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Linear projects are a special type of repetitive projects. Major disadvantages have been shown when using the critical path method (CPM) for linear project problems. So, to overcome these shortcomings linear scheduling method (LSM) was used to analyze linear projects. There are different types of activities in linear projects. However, existing mathematical models for LSM cannot represent all types of linear project activities. Therefore, this paper presents a mathematical model that can represent all types of activities using matrices. Moreover, the mathematical model is then used to create an optimization model that minimizes the project duration and cost using non-dominated sorting genetic algorithm II (NSGA-II). The two models can help project managers in scheduling real-life linear projects and find optimum linear project schedules. This paper introduces an optimization model for linear projects that utilizes matrices, offering a different approach in the field of linear project optimization. • Different types of activities in linear schedule method (LSM) are identified • New mathematical formation for (LSM) is developed using matrices • Mathematical formation helps in representing all types activities • Mathematical formation was used to build an optimization model • Optimization model solves time cost tradeoff problem for linear project [ABSTRACT FROM AUTHOR]

Risks are uncertain events that can affect criteria such as project cost, quality, and completion time and ultimately lead to project failure. That is why the project risk management process, which is one of the most fundamental parts of project management, must be done properly. In this paper, a new multi-objective fuzzy model is proposed to respond appropriately to the primary and secondary project risks. The contributions, such as risk interdependency, considering the project with multi-mode activities, resource considerations, as well as attention to interval-valued fuzzy uncertainties are regarded simultaneously for the first time. The purpose of the proposed multi-objective mathematical model is to minimize cost, quality reduction, and project completion time. Then, a new two-stage uncertain solution approach is introduced in this paper. In this solution approach, using an equivalent method in the first step and then using an extended multi-choice goal programming method in the second step, for both lower and upper limits of the membership functions for interval-valued fuzzy numbers, the computational processes are performed. To show the application and effectiveness of the proposed model, a case study adapted from the literature is given. Finally, sensitivity analysis is conducted to analyze the behavior of the developed mixed-integer programming model. The analysis of obtained results indicates that the utilization of the proposed model leads to better and more appropriate solutions. • Presenting a new multi-objective programming model for project risk responses. • Proposing multi-mode activity and resource considerations in project risk modeling. • Introducing a new interval-valued fuzzy solution approach to handle uncertainty. • Focusing on primary and secondary risks along with project risk interdependency. • Implementing the proposed model in a case study for electricity industry projects. [ABSTRACT FROM AUTHOR]

Abstract: This paper concerns the modelling of an accumulator used in industrial elastic web processing plant such as paper mills, fabric, rolling mills etc. Accumulators are used to allow rewind or unwind core changes while the process continues at a constant web velocity. A new nonlinear model of a pneumatic actuated industrial accumulator including pneumatic jack model, static friction representation and web weight is first detailed which enables to deduce a linear model. These models are derived from physical laws that describe web tension and velocity dynamics in each web span. In a second part, the effects of time-varying mechanical parameters, such as web Young modulus, web length and rollers inertia on accumulator dynamics are presented. The performances of the modeled accumulator are illustrated by simulations in Matlab/Simulink software environment. [Copyright &y& Elsevier]

This paper describes an accurate model of the Electrical Power Subsystem (EPS) of the Thermal Analysis Support and Environment Characterization Laboratory (TASEC-Lab), a university experiment developed for using in high-altitude balloon missions to measure and analyze the convection heat transfer. A Li-ion battery and two high efficient DC–DC converters have been characterized through laboratory tests and fitting to the experimental results. The developed mathematical models described in this paper are used to carry out accurate EPS simulations and are validated by comparison with the experimental data. • Design and modeling of the electrical power subsystem of a stratospheric balloon experiment. • New Li-lion battery discharging model that describes the three main parts: initial decay, linear, and exponential decay. • Formulation of a new DC/DC converter efficiency model. • Simulation and model validation of the electrical power subsystem. [ABSTRACT FROM AUTHOR]

A new improved three-dimensional continuous chaotic system (ImproBsys) is designed in this paper. It can achieve from an ordinary chaotic state to a hyperchaotic state, that is, chaotic behavior tends to become more complex. Furthermore, by using ImproBsys, this paper proposes a double image encryption algorithm based on compressive sensing and public key elliptic curve. First, the two plain images of the same size are excuted by discrete wavelet transformation (DWT), and then the DWT coefficients are thresholded. Second, the quantization matrix is compressed by compressive sensing, and the size is reduced to half of the original one, and then the two compressed matrices are spliced together to form a new matrix. Finally, the new matrix is encrypted by elliptic curve cipher to get the cipher image. Our contributions are: (1) A new ImproBsys is designed with better chaotic behavior, which has two positive Lyapunov exponents to show hyperchaos phenomenon. (2) Compressive sensing technique is employed to reduce the amount of data transmission for two single images, and then we use ImproBsys to control the measurement matrix. (3) The initial values of the ImproBsys depend on the information entropy of the plain image by a new constructed mathematical model. [ABSTRACT FROM AUTHOR]

This paper proposes a novel method to address coherent interference (pilot contamination) in Massive MIMO by incorporating control over propagation environment through Intelligent Reflecting Surfaces. In earlier research it was established that each mobile device has unique spatial signature which can be used as identifier even if they are sharing same pilot sequence. However in certain circumstances when their signals are received at BS with same Angle of Arrival their spatial structure become similar thus their individual identity is lost. This situation adds error in acquisition of channel state information, the accuracy of which is the key to benefit from Massive MIMO. This paper present a method to resolve the mentioned accepted gap using mathematical basis and simulation methods. A mathematical model of Massive MIMO is presented which is widely accepted by the subject modeling community. The model is then used to generate the basis for the presented algorithm through further mathematical studies and simulations. The basic algorithm used for the resolution of pilot contamination problem is finally presented in this paper. The algorithm was simulated using MATLAB and simulation results are tabulated to identify the results of pilot de-contamination after incorporating signal propagation control. [ABSTRACT FROM AUTHOR]

In this paper, a novel four-dimensional autonomous chaotic system based on memristive diode bridge is presented, and it consists of a simple linear oscillation and a memristor. According to the mathematical model of the system, the equilibrium point is analyzed, and the phase portraits, time-domain sequences, bifurcation diagrams and Lyapunov exponent spectrums are numerically simulated. The rich dynamical behavior of proposed system is investigated. It includes multistability, offset boosting and chaotic bursting. In addition, the circuit simulation and Field-Programmable Gate Array (FPGA) hardware experiment are carried out to verify the feasibility of the system. Then the application of proposed system in chaotic image encryption is presented. By carrying out some security performance analyses, we show that the proposed system has good security performance. • A memristor chaotic system with simple circuit structure is proposed. • The memristive chaotic system presented in this paper has rich dynamical behaviors. • The dynamical behavior of offset boosting and multi-stable is proposed. [ABSTRACT FROM AUTHOR]

Abstract: The possibility to develop an absolute technique, independent from the paper conservation conditions, to date recent paper documents (i.e. less than 50 years old) for forensics purposes is discussed. We suggest the possibility to use the curve representing the strong increase in the atmospheric radiocarbon concentration induced in the last 50 years by nuclear weapons tests as reference to date paper documents, with a resolution down to a few months. The results obtained in the analysis of two known age documents are presented together with a first order mathematical model developed in order to take into account the contributions of the different tree rings employed in the paper production. [Copyright &y& Elsevier]

