investigated in the presence of negative data. The problem of merging units refers to the fact that a set of units create a new unit based on synergy to improve their performance. We use multiple objective programming for this purpose and suggest new models based on predetermined conditions for new units. The proposed models estimate inputs and outputs simul- taneously. Importance advantages of the proposed models are: i) We can follow multiple goals in the problem of merging units because mul- tiple objective programming is applied. ii) Models can simultaneously estimate the inputs and outputs of the combined unit. iii) Unlike the existing methods in the InvDEA-based merging literature, the negative data do not need to be transferred to positive data. Finally, a numerical example is used to explain and validate the model proposed in this paper. [ABSTRACT FROM AUTHOR]

This document discusses recent trends in mathematical models and solitons used to analyze real-world problems. The focus is on the application of fractional calculus in modeling phenomena such as anomalous diffusion, non-Markovian processes, and random walk. The document provides summaries of 15 papers accepted for publication in a special issue, covering topics such as digestive system modeling, COVID-19 pandemic modeling, control systems for motors, symmetry in pine wilt disease, soliton solutions for various equations, and epidemic modeling. The papers employ various mathematical techniques and provide insights into different aspects of real-world problems. [Extracted from the article]

In this paper, an analysis of a mathematical model of the coronavirus is carried out by using two fractal-fractional parameters. This dangerous virus infects a person through the mouth, eyes, nose or hands. This makes it so dangerous that no one can get rid of it. One of the main factors contributing to increasing infections of this deadly virus is crowding. We believe that it is necessary to model this effect mathematically to predict the possible outcomes. Hence, the study of neural network-based models related to the spread of this virus can yield new results. This paper also introduces the use of artificial neural networks (ANNs) to approximate the solutions, which is a significant contribution in this regard. We suggest employing this new method to solve a system of integral equations that explain the dynamics of infectious diseases instead of the classical numerical methods. Our study shows that, compared to the Adams-Bashforth algorithm, the ANN is a reliable candidate for solving the problems. [ABSTRACT FROM AUTHOR]

The 2023 Mathematical Contest in Modeling (MCM) results are presented in this article. The contest attracted a large number of teams from around the world, including both undergraduate and high school students. The teams worked on interdisciplinary modeling problems, such as species diversity, wildlife management, data analysis, and sailboat pricing. The article highlights the importance of proper citation and attribution, as some teams were disqualified for plagiarism. The text also includes information about the sponsors of the contest and the authors of the article, who are mathematics professors. [Extracted from the article]

The paper is focused on recent advances in uncertainty quantification using polynomial chaos expansion (PCE). PCE is a well-known technique for approximation of costly mathematical models with random inputs - surrogate model. Although PCE is a widely used technique and it has several advantages over various surrogate models, it has still several limitations and research gaps. This paper reviews some of the recent theoretical developments in PCE. Specifically a new active learning method optimizing the experimental design and an extension of analytical statistical analysis using PCE will be reviewed. These two topics represent crucial tools for efficient applications: active learning leads generally to a significantly more efficient construction of PCE and improved statistical analysis allows for analytical estimation of higher statistical moments directly from PCE coefficients. Higher statistical moments can be further used for the identification of probability distribution and estimation of design quantiles, which is a crucial task for the probabilistic analysis of structures. Selected applications of the theoretical methods are briefly presented in a context of civil engineering as well as some preliminary results of further research. A part of the paper also presents UQPy package containing state-of-the-art implementation of the PCE theory. [ABSTRACT FROM AUTHOR]

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