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The aim of this paper is the development of a mathematical model to compute the optimal inventory mix to face stochastic demand at minimum cost in a two-level supply chain. The paper addresses a multi-product dynamic lot-sizing problem under stochastic demand subject to capacity and service level constraints. This model is executed to compare a Make To Order (MTO) strategy to a Vendor Managed Inventory (VMI) partnership between the supplier and their customers. Both strategies provide the demand order to be produced. A schedule of production orders is determined over the planning horizon in order to minimize the inventory holding costs of the supply chain, taking into consideration that the supplier is also responsible of initiating the replenishment orders and deliveries of their customers according to the VMI partnership. The simulation model is illustrated empirically using a real case study: a paper manufacturing company that pursues to improve customer service level and supply chain inventory costs through a proper production planning of their paper machines and a suitable VMI order replenishment schedule. [ABSTRACT FROM AUTHOR]

Stochastic cellular automata for rock-paper-scissors games are related to Lotka-Volterra model. Simulations are usually performed by two methods local and global interactions. It is well known that the population dynamics with local interaction is stable, where all species coexist. In contrast, global interaction leads to extinction. So far, theories such as mean-field theory and pair approximation have been presented, but they never explained the stable dynamics in local simulation. In the present article, we apply effective medium approximation (EMA) which has been developed in Physics. The effective medium is determined in a self-consistent way. The EMA theory well predicts the stability of population dynamics. Moreover, it fairly explains the aggregation of each species observed in the stationary state. [ABSTRACT FROM AUTHOR]

We propose a new concept which is a generalization of fuzzy soft subset and fuzzy soft equal. Using such notions, we will be able to consider the distributive law of fuzzy soft sets. Using the distributive law of fuzzy soft sets, we point out that the distributive law of trapezoidal fuzzy soft sets as proposed by Xiao et al. (2012) is not true. The correction will further improve further extensions of the results of Xiao et al. (2012). We will also establish the generalized distributive law of trapezoidal fuzzy soft sets along with illustrative examples. [ABSTRACT FROM AUTHOR]

The mealybug (Paracoccus marginatus) is one of the most important pests of papaya (Carica papaya L.). The high potential damage of this pest threatens papaya production. The objective of this paper is to explore the impact of biocontrol and temperature variations on the population dynamics of Paracoccus marginatus (P. marginatus). We first propose and study a mathematical model for the dynamics of P. marginatus within a papaya field. This model consists of a time-delayed non-autonomous system of differential equations that takes into account the egg incubation period, temperature variations, plant compensation and predators that are natural enemies of the papaya pest. We provide the basic properties of the model, compute the basic offspring number N 0 and show that there exists two threshold parameters N _ 0 and ξ 0 such that N _ 0 ≤ N 0 ≤ ξ 0 ≤ 1 and N 0 ≥ N _ 0 > 1 provide conditions for the extinction and persistence of the pest within the papaya field, respectively. After, we investigate the impact of biocontrol on the pest population. We found that the use of a control strategy based on constant releases of predators could reduce the pest population by 35.62 percent and increase the biomass by 77.50 percent, while the use of impulsive releases of predators result in a decrease of 96.31 percent of the pest population and an increases of 55.74 percent of the biomass. We also combine the use of continuous predator releases and bio-pesticides and discovered that a spray applied 90 days after germination could completely eliminate the pest population and boost the biomass by 81.58 percent. • The population dynamics of Paracoccus marginatus , papaya pest is modeled. • The model includes the egg incubation period, temperature variations and biocontrol. • The warm temperatures are favorable to the development and survival of the pest. • The use of impulsive releases of predators can reduce the pest by 96.31%. • The use of continuous releases of predators and bio-pesticides can eradicate the pest. [ABSTRACT FROM AUTHOR]

