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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]

One of the main issues in a paper mill is the minimization of trim loss when cutting master reels and stocked reels into reels of smaller required widths. The losses produced in trimming at a paper mill are reprocessed by using different chemicals which contributes to significant discharge of effluent to surface water and causes environmental damage. This paper presents a real-world industrial problem of production planning and cutting optimization of reels at a paper mill and differs from other cutting stock problems by considering production and cutting of master reels of flexible widths and cutting already stocked over-produced and useable leftover reels of smaller widths. The cutting process of reels is performed with a limited number of cutting knives at the winder. The problem is formulated as a linear programming model where the generation of all feasible cutting patterns determines the columns of the constraint matrix. The model is solved optimally using simplex algorithm with the objective of trim loss minimization while satisfying a set of constraints. The solution obtained is rounded in a post-optimization procedure in order to satisfy integer constraints. When tested on data from the paper mill, the results of the proposed model showed a significant reduction in trim loss and outperformed traditional exact approaches. The cutting optimization resulted in minimum losses in paper trimming and a lesser amount of paper is reprocessed to make new reels which reduced the discharge of effluent to the environment. [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]

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]

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

This paper strives to achieve a comprehensive review of chaos in analog circuits and lumped electronic networks. Readers will be guided from the beginning of the investigations of simple electronic circuits to the current trends in the research into chaos. The author tries to provide the key references related to this issue, including papers describing modern numerical algorithms capable of localizing chaotic and hyperchaotic motion in complex mathematical models, interesting full on-chip implementations of chaotic systems, possible practical applications of entropic signals, fractional-order chaotic systems and chaotic oscillators with mem-elements. [ABSTRACT FROM AUTHOR]

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

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

Bibliometric analysis is the quantitative study of bibliographic material. In this paper, a systematic review of papers, authors, and journals is carried out. This is necessary to determine and set targets to be achieved in further research. The main objective of this study is to identify some of the most relevant research and the latest trends according to the information found in the Google Scholar, Publish or Perish, Science Direct, and Dimension databases. The methods used are classification, analysis of the most cited journals of all time, and the most prolific and influential authors. The results are information on the number of papers, citations, researchers, h-index, g-index, major reference journals, and visualization of research roadmaps for the topic of agricultural insurance mathematical models. The research findings identify the core themes, which are used as research gaps for future research. [ABSTRACT FROM AUTHOR]

This paper examines the added value of a digital tool that constitutes a new model to introduce students to multiplication. Drawing on the theory of semiotic mediation, the semiotic potential of this new model is analysed with respect to the same task that can be solved in two different settings (the digital tool and pencil and paper). The analysis shows that the task solutions undergo significant changes depending on to the technological settings. Even though the end product of the model–task dyads might look the same in both settings, the product emerges from the different processes that would mediate quite different meanings for multiplication. This suggests that while designing tasks that involve mathematical models, rather than focusing only on the end product, considering the whole process would reveal the extensive potential meanings the model–task dyad can mediate. [ABSTRACT FROM AUTHOR]

A. Montisci, S. Cargangiu, G. Sias, B. Cannas and A. Fanni, in [[16]], present a real time bolometer tomographic reconstruction algorithm in nuclear fusion reactors based on the combination of highly correlated grid elements to yield a square coefficient matrix with sufficiently low condition number. The procedure was derived from the polynomial reproduction properties satisfied by the Hermite splines without requiring the explicit construction/evaluation of the basic functions. The paper authored by Y.E. Shao and S.C. Lin [[1]] presents an innovative time-delay neural network-based classifier to diagnose the quality variables that cause out-of-control signals for a normal multivariate process with variance shifts. It is now clear that cooperation between academia and industries is crucial for social, cultural, technological and economic progress and innovation. [Extracted from the article]

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

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

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

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]

