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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]

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

In recent years, the accuracy of visual SLAM (Simultaneous Localization and Mapping) technology has seen significant improvements, making it a prominent area of research. However, within the current RGB-D SLAM systems, the estimation of 3D positions of feature points primarily relies on direct measurements from RGB-D depth cameras, which inherently contain measurement errors. Moreover, the potential of triangulation-based estimation for ORB (Oriented FAST and Rotated BRIEF) feature points remains underutilized. To address the singularity of measurement data, this paper proposes the integration of the ORB features, triangulation uncertainty estimation and depth measurements uncertainty estimation, for 3D positions of feature points. This integration is achieved using a CI (Covariance Intersection) filter, referred to as the CI-TEDM (Triangulation Estimates and Depth Measurements) method. Vision-based SLAM systems face significant challenges, particularly in environments, such as long straight corridors, weakly textured scenes, or during rapid motion, where tracking failures are common. To enhance the stability of visual SLAM, this paper introduces an improved CI-TEDM method by incorporating wheel encoder data. The mathematical model of the encoder is proposed, and detailed derivations of the encoder pre-integration model and error model are provided. Building on these improvements, we propose a novel tightly coupled visual-inertial RGB-D SLAM with encoder integration of ORB triangulation and depth measurement uncertainties. Validation on open-source datasets and real-world environments demonstrates that the proposed improvements significantly enhance the robustness of real-time state estimation and localization accuracy for intelligent vehicles in challenging environments. [ABSTRACT FROM AUTHOR]

The integration of numerous distributed energy sources into the power system offers exciting opportunities to enhance the resilience of distribution networks. It is worth noting that the renewable-to-ammonia system has the potential to alleviate the multi-temporal and spatial imbalance of the power system. Therefore, this paper proposes a mathematical model for a renewable-to-ammonia system, taking into account the material balance and power balance of each unit. Based on this, this paper further explores the optimization scheduling method for flexible ammonia loads in distribution networks. A relaxation method for branch flow models in distribution networks based on second-order cone programming is proposed. An optimization scheduling model for flexible ammonia loads in distribution networks is constructed to minimize network loss. Moreover, considering the environmental advantages of the renewable-to-ammonia system, this paper compares the changes in hydrogen production technologies under different carbon emission constraints. Finally, a case study of the IEEE 33-node system is adopted to verify the effectiveness of the proposed model and method. It indicates that the renewable-to-ammonia system has environmental benefits and can reduce network loss to a certain extent. [ABSTRACT FROM AUTHOR]

In this paper, a spatial two-degree-of-freedom (2DOF) parallel platform based on electromagnetic redundant drive and its control method are investigated. The platform is redundantly driven by three electromagnetic-spring conforming branched chains, and the design provides better flexibility and responsiveness than conventional parallel structures. The introduction of the electromagnetic drive alleviates the stresses within the conventional rigid redundant drive structure and reduces the detrimental effects associated with rigid redundancy. In this paper, the structure and equivalent SPU model of the platform are first introduced, with S referring to the kinematic sub, P to the spherical sub, and U to the universal joint. The degrees of freedom of the platform are analyzed, and the inverse kinematic model and velocity Jacobi matrix are derived, so as to derive the relationship between the pitch, roll angles, and length of the gimbal chain, and the relational equation between the angle and the current is further established to realize the electromagnetic control of the parallel redundant platform. The control part is realized as follows. Firstly, the angle information of the platform is obtained from the gyroscope to the microcontroller, the filtered angle is derived through the Untraceable Kalman Filter (UKF), and the angle value can be fused with data by both the mathematical model and PID algorithm to introduce the current value required to achieve the balance and realize the balance. In the simulation part, this paper uses Simulink and Simscape in MATLAB for joint simulation, and by giving the simulated trajectory and the desired trajectory of the joints, the driving force diagrams of the three branched chains based on the Least-Second Paradigm method are derived, and the trajectory error and driving force error are given to validate the reliability of the method of this paper. [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]

In dietary assessment using a single-view food image, an object of known size, such as a checkerboard, is often placed manually in the camera's view as a scale reference to estimate food volume. This traditional scale reference is inconvenient to use because of the manual placement requirement. Consequently, utensils, such as plates and bowls, have been suggested as alternative references. Although these references do not need a manual placement procedure, there is a unique challenge when a dining bowl is used as a reference. Unlike a dining plate, whose shallow shape does not usually block the view of the food, a dining bowl does obscure the food view, and its shape may not be fully observable from the single-view food image. As a result, significant errors may occur in food volume estimation due to the unknown shape of the bowl. To address this challenge, we present a novel method to premeasure both the size and shape of the empty bowl before it is used in a dietary assessment study. In our method, an image is taken with a labeled paper ruler adhered to the interior surface of the bowl, a mathematical model is developed to describe its shape and size, and then an optimization method is used to determine the bowl parameters based on the locations of observed ruler makers from the bowl image. Experimental studies were performed using both simulated and actual bowls to assess the reliability and accuracy of our bowl measurement method. [ABSTRACT FROM AUTHOR]

As large-scale renewable energy sources are increasingly integrated into AC grids via voltage source converters (VSCs), the transient synchronization stability of phase-locked loop (PLL)-based VSCs during fault ride-through is gaining more attention. Most existing studies assume that the positive and negative sequence separation and current control dynamics are much faster than the PLL dynamics, thereby neglecting their impact on the transient synchronization stability of the system. However, when the PLL bandwidth is relatively large, ignoring the positive and negative sequence separation and current control dynamics may result in incorrect stability assessments. To address this issue, this paper first considers the multiple control loop coupling, including positive and negative sequence separation, current control, and PLL, to construct a full-order nonlinear mathematical model of the VSC grid-connected system under asymmetric fault conditions. Based on this, the phase trajectory method is employed to analyze the transient synchronization stability of the system. Additionally, this full-order mathematical model is used to determine the PLL bandwidth boundary beyond which the effects of positive and negative sequence separation and current control dynamics cannot be neglected. Finally, PSCAD/EMTDC simulation results validate the effectiveness of the theoretical analysis presented in this paper. [ABSTRACT FROM AUTHOR]

This paper focuses on the active removal of spent upper stages from LEO using de-orbiting devices. It proposes a method of regulating aerodynamic loads on the target during its re-entry by utilizing the features of spatial attitude motion. A mathematical model of the re-entry process is developed, and numerical simulations are conducted, demonstrating that the nature of the attitude motion during the descent influences the load factors and, thus, the breakup altitude. It is shown that the respective de-orbiting devices should control both the initial tumbling and spin of the target to achieve different mission outcomes, such as minimizing the debris footprint size or maximizing the breakup altitude. [ABSTRACT FROM AUTHOR]

To accurately quantify the time-varying pattern of concrete's compressive strength, selecting an appropriate curve model is of paramount importance. Currently, widely adopted models such as polynomial, hyperbolic, and exponential models all possess limitations, particularly in terms of low fitting accuracy during the ultra-early-age stage. This paper innovatively introduces a mathematical model that utilizes a combined curve approach. This model boasts a simplified structure with only two fitting parameters. Compared to traditional models, when utilizing three or more sets of experimental data on compressive strength across different ages, the new model is capable of yielding more precise strength predictions. Due to its minimal reliance on experimental data, the new model exhibits high practicality and convenience in real-world applications. To validate its superiority, a detailed comparison between the new model and existing models was conducted based on several sets of experimental data. The results demonstrate that the new model has significant advantages in terms of mean fitting error and standard deviation, making its predictions the most reliable. For most cases, the standard deviation of the new model is reduced by approximately 30% to 80% compared to the second-best model, underscoring its exceptional stability and consistency. Additionally, the predicted long-term compressive strength values of the new model are closer to the design strength grade of the concrete. This model can also be successfully applied to predict the tensile strength of concrete during its ultra-early age. It has been demonstrated that the combined model proposed in this paper shows promising application prospects in evaluating the time-varying behavior of concrete strength. [ABSTRACT FROM AUTHOR]

The dual-active hybrid full-bridge (H-FDAB) DC–DC converter has great potential in medium-voltage high-power photovoltaic power station applications by introducing a three-level bridge arm to increase the output voltage range. However, its mathematical model and optimum modulation schemes have not been fully explored. Under the traditional PI control, the H-FDAB DC–DC converter will produce significant reflux power, which will lead to a decrease in converter efficiency and output voltage fluctuation. On this basis, this paper proposes a reflux power optimization strategy for an H-FDAB DC-DC converter based on active disturbance rejection control (ADRC). Firstly, the structure and power characteristics of the H-FDAB DC–DC converter are analyzed, and the relationship among the reflux power, the transmission power, and the phase shift angle is derived. Secondly, to reduce the complexity of the control calculation, upon the foundation of dual phase-shifting modulation, the Karush–Kuhn–Tucker (KKT) condition is used to solve for the phase shift angle that corresponds to the minimum reflux power. Simultaneously, we develop an ADRC loop utilizing an extended state observer (ESO) for the real-time estimation of system states. We also consider the sudden changes in input voltage, load switching, and transmission power fluctuations caused by reflux power optimization strategies as system disturbances and compensate for them accordingly. Finally, the experiments conclusively validate the designed control strategy's correctness and feasibility. [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]

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 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]

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]

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

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

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]

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]

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]

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

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

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]

We take into account a nonlinear Caputo fractional-order differential equation including several variable delays. We examine whether the solutions to the Caputo fractional-order differential equation taken under consideration, which has numerous variable delays, are unique. In the present study, first, we will apply the method of progressive contractions, which belongs to T.A. Burton, to Caputo fractional-order differential equation, including multiple variable delays, which has not yet appeared in the relevant literature by this time. The significant point of the method of progressive contractions consists of a very flexible idea to discuss the uniqueness of solutions for various mathematical models. Lastly, we provide two examples to demonstrate how this paper's primary outcome can be applied. [ABSTRACT FROM AUTHOR]

Non-Tarskian interpretations of many-valued logics have been widely explored in the logic literature. The development of non-tarskian conceptions of logical consequence set the theoretical foundations for rediscovering well-known (Tarskian) many-valued logics. One may find in distinct authors many novel interpretations of many-valued systems. They are produced through a type of procedure which consists in altering the semantic structure of Tarskian many-valued logics in order to output a non-Tarskian interpretation of these logics. Through this type of transformation the paper explores a uniform way of transforming finitely many-valued Tarskian logics into their non-Tarskian interpretation. Some general properties of carrying out this type of procedure are studied, namely the dualities between these logics and the conditions under which negation-explosive and negation-complete Tarskian logics become non-explosive. [ABSTRACT FROM AUTHOR]

In this paper, we consider some problems that arise in connected and autonomous vehicle (CAV) systems. Their simplified variants can be formulated as scheduling problems. Therefore, scheduling solution algorithms can be used as a part of solution algorithms for real-world problems. For four variants of such problems, mathematical models and solution algorithms are presented. In particular, three polynomial algorithms and a branch and bound algorithm are developed. These CAV scheduling problems are considered in the literature for the first time. More complicated NP-hard scheduling problems related to CAVs can be considered in the future. [ABSTRACT FROM AUTHOR]

The red palm weevil (Rhynchophorus ferrugineus) is a highly destructive pest, causing severe damage to palm trees and significantly reducing their productivity. This paper aims to develop and analyze a mathematical model that captures the interactions between palm trees, Rhynchophorus ferrugineus, and entomopathogenic nematodes as a means of integrated control. We identify the equilibrium points of the system and perform a stability analysis to assess the system's behavior. Additionally, we design a linear quadratic regulator (LQR) to limit the spread of the red palm weevil within a locally linearized framework. The feedback control law, which is both straightforward and immediately implementable, is employed to avoid the need for complex cost calculations, thus simplifying the solution to the optimal control problem. Numerical simulations demonstrate that the proposed control strategy is effective in reducing the number of infected palm trees. The results indicate that increasing the population of entomopathogenic nematodes can significantly decrease the red palm weevil population, offering a promising approach to mitigating this pest's impact. [ABSTRACT FROM AUTHOR]

At present, the International Maritime Organization (IMO) has issued interim guidelines for the direct stability assessment of surf-riding and broaching for the second-generation intact stability criteria. Accurately and efficiently predicting surf-riding and broaching remains a key problem to be solved for the direct stability assessment of surf-riding and broaching. Therefore, a six-degree-of-freedom(6DOF) coupled mathematical model is established in this paper. Firstly, the four-degree-of-freedom(4DOF) coupled equations of surge–sway–roll–yaw motions are built based on the traditional MMG maneuvering mathematical model by considering Froude–Krylov forces, diffraction forces and restoring forces, and the heave and pitch are approximately calculated by iteratively solving improved static equilibrium equations in real-time, effectively solving the divergence problem in direct time-domain seakeeping calculations of high-speed ships in stern-quartering waves. Secondly, the hydrodynamic lift forces due to the coexistence of wave particle velocity and ship forward velocity are taken into account in the propeller-thrust and rudder-force models. In addition, the real-time emersion of twin rudders in waves is considered in the rudder-force models. At the same time, the free-running model experiments with a ONR tumblehome vessel are carried out in stern-quartering waves, and the pure loss of stability and broaching motions are observed. Finally, comparative validations between the calculations and the experiments of surf-riding and broaching in stern-quartering waves are carried out, and the effects of the ship speed, the instantaneous wetted surface of the hull, rudder exposure, heave and pitch motions on predicting surf-riding and broaching motions are investigated. The computation results show that the established 6DOF mathematical model has enough accuracy to be used for the direct stability assessment of the surf-riding and broaching failure modes. [ABSTRACT FROM AUTHOR]

Model-Based Systems Engineering (MBSE) supports the system-level design of complex products effectively. Currently, system design and optimization for complex products are two distinct processes that must be executed using different software or platforms, involving intricate data conversion processes. Applying multidisciplinary optimization to validate system optimization often necessitates remodeling the optimization objects, which is time-consuming, labor-intensive, and highly error-prone. A critical activity in systems engineering is identifying the optimal design solution for the entire system. Multidisciplinary Design Optimization (MDO) and reliability analysis are essential methods for achieving this. This paper proposes a SysML-based multidisciplinary reliability design optimization modeling method. First, by analyzing the definitions and mathematical models of multidisciplinary reliability design optimization, the SysML extension mechanism is employed to represent the optimization model based on SysML. Next, model transformation techniques are used to convert the SysML optimization model generated in the first stage into an XML description model readable by optimization solvers. Finally, the proposed method's effectiveness is validated through an engineering case study of an in-vehicle environmental control integration system. The results demonstrate that this method fully utilizes SysML to express MDO problems, enhancing the efficiency of design optimization for complex systems. Engineers and system designers working on complex, multidisciplinary projects can particularly benefit from these advancements, as they simplify the integration of design and optimization processes, facilitating more reliable and efficient product development. [ABSTRACT FROM AUTHOR]

When the landing position of a shipborne helicopter on the deck does not meet the requirements for towing it into the hangar, its position must first be corrected before towing can proceed. This paper studied the methods for using Shipborne Rapid Carrier Robots (SRCRs) to correct helicopter positions on the deck and proposed two correction methods, the stepwise correction method and the continuous correction method, aiming to improve the efficiency of the position adjustment process. Firstly, the actual helicopter landing position deviation was divided into two components—lateral offset and fuselage yaw angle—to quantitatively assess the deviations. Then, a mathematical model of the SRCR traction system was established, and its traction motion characteristics were analyzed. The kinematic characteristics and control processes of the two proposed position correction methods were subsequently studied, revealing the coordinated control relationships between key control elements. Finally, simulations were conducted to validate the feasibility of the proposed correction methods and compare their efficiencies. The results indicated that both the stepwise and continuous correction methods effectively achieved the position correction objectives. The stepwise method was more efficient when the initial yaw angle was small, while the continuous method proved more efficient when the initial yaw angle was large and the lateral offset was minimal. The results of this study may provide a valuable reference for correcting the positions of helicopters on deck. [ABSTRACT FROM AUTHOR]

During the operation of maglev trains, they are subjected to various disturbances. The presence of these disturbances presents a significant challenge for attaining high-performance control and even poses the risk of system instability. To further enhance the anti-disturbance capability of maglev trains, this paper proposes a model information-assisted modified active disturbance rejection control (MADRC) approach. A mathematical model of the single-point suspension system of maglev trains is constructed for the design of the extended state observer (ESO), which is a modified extended state observer (MESO), and a nonlinear mechanism is incorporated to boost the performance of the ESO. Owing to the introduction of model information, the estimated quantity of disturbances by MESO no longer considers the system model deviation as a disturbance. Hence, the linear feedback control law is modified accordingly. The MESO is regarded as an ESO with time-varying gain using the equivalent gain method, and its stability is proven using the Lyapunov method. The tracking and anti-disturbance performances of different controllers are compared via simulation experiments. Suspension and anti-disturbance experiments are conducted on the single-point suspension experimental platform, verifying that the proposed MADRC has a more potent suppression ability for load disturbances in the suspension system. [ABSTRACT FROM AUTHOR]

For the research on real-time accurate testing technology for the explosion point spatial coordinate of munitions, its currently commonly used methods such as acoustic–electric detection or high-speed imaging are limited by the field conditions, response rate, cost, and other factors. In this paper, a method of spatial coordinate testing for the explosion point based on a 2D PSD (position-sensitive detector) intersection is proposed, which has the advantages of a faster response, better real-time performance, and a lower cost. Firstly, a mathematical model of the spatial coordinate testing system was constructed, and an error propagation model for structural parameters was developed. The influence of the position of the optical axes' intersection as well as the azimuth angle and pitch angle on the test accuracy of the system was simulated and analyzed, thus obtaining the distribution and variation trend of the overall error propagation coefficient of the system. Finally, experiments were designed to obtain the test error of the system for validation. The results show that the system test accuracy is high when the azimuth angle is 20°–50°, the overall error propagation coefficient does not exceed 48.80, and the average test error is 56.17 mm. When the pitch angle is −2.5°–2.5°, the system has a higher test accuracy, with the overall error propagation coefficient not exceeding 44.82, and the average test error is 41.87 mm. The test accuracy of the system is higher when the position of the optical axes' intersection is chosen to make sure that explosion points fall in the region of the negative half-axis of the Z w -axis of the world coordinate system, with an overall error propagation coefficient of less than 44.78 and an average test error of 73.38 mm. It is shown that a reasonable selection of system structure parameters can significantly improve the system test accuracy and optimize the system deployment mode under the long-distance field conditions so as to improve the deployment efficiency. [ABSTRACT FROM AUTHOR]

We discuss 1D, 2D and 3D bifurcation diagrams of two nonlinear dynamical systems: an electric arc system having both chaotic and periodic steady-state responses and a cytosolic calcium system with both periodic/chaotic and constant steady-state outputs. The diagrams are mostly obtained by using the 0–1 test for chaos, but other types of diagrams are also mentioned; for example, typical 1D diagrams with local maxiumum values of oscillatory responses (periodic and chaotic), the entropy method and the largest Lyapunov exponent approach. Important features and properties of each of the three classes of diagrams with one, two and three varying parameters in the 1D, 2D and 3D cases, respectively, are presented and illustrated via certain diagrams of the K values, − 1 ≤ K ≤ 1 , from the 0–1 test and the sample entropy values S a E n > 0 . The K values close to 0 indicate periodic and quasi-periodic responses, while those close to 1 are for chaotic ones. The sample entropy 3D diagrams for an electric arc system are also provided to illustrate the variety of possible bifurcation diagrams available. We also provide a comparative study of the diagrams obtained using different methods with the goal of obtaining diagrams that appear similar (or close to each other) for the same dynamical system. Three examples of such comparisons are provided, each in the 1D, 2D and 3D cases. Additionally, this paper serves as a brief review of the many possible types of diagrams one can employ to identify and classify time-series obtained either as numerical solutions of models of nonlinear dynamical systems or recorded in a laboratory environment when a mathematical model is unknown. In the concluding section, we present a brief overview of the advantages and disadvantages of using the 1D, 2D and 3D diagrams. Several illustrative examples are included. [ABSTRACT FROM AUTHOR]

Many problems in scientific research are reduced to a nonlinear equation by mathematical means of modeling. The solutions of such equations are found mostly iteratively. Then, the convergence order is routinely shown using Taylor formulas, which in turn make sufficient assumptions about derivatives which are not present in the iterative method at hand. This technique restricts the usage of the method which may converge even if these assumptions, which are not also necessary, hold. The utilization of these methods can be extended under less restrictive conditions. This new paper contributes in this direction, since the convergence is established by assumptions restricted exclusively on the functions present on the method. Although the technique is demonstrated on a two-step Traub-type method with usually symmetric parameters and weight functions, due to its generality it can be extended to other methods defined on the real line or more abstract spaces. Numerical experimentation complement and further validate the theory. [ABSTRACT FROM AUTHOR]

Almost every branch of industry, at a certain point, utilizes omnifarous materials in their granular form. A key constituent in many bulk material logistic systems is the hopper, which usually acts as a buffering component. In order to achieve the desired throughput, the geometry of the particular hopper must be carefully determined. Considering the geometric properties of the given hopper, the inclination of the walls and the outlet orifice characteristics are the pivotal determinants of hopper functionality. In this paper, the authors have developed an analytical model of the conical hopper's mass efficiency and compared the model with the experimental results for two distinctive granular materials. The model inputs were: the density of the bulk material, critical angle of material repose, generatrix inclination angle of the cone, and diameter of the circular outlet. The experiment was conducted according to a 32 full factorial design. The repeatability of the results was examined according to Cochran's theorem and the adequacy of the data was evaluated via Fisher's criterion, which confirmed the quality of the mathematical model. The error of the developed model does not exceed 4.5%. [ABSTRACT FROM AUTHOR]

In the everchanging landscape of human mobility and commerce, efficient route planning has become paramount. This paper addresses the open vehicle routing problem (OVRP), a major logistical challenge in route optimization for a fleet of vehicles serving geographically dispersed customers. Using a heuristic approach, we explore the complexities of OVRP, comparing the results with advanced optimization methods. This study not only highlights the effectiveness of mathematical modeling, but also explores the practicality of heuristic algorithms such as Greedy, Nearest Neighbor and 2-opt to provide quality solutions. The findings highlight the nuanced interplay between solution quality and computational efficiency, providing valuable insights for addressing real-world logistics challenges. Recommendations delve into optimization opportunities and the integration of emerging technologies, ensuring adaptable solutions to the intricate the problem of open vehicle routing. [ABSTRACT FROM AUTHOR]

This paper presents a novel approach to studying divorce dynamics and elimination strategies using nonlinear differential equations. A mathematical model is formulated to capture the key factors influencing divorce rates. The model undergoes a rigorous theoretical analysis, including parameter estimation, solution existence/uniqueness, positivity, boundedness, and invariant regions. A qualitative analysis explores equilibria, stability conditions, and a sensitivity analysis. Numerical simulations and discussions are presented to validate the model and shed light on divorce dynamics. Finally, conclusions and future research directions are outlined. This work offers valuable insights for understanding and potentially mitigating divorce rates through targeted interventions. [ABSTRACT FROM AUTHOR]

This paper primarily investigates the effect of the tilt of corner cube reflector (CCR) arrays on lunar laser ranging (LLR). A mathematical model was established to study the random errors caused by the tilt of the CCR arrays. The study found that, ideally, when the laser ranging pulse width is 10 picoseconds or less, it is possible to distinguish from which specific corner cubes within the CCR array each peak in the echo signal originates. Consequently, partial data from the echo can be extracted for signal processing, significantly reducing random errors and improving the single-shot precision of LLR. The distance obtained by extracting part of the echo can be reduced to the center position of the array, thereby providing multiple higher-precision ranging results from each measurement. This not only improves the precision of LLR but also increases the data volume. A simulation experiment based on the 1.2 m laser ranging system at Yunnan Observatories was conducted. By extracting one peak for signal processing, the single-shot precision improved from 32.24 mm to 2.52 mm, validating the theoretical analysis results. Finally, an experimental laser ranging system based on a 53 cm binocular telescope system was established for ground experiments. The experimental results indicated that the echo signal could identify the tilt state of the CCR array. By extracting the peak returned by the central CCR for signal processing, the ranging precision was greatly improved. Through theoretical analyses, simulation experiments, and ground experiments, a solution to reduce the random errors caused by the tilt of the CCR array was provided. This offers an approach to enhance the single-shot precision of future LLR and provides a reference for upgrading ground-based equipment at future laser ranging stations. [ABSTRACT FROM AUTHOR]

The paper presents the application of a new bio-inspired metaheuristic optimization algorithm. The popularity and usability of different swarm-based metaheuristic algorithms are undeniable. The majority of known algorithms mimic the hunting behavior of animals. However, the current approach does not satisfy the full bio-diversity inspiration among different organisms. Thus, the Birch-inspired Optimization Algorithm (BiOA) is proposed as a powerful and efficient tool based on the pioneering behavior of one of the most common tree species. Birch trees are known for their superiority over other species in overgrowing and spreading across unrestricted terrains. The proposed two-step algorithm reproduces both the seed transport and plant development. A detailed description and the mathematical model of the algorithm are given. The discussion and examination of the influence of the parameters on efficiency are also provided in detail. In order to demonstrate the effectiveness of the proposed algorithm, its application to selecting the parameters of the control structure of a drive system with an elastic connection is shown. A structure with a PI controller and two additional feedbacks on the torque and speed difference between the drive motor and the working machine was selected. A system with rated and variable parameters is considered. The theoretical considerations and the simulation study were verified on a laboratory stand. [ABSTRACT FROM AUTHOR]

To ensure the stable operation of a wind turbine generator system when the wind speed exceeds the rated value and address the issue of excessive rotor speed during high wind speeds, this paper proposes a novel variable pitch controller strategy based on a back-propagation neural network and optimal control theory to solve this problem. Firstly, a mathematical model for the wind turbine is established and linearized. Then, each optimal sub-controller is designed for different wind speed conditions by optimal theory. Subsequently, a back-propagation neural network is utilized to learn the variation pattern of controller parameters with respect to wind speed. Finally, real-time changes in wind speed are applied to evaluate and adjust controller parameters using the trained back-propagation neural network. The model is simulated in MATLAB 2019b, real-time data are observed, and the control effect is compared with that of a Takagi–Sugeno optimal controller, firefly algorithm optimal controller and fuzzy controller. The simulation results show that the rotor speed overshoot of the optimal controller under the step wind speed is the smallest, only 0.05 rad/s. Under other wind speed conditions, the rotor speed range fluctuates around 4.35 rad/s, and the fluctuation size is less than 0.2 rad/s, which is much smaller than the fluctuation range of other controllers. It can be seen that the back-propagation optimal controller can ensure the stability of the rotor speed above the rated wind speed. At the same time, it has better control accuracy compared to other controllers. [ABSTRACT FROM AUTHOR]

When the battery or supercapacitor is connected to the output of a PV system, the conventional voltage equation expressing its mathematical model usually must be replaced by the current relationship to study the maximum power point tracking (MPPT) control theory. However, hitherto, there is a lack of an attempt to disclose the current constraint relationships at the maximum power point (MPP), which leads to the potential risk of MPPT failure. To solve this problem, in this paper, the MPPT constraint conditions on the basis of currents are built and then a new MPPT control strategy is proposed. In this strategy, a linearized model parameter of a PV cell is used as the bridge to find the current relationships. On the basis of them, some expressions involving the duty cycle are built to directly calculate the control signal of the MPPT controller. Meanwhile, an implementation method is designed to match this proposed MPPT strategy. Finally, some simulation experiments are conducted. The simulation results verify that the proposed MPPT constraint expressions are accurate and workable and that the proposed MPPT strategy and its implementation process are feasible and available. In addition, the simulation results also show that the proposed MPPT strategy has a better MPPT speed and the same MPPT accuracy when the P&O method and fuzzy algorithm are compared. By this work, the MPPT constraint conditions based on current relationships are first found, representing a breakthrough in disclosing the inherent relationships between different currents when the PV system is operating around the MPP. [ABSTRACT FROM AUTHOR]

The operating room is the environment where harm to the patient is most likely. Robotic surgery was listed as one of the top 10 health hazards as late as 2020. Taking inspiration from other fields of application, such as aeronautics, checklists have been increasingly implemented in medical practice over the years, becoming essential components of the operating theatre. In addition to checklists, simulation has taken on a fundamental importance in reducing errors. This paper aims to provide a narrative review to assess the importance of checklists and training in robotic surgery and how they improve the outcome. A comprehensive literature search from January 2000 to September 2023 was conducted. A total of 97 articles were included in the initial search. Eleven studies were deemed relevant and were considered eligible for full-text reading. Among these, ten studies focused on the analysis of training effectiveness. An article in our review assessed the benefits of introducing checklists in the operating room. Innovations created in aviation, such as checklists and simulation, have entered the medical field to prevent human error. Developing dedicated checklist and surgical teams, through theoretical and practical training, has become essential in modern medicine. Tools such as checklists, training, and simulation are among the best methods to reduce adverse medical events. [ABSTRACT FROM AUTHOR]

In the midst of global efforts to curb the spread of infectious diseases, researchers worldwide are striving to unravel the intricate spatial and temporal patterns of disease transmission dynamics. Mathematical models are indispensable tools for understanding the dissemination of emerging pathogens and elucidating the evolution of epidemics. This paper introduces a novel approach by investigating city transmission networks as a framework for analyzing disease spread. In this network, major cities are depicted as nodes interconnected by edges representing disease transmission pathways. Subsequent network analysis employs various epidemiological and structural metrics to delineate the distinct roles played by cities in disease transmission. The primary objective is to identify superspreader cities. Illustratively, we apply this methodology to study COVID-19 transmission in Saudi Arabian cities, shedding light on the specific dynamics within this context. These insights offer valuable guidance for decision-making processes and the formulation of effective intervention strategies, carrying significant implications for managing public health crises. [ABSTRACT FROM AUTHOR]

In recent years, the cost-effectiveness and versatility of Unmanned Aerial Vehicles (UAVs) have led to their widespread adoption in both military and civilian applications, particularly for operations in remote or hazardous environments where human intervention is impractical. The use of multi-agent UAV systems has notably increased for complex tasks such as surveying and monitoring, driving extensive research and development in control, communication, and coordination technologies. Evaluating and analysing these systems under dynamic flight conditions present significant challenges. This paper introduces a mathematical model for leader–follower structured Quadrotor UAVs that encapsulates their dynamic behaviour, incorporating a novel multi-agent ad hoc coordination network simulated via COOJA. Simulation results with a pipeline surveillance case study demonstrate the efficacy of the coordination network and show that the system offers various improvements over contemporary pipeline surveillance approaches. [ABSTRACT FROM AUTHOR]

This paper presents a method of calculating and correcting grinding face gears on an internal gear grinding machine. The generating principle of face gears is studied, and the feasibility of grinding motion on an internal gear grinding machine is analyzed. Then, the motions that need to be followed for grinding are analyzed based on the gear machine tool structure. Four main error sources causing tooth surface deviation in the grinding movements are proposed. The mathematical modeling of the grinding of face gears containing proposed error sources on an internal gear grinding machine is accurately established. The influence of the error sources on the topological deviations of the tooth surface is explored. A sensitivity matrix is established for the influence of various error factors on the tooth surface deviations. The correction values of each error factor are obtained in the case of existing tooth surface deviations. Finally, a virtual machining experiment is conducted, which proves the accuracy of the proposed method for characterizing grinding and realizing corrections. [ABSTRACT FROM AUTHOR]

This paper aims to analyze the stability of a special class of single-channel slow-rotating homing missiles using the Frank–Wall stability criterion. To achieve this, starting from the model of a slow-rolling missile with six degrees of freedom (6 DOFs) in the body frame, a 6-DOFs model in the Resal frame is obtained, which is used to linearize the coupled commanded motion. Based on the linearized model, we obtain the structural scheme of the commanded object and define the flight quality parameters. The obtained linear model has a complex representation (with real and imaginary parts) due to the coupling between longitudinal channels for the rolling missile. Then, the kinematic guidance equations, the seeker equations and the actuator relations using a switching function, specific to the slow-rolling single-channel missile, are defined. The guidance kinematic equations, the seeker equations and the actuator model are linearized in the Resal frame, and the structural diagram of the homing missile is constructed. Starting from this, the characteristic polynomial having complex coefficients is determined and then analyzed with the Frank–Wall stability criterion. Based on the analysis, a stability range is determined for the navigation constant (k) , and a minimum and possibly a maximum limit for the time to hit the target t g o is obtained. The stability range defined for the navigation constant in the linear model is finally validated in the nonlinear model in the body frame. [ABSTRACT FROM AUTHOR]

Orbital flybys have been extensively studied for spacecraft missions, resulting in effective mathematical and physical models. However, these models' applicability to natural encounters involving asteroids has not been explored. This paper examines the applicability of two such theories, patched conics (PC) and the Keplerian map (KM), to asteroid encounters. A review of the two methods will be provided, highlighting their assumptions and range of applicability. Simulations of asteroid–asteroid encounters will then be performed to evaluate their effectiveness in these scenarios. The simulation parameters are set by collecting data on actual asteroid–asteroid encounters, hereby presented, generally characterised by high close approach distances and small masses of the perturbing bodies, if compared to those used to build the flyby theories. Results show that the PC theory's effectiveness diminishes with increasing approach distances, aligning with its assumptions. Moreover, the prediction of the model is better in the geometric configurations where the flyby has major effects on the orbital energy change. The KM theory has shown good effectiveness for encounters occurring outside the sphere of influence of the perturbing body, even for very high distances. This research investigates flyby models' strengths and weaknesses in asteroid encounters, offering practical insights and future directions. [ABSTRACT FROM AUTHOR]

The number of real-time dynamic satellite observation missions has been rapidly increasing recently, while little attention has been paid to the dynamic mission-scheduling problem. It is crucial to reduce perturbations to the initial scheduling plan for the dynamic mission-scheduling as the perturbations have a significant impact on the stability of the Earth observation satellites (EOSs). In this paper, we focus on the EOS dynamic mission-scheduling problem, where the observation profit and perturbation are considered simultaneously. A multi-objective dynamic mission-scheduling mathematical model is first formulated. Then, we propose a multi-objective dynamic mission-scheduling algorithm (MODMSA) based on the improved Strength Pareto Evolutionary Algorithm (SPEA2). In the MODMSA, a novel two-stage individual representation, a minimum perturbation random initialization, multi-point crossover, and greedy mutation are designed to expand the search scope and improve the search efficiency. In addition, a profit-oriented local search algorithm is introduced into the SPEA2 to improve the convergence speed. Furthermore, an adaptive perturbation control strategy is adopted to improve the diversity of non−dominated solutions. Extensive experiments are conducted to evaluate the performance of the MODMSA. The simulation results show that the MODMSA outperforms other comparison algorithms in terms of solution quality and diversity, which demonstrates that the MODMSA is promising for practical EOS systems. [ABSTRACT FROM AUTHOR]