Two-phase flows under microgravity conditions play a crucial role in Space technology and science. Studying the behavior of dispersed droplets suspended in a gas flow and their influence on the characteristics of the carrier flow is the main task of computational modeling of turbulent two-phase flows. To understand the features and predict the behavior of such flows, along with experimental studies, it is necessary to develop mathematical models, which adequately describe all the basic physical and chemical processes in a gas-droplet environment at different scales. In this paper we obtain solutions for the problem of two droplets collision, using solutions for cumulative jets, and propose droplet collision outcome criterion. This research will focus on the process of two interacting droplets coalescence into one and coalescence with subsequent separation into two or more droplets. A semi-analytical method has been developed for application of the solution of the cumulative jet problem to the problem of droplet collision. A differential equation has been obtained that describes the following possible outcomes of droplet collision: coalescence and coalescence with subsequent separation. A criterion for determining the outcome of on-head droplet collision has been obtained. In accordance with the developed criterion, the number and size of formed droplets are obtained. The effect of collision on moving droplet evaporation in a heated atmosphere was regarded. • Solutions for the problem of two droplets collision and fragmentation are obtained. • A differential equation has been obtained that describes droplet coalescence or atomization. • A criterion for droplet fragmentation has been obtained. • The effect of collision on moving droplet evaporation in a heated atmosphere was regarded. [ABSTRACT FROM AUTHOR]

Earth observation satellite (EOS) scheduling is critical for improving the performance of Earth observation system. Most of the existing studies on satellite observation scheduling problems focus on static tasks and real-time dynamic tasks also known as emergency tasks while few attempts have been made for common dynamic tasks yet. The common dynamic tasks are characterized by uncertain arrival times and delayable observations while the emergency tasks require immediate observations. The number of common dynamic tasks is rapidly increasing with the expansion of satellite observation applications, which poses great challenges to EOS observation scheduling. To address this issue, this paper investigates the satellite observation scheduling problem with common dynamic tasks. Firstly, a centralized onboard dynamic scheduling framework based on a periodic-triggered rolling horizontal optimization (RHO) strategy is proposed and a novel two-stage mathematical model is established for the periodic rescheduling problem. Secondly, we propose a low-complexity onboard periodic rescheduling algorithm (OPR), which consists of a greedy-based task allocation algorithm, a pointer network (Ptr-network) based task scheduling algorithm and an iterative local search algorithm. In the greedy-based task allocation algorithm, we define a Task-EOS Fitness Indicator (TEFI) and each task is greedily allocated to the EOS with maximum TEFI. In the Ptr-network based task scheduling algorithm, the allocated task sets of all EOSs are fed into the Ptr-network in parallel to generate the observation scheduling result. Afterward, an iterative local search algorithm is proposed to further improve the quality of the observation scheduling result. Finally, extensive experiments are conducted to demonstrate the superiority of the OPR algorithm for the satellite observation scheduling problem with common dynamic tasks. [ABSTRACT FROM AUTHOR]

• Reviews the mathematics of the EOQ/EPQ-based reverse logistics models. • It provides a condensed review of the works that stemmed from the work of Schrady (1967). • It identifies significant research gaps and provides future research directions. This paper reviews the mathematics of the economic order/production quantity (EOQ/EPQ)-based models in the reverse logistics (RL) literature. It starts with the seminal work of Schrady (A deterministic inventory model for reparable items. Naval Research Logistics Quarterly, 14(3), 1967, 391–398) up until December 31, 2022. It provides researchers with a road map of how the mathematics has evolved since the work of Schrady and saves them time and effort by avoiding the need to review the entire RL literature. As it unifies the notations for all reviewed models, it also provides some research pointers for promising topics to be pursued. [ABSTRACT FROM AUTHOR]

Significant dimensional variations may occur in paper-based materials when subjected to changes in moisture content. Moisture induced deformations are governed by the swelling of individual fibres, which is transferred through inter-fibre bonds to the entire fibrous network. Complex interactions between mechanical and hygro-expansive properties take place in the bonding areas, affecting the overall material response. In most network models, the role of these inter-fibre bonds is not explicitly incorporated. This work presents a periodic meso-structural model for the discrete fibrous network, which considers the free-standing fibre segments and inter-fibre bonds. Despite its simplicity, the reference unit-cell enables the incorporation of relevant micro- and meso-structural features such as network structure, fibres and bond geometry and hygro-elastic properties. The proposed model is solved analytically through a proper homogenization strategy, allowing to recover the paper’s anisotropic hygro-mechanical response in terms of effective elastic constants and effective hygro-expansive coefficients, exploiting the coupling at the meso-structural level between hygroscopic and mechanical behavior. A comparison with experimental results obtained from the literature shows that the presented approach is quite accurate in predicting the overall paper response, thereby revealing the influence of several meso-scale parameters (e.g. fibre orientation, dimensions, mechanical strength). [ABSTRACT FROM AUTHOR]