Fuzzy logic is becoming one of the most-influential fields of modern mathematics with applications that impact not only other sciences, but society in general. This newly found interest in fuzzy logic is in part due to the crucial role it plays in the development of artificial intelligence. As a result, new tools and practices for the development of the above-mentioned field are in high demand. This is one of the issues this paper was composed to address. To be more specific, a sizable part of fuzzy logic is the study of fuzzy connectives. However, the current method used to generalize them is restricted to the use of basic automorphisms, which hinders the creation of new fuzzy connectives. For this reason, in this paper, a new method of generalization is conceived of that aims to generalize the fuzzy connectives using polynomial automorphism functions instead. The creation of these automorphisms is achieved through numerical analysis, an endeavor that is supported with programming applications that, using mathematical modeling, validate and visualize the research. Furthermore, the automorphisms satisfy all the necessary criteria that have been established for use in the generalization process and, consequently, are used to successfully generalize fuzzy connectives. The result of the new generalization method is the creation of new usable and flexible fuzzy connectives, which is very promising for the future development of the field. [ABSTRACT FROM AUTHOR]

A System-of-Systems (SoS) is characterized both by independence and by inter-dependency. This inter-dependency, while allowing an SoS to achieve its objectives, also means that failures can cascade throughout the SoS. An SoS needs to be resilient to deal with the impact of complex internal and external environments. In this paper, we propose a resilience analysis method of an SoS based on a hierarchy structure. Firstly, we establish a hierarchy structure, which is ranked from high to low as capability level, activity level and system level. Then, Bayesian Networks (BNs) and Dynamic Bayesian Networks (DBNs) are used to analyze the resilience of the SoS. A resilience-based system importance metric is introduced, which is used in the budget allocation optimization problem during the development domain of an SoS. This paper proposes a mathematical programming model aimed at optimizing SoS resilience by optimally using budget to the subsystem. The application of the proposed approach is demonstrated using a case study: a Next Generation Air Transportation setting. The study results provide evidence that the proposed inter-dependency analysis based on Bayesian theory and the SoS resilience design approach can assist SoS system engineers in increasing expected SoS resilience during the development domain. [ABSTRACT FROM AUTHOR]

To improve the performance of the tension control system in gravure printed electronic equipment, it is necessary to study the tension system model of gravure-printing electronic equipment. This paper focuses on the coupling characteristics of multi-span tension systems. Firstly, based on the single-span tension model, the mathematical model of the printing tension subsystem is established and simplified into a general multi-span tension coupling model. Then, using the relationship between the inputs and outputs of the system, the coupling model is simulated using MATLAB/Simulink and verified through experiments on the gravure printed electronic platform. Finally, the coupling relationship and influence laws among multi-physical quantities of the system are analyzed. The research results show that changes in the input web tension of the multi-span system will affect the steady-state tension values of all subsequent spans. Moreover, the speed change in a roller in the multi-span system will not only affect the steady-state tension value of its own span, but also cause transient tension fluctuations in all subsequent spans. The findings of this paper provide an important theoretical basis for the research of the tension system in gravure printed electronic equipment, contributing to the enhancement of printed electronic product quality. [ABSTRACT FROM AUTHOR]

A 360° video offers a more immersive experience, gaining increasing popularity among users. However, enhancing the transmission efficiency of 360° videos under limited bandwidth conditions remains a significant challenge. This paper segments the video into three areas: the attention area, the edge area, and the viewpoint-switching transition area. Based on the segmentation of these three distinct video areas, a novel non-uniform coding transmission method for 360° videos is presented, along with mathematical modeling to define the optimization problem. A heuristic algorithm is subsequently introduced, which adaptively determines the optimal number of tiles and allocates the bitrate for each tile in real time to enhance the user's quality of experience (QoE). Finally, a simulation platform has been developed to validate the efficacy of the proposed algorithm by conducting comparative analyses with existing algorithms. [ABSTRACT FROM AUTHOR]

Mathematical models play a crucial role in evaluating real-life processes qualitatively and quantitatively. They have been extensively employed to study the spread of diseases such as hepatitis B, COVID-19, influenza, and other epidemics. Many researchers have discussed various types of epidemiological models, including deterministic, stochastic, and fractional order models, for this purpose. This article presents a comprehensive review and comparative study of the transmission dynamics of fractional order in epidemiological modeling. A significant portion of the paper is dedicated to the graphical simulation of these models, providing a visual representation of their behavior and characteristics. The article further embarks on a comparative analysis of fractional-order models with their integer-order counterparts. This comparison sheds light on the nuances and subtleties that differentiate these models, thereby offering valuable insights into their respective strengths and limitations. The paper also explores time delay models, non-linear incidence rate models, and stochastic models, explaining their use and significance in epidemiology. It includes studies and models that focus on the transmission dynamics of diseases using fractional order models, as well as comparisons with integer-order models. The findings from this study contribute to the broader understanding of epidemiological modeling, paving the way for more accurate and effective strategies in disease control and prevention. [ABSTRACT FROM AUTHOR]

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

With the widespread application of electrochemical energy storage technology, the safety issues of lithium-ion batteries have garnered significant attention. The issue of arc faults resulting from electrical failures is especially critical, as it can lead to catastrophic battery disasters. Therefore, this paper first established an arc testing platform and conducted experiments on top cover and body of prismatic lithium-ion batteries to analyze the thermoelectric characteristics between arc and battery. Under experimental conditions of 300 V and 15 A, it was found that arcs can induce thermal runaway in batteries. Subsequently, based on the experimental conditions, a mathematical model was established to induce thermal runaway in batteries through an equivalent method of arc heat source. By comparing the temperature curves of model and experiment, the RMSE of temperature at the center point of large surface was 5.09 °C (with a maximum temperature of 212 °C), indicating the accuracy of the model. This paper's research on arc faults in battery systems revealed the evolution pattern and realized that arcs can trigger thermal runaway in batteries. The model for arc-triggered thermal runaway in batteries is highly accurate, capable of reducing the number of experiments, accelerating experimental progress, and is of significant importance for guiding the design of arc experiments about batteries. [ABSTRACT FROM AUTHOR]

Ship maneuvering in ports is increasingly reduced because the increase in ship size is not proportional to the increase in port areas. Furthermore, the number of assisted vessels and the need for tugboats working in densely populated areas make it necessary to reduce the number of involved tugboats, reducing pollution and costs. Therefore, shiphandlers must know, in addition to the pivot point, the center of lateral resistance under any circumstance to optimize the assistance from tugboats and improve maritime navigation. From the literature, it is evident that the practical determination of the center of lateral resistance is still unknown. This paper aims to propose novel mathematical models to identify the position of this point and the most important variables that determine its position. For that, data of different ships in different conditions were obtained from a full mission bridge simulator. Afterwards, 15 novel mathematical models were developed, making use of artificial intelligence tools and training neural networks. The high determination factor reached in some models shows the accuracy of the obtained models. One advantage of the presented models is that they are very easy to be applied by shiphandlers, because highly well-known parameters are involved. Moreover, original 3D charts showing the combination of the input variables were generated to identify the map of the whole process. The very simple new models obtained and the novel 3D charts shown in the present paper can be considered useful and applicable by the shiphandlers of most of the merchant fleet to improve the efficiency and safety of maritime navigation in increasingly restricted waters. [ABSTRACT FROM AUTHOR]

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

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

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

This paper introduces an autonomous robot designed for in-pipe structural health monitoring of oil/gas pipelines. This system employs a 3D Optical Laser Scanning Technical Vision System (TVS) to continuously scan the internal surface of the pipeline. This paper elaborates on the mathematical methodology of 3D laser surface scanning based on dynamic triangulation. This paper presents the mathematical framework governing the combined kinematics of the Mobile Robot (MR) and TVS. It discusses the custom design of the MR, adjusting it to use of robustized mathematics, and incorporating a laser scanner produced using a 3D printer. Both experimental and theoretical approaches are utilized to illustrate the formation of point clouds during surface scanning. This paper details the application of the simple and robust mathematical algorithm RANSAC for the preliminary processing of the measured point clouds. Furthermore, it contributes two distinct and simplified criteria for detecting defects in pipelines, specifically tailored for computer processing. In conclusion, this paper assesses the effectiveness of the proposed mathematical and physical method through experimental tests conducted under varying light conditions. [ABSTRACT FROM AUTHOR]

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

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

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]

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]

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]

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 order to fulfill the practical application demands of precisely localizing underwater vehicles using passive electric field localization technology, we propose a scalar-potential-based method for the passive electric field localization of underwater vehicles. This method is grounded on an intelligent differential evolution algorithm and is particularly suited for use in three-layer and stratified oceanic environments. Firstly, based on the potential distribution law of constant current elements in a three-layer parallel stratified ocean environment, the mathematical positioning model is established using the mirror method. Secondly, the differential evolution (DE) algorithm is enhanced with a parameter-adaptive strategy and a boundary mutation processing mechanism to optimize the key objective function in the positioning problem. Additionally, the simulation experiments of the current element in the layered model prove the effectiveness of the proposed positioning method and show that it has no special requirements for the sensor measurement array, but the large range and moderate number of sensors are beneficial to improve the positioning effect. Finally, the laboratory experiments on the positioning method proposed in this paper, involving underwater simulated current elements and underwater vehicle tracks, were carried out successfully. The results indicate that the positioning method proposed in this paper can achieve the performance requirements of independent initial value, strong anti-noise capabilities, rapid positioning speed, easy implementation, and suitability in shallow sea environments. These findings suggest a promising practical application potential for the proposed method. [ABSTRACT FROM AUTHOR]

The issues of the evaluation and prediction of the reliability and testability of mining machinery and equipment are becoming particularly relevant, since the safety of technological processes and human life is reaching a new level of realisation due to changes in mining technology. The work is devoted to the development of a logical model for analysing the controllability of mining equipment. The paper presents a model of reliability of the operation of mining equipment on the example of a mine load and passenger hoist. This generalised model is made in the form of a graph of transitions and supplemented with a system of equations. The model allows for the estimation of the reliability of equipment elements and equipment as a whole. A mathematical and logical model for the calculation of the availability and downtime coefficients of various designs of mining equipment systems is proposed. This model became the basis for the methods to calculate the optimal values of diagnostic depth. At these calculated values, the maximum value of availability factor will be obtained. In this paper, an analytical study was carried out and dependences of the readiness factor of parameters of the investigated system such as the intensity of control of technical systems, intensity of failures, etc., were constructed. The paper proposes a mathematical model to assess the reliability of mine hoisting plants through its integration into the method of improving the reliability of mine hoisting plants. [ABSTRACT FROM AUTHOR]

The basic reproduction, or reproductive number, is a useful index that indicates whether or not there will be an epidemic. However, it is also very important to determine whether an epidemic will eventually decrease and disappear or persist as an endemic. Different infectious diseases have different behaviors and mathematical models used to simulated them should capture the most important processes; however, the models also involve simplifications. Influenza epidemics are usually short-lived and can be modeled with ordinary differential equations without considering demographics. Delays such as the infection time can change the behavior of the solutions. The same is true if there is permanent or temporary immunity, or complete or partial immunity. Vaccination, isolation and the use of antivirals can also change the outcome. In this paper, we introduce several new models and use them to find the effects of all the above factors paying special attention to whether the model can represent an infectious process that eventually disappears. We determine the equilibrium solutions and establish the stability of the disease-free equilibrium using various methods. We also show that many models of influenza or other epidemics with a short duration do not have solutions with a disappearing epidemic. The main objective of the paper is to introduce different ways of modeling immunity in epidemic models. Several scenarios with different immunities are studied since a person may not be re-infected because he/she has total or partial immunity or because there were no close contacts. We show that some relatively small changes, such as in the vaccination rate, can significantly change the dynamics; for example, the existence and number of the disease-free equilibria. We also illustrate that while introducing delays makes the models more realistic, the dynamics have the same qualitative behavior. [ABSTRACT FROM AUTHOR]

