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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]

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]