Safe operation of orbital platforms relies heavily on stability of fluid flows in microgravity, which are strongly affected by capillary forces. The paper considers multiphase fluid seepage through a porous medium. Questions of instability of the interface between liquids are discussed. The effect of capillary instability is shown, which was revealed during the processing of experimental data on the imbibition of a porous structure in microgravity conditions during parabolic flights. A mathematical model is proposed to describe the process of multiple imbibition of a porous medium under conditions of variable gravity. The model takes into account hysteresis, various models of capillary pressure are used during imbibition and drainage. The paper also considers a method for modeling the instability by transforming the constitutive equations. The method allows modeling additional blurring of the imbibition front. The results of modeling based on this method for capillary imbibition of a porous medium under microgravity conditions, as well as for the case when chemical interactions occur between flowing fluids, are considered. • The instability of the phase boundary during seepage is considered. • Flows are studied controlling safe operation of spacecraft fluid supply systems. • A new mathematical model for describing the multiple imbibition is proposed • The seepage with chemical interactions between the phases is considered. [ABSTRACT FROM AUTHOR]

The paper considers a process of a controlled attitude motion of a dual-spin nanosatellite. The main goal of control is to achieve a gravitationally stabilized position in a circular orbit in the shortest possible time. The dual-spin nanosatellite contains a gravitational damper and an internal rotor inside a movable unit. The movable unit can fulfill small controlled inclination relative to the main body of the nanosatellite. The mathematical model of the attitude dynamics of the nanosatellite is built and appropriate control laws are developed. Simulation results confirm the performance of the gravitational damper and efficiency of the control algorithm. [ABSTRACT FROM AUTHOR]

Southeastern Turkey perished by the M w 7.8, Kahramanmaras earthquake on February 6, 2023, at 01:17 UT (04:17 LT). The Kahramanmaras-centered event, hit by the break of the East Anatolian Fault Line, is felt in Syria, Egypt, Lebanon, Iraq, and Cyprus on the border of Turkey. Together with Syria, it causes loss of lives and severe damage in 10 cities. This work is dedicated to the people of the region. The study discusses the causality of anomalies by conducting ionospheric anomaly research via the interpolated TEC map obtained from the CODE according to the coordinates of the epicenter of the earthquake (latitude, longitude). The TEC amplitudes are observed by evolving the time-domain TEC map into the frequency-domain with the Fourier transform. The peaks of the amplitudes allow preliminary information for the anomaly days. For the anomaly, the TEC (TECU) boundaries are drawn by the statistical specification. The TEC map outside these boundaries is marked as an anomaly. The causality of abnormalities is tried to be read through the triad of the geomagnetic storm(s) , solar activity , and the earthquake effect. One can find seven anomaly days in the paper. January 30, February 2, 3, 11, 15, 16, and 21 are the anomaly days. The essay probably detects the anomaly before 3 days related to the Southeastern earthquake. • Reads the causality of the earthquake in southeast Turkey (Mw 7.8), through the ionosphere-earth crust relationship. • Notices potential anomalies by presenting the time-domain TEC atlas in the frequency domain with Fourier spectral analysis. • Considering all possible TEC anomaly essentials detect the precursors of the earthquake 3 days before the event day. [ABSTRACT FROM AUTHOR]

Exploring special multi-scroll chaotic systems is meaningful work. This paper studies an expanded multi-scroll chaotic system consisting of eight terms with one nonlinearity. It is generated by modifying the nonlinear term of the newly constructed chaotic system by a polynomial function. The unique mathematical model makes the unstable index-2 equilibria increase in four dimensions, which contributes to the number of scrolls expanding in each phase plane unidirectionally. Dynamic analysis finds that the system can yield complex nested multi-scroll attractors and has single-parameter-based synchronization control of amplitude and offset boosting behavior. Moreover, circuit implementation verifies the physical existence of the proposed system. Also, an image encryption algorithm for remote sensing images is established. Permutation and diffusion operations are performed using new pixel coordinates derived from the data of the chaotic matrix, which comes from the same position as the pixel matrix. Relevant tests suggest that the algorithm is secure and able to resist undesirable interference. • Simple multiscroll chaotic system with various signal control features is proposed. • Complex dynamics, circuit implementation of the proposed system is studied. • New chaos-based image encryption algorithm with high security is designed. [ABSTRACT FROM AUTHOR]

This paper investigates the effects of model fidelity and parameter uncertainty on the performance of a hybrid model-based feedback-feedforward control scheme for attitude tracking of a satellite with flexible appendages. The feedforward component is an inverse model-based term produced through a computational approach known as inverse simulation (InvSim), which works by iteratively solving a discretised reference trajectory. The hybrid controller's feedback is proportional-derivative (PD) based, using body attitude and rate feedback to provide stability and robustness. Furthermore, to ensure that the flexible modes do not trigger instability, the PD control gains are tuned to give a closed-loop response that is significantly slower than the flexible modes. Additionally, excitation of the flexible modes is reduced by minimising jerk through polynomial rest-to-rest manoeuvres, following the shortest quaternion path using spherical–linear-interpolation (SLERP). The effects of the appendage flexing on attitude tracking are then compensated through the feedforward element of the hybrid controller, with performance being compared to a traditional PD tracking law. The effect of the model fidelity on the performance of the hybrid controller is investigated through the use of both rigid body and multiple-fidelity finite-element mathematical models. Additionally, the effect of uncertainties in the model parameters is investigated to determine the accuracy of the model required to obtain significant improvement in attitude tracking. It is found that in the absence of any model parameter uncertainty, the hybrid controller outperforms the PD tracking control law by at least one order of magnitude when the finite-element model is used. Increasing the number of finite elements was found to provide no significant improvement in performance, with one element being sufficient and favourable with its lower computational overhead. It was also found that to ensure good performance compared to the PD tracking controller, the uncertainty in the inertia tensor should be < 1%. Similarly, uncertainty in the first flexible modal frequency should be < 0.5 rad/s. • Inverse simulation (InvSim) used to produce model-based feedforward control. • Combined with PD feedback to improve attitude tracking. • Effects of model uncertainty and fidelity on model-based control investigated. [ABSTRACT FROM AUTHOR]

Physics-informed neural networks (PINN) architectures have been recently explored to accelerate hemodynamics simulations by leveraging mathematical models for blood flow and empirical data. In this paper, a variable separated physics-informed neural networks based on adaptive weighted loss functions (AW-vsPINN) is developed for blood flow model in arteries. In particular, sub-neural networks are proposed to separately predict the unknown scalar state variables by sharing the same input layer. The AW-vsPINN adaptively adjusts the weights of loss terms by the minmax algorithm, which will be updated synchronously along with the network parameters and can balance the contributions of different loss terms during training. The two-stage optimization is implemented to train the neural networks. Specifically, the Adam optimizer is iterated for initial steps with the learning rate generated by the inverse time decay scheduler, and then the L-BFGS optimizer continues to train until the loss converges. Numerical results illustrate that the AW-vsPINN can remarkably improve prediction accuracy and enhance the ability of generalization compared to the conventional PINN. The proposed AW-vsPINN framework has high potential in predicting the blood flow information in cardiovascular disease. [ABSTRACT FROM AUTHOR]

• 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]

• 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 present comment concerns some doubtful results included in the above papers. [ABSTRACT FROM AUTHOR]

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]

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]

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]

• 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]

• 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]

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]

• 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]

• A mathematical methodology to find the optimal NIR light protocol in transdermal drug delivery; • Strategy based on an optimization problem minimizing the difference between target and simulated drug absorption profile; • The optimization problem relies on a 2D mathematical model for NIR light controlled transdermal drug delivery; • Validation of the transdermal model against laboratory data; • Convergence and stability analysis of a finite difference spatial scheme for a generalization of the transdermal model. Near-infrared light-controlled transdermal drug delivery (NIRTDD) has several advantages over traditional delivery methods, and it is now undergoing extensive research. One prominent aspect of NIRTDD is the possibility of keeping the drug concentration in its optimal therapeutic window using a suitable near-infrared light protocol. The problem is that this ideal protocol is usually unknown. In this paper, we propose a computational tool that aims at solving this issue. The computational tool relies on an optimization problem involving the numerical simulation of a two-dimensional mathematical model for NIRTDD. We also analyze the convergence and stability of a finite difference spatial scheme for a generalized version of this mathematical model. [ABSTRACT FROM AUTHOR]