Active disturbance rejection control (ADRC) is widely used in airborne optoelectronic stabilization platforms due to its minimal reliance on the mathematical model of the controlled object. The extended state observer (ESO) is the core of ADRC, which treats internal parameter variations and external disturbances as total disturbances, observes the disturbances as extended states, and then compensates them into the control loop to eliminate their effects. However, the ESO can only achieve a precise estimation of constant or slowly varying disturbances. When the disturbance is periodically changing, satisfactory results cannot be obtained. In this paper, a generalized high-order extended state observer (GHOESO) is proposed to achieve the precise estimation of known frequency sinusoidal disturbance signals and improve disturbance suppression levels. Through numerical simulations, a traditional ESO and GHOESO are compared in terms of disturbance observation capability and disturbance suppression ability for single and compound disturbances based on our prior knowledge of disturbance frequency. The effectiveness of the proposed GHOESO method is verified. Finally, the algorithm is applied to an airborne optoelectronic stabilization platform for a 1°/1 Hz swing experiment on a space hexapod swing table. The experimental results demonstrate the superiority of the GHOESO proposed in this paper. [ABSTRACT FROM AUTHOR]

Economic globalization and the rapid development of the Internet make logistics systems more and more diversified, people and enterprises have greatly increased their requirements for logistics systems, and fourth party logistics has received more and more attention from people and related enterprises. In order to further study the routing problem under uncertain stochastic environments, this paper considers the fourth party logistics routing problem from a single manufacturer to multiple distributors with uncertain times and random supplies under the complete information symmetry scenario and symmetric transportation volume decision space. Then, an uncertain stochastic programming model is established with the minimum total cost as its core objective, and the total transportation time, manufacturer's supply, and distributor's demand as constraints. In order to solve the optimal path of the above problems, this paper transforms the uncertain stochastic programming model into a classical mathematical programming model based on the distribution functions of uncertain time and random supply. Finally, two numerical examples are given to verify the effectiveness of the proposed model. [ABSTRACT FROM AUTHOR]

This paper presents a centralized disturbance suppression strategy for distributed drive electric vehicles which is based on model predictive direct motion control. This strategy is capable of addressing issues such as parameter uncertainties and external disturbances in vehicles. Firstly, the paper provides a brief introduction to model predictive direct motion control. Secondly, it analyzes the impact of vehicle parameter uncertainties and external disturbances on the mathematical model. Finally, a centralized disturbance suppression strategy based on a sliding mode observer is proposed. Simulation results demonstrate that this strategy exhibits excellent disturbance rejection capabilities. [ABSTRACT FROM AUTHOR]

The reliability of power electronic switching components is of great concern for many researchers. For their usage in many mission profiles, it is crucial for them to perform for the duration of their intended lifetime; however, they can fail because of thermal stress. Thus, it is essential to analyze their thermal performance. Non-linear switching action, bifurcation and chaotic events may occur in DC-DC power converters. Consequently, they show different behaviors when their parameters change. However, this is an opportunity to study these bifurcation phenomena and the existence of chaos, e.g., in boost converters, on their performance as the effects of load variations (mission profiles) on the system's behavior. These variations generate many non-linear phenomena such as periodic behavior, repeated period-doubling bifurcations and chaos in the MOSFET drain-source current. Thus, we propose, for the first time, an analysis of the influence of chaos on the junction temperature. First of all, this paper provides a step-by-step procedure to establish an electrothermal model of a C2M0080120D MOSFET with integrated power loss. Then, the junction temperature is estimated by computing the power losses and a thermal impedance model of the switch. Additionally, this model is used to investigate the bifurcation and chaotic behavior of the MOSFET junction temperature. The paper contributes by providing a mathematical model to calculate several coefficients based on experimental data and thermal oscillations. Estimation of the number of cycles to failure is given by the Coffin–Manson equation, while temperature cycles are counted using the rainflow counting algorithm. Further, the accumulated damage results are calculated using the Miner's model. Finally, a comparison is made between the damage accumulated during different mission profiles: significant degradation of the MOSFET's lifetime is pointed out for chaotic currents compared to periodic ones. [ABSTRACT FROM AUTHOR]