• The mathematical model of the reachable domain of the contingency return trajectories. • Reachable domain calculation method of the contingency return trajectories based on interval analysis. • Parameter characteristic analysis of reachable domain. The investigation on reachable domain based on interval analysis is performed, which is aimed for the contingency return trajectories during the circumlunar flight stage in manned lunar landing engineering. First, the issue of contingency return trajectory, which adopts a non-coplanar maneuver during the circumlunar flight phase, is expounded upon. The mathematical model of the reachable domain of contingency return trajectories is established. Second, the contingency return trajectory is designed. An improved interval branch and bound algorithm is introduced and a reachable domain calculation method of the contingency return trajectories is proposed. Third, in numerical simulations, by comparing the reachable domain obtained by the traditional brute force method, the accuracy of the method presented in this paper is verified. It also indicates that this method has a higher calculation efficiency. Finally, numerous simulations are conducted to discuss the parameter characteristic of reachable domain by adopting this method. The study conclusions can serve as an important reference for the selection and decision of contingency return trajectory plans in the future manned lunar landing engineering. [ABSTRACT FROM AUTHOR]

In this paper, we propose a simple and fast shape transformation method. This method is based on the Allen-Cahn (AC) partial differential equation and uses the edge stop function to constrain evolution. We use the operator splitting method to control the equation for splitting, and use the explicit Euler's method to solve the discrete equation. Based on the source shape and the target shape, our phase-field model can perform rapid shape transformation when the appropriate parameters are selected. In order to verify the feasibility of our proposed phase-field model, numerical experiments on shape transformation are carried out in two-dimensional and three-dimensional space. The results show that the established mathematical model can not only perform shape transformation between simple shapes, but also have a good effect on shape transformation between complex shapes. We also propose a numerical solution using the Crank-Nicolson numerical scheme to handle the model we introduced. This numerical scheme utilizes the multigrid method and Gauss-Seidel iteration for solving. The results of the numerical experiments demonstrate the effectiveness of this numerical method in handling shape transformations in three-dimensional space. [ABSTRACT FROM AUTHOR]

The paper considers the process of imbibition in a porous medium under the action of capillary forces in microgravity. A description of experiments on the repeated imbibition of an artificial porous medium during parabolic flights is given. In some experiments, the porous medium is homogeneous; in others, the experimental cell contains regions with different permeability. The analysis of non-stationary and convective terms in the equation of momentum conservation and their influence on the imbibition process is carried out. The results of numerical modeling of the process of repeated imbibition under the action of capillary forces under microgravity in an inhomogeneous porous medium are presented. The results of numerical modeling are compared with experimental data. • The paper considers the imbibition of fluid into a porous medium in microgravity. • The mathematical model that takes into account hysteresis is proposed. • The experimental results for various porous media are described. • The results of numerical modeling are compared with experimental data. [ABSTRACT FROM AUTHOR]

• Determining the urban critical infrastructures in the event of an earthquake. • Designing Location-Routing-Inventory decisions in humanitarian relief chain. • Simulation of interaction of urban infrastructure in earthquake conditions. • Using a cooperative game to examine the manner of cooperation of disaster relief supply chain players. • Application of the model to a real-world disaster relief logistic case study. This paper describes a new simulation based mathematical model for locating distribution centres, vehicle routing, and inventory problems under earthquake conditions. In this paper, the proposed network includes affected areas, suppliers, distribution centres, and hospitals. Additionally, the basic infrastructures of the city, which are very fragile at the time of the earthquake, are identified. Then, the demand of each relief commodity is calculated depending on the different earthquake scenarios using simulation. The estimated demand is incorporated into the mathematical model as an uncertain parameter. The proposed methodology is designed as a two-stage model so that in the first stage the location and inventory of distribution centres are addressed. Thereafter, in the second stage the routing decisions are taken for the distribution of relief commodities from the distribution centres and suppliers to the affected areas. Due to the NP-hardness of the second stage model, this model is solved using multi-objective stochastic fractal search. This algorithm is one of the population-based and stochastic optimization techniques and inspired by the natural phenomenon of fractal growth. It should be noted that in the second stage, a cooperative game theory of coalition type is considered, which resulted in synergies that minimize the relief golden time. The kind of cooperation is the use of potential of co-operators' vehicle. In this stage, the possibility for the players to cooperate by sharing people and commodities transportation requests is considered. Also, to validate the model, a real case study is provided for a possible earthquake in Tehran. Finally, the comparison between the simulation results and the values obtained from the real system evaluates the performance of the implemented model. Considering normality and a 95% confidence interval, it can be concluded that the proposed model provides a precise representation of the real system's performance. [ABSTRACT FROM AUTHOR]

Intelligent Reflection Surface (IRS) will be widely used in future communication system construction to reduce construction costs and improve coverage. However, IRS systems are generally equipped with controllers to receive wireless signal instructions, this increases the vulnerability of future communications. In this paper, we present an attack tactic to provide a way of thinking for the future defense deployment. At the beginning, the hacker cannot know the whole communication system, then it continuously attacks the IRS system, monitor the communication system, and sequentially learns new information about the system in each attacking round in order to attack more effectively in the next round. A two-layer optimal mathematical model is presented to describe the BS and the hacker's decision. And the two-layer optimization which is difficult to solve is transformed into a single layer linear optimization by using equivalent transformation and dual transformation. A series of mathematical experiments are used to test different scenarios applicable to different monitoring style, and verify that the tactic proposed in this paper can effectively interfere with the system. [ABSTRACT FROM AUTHOR]

This paper presents a method to automatically improve simulation model accuracy by using a stochastic gradient descent algorithm. The proposed algorithm updates models' parameters based on data collected from the actual domain under investigation. Collected data and feedback are fed into the simulation model to get predictions. In a linear prediction model, this data, along with the predictions, would form a typical regression problem; however, the stochastic gradient descent algorithm was modified to update the simulation model parameters. A tunneling case study is presented here, and the results show that the proposed algorithm can decrease simulation error by more than 50%, even in the case of incomplete simulation models or a missing inter-relationship between elements. Besides improving initial models, this paper provides a new approach for achieving data-driven simulation models that are updated in real time based on feedback from the actual domain. • Proposing a data-driven approach to enhance simulation performance. • Using stochastic gradient descent algorithm to update simulation parameters. • Deriving mathematical model to calculate error rate from a simulation model. • Applying the proposed method in a real case study of a tunneling project. • Suggesting a new approach for fitting data to model a simulation. [ABSTRACT FROM AUTHOR]

This paper aims to explore the development of a flight dynamics model for a small-scale side-by-side helicopter and describe its trim and stability characteristics. The helicopter is considered a suitable candidate for Urban Air Mobility (UAM) solutions, because of its reliable design and low noise characteristics, but still very small knowledge is present on the mathematical modeling approaches and dynamic properties. A 14 degrees of freedom nonlinear mathematical model is developed and semi-analytical models are employed to account for the presence of the shrouds. An iterative trim routine is developed and applied with a suitable control mix that allows the use of classic helicopter controls. To control the vertical speed and roll rate, the paper assumes an equal collective pitch and lateral cyclic in the two rotors, while a uniform plus a differential longitudinal cyclic is adopted for pitch and yaw maneuvers. The paper discusses unique characteristics of the side-by-side configuration as obtained from the stability analysis: an unstable high-frequency mode, governed by the vertical velocity and pitch angle arises when the center of gravity (CG) of the vehicle is aligned or placed in front of the two main rotors. Similarly, both lateral phugoid and roll subsidence modes are sensitive to the CG location. The side-by-side configuration presents also a stable spiral mode which needs to be carefully designed. [ABSTRACT FROM AUTHOR]

This paper is the second in a two-part series on the concavity-convexity of the distribution system security region (DSSR). In Part I, the concave-convex characteristics and mechanism of DSSR are revealed by observing many case grids. In Part II (this paper), the concave-convex principle of DSSR is revealed through mathematical deduction. Firstly, the relevant concepts of sub-regions are proposed, and a DSSR model based on the union of sub-regions is developed. Secondly, the concave-convex principle of DSSR is proposed. The proposed criteria show that the security region of a distribution system with a single load transfer path for each feeder is convex, while that with multiple load transfer paths for some feeders can be concave or convex. Thirdly, the proposed criteria are deduced mathematically. Fourthly, based on the criteria, a method is proposed to judge whether a DSSR is concave or convex. Fifthly, the proposed criteria and method are verified through several cases, and the DSSR concavity-convexity of real distribution systems in China is also analyzed. Finally, the applications of DSSR concavity-convexity are illustrated. This work lays a mathematical foundation for the research of the topological properties of DSSR and is also useful for the application of DSSR. • The DSSR mathematical model based on the union of sub-regions is developed. • Three criteria are proposed and proved, revealing the concave-convex principle of DSSR. • A judgment method for DSSR concavity-convexity is proposed based on these criteria. • The DSSR concavity-convexity of real distribution systems in China is analyzed. • The application values of DSSR concavity-convexity are demonstrated. [ABSTRACT FROM AUTHOR]

With the development of economic globalization, distributed hybrid flow shop scheduling problem (DHFSSP) has become prevalent in realistic manufacturing systems. Moreover, to accord with the actual production scenarios and satisfy the requirement of manufacturing market, it is imperative to comprehensively explore various complex manufacturing scenarios (e.g., production assembly) and production-constrained resources (e.g., worker resources) in DHFSSP. However, the integration mode of DHFSSP, assembly shop problem (ASP), and dual-resource constraints (DRC) has not been reported in existing literature. Thus, to fill out this research gap, this paper first attempts to investigate DAHFSSP-DRC with minimization the total tardiness (T T D). To solve this problem, a mixed-integer linear programming (MILP) model and a knowledge-based iterated greedy algorithm (KBIG) are presented. The novelties of KBIG are as follows: (1) An efficient decoding is developed to improve the solution's quality; (2) A knowledge-based NEH (KB-NEH) initialization strategy is presented to generate an initial solution; (3) A knowledge-based destruction and construction is designed to improve the exploration capability; (4) A product-based local search is proposed to enhance the exploitation capability. Additionally, to validate the proposed model, we implement CPLEX to solve it on 24 small-sized instances. To verify the effectiveness of the proposed KBIG, extensive experiments are conducted to compare with other 7 comparison algorithms on 405 large-sized instances. Experimental results illustrate that KBIG is superior to its competitors. • This paper first investigates DAHFSSP-DRC with minimization TTD. • A MILP model and a KBIG are proposed for DAHFSSP-DRC. • The importance level of different knowledge is considered in KBIG. • Experimental results prove the effectiveness of MILP model and KBIG. [ABSTRACT FROM AUTHOR]

Listeriosis is one of the zoonotic diseases affecting most parts of the Sub-Saharan countries. The infection is often transmitted by eating and it can also pass by respiratory and direct contact. In this paper, a listeriosis mathematical model is formulated involving fractal-fractional orders in both Caputo and Atangana–Baleanu derivatives. Moreover, future behaviors of the disease are investigated by considering the fractal–fractional operators that are very effective in modeling the real-life phenomena by virtue of their memory effect. The basic properties and steady states are also obtained. The threshold parameter for determining the spread of the disease is computed. Numerical results are presented for each fractal-fractional-order operator. The results obtained in the paper show that the numerical schemes are effective for predicting and analyzing complex phenomena. [ABSTRACT FROM AUTHOR]

This paper presents a dynamical analysis of a tethered aerostat using a multibody simulation tool called SimscapeMultibody™. Tethered aerostats are lighter than air vehicles that float in the air and are connected to the ground through the tether. Atmospheric winds are a source of disturbance to the aerostat. The wind produces drag force that causes the aerostat to displace from its mean position. This phenomenon is called blow-by. Solving the mathematical model of the motion dynamics with time step is the conventional method used for simulating the flight dynamics of the aerostat. This paper discusses the application of Simscape Multibody™ for the three-degrees-of-freedom flight dynamic simulation of spherical tethered aerostat. Simscape Multibody™, an extension of MATLAB®/Simulink, is a multibody modeling tool in which physical bodies and their interactions have to be defined to simulate the dynamics. The mathematical model of the defined system is automatically generated by the SimscapeMultibody™ solver, and the system dynamics is simulated. The simulation of dynamics using multibody modeling tools provides high fidelity simulation for the tethered aerostats. [ABSTRACT FROM AUTHOR]

Renewable powered dc microgrid is more cost-effective, simple, reliable, highly efficient, and scalable than the traditional electric grid. This paper provides an overview of high gain dc converter topologies for dc microgrids. This research's primary objective is to impart a unique extensive, comparative, and perceptive analysis in high gain converter configurations. The most recently reported research articles are considered for discussion in this paper. Initially, based on the structural configurations, the converters are segregated and are grouped into four categories, such as Replacement, Reduced Redundant Power Processing (R2P2), Incorporation, Integration (R2I2) techniques. Secondly, based on the dynamic and steady-state analysis, the topological converter configurations are comparatively analyzed. A few topologies' mathematical modeling is also discussed to obtain a comprehensive insight into the converter's dynamic behavior. An extensive analysis, comparisons, and assessment of these converters with diverse configurations are acquainted with tables and figures are presented for choosing an appropriate converter suitable for dc grid application. The pros and cons of the topology derivation under each categorization are presented for benefitting the researchers in selecting the topological configuration method. In the end, the comparison results of the high gain converter clusters are summarized, and recommendations are given, which leads to the guidelines for selecting a significant high gain topology for a specific application. Furthermore, the constraints considered for topology derivation with the type of analysis carried out are presented. This gives a way to find the scope for future research under this area which is finally offered. This study will also provide an insight into the derivation of several configurations of the novel high gain dc-dc converter in the field of dc microgrid. [ABSTRACT FROM AUTHOR]

Abstract: Papermaking is known as an energy-intensive, but not always efficient industry. This is at least partly due to the fact that the majority of papermaking technologies and procedures were established at a time when energy was both cheap and plentiful. A considerable fraction of the energy required for papermaking is consumed in removing water by the use of steam in the paper machine’s drying section. It is also known that even a small reduction in steam use can result in a significant reduction in production costs and environmental effects. To date, a great deal of research has been undertaken, aimed at improving the performance of the drying section by making more efficient use of dryer steam. This paper investigates a new approach to reducing thermal energy use in paper making by seeking to enhance the amount of water removed in sections of the machine prior to the drying section. The proposed method is focused on sequential modelling of the effect of vacuums used in the forming section on the thermal energy consumption in the drying section. The primary models explain how different vacuum pressures can affect the flow of water from the sheet in the forming section whilst the secondary models describe the effect of increased drainage on the steam requirements in the dryer. Operational data from a UK paper mill are used to illustrate the proposed method. The models developed can have subsequent application to optimising the use of thermal energy in paper making. [Copyright &y& Elsevier]

• In this article, an optimal evaluation of re-opening policies for COVID-19 is developed. • The method provides effective re-opening policies using agent-based models and the whale optimization algorithm. • Agent-based models simulate the transmission risk in scenarios that are impossible to evaluate in real conditions. • The whale optimization algorithm is used to find the best scenario where the lowest risk of infection is reached. • Experiments demonstrate that the proposed approach delivers realistic predictions to formulate re-opening policies. A new contagious disease or unidentified COVID-19 variants could provoke a new collapse in the global economy. Under such conditions, companies, factories, and organizations must adopt reopening policies that allow their operations to reduce economic effects. Effective reopening policies should be designed using mathematical models that emulate infection chains through individual interactions. In contrast to other modeling approaches, agent-based schemes represent a computational paradigm used to characterize the person-to-person interactions of individuals inside a system, providing accurate simulation results. To evaluate the optimal conditions for a reopening policy, authorities and decision-makers need to conduct an extensive number of simulations manually, with a high possibility of losing information and important details. For this reason, the integration of optimization and simulation of reopening policies could automatically find the realistic scenario under which the lowest risk of infection was attained. In this paper, the metaheuristic technique of the Whale Optimization Algorithm is used to find the solution with the minimal transmission risk produced by an agent-based model that emulates a hypothetical re-opening context. Our scheme finds the optimal results of different generical activation scenarios. The experimental results indicate that our approach delivers practical knowledge and essential estimations for identifying optimal re-opening strategies with the lowest transmission risk. [ABSTRACT FROM AUTHOR]

• A model for edema growth coupled with degradation and drug delivery from a PLGA intravitreal implant is proposed. • The edema growth model can be fitted with respect to one parameter to match patient-specific data. • The proposed methodology can be used to provide insights into the pharmacokinetics of a dexamethasone PLGA implant. • The model presented provides a general framework for the study of problems in tissue growth in other contexts. In this paper, we introduce a mathematical model for the drug release from an intravitreal implant and the subsequent effect of the drug on the inflammation process of macular edema. Coupling the drug transport problem with the growth of the edema, we compare the numerical simulations with patient-specific medical images. We fit the model with respect to one parameter and match the retinal thickness observed in the patient. After the validation of the proposed model, we perform numerical experiments regarding patient-specific treatments. In particular, we analyze the drug concentration in the different sub-domains (e.g., the implant and the retina) and simulate the scenario of edema recurrence and implant re-injection. The proposed mathematical model has the potential to provide important insights into the use of intravitreal dexamethasone implants and the treatment of macular edema. [ABSTRACT FROM AUTHOR]

The recent outbreak of rabies virus has affected numerous individuals in the community, highlighting the importance of studying the disease mathematically in epidemiology. In this paper, we develop a mathematical model for the spread of rabies disease using the harmonic mean incidence rate and determine the reproduction number R 0 using the next generation matrix approach. The fractional dynamics of the model incorporate the interaction between infected individuals and environmental factors. We analyze the model using both Atangana-Baleanu-Caputo (ABC) and Caputo-Fabrizio (CF) techniques, drawing on both modern and classical approaches. For qualitative investigation using fractional operators, we utilize the Banach fixed-point theory and derive the Hyers-Ulam stability concept. We assign values to the model parameters and utilize the Newton interpolation technique to obtain a numerical scheme. Additionally, we perform sensitivity analysis on the model. In conclusion, our findings provide important insights for the study of epidemics. [ABSTRACT FROM AUTHOR]

In this paper, the stabilization and set point tracking of the utility boiler is achieved via the Proportional-Integral-Derivative (PID) controller, tuned using the versions of metaheuristic Particle Swarm Optimization (PSO) algorithms. The utility boiler model dynamics are based on the Bell and Astrom boiler turbine system. Initially, the non-linear mathematical model is obtained using the first principles data from the plant model. Further, Taylor series approximation is applied to linearize the non-linear equations around the equilibrium point to implement a stable controller for the plant. Finally, the PID controller gains for the plant model are determined using the PSO algorithms to achieve the desired response. For tuning the PID controller, three PSO algorithms namely standard PSO, Adaptive PSO (APSO) and Improved Adaptive PSO (IAPSO) are proposed. The performance of the proposed PSO based PID control algorithms are evaluated using error metrics such as Integral Absolute Error (IAE), Integral Time Absolute Error (ITAE) and Integral Square Error (ISE). The simulation results show that the proposed APSO and IAPSO algorithms have improved performance when compared to regular PSO algorithms and are capable of optimizing the control parameters. [ABSTRACT FROM AUTHOR]

The problem of motion of coupled harmonic oscillators can be modeled in the terms of system of ordinary differential equations (SODEs). In the present paper, authors used Sawi transformation for finding the solution of SODEs with application to determine the concentration of chemical reactants of chemical reaction in series. Authors have considered four numerical problems and determined their solutions step by step for explaining the complete method. After it, authors have taken a problem of physical chemistry for determining the concentration of chemical reactants (substances) of chemical reaction in series. Authors have obtained the solution of this problem by developing its mathematical model in terms of SODEs and then applying Sawi transformation on it. Results of this problem are visualized using tables and graphs. Results of the present paper show that the Sawi transformation provides us the exact solution of SODEs without large computational work. [ABSTRACT FROM AUTHOR]

In recent times, origami-inspired deployable structures have received significant interest from the research community as a major area of research in the fields of science and technology. This paper deals with the geometry and the deformation behavior of deployable cones based on the four-fold line origami concept. First, a novel geometric design algorithm is presented to develop axially foldable conical structures based on generalized Miura-ori pattern, which is then utilized to investigate the influence of four design parameters on folding geometry. The foldability of thus obtained origami patterns is verified with the help of physical models. The geometric incompatibilities during the deployment are highlighted using a simple experiment, showing the unfolding sequence of a paper model. The deformations due to incompatibilities are analyzed by adopting the concept of pin-jointed truss modeling of the origami structures. A mathematical model of the deployment problem is formulated to capture the deployment deformations of the structure, on the basis of which an algorithm for deformation analyses is developed. One example is considered to characterize the deformation behavior of the conical origami structures as the design parameters of the folding pattern are varied. The analytical findings demonstrate that the fold line strains of the origami cone are very sensitive to the changes in three design parameters, number of origami units (m), fold angle (α 0), and angle θ 2 ; except the length ratio (l r 0). The variation in design parameters may induce bi-stability in the deployment path of the conical structure. The findings of the analytical investigation are verified numerically, demonstrating that the strain responses obtained from the numerical analyses are completely consistent with the analytical results. [ABSTRACT FROM AUTHOR]

Tourist trip design is a fast-growing area of research. Tourist interest, budget, travel style, safety, and the existence of travelers with special needs (for example, wheelchair accessibility) are some of the elements to consider for obtaining personalized routes. Including these elements in a single mathematical model can considerably complicate the solution process. Also, route decision-making is affected by the context (health, social, political, economic, etc.) in which decisions are made. In this paper, the first aim is to propose a three-step methodology to obtain contextualized solutions to a tourist trip design problem (TTDP) with time-dependent recommendation factors. The methodology consists of (1) providing a basic TTDP model that avoids the complexity of including contextual information, (2) obtaining a set of solutions to the problem using a Modeling to Generate Alternatives (MGA) approach, and (3) using a recently developed a posteriori method to include the contextual information through fuzzy propositions. The second aim of the paper is to evaluate three algorithmic strategies for the MGA step. Lastly, considering a context for people with mobility impairments, an example is solved using real data. The results show the usefulness of the proposed methodology in solving the TTDP with contextual information. • A tourist trip design problem with time-dependent recommendations factors is solved. • A methodology to obtain contextualized solutions is developed. • An accessibility context is modeled with fuzzy propositions. • Solutions are obtained by using the modeling-to-generate-alternatives approach. • Best solutions are suitable for the accessibility context. [ABSTRACT FROM AUTHOR]

• The model allocates safety stocks in supply chains at minimum cost. • An MIQCP reformulation with piecewise approximation greatly improves computational efficiency. • The piecewise function yields an improved estimation for the fill rates. • The GSM is extended to handle non-normally distributed demands. • Real-world case studies solved to optimality within few seconds of computational time. This paper presents a Multi-Echelon Inventory Optimization (MEIO) framework, based on the Guaranteed-Service Model (GSM), to allocate safety stocks across a supply chain with several locations and products, minimizing costs while meeting service level objectives. Extending previous work by Achkar et al. (2023), this paper enhances the Mixed-Integer Quadratically Constrained Program (MIQCP) with a highly efficient solution approach. The model introduces a piecewise linear approximation, significantly improving computational efficiency and the accuracy of the approximation for the fill rate function. It also introduces a different and more efficient approach to account for stochastic lead times using a discrete function. Moreover, an extension of the approach to account for non-normally distributed demands is proposed. The model is applied to several instances of a real-world case study from a pharmaceutical company, with more than 7300 product-location combinations, showing that optimal solutions can be obtained within few seconds of computational time. [ABSTRACT FROM AUTHOR]

Grey prediction evolutionary algorithm (GPE) is an emerging category of meta-heuristic algorithm based on mathematical model. It generates offspring by predicting the macroscopic evolutionary trend of population series. On the contrary, the mining of local evolutionary trend are flawed. To address this imperfection, this paper introduces a quadratic function as a surrogate model to mine the local evolutionary trend of population series for the first time. Thereby an improved grey prediction evolutionary algorithm called grey prediction evolutionary algorithm with a surrogate model based on quadratic interpolation (GPE-QI) is designed. The surrogate model based on quadratic interpolation is regarded as an external auxiliary tool to mine the local evolutionary trend of population series by using currently superior individuals. Through utilizing the mined local trend information, a donor population closer to the optimal solution is formed to improve the prediction direction of the algorithm. The performance of GPE-QI is tested on CEC2019, CEC2020 benchmark functions and six engineering design problems. The experimental results demonstrate the stronger competitiveness of GPE-QI to well-established algorithms in terms of solving accuracy and convergence rate. If this paper is accepted, MATLAB codes associated with this paper will be uploaded to https://github.com/Zhongbo-Hu/Prediction-Evolutionary-Algorithm-HOMEPAGE. • Improvement can be made by enhancing local search of grey prediction evolution. • Mine local evolutionary trend of population series by quadratic interpolation. • Construct a surrogate model by using the local evolutionary trend. • Design an improved grey prediction evolutionary algorithm with a surrogate model. • The proposed algorithm is more competitive than the well-established. [ABSTRACT FROM AUTHOR]

Periodic cleaning of photovoltaic (PV) panels, such as every three months, is a common industry practice. However, this fixed period may not be optimal for maximizing the profit of a PV power generation system, due to numerous time-variant influencing factors, such as weather, temperature, etc. To increase the overall profit of a solar farm, it is highly desirable to have a flexible cleaning schedule that considers time-variant influencing factors. For this requirement, a rolling-horizon cleaning recommendation system is presented in this paper. Within this cleaning recommendation system, a prediction model and profit model are proposed. The prediction model, called the ensemble long-term and nonlinear autoregressive, can provide a time-variant future horizon by analyzing and compressing the time-variant characteristics in historical information. The profit model based on mathematical constraints, can process time-variant future horizon output from prediction model to generate a flexible optimized recommendation for cleaning schedule. The effectiveness of the proposed system is validated in real farms and all data used in this paper is collected from real world. The two case studies in experiments show that the profit improvement can reach up to 6% and 30%, respectively. [Display omitted] • A rolling-horizon cleaning recommendation system for PV panels. • A novel long-term and nonlinear predictive method. • A concise profit model for easy deployment in industry. • Flexible cleaning schedule considering time-variant characteristics. • Improvements of 6% and 30% in two different real farms, respectively. [ABSTRACT FROM AUTHOR]

In this paper the aerothermal heating of a reusable launch vehicle is reconstructed on the basis of temperature measurements taken in the thermal protection system of this vehicle. The discussed integrated thermal protection system is composed of three layers. Mathematical model, describing the problem, takes into account the dependence on temperature of the material parameters as well as the thermal resistances occurring in the contact zones of the layers, which is a novelty in the proposed approach. For solving the direct problem, the implicit scheme of the finite difference method is applied. Next, by using the solution of the direct problem, the Tikhonov functional is created, which describes the error of the current approximate solution. Whereas for determining the solution of the inverse problem the Levenberg-Marquardt method, modified and adapted to the Tikhonov functional, is used. The paper presents the mathematical model of the problem and the method of solution together with the selected examples illustrating its exactness and stability. In order to better examination of the solution method some various values of parameters are taken in the demonstrated examples. • Reconstructing an aerothermal heating in space vehicle protection system with temperature dependent material properties. • Reconstructing an aerothermal heating taking into account the thermal resistance between layers. • Solving the problem for three layers model of the thermal protection system. • Inverse problem solved for input data taken from NASA measurements. • Heat flux measured by NASA reconstructed with good precision and stability. [ABSTRACT FROM AUTHOR]

Magnetic localization techniques are used in in vivo therapy, drug delivery, and surgical localization widely due to their ability to locate in an unobstructed environment precisely. The Levenberg-Marquardt (L-M) algorithm is one of the most common magnetic localization algorithms due to its fast optimization speed and high precision, but it requires high initial values such that improper initial values can easily lead to local optimization. In this paper, the performance of ten commonly used intelligent optimization algorithms is compared based on the mathematical model of the permanent magnet. The final position of the magnet is obtained by a fusion algorithm that uses the result of the intelligent optimization algorithm as the initial value of L-M. The real-time localization accuracy of this fusion algorithm is verified on a hardware platform and experiments demonstrate that the integration of the TSA algorithm and L-M algorithm fusion yields higher performance of the magnetic positioning system. [ABSTRACT FROM AUTHOR]

Mitogen-activated protein kinase (MEK) inhibitors and oncolytic virotherapy are identified as promising cancer therapies that can enhance the efficacy of other cancer treatments. A few studies demonstrate that cancer cells proliferate when exposed to virotherapy with MEK inhibitors in an integer order model or without them in a fractional order model. None of them are intended to investigate tumor cell growth under the combined treatment strategy of chemo-virotherapy with a MEK inhibitor in a fractional order model. In this paper, a mathematical model based on fractional order ordinary differential equations (ODEs) is developed for the mutual interactions among tumor cells, as well as a therapeutic combination of chemotherapy, oncolytic viruses and the functional consequence of MEK inhibitor, to investigate how virotherapy could enhance chemotherapy under the action of MEK inhibitor. The numerical results show that virus burst size and MEK inhibitors have a noticeable impact on regulating the trend of tumor cell proliferation. While virotherapy responses to tumor cell proliferation are undoubtedly quicker than chemotherapeutic treatment responses, MEK intensity clearly affects the success of the treatment regimen. The results of this study can contribute to the development of a therapeutic strategy that combines MEK inhibitor functional monitoring with tumor cell growth control. [ABSTRACT FROM AUTHOR]

Traditional linear active disturbance rejection control (LADRC) may have difficulty to achieve a rapid precise disturbance rejection for a permanent magnet synchronous linear motor (PMSLM). By making use of model information, a model predictive and compensated LADRC (MPLADRC) method is proposed in this paper. In this method, a model compensated extended state observer (MESO) is designed to transform the controlled object into an established mathematical model through total disturbance compensation. Meanwhile, considering the delay problem of MESO, a phase advance module is designed to improve the estimation speed of MESO for system disturbance and state, thus the MESO can rapidly compensate various uncertainty disturbances to the controlled object in real time. The model predictive controller (MPC) is then designed based on the mathematical model, and its optimal control law is then obtained through a quadratic objective function to further suppress the disturbance unobserved by the designed MESO. The proposed method can thus realize a dual-degree-of-freedom disturbance rejection through the MESO and MPC. The simulation and experimental results validate the effectiveness of the proposed MPLADRC in rapid anti-disturbance and fast positioning for the motion control of the PMSLM. • An MPLADRC method for achieving real-time disturbance rejection is proposed. • A model compensation ESO is designed to accurately estimate the total disturbance. • A phase advance module is designed to solve the ESO delay problem. • A predictive controller is designed to further suppress the disturbance. [ABSTRACT FROM AUTHOR]

• Mathematical model to describe drug delivery to the posterior segment of the eye. • Efficacy of intravitreal (IVI), suprachoroidal (SCS) and subretinal (SRS) injections enhanced by iontophoresis. • Protocols based on the use of a series of electric pulses at fixed times, can lead to an optimized SRS or SCS release. • In case of choroidal, retinal or vitreous diseases, SRS injection is the right option. Drug and gene delivery to the eye, namely to the posterior segment of the eye, is one of the most challenging problems for ophthalmologists and pharmacologists. The reason lies in the fact that the eye is protected by multiple barriers that prevent the permeation of xenobiotics and consequently prevent drugs from permeating ocular tissues. Intravitreal injection (IVI), a procedure that releases the drug directly into the vitreous, has become the gold standard for the treatment of posterior diseases. However, due to its invasiveness, several complications can occur. Medical and pharmaceutical researchers are continuously looking for new compounds, new access routes and new ways of enhancing the release. In recent years, two less invasive routes, subretinal space (SRS) and suprachoroidal space (SCS), have received considerable attention, to target the posterior segment of the eye. The aim of the paper is to present a mathematical model that simulates the coupling of an electric field with SRS or SCS injections, and to show how drug distribution compares with the gold standard, IVI. The model is represented by coupled systems of parabolic and elliptic partial differential equations. The ocular barriers are described with a certain detail. A priori estimates establish qualitative properties of the total mass released. Numerical simulations, in different scenarios, illustrate the comparative behaviour of the three treatments for short and long times. The evolution of mean drug concentration in the different ocular tissues, with and without electrical assistance, is studied. [ABSTRACT FROM AUTHOR]

This research paper proposes a hybrid Whale Optimization Algorithm (WOA) variant based on Equilibrium Optimizer (EO), named Equilibrium Whale Optimization Algorithm (EWOA). The major finding lies in an efficient hybridization of bio-inspired (WOA) and physics-based (EO) metaheuristic algorithms. Upon mathematical modelling, EWOA proposes a main architecture that combines WOA's encircling and net-bubble attacking mechanisms via EO's weight balance strategy. The proposed algorithm was tested on 23 classical, 28 constrained CEC 2017, 30 unconstrained CEC 2017, 10 CEC 2019, and 10 CEC 2020 benchmark problems, in comparison with six recently proposed state-of-the-art algorithms (including WOA and EO). EWOA outperforms other algorithms with the best statistical mean performance on 46 out of 101 functions and the most promising clustering data in the graph, respectively. The fact that EWOA could achieve best statistical SD performance on 2 of the total 5 benchmark sets proves that EWOA is competitively robust. EWOA can converge to the optimum before 50% iterations of most benchmark functions, achieving the fastest convergence rate compared to other algorithms. The major contribution thereby lies in the successful development of this hybrid algorithm, which yields better optimization efficiency than the original and other state-of-the-art algorithms in terms of statistics, convergence and clustering. [ABSTRACT FROM AUTHOR]

Spherical wind-blown Tumbleweed rovers have the potential to significantly expand the type of interplanetary terrain that can be explored on planets such as Mars. Multiple tumbleweed designs have been studied by NASA's Langley Research Center and Jet Propulsion Laboratory, and one promising design, the box-kite model, relies on internal sails to maneuver over rough terrains with the help of mass actuation within the rover chassis for directional control. This paper sets out to parametrically study the effect of actuating masses on Tumbleweed rover performance. As a first step towards evaluating the performance of a spherical Tumbleweed rover, we study a planar model in this paper. To accomplish our parametric study, a dynamic model and control scheme for a planar tumbleweed rover has been developed with four moving masses within the structure, and a prototype was built based on the model and proposed control scheme. The prototype was used to establish the validity of the dynamic model, and the dynamic model was then used to study the effect of rover diameter, mass actuation speed, and chassis-mass-to-actuating-mass ratios on the performance of the tumbleweed rover. From these studies it was found that the final angular speed of the rover decreases with increasing rover diameter, while the rover linear speed increases with diameter. The time taken to reach a desired angular speed was found to increase with increasing rover diameter for all cases. Additionally, final rover angular speed and linear speed were shown to increase with actuating-mass-to-chassis-mass ratio, and the time taken for reaching a desired angular speed and linear speed, i.e. settling time, was found to decrease with increasing actuating-mass-to-chassis-mass ratio. • Dynamic model of planar tumbleweed rover derived and validated via prototype. • Parametric study conducted on the effect of design parameters on rover performance. • Rover speed found to increase with increasing moving-mass- to-chassis-mass ratio. • Rover speed found to increase with increase in control mass speed. • Smaller rovers found to be more apt at braking as compared to larger rovers. [ABSTRACT FROM AUTHOR]

In this paper, a model predictive direct power control (MP-DPC) with power compensation and circulating current reduction is proposed for modular multilevel converter under unbalanced grid conditions. The main objectives of this paper are to achieve the circulating currents reduction and the power ripples elimination under unbalanced grid-side voltage conditions. In order to realize the aforementioned objectives, a triple-stage MP-DPC method based on a decoupled mathematical model of circulating current and DC-link current components is presented, which results in the elimination of weighting factors. Meanwhile, a power compensation term is embedded in the proposed design so as to eliminate the power ripples. In this sense, the power compensation terms are expressed by grid voltages and their quadrature signals without the complex positive/negative sequences extraction of grid voltage/currents and phase-locked loop. The proposed methodology can not only relieve the effect of circulating currents but also eliminate the active and reactive power ripples while remaining computationally feasible under unbalanced grid conditions. Additionally, a reduced switching frequency approach is introduced to decrease the power loss. Finally, the effectiveness of the proposed MP-DPC method is validated by both simulation and experimental results. • A triple-stage FCS-MPC method is proposed to regulate multiple control objectives of MMC, which results in the elimination of weighting factors. • To enhance the grid-side power quality, the proposed strategy takes power compensation scheme into consideration under unbalanced grid-side conditions. • Compared with the conventional MP-DPC method, the circulating current and switching frequency are restrained in this design while not punishing the computational complexity. [ABSTRACT FROM AUTHOR]

This paper analyzes the system describing the absorption solar collector as an application of nanoparticles for the storage of solar energy. The system involves two fractional partial differential equations (FPDEs) utilizing the Caputo fractional definition (CFD). Explicit solutions are determined for the temperature and velocity in terms of the Wright function (WrFn) via Laplace transform (LT). In addition, the solutions are expressed in terms of some well–known special functions at selected values of the fractional–order. Moreover, the behaviors of the temperature and velocity are investigated graphically using the thermo–physical data of the Cu/Al 2 O 3 –nanoparticles. Furthermore, some numerical results are conducted about the performance of the Cu and Al 2 O 3. The results reveal the higher efficiency/performance of the Cu–nanoparticles over the Al 2 O 3 and thus copper enjoys higher capability than alumina for the purpose of solar energy storage. In addition, it is found that 1.41% in the enhancement of heat transfer is achieved by adding 1% of the Cu–nanoparticles while the corresponding enhancement rate of the other three nanoparticles was less. Besides, the enhancement rate reaches 7.1% by increasing the volume fraction of the Cu–nanoparticles to 5%. Furthermore, the enhancement rates for the TiO 2 , Ag, and Al 2 O 3 are 5.41%, 6.47%, and 6.53%, respectively when using 5% of these nanoparticles. Finally, the advantages/effectiveness of the current approach over a previous work in the literature are discussed in detail. [ABSTRACT FROM AUTHOR]

In this paper, the application of spatial partial differential equation in user intent oriented information mining is proposed. The hybrid mining algorithm is used to avoid the defects of a single algorithm, which makes the discovery and identification of user intent efficient and practical. The v-svc algorithm can suppress the classification of errors, the hierarchical generation based on attributes can easily get the focus of services, and the fuzzy clustering method can get the service level or service quality of users. This method can be used for any complex object research similar to user intention and the evaluation mechanism of a research object. In view of the problems of traditional methods, this paper puts forward the technology of association mining based on the mathematical model of partial differential classification, and makes an experimental comparative analysis. The results show that the convergence, stability and performance of this method are good. [ABSTRACT FROM AUTHOR]

Three-phase PWM rectifiers are adopted extensively in industry because of their excellent properties and potential advantages. However, while the IGBT has an open-circuit fault, the system does not crash suddenly, the performance will be reduced for instance voltages fluctuation and current harmonics. A fault diagnosis method based on deep feedforward network with transient synthetic features is proposed to reduce the dependence on the fault mathematical models in this paper, which mainly uses the transient phase current to train the deep feedforward network classifier. Firstly, the features of fault phase current are analyzed in this paper. Secondly, the historical fault data after feature synthesis is employed to train the deep feedforward network classifier, and the average fault diagnosis accuracy can reach 97.85% for transient synthetic fault data, the classifier trained by the transient synthetic features obtained more than 1% gain in performance compared with original transient features. Finally, the online fault diagnosis experiments show that the method can accurately locate the fault IGBTs, and the final diagnosis result is determined by multiple groups results, which has the ability to increase the accuracy and reliability of the diagnosis results. [ABSTRACT FROM AUTHOR]

Radio-Frequency (RF) energy harvesting must cope with the limited availability and high variability of the energy source. In this paper, the modeling of an RF harvester for ultra low power environments is presented. A mathematical model based on theoretical analysis is developed. The model demonstrates that the maximum transferred power point is located in a three-dimensional space defined by the input capacitance, the output voltage, and the load resistance of the rectifier circuit. Moreover, the mathematical model returns results in substantial agreement with the SPICE simulation results, while guaranteeing a remarkable reduction of the required computation time. Furthermore, the paper reports the implementation of a mixed signal system for the 3-D MPPT, to be embedded in an RF harvester, in a 65 nm CMOS technology. The circuit exhibits a simulated power consumption lower than 100 nW, making this solution suitable for ultra low power harvesting. Measurement of 24 h of power spectral density, over the [0.7–1] GHz band, in an urban environment in Northern Italy. Image 1 • Theory of the large signal model of an RF rectifier. • Detailed mathematical model of an RF rectifier. • Behavioural simulation of the developed model for 3-D MPPT. • Multiple model validations. • Circuit implementation for the 3-D MPPT and validation. [ABSTRACT FROM AUTHOR]

• A truly meshless method is extended in this paper for solving coupled bedload sediment transport equations. • The method can solve problems which their domains discretized by irregularly distributed nodes , and shows good accuracy. • The method is applicable to cope with complex geometry in practical problems. The discrete least squares meshless (DLSM) method is extended in this paper for solving coupled bedload sediment transport equations. The mathematical formulation of this model consists of shallow water equations for the hydrodynamical component and an Exner equation expressing sediment continuity for the bedload transport. This method uses the moving least squares (MLS) function approximation to construct the shape functions and the minimizing least squares functional method to discretize the system of equations. The method can be viewed as a truly meshless method as it does not need any mesh for both field variable approximation and the construction of system matrices; it also provides the symmetric coefficient matrix. In the present work, several benchmark problems are studied and compared with the work of other researchers; the proposed method shows good accuracy, high convergence rate, and high efficiency, even for irregularly distributed nodes. At the end, a real test problem is performed to show and verify the main benefit and applicability of the proposed method to cope with complex geometry in practical problems. [ABSTRACT FROM AUTHOR]

• Differential manifolds and their tangent spaces are used for motion modelling. • Motions of parallel mechanisms with different constraint singularities are modelled. • Constraint singularities of parallel mechanisms are classified into two kinds. • Singularities causing bifurcated motions, instantaneous DoFs are separated. • Two examples are given to verify the theoretical results. This paper presents investigations into classification and analysis of constraint singularities for parallel mechanisms. Parallel mechanisms (also called parallel manipulators or parallel robots) have wide applications in industry. The singularities tremendously affect their applications. Existing research works show that constraint singularity causes a mechanism to have instantaneous degree-of-freedoms (DoFs) or bifurcated finite motions. However, the intrinsic differences among the conditions under which the specific constraint singularities happen have not been discussed. This paper is focused on these topics by using differential manifolds as mathematical tools. Firstly, the general mathematical models of parallel mechanisms are formulated by respectively describing their finite motions and instantaneous motions in forms of differential manifolds and their tangent spaces. Then, parallel mechanisms having bifurcated finite motions and instantaneous DoFs are modelled accordingly, and the constraint singularities are thus classified into two kinds by considering their influences on motions of mechanisms in both finite and instantaneous motion levels. Finally, two examples are given to further illustrate the theoretical analysis. This paper lays foundations for mathematical modelling and applications of parallel mechanisms with constraint singularities. [ABSTRACT FROM AUTHOR]

• A general mathematical spiral model is deduced for forming the skeleton of rope. • Costello's conclusion is extended to suit universal cases with rigorous proofs. • A novel cross section method (SCM) is put forward and proofed strictly for solving adjacent wires overlapping problem. • A precise geometric modeling of wire rope strands procedure is proposed. • The critical graph of wire radius determination is obtained for simple straight strand. Based on the Frenet frame, this paper proposes a general mathematical spiral model with an arbitrary smooth space curve as the center path, which can accurately build complex skeleton lines of wire rope strands. From the aspect of geometry, all the wires are spatial cylinders and must meet the actual geometric requirements: 1. The center cylinder is tangent or separated from the spiral cylinder; 2. The adjacent spiral cylinders do not overlap each other. For requirement 1, Costello' conclusion is referenced and extended universally to suit an arbitrary smooth space central curve case with rigorous proofs. For requirement 2, the overlapping problem is described as obtaining the minimum distance between the two adjacent spatial path curves, which is deduced by a novel cross section method (SCM) with rigorous proofs and solved by the General Particle Swarm Optimization (PSO) algorithm. Based on the above models, the geometric modeling of wire rope strands procedure is proposed and implemented on the platforms of MATLAB and SolidWorks. Validations are conducted through geometric graphical representations, compared with those from some previous researches. For the simple straight strand case, when the number of spiral cylinders and spiral radius are given, the critical relationship between the ratio of spiral wire radius to spiral radius and the spiral angle is firstly obtained, which can be a precise dimension design reference of simple straight strand for eliminating initial geometric overlap. Further, to show the advance, some precise graphical examples of complex wire rope strands like independent wire rope core (IWRC) and multilayered rope are presented. The wire rope strands geometric modeling method proposed in this paper is precise enough averting initial geometric overlap between the wires for the benefit of subsequent mechanical computation accuracy and efficiency. [ABSTRACT FROM AUTHOR]

• The paper focuses on a pick-up routing problem with a three-dimensional (3D-PRP) loading constraint. • The paper combines genetic algorithm for pick-up routing with machine learning for three-dimensional loading problem. • K-means algorithm is developed for clustering phase. • The paper includes four expert systems. • Results of a real dataset are highly promising. This paper presents a combinatorial problem called a pick-up routing problem with a three-dimensional (3D-PRP) loading constraint, clustered backhauls at the operational level, and train loading at the tactical level for an intermodal transportation network. A two-phase approach, called clustering first, packing-routing second, is proposed for use during the first stage. The clustering of backhauls is carried out using the k-means algorithm. A hybrid approach is provided, which combines the packing of orders by first solving a 3D loading problem for each cluster using machine learning with a best-fit-first strategy, with routing using a genetic algorithm. During the second stage, the train-loading problem is solved using a mixed integer programming approach to minimise the total costs by incorporating various cost types, in which detention and demurrage costs are taken into account. All solution approaches are computationally evaluated on real-world data provided by an international logistics firm and new randomly generated instances. Comparisons are carried out using both exact solution methods and heuristic approaches, and the proposed approach was shown to be more effective for real-world problems. [ABSTRACT FROM AUTHOR]

• Evolution and disappearance of condensation of R507A refrigerant in pipe mini-channels. • Condensation process occurring in mini-channels. • Comparison of the results of experimental studies with R404A obtained for R507A. • Proposition of a regression function for the description of dynamic instability. This paper presents the results of experimental research and mathematical modelling on the influence of dynamic instabilities on the condensation phase change of R507 refrigerant in tubular mini-channels. This agent is currently being utilised as a temporary substitute for R404A, with R448A intended as the target substitute. In addition to the results, this paper contains a dimensional analysis procedure based on the Π-Buckingham theorem that has allowed for the development of a regressive model for the velocities of the dynamic instabilities. The experimental part of this paper was conducted using tubular mini-channels with internal diameters of 1.44, 2.3, and 3.3 mm. [ABSTRACT FROM AUTHOR]

Mathematical modelling and simulation represent a significant portion of quantitative modelling efforts in the field of construction supply chain management. A gap exists in understanding the current research status of mathematical and simulation modelling in this field. This paper provides a systematic literature review from 179 journal articles to synthesise these modelling techniques that are applied to construction supply chain management. Three research questions, focusing on characteristics of construction supply chains captured, model applications, and construction supply chain problems modelled, are proposed. A framework comprising three structural dimensions is developed to answer formulated research questions. Findings suggest mathematical modelling dominates current research in construction supply chain modelling. Ten future research trends are also proposed. This paper successfully outlines how mathematical, simulation and hybrid models can contribute to construction supply chain management. • Mathematical and simulation models in CSCM are reviewed based on 179 articles. • Mathematical optimisation dominate this field, and the use of simulations should be revisited. • More effort should be dedicated to modelling how to close the CSC loop. • Research gaps are identified, and ten future directions are proposed. [ABSTRACT FROM AUTHOR]

• The mathematical model of ASC and its calculation method are proposed. • The model of optimized ASC (OASC) is proposed, which can further exploit the ASC. • The ASC obtained is complete and precise as it considers all load growth patterns. • The ASC obtained can be used for real-time evaluation of supply capability margin. This paper proposes the mathematical model, and calculation method of available supply capability (ASC) for distribution systems. Firstly, the mathematical model for ASC is established, considering all allowed load increments from the present operating point to the security boundary of a distribution system. Secondly, the calculation method for the ASC model is proposed. The results of the proposed method can describe the available supply capability of a distribution system completely, including not only the ASC values, but also some other important data, such as all load growth patterns and cross-boundary points when the system reaches its security boundary. Finally, an IEEE RBTS test system with DGs is used to demonstrate the proposed models and method. Similar to the ATC of the transmission systems, the proposed ASC is an important operational index that can help operators accurately evaluate the supply capability margin of a distribution system. The ASC relevant operational guides are also given in this paper. This work lays the foundation for establishing the ASC theory for distribution systems, which corresponds to the ATC theory for transmission systems. [ABSTRACT FROM AUTHOR]