• An industrial cargo routing problem with split loads motivated from a major steel company is studied. • Cargo-cargo and cargo-ship compatibility and the minimum loading amount for using a ship are considered. • An efficient path flow-based mathematical model is proposed. • The proposed model can reduce the computation time by 67% compared to an arc flow model. This paper presents an industrial ship routing problem with split loads faced by a steel company that exports its steel products to neighboring countries. The problem considers two types of ships: ships with contracts of affreightment and spot ships. It also considers other practical constraints, such as cargo–cargo and cargo–ship compatibility and the minimum loading amount for using a ship. Due to high surcharges for multiple port visits, each ship is allowed to visit at most two loading and two unloading ports. Herein, arc flow-based and path flow-based mathematical models are proposed to solve the problem. Computational experiments show that the path flow model is more efficient than the arc flow model. The path flow model can reduce the computational time by 67% on average and find optimal solutions to real-world ship routing problems in acceptable computational time in most cases. [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]

Compared with the two-valued memristor, the three-valued memristor has higher data density, richer dynamic characteristics, and more potential in digital logic and chaotic circuit. The present model of the three-valued memristor has several limitations. It doesn't perform well enough in three-valued applications since its hysteresis loops are linear and asymmetric. The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this research. To further investigate the electrical characteristics of the three-valued memristor, a circuit emulator of the memristor has been constructed with fundamental components. Multisim simulations and hardware experiments demonstrate the emulator's effectiveness. The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics and lays the foundation for future research. • The mathematical model of the three-valued memristor with nonlinear and symmetric hysteresis loops is proposed in this paper. • A circuit emulator of the three-valued memristor is proposed and verified using hardware and software. • The three-valued memristor application in chaotic circuits shows fascinating dynamic characteristics. [ABSTRACT FROM AUTHOR]

The electrodynamic tether (EDT) system is used as one of the end-of-life disposal technologies to deorbit defunct satellites with the benefit of Earth's magnetic field and plasma environment. However, due to the flexibility of the conductive tether, the orbit-attitude coupling effects as well as the influence of Multiphysics fields, this system suffers from time-consuming computations using complicated mathematical model in long-term simulations. Therefore, this paper proposes a high-fidelity high-efficiency dynamics model for the EDT system, in which the tether libration and transverse motions are described by the articulated model, and the system equations are formulated using recursive dynamics algorithm. Computational cost of the recursive method is compared with a nonrecursive method, and the result shows that with the number of tether elements larger than 15, the recursive method would show better computational efficiency. Since the conductive tether tends to be kilometers long in application, this new model would definitely contribute to the numerical efficiency. In addition, simulations are conducted with 2 and 16 tether elements solutions. By comparing the obtained results, it is found that the two cases show large differences over time. For a long tether, it is reasonable to use a larger number of elements in the dynamics analysis. Besides, in order to suppress the libration motion and avoid unstable states in the EDT system, a current control strategy is proposed and verified by a deorbit simulation in low Earth orbit. • A high-fidelity high-efficiency model is proposed for the electrodynamic tether system. • The recursive method shows better efficiency with the number of elements larger than 15. • Different tether elements would result in large differences in simulation. • A current control strategy is proposed to stabilize the libration motion. [ABSTRACT FROM AUTHOR]

• A model for the population dynamics of age-structured criminal gangs with correctional intervention measures is proposed. • The existence of backward bifurcation is determined by the adolescent population. • We fitted the gang model against the crime data and provide forecast for the cumulative number of reported cases. • Global sensitivity analysis is carried out to determine the parameters that strongly drive the dynamics of the model. • The existence of periodic trajectories (Hopf bifurcation) for the criminal gang model is studied. The prevalence of criminal gang activities in the society has continued to be a huge burden to mankind. Despite several attempts by the government and non-governmental organizations in curtailing the activities of criminal gangs, new criminal gangs are beginning to emerge with associated criminal cases on the high side, thereby causing social unrest. This paper examines the impact of correctional intervention measures on the population dynamics of the criminal gangs in Nigeria, following an age-structured paradigm. The existence of backward bifurcation is presented sequel to the coexistence of gang free equilibrium and gang endemic equilibrium when the reproduction number is less than unity. Also, the model exhibits periodic trajectories (Hopf bifurcation) as a result of coexistence among the criminal gang classes. Using the Nigeria crime data (from 1993 to 2013) as obtained from Elsevier Data in Brief, we analyze the criminal gang model quantitatively and provide the sociological implications of the results. The numerical results obtained from this work show that if at least 60 % of adolescents between 8–17 years who commit crimes are apprehended with prompt prosecution and correction, we can potentially eradicate adolescent delinquencies from the population and thus control the entire criminal gangs' population. [ABSTRACT FROM AUTHOR]

In the state of the art of steel production, the temperature evolution of steel strips is typically controlled to regulate the phase contents indirectly and, with this, their material properties. This paper proposes a novel computationally efficient, real-time capable dynamic model that captures both the temperature evolution and the phase transformations in the steel strip. The steel strip is processed in a cooling section after a continuous annealing furnace. The phase transformations cover the austenite decomposition which is mainly controlled by specifically decreasing the temperature during the cooling process. For this, a phenomenological state-space model is derived, which is inspired by the Johnson-Mehl-Avrami-Kolmogorov and the Koistinen-Marburger model. Phase transformations generally change the specific latent heat of the material, which is captured in the proposed distributed-parameter model of the strip temperature by an energy balance. Lumped-parameter models are used for the temperature evolution of the wall, the rolls, and the radiant tubes. Heat transfer due to convection, radiation, and conduction couple the individual thermal submodels. A comparison of simulation results and measurements from both experimental material tests and the real plant operation demonstrate the accuracy and feasibility of the proposed model. The model is computationally inexpensive and serves as a solid basis for advanced real-time control and optimization. • A mathematical model is proposed to describe the evolution of temperature and phases in a steel strip during cooling. • The austenite decomposition is captured by a phenomenological phase transformation model. • The model is computationally efficient and real-time capable. • The accuracy and the suitability of the proposed model is demonstrated by comparing simulation results with measurements. [ABSTRACT FROM AUTHOR]

Due to motion coupling and increased model dependence, the use of nonlinear controllers in real-time applications for aircraft is extremely constrained. This explains why proportional, derivative, and integral (PID) controls are frequently used in practice. However, fast changes in the commanded path and the requirement for high accuracy and tracking performance limit use of PID in landing. This paper presents a design of a decoupled incremental nonlinear dynamic inversion (INDI) controller for performing autonomous landing of a fixed-wing aircraft. The investigation is carried out using the ground effect model and is compared without it. A carrot chasing guidance algorithm is implemented for waypoint navigation to generate the command for the proposed controller's outer loop. The navigational state estimate issue has been resolved using the Cubature Kalman Filter (CKF) approach. Two decoupled CKF algorithms named complementary Cubature Kalman Filter (C CKF) and Integrated Cubature Kalman Filter (I-CKF) are proposed to estimate aircraft navigational states comprised of attitudes, navigational position in terms of latitude, longitude altitudes, and North-East-down velocities. The mathematical model for flare and approach trajectory is designed and commanded to follow the same by the proposed INDI controller. The effectiveness of INDI have been evaluated in a simulation environment by landing the aircraft in the same runway position at arbitrary wind conditions. The performance of the proposed INDI controller is juxtaposed with a conventional proportional integrator and derivative (PID) based landing controller. The simulation findings demonstrate that the INDI has a competitive edge over traditional PID approaches due to its robust performance, less dependence on model dynamics, and fast command tracking capability required during the flare phase. [ABSTRACT FROM AUTHOR]

This research paper presents a new flexural design approach for cold-formed steel (CFS) built-up sections failing in local buckling, developed following an extensive numerical investigation involving two novel closed built-up sections. At first, a finite element (FE) model using the widely adopted ABAQUS software was constructed and carefully validated against pertinent experimental data available in the literature. A comprehensive validation process which included comparing flexural strengths, deformed shapes, moment-curvature, and moment-displacement curves was performed. Afterwards, the validated FE model was extended to a numerical parametric investigation comprising of 108 simulations involving both three-point and four-point bending cases. Key parameters, including cross-sectional shapes, slenderness, and screw spacing, were varied primarily to facilitate the formulation of the novel design method. The outcomes of this investigation revealed that the current direct strength method (DSM) available in the North American Specifications (NAS) underestimated the bending strength, particularly for the ultra-thin sections. Considering this observation which is consistent with the findings of past research on similar cross-sections, a Generalised Direct Strength Method (DSM-G) was developed by introducing a new mathematical model, which differs from the traditional slenderness limit equations, instead relying on a conservativeness degree-based approach used for modifying the original DSM equations. The DSM-G method demonstrated a better accuracy in predicting the flexural strengths of different built-up sections (including the ones investigated by other researchers), all failing by local buckling. Moreover, the reliability of DSM-G equations was assessed, satisfying the prescribed threshold index limit suggested in NAS. A comprehensive set of guidelines, along with a design example for implementing the DSM-G method, has been presented to facilitate practical application. • FE investigation on novel CFS closed built-up sections is carried out. • Key parameters like cross-sectional profiles/sizes and screw spacing are varied. • Current DSM predictions of the novel sections are inconsistent. • A new mathematical model is proposed for a new generalized DSM (DSM-G). • DSM-G is reliable and is verified against results from current and previous studies. [ABSTRACT FROM AUTHOR]

In the last years, many areas in science, business, and engineering have experienced an enormous growth in the amount of data that they are required to analyze. In many cases, this analysis relies intimately on data visualization and, as a result, graph drawing has emerged as a new field of research. This paper addresses the challenge of drawing hierarchical graphs, which is one of the most widely used drawing standards. We introduce a new mathematical model to automatically represent a graph based on the alignment of long arcs, which we combine with the classic arc crossing minimization objective in hierarchical drawings. We complement our proposal with a heuristic algorithm that can obtain high-quality results in the short computational time required by graph drawing systems. Our algorithm joins two methodologies, tabu search and strategic oscillation (SOS), to perform a fast and effective exploration of the search space. We conduct extensive experimentation that integrates our new mathematical programming formulation and the SOS tabu search that targets large instances. Our statistical analysis confirms the effectiveness of this proposal. [ABSTRACT FROM AUTHOR]

Partial destructive disassembly (PDD) is a crucial tool for enhancing efficiency and reducing disassembly costs when recycling complex end-of-life (EOL) products. Evaluating the feasibility of PDD is crucial for determining its implementation. However, the existing partial destructive disassembly line balancing (PDDLB) problem prioritizes profitability and randomly selects components for destructive, disregarding the feasibility of PDD and the noise pollution resulting from destructive operations. To address this concern, this paper introduces the integration of feasibility evaluation and noise considerations into the PDDLB problem for the first time. Subsequently, a mathematical model is established for the PDDLB problem, aiming to minimize disassembly costs, achieve smoothness balance, minimize the number of stations, and mitigate the adverse effects of noise. Then, an improved grey wolf optimization algorithm (IGWOA) considering feasibility evaluation and noise limitations is developed. It non-linearizes the convergence factor to enhance accuracy in the search for optimality, introduces a Lévy flight operation to further expand the search solution space, and incorporates an interference factor to prevent local optimality. In addition, the superiority of the proposed algorithm in solving different cases is verified by comparing five algorithms for the 25-task example and seven algorithms for the 52-task example in the latest literature. Finally, the proposed method is applied to a real engine case. The obtained results are compared with several classical Swarm Intelligence methods. The comparison results show that IGWOA has advantages due to other group intelligence methods in solving small, medium, and large-scale example. Moreover, the disassembly cost is comparatively low. [ABSTRACT FROM AUTHOR]

This paper presents the calibration of the volume of a tank prover using the gravimetric method. A mathematical model of this calibration has been developed and it is non-linear. An evaluation of measurement uncertainty of the tank prover calibration has been carried out using the "Guide to the Expression of Uncertainty in Measurement" (GUM) and the Monte Carlo method. The measurement results have been compared. The influence of calibration conditions on the validation of GUM method by means of the Monte Carlo method (MCM) has been investigated computationally, as well as the behavior of the expanded uncertainty (GUM method) as a function of these calibration conditions. Seven case studies have been analyzed in this research work. In reference case, the tank prover calibration is carried out in the normal laboratory condition. In other case studies, the tank prover calibration is modeled in various hypothetical situations, such as change in tank prover scale quality, variation of calibration water density during calibration, large temperature gradient of water inside the tank prover and combination of the above conditions. In general, GUM method has not been validated by MCM due to one or more of the following conditions: a) the dominant source of uncertainty is a rectangular distribution; b) the uncertainty budget contains large uncertainty and the measurand model is non-linear; c) the measurand probability distribution is not normal. • The tank prover volume has been calibrated using the gravimetric method. • A mathematical model of the measurand has been conceived and it is non-linear. • The analysis of uncertainty of the tank prover calibration has been developed using GUM approach and Monte Carlo method (MCM). • The influence of calibration conditions on the validation of GUM method by MCM has been investigated in case studies. [ABSTRACT FROM AUTHOR]