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Drying of a coated paper is modeled and simulated. The paper sheet is assumed to form three zones, and each zone has its own drying mechanism. Coupling of energy and mass balances must be used in order to solve differential equations. The simulations are carried out in various drying conditions i.e., only hot air drying, only radiant drying, and mixed hot air-radiant drying. Also the effect of one side and two side assumption on evaporation is studied. Effect of venting air speed and radiant heat source presence and its distance from the drying surface on the drying of a coated paper has been studied. It is found that both distance and venting air speed are inversely related to drying in mixed hot air-radiant drying. Both surfaces participate in evaporation however, during the last time of drying, no difference between the upper and the bottom surfaces exist. [ABSTRACT FROM AUTHOR]

Calendaring is an important operation in pulp and paper mill, with an objective to increase the smoothness or reduce the roughness of paper. Bypassing calendering operation in paper machine, paper of desired quality cannot be produced. In the present investigation, a nip mechanics model for supercalendering has been developed by expanding Meijers nip mechanics model up to fourth term, and using this model the effect of additional fourth term and various design and process parameters on results of supercalendering has been discussed using the data taken from paper industry. [ABSTRACT FROM AUTHOR]

This editorial paper presents the papers published in a special issue devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is proposed in three parts. First, motivations and objectives are presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous features of the complex system under consideration. Subsequently, the contents of the papers in this issue are presented referring to the aforementioned complexity features. Finally, a critical analysis of the overall contents of the issue is proposed, with the aim of providing a forward look to research perspectives. [ABSTRACT FROM AUTHOR]

The unrelenting trend of larger and larger sizes of Software Systems and data has made software comprehensibility an increasingly difficult problem. However, a tacit consensus that human understanding of software is essential for most software related activities, stimulated software developers to embed comprehensibility in their systems' design. On the other hand, recent empirical successes of Deep Learning neural networks, in several application areas, seem to challenge the tacit consensus: is software comprehensibility a necessity, or just superfluous? This introductory paper, to the 2020 special issue on Theoretical Software Engineering, offers reasons justifying our standpoint on the referred controversy. This paper also points out to specific techniques enabling Human Understanding of software systems relevant to this issue's papers. [ABSTRACT FROM AUTHOR]

The paper is devoted to the theoretical analysis of one-dimensional (1D) models of blood flow. The non-Newtonian nature of blood is taken into account. The generalized Newtonian models, in which the dynamic viscosity is dependent only on the shear rate, are considered. The models are constructed by averaging the simplified Navier–Stokes system in cylindrical coordinates. The 1D models, corresponding to Newtonian, Power Law, Carreau, Carreau–Yasuda, Cross, Simplified Cross, Yeleswarapu, Modified Yeleswarapu, and Quemada models, are compared in this paper. The comparison is performed in order to estimate the influence of non-Newtonian frictional terms, velocity profiles and hematocrit values on the deviations of the solutions from the solution for the Newtonian case. For this purpose, two problems that can be solved analytically are considered: problems for the infinite interval and finite interval with periodic conditions. For the quantitative comparison of solutions, the non-Newtonian factor, which characterizes the relative deviations of solutions from the solution for the Newtonian model, is introduced. The analytical solutions of nonlinear problems are obtained by the perturbation method. As it is demonstrated for both solved problems, the relative deviations increase with the flattening of the velocity profile. For the models that depended on hematocrit, the non-Newtonian factor values increased with the increase in hematocrit value. The solutions obtained in the paper can be used as a tool for the comparison of different 1D models of blood flow and for the testing of programs that implement numerical algorithms. [ABSTRACT FROM AUTHOR]

Asynchronous temporal Boolean Networks (ATBNs) are more complex in structure and have different linear expressions compared to traditional synchronous Boolean networks. The complexity depends on the number of updated nodes. The main contribution of this paper is to propose results of synchronization and anti-synchronization problems of ATBNs. First, this paper abstracts two Temporal Boolean Networks (TBNs) into a mathematical model, and provides a linear expression of the network by means of the semi-tensor product (STP) tool. Second, based on the asynchronous updating scheme of temporal Boolean networks, we investigate the synchronization (including complete synchronization and anti-synchronization) of ATBNs, and provide two results to guarantee the synchronization and anti-synchronization. Finally, we provide two examples to verify the correctness of our theorems and corollaries. [ABSTRACT FROM AUTHOR]

This paper surveys the theory of functional identities and its applications. No prior knowledge of the theory is required to follow the paper. [ABSTRACT FROM AUTHOR]