Many optimization mathematical models, associated with the technical-economic processes of real-world problems, have elements of uncertainty in their structure, which places them in stochastic optimization programming. Their diversity and complexity, due to the large uncertainty space, require special methods of solving, because there is no general solution method. Within this context, in this paper we consider the category of optimization models that can contain random variable type coefficients and/or imposed probability levels on the constraints. The purpose of the paper is to propose a methodology dedicated to these studied models. Applying the methodology leads to developing a deterministic linear programming model, associated with the initial stochastic model. In fact, the proposed methodology reduces the stochastic formulation to a deterministic formulation. The methodology is illustrated with a numerical case study based on a manufacturing problem. Solving the obtained deterministic model is carried out in the version assisted by a specialized software product (WinQSB Version 2.0). It allows for the performing of a sensitivity analysis of the optimal solution, and/or a parametric analysis relative to certain model coefficients, both also presented in the paper. The main result of the study in this paper is the proposed methodology, which is applicable on a large scale, for any mathematical model of stochastic optimization of the mentioned type, regardless of complexity, dimensions and the domain of the process to which it is associated. The numerical results obtained when applying this methodology indicate its efficiency and effectiveness in finding the solution for the studied models. The approach to this issue in the present paper is determined by the wide range of stochastic optimization problems in the various studied real-life processes and by the imperative need to adopt the best decisions in conditions of uncertainty. [ABSTRACT FROM AUTHOR]

The article is an editorial introducing a special issue of the scientific journal Axioms titled "Mathematical Models and Simulations." The issue contains 13 papers that cover various mathematical models and simulations in fields such as physics, biology, finance, and engineering. The papers explore different types of mathematical models, including deterministic and stochastic models, and discuss their applications and numerical simulations. The authors provide a brief overview of each paper, highlighting their main findings and methodologies. The article aims to provide library patrons with a concise summary of the special issue, allowing them to decide if they want to explore the individual papers further. [Extracted from the article]

This document is a summary of a special issue of the journal Mathematics, titled "Mathematical Modeling and Simulation in Mechanics and Dynamic Systems, 2nd Edition." The special issue focuses on the development of sophisticated models to predict phenomena in dynamic systems using experiments and computer models. The issue includes papers on topics such as modeling mechanical systems, new methods in dynamic systems, and the behavior simulation of mechanical systems. The papers were written by authors from 13 different countries, and the majority of the articles adhere well to the theme of the special issue. The document also provides a table showing the geographic distribution of authors by country. The authors of the special issue have made significant contributions to the field, and the document concludes by stating that the authors have no conflicts of interest. [Extracted from the article]

Detecting small targets and handling target occlusion and overlap are critical challenges in weld defect detection. In this paper, we propose the S-YOLO model, a novel weld defect detection method based on the YOLOv8-nano model and several mathematical techniques, specifically tailored to address these issues. Our approach includes several key contributions. Firstly, we introduce omni-dimensional dynamic convolution, which is sensitive to small targets, for improved feature extraction. Secondly, the NAM attention mechanism enhances feature representation in the region of interest. NAM computes the channel-wise and spatial-wise attention weights by matrix multiplications and element-wise operations, and then applies them to the feature maps. Additionally, we replace the SPPF module with a context augmentation module to improve feature map resolution and quality. To minimize information loss, we utilize Carafe upsampling instead of the conventional upsampling operations. Furthermore, we use a loss function that combines IoU, binary cross-entropy, and focal loss to improve bounding box regression and object classification. We use stochastic gradient descent (SGD) with momentum and weight decay to update the parameters of our model. Through rigorous experimental validation, our S-YOLO model demonstrates outstanding accuracy and efficiency in weld defect detection. It effectively tackles the challenges of small target detection, target occlusion, and target overlap. Notably, the proposed model achieves an impressive 8.9% improvement in mean Average Precision (mAP) compared to the native model. [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]

Variable (feature) selection plays an important role in data analysis and mathematical modeling. This paper aims to address the significant lack of formal evaluation benchmarks for feature selection algorithms (FSAs). To evaluate FSAs effectively, controlled environments are required, and the use of synthetic datasets offers significant advantages. We introduce a set of ten synthetically generated datasets with known relevance, redundancy, and irrelevance of features, derived from various mathematical, logical, and geometric sources. Additionally, eight FSAs are evaluated on these datasets based on their relevance and novelty. The paper first introduces the datasets and then provides a comprehensive experimental analysis of the performance of the selected FSAs on these datasets including testing the FSAs' resilience on two types of induced data noise. The analysis has guided the grouping of the generated datasets into four groups of data complexity. Lastly, we provide public access to the generated datasets to facilitate bench-marking of new feature selection algorithms in the field via our Github repository. The contributions of this paper aim to foster the development of novel feature selection algorithms and advance their study. [ABSTRACT FROM AUTHOR]

In this paper, we investigate mathematical models of meteorological forecasting based on the work of neural networks, which allow us to calculate presumptive meteorological parameters of the desired location on the basis of previous meteorological data. A new method of grouping neural networks to obtain a more accurate output result is proposed. An algorithm is presented, based on which the most accurate meteorological forecast was obtained based on the results of the study. This algorithm can be used in a wide range of situations, such as obtaining data for the operation of equipment in a given location and studying meteorological parameters of the location. To build this model, we used data obtained from personal weather stations of the Weather Underground company and the US National Digital Forecast Database (NDFD). Also, a Google remote learning machine was used to compare the results with existing products on the market. The algorithm for building the forecast model covered several locations across the US in order to compare its performance in different weather zones. Different methods of training the machine to produce the most effective weather forecast result were also considered. [ABSTRACT FROM AUTHOR]

This paper proposes a modeling and analysis method for a Caputo–Fabrizio (C-F) definition-based fractional-order Boost converter with fractional-order inductive loads. The proposed method analyzes the system characteristics of a fractional-order circuit with three state variables. Firstly, this paper constructs a large signal model of a fractional-order Boost converter by taking advantage of the state space averaging method, providing accurate analytical solutions for the quiescent operating point and the ripple parameters of the circuit with three state variables. Secondly, this paper constructs a small signal model of the C-F definition-based fractional-order Boost converter by small signal linearization, providing the transfer function of the fractional-order system with three state variables. Finally, this paper conducts circuit-oriented simulation experiments where the steady-state parameters and the transfer function of the circuit are obtained, and then the effect of the order of capacitor, induced inductor, and load inductor on the quiescent operating point and ripple parameters is analyzed. The experimental results show that the simulation results are consistent with those obtained by the proposed mathematical model and that the three fractional orders in the fractional model with three state variables have a significant impact on the DC component and steady-state characteristics of the fractional-order Boost converter. In conclusion, the proposed mathematical model can more comprehensively analyze the system characteristics of the C-F definition-based fractional-order Boost converter with fractional-order inductive loads, benefiting the circuit design of Boost converters. [ABSTRACT FROM AUTHOR]

Fractional calculus is defined by expanded integer order integration and differentiation. In this paper, multiple mathematical models of a nonlinear dual-tank device are precisely formulated by fractional calculus. Using the accurate model, a multivariable fractional-order controller is designed for nonlinear devices. The merits of the fractional-order design include: (1) control of multivariable nonlinearities, (2) compensation of uncertainties, and (3) elimination of coupling effects. Simulations and experiments are conducted to verify the precision of the fractional order models and the effectiveness of the multivariable fractional-order control system design. [ABSTRACT FROM AUTHOR]