In the present scenario, the main aim of each and every organization is to be competitive, eco-friendly, and sustainable in order to run effectively and efficiently. Therefore, to meet and fulfill the above objectives, each organization must identify and choose the appropriate and best green and sustainable supplier, as a green supplier considers green technology, green products, green packaging, etc., while a sustainable supplier considers all three characteristics of sustainability, namely social, economic, and environmental. The problem of the evaluation and selection of green and sustainable suppliers is an example of a multi-criteria decision-making (MCDM) problem. In this research paper, to handle the uncertainty hidden in the green supply chain, the extended version of a MCDM technique named fuzzy additive ratio assessment (F-ARAS) is implemented for the evaluation of the relative weights of the green and sustainable supplier selection criteria, namely social, economic, and environmental, and also to determine the best green and sustainable supplier through fuzzy theory by using linguistic terms, which includes the application of interval-valued triangular fuzzy numbers (IVTFNs) in an organization. Finally, the technique, F-ARAS, has performed well and enables the organization's managers to attain their required solution and final decision. [ABSTRACT FROM AUTHOR]

Load flow (LF) analysis is one of the most important aspects in power system studies. It is the most significant and necessary way to investigate the problems in power system operation and planning. The LF problem comprises a set of nonlinear algebraic equations that must be solved mathematically through iterations. The solution convergence is the most important criteria that is largely affected by the size of power system, which continues to increase in the current modern power system field. Thus, there is no guarantee that the iterative approaches will converge to a valid solution for problems with such large dimensions. This paper develops generalized, effective and simple mathematical models for the solution of the LF problem. The problem is first solved by Gauss–Seidel (GS) method in order to generate the training data. Eureqa software is then adopted for the purpose of data training and mathematical models generation. The models relate bus voltage magnitudes and angles as output parameters with the load active and reactive power values as input parameters. To study the validity of the proposed approach, the mathematical models have been developed for two benchmark test systems; IEEE 5-bus test system and 9-bus test system developed by Western Systems Coordinating Council (WSCC). When compared with the outputs resulting from GS technique, the results have shown efficient and accurate capability of the generated models for evaluating bus voltages magnitudes and angles as well as generated reactive power. The models have also been compared with other published research. The results have shown efficient performance of the developed models. [ABSTRACT FROM AUTHOR]

This paper presents an analytical solution to the model. By solving the system of nonlinear reaction-diffusion equations using Akbari–Ganji's method (AGM), we can derive the semi-analytical expressions for substrate and oxidized and reduced mediator concentrations. These models provide information about enzyme electrode mechanisms and their kinetics. These modeling results can be helpful for sensor design, optimization, and determining how the electrode will react. Further, we studied the effects of many physical and biological parameters on model prediction. The mathematical equations, which are nonlinear partial differential equations, are solved using AGM. Also, we derived the semi-analytical results for concentrations for saturated and unsaturated kinetics. It is verified that the proposed solution is validated by comparing it with numerical solutions. [ABSTRACT FROM AUTHOR]

A signed network Σ = (G , σ) with the underlying graph G = (V , E) , used as a mathematical model for analyzing social networks, has each edge in E with a weight 1 or − 1 assigned by the signature function σ. In this paper, we deal with two types of Detour Distance Laplacian (DDL) matrices for signed networks. We characterize balance in signed social networks using these matrices and we compute the DDL spectrum of certain unbalanced signed networks, as balanced signed networks behave like unsigned ones. [ABSTRACT FROM AUTHOR]

Traditional physics-based mathematical models of viscoelastic (VE) damper often exhibit different degrees of prediction errors under complex working conditions, whereas data-driven approaches have shown significant potential for overcoming such problems, and have not been introduced into any study to describe the dynamic mechanical properties of VE damper. In this paper, the architecture of microsphere model is adopted to represent the spatial distribution of molecular chain structure of VE damping material, which is categorized into free chains and elastic chains. Then, the physics-informed neural network surrogates are introduced to describe the statistical stress–strain behaviors of free chains and elastic chains. Finally, by constructing the physics-constrained loss function based on the combination of physics-based model and data-driven model, a physics-constrained data-driven model is proposed to characterize the dynamic mechanical behaviors of VE damper used for structure vibration control. Based on the existing experimental data, the prediction ability and robustness of the proposed model are comparatively verified, the results reveal that the proposed model can accurately reflect the stiffness and energy dissipation of VE damper under different ambient temperatures, excitation frequencies, and deformation conditions. This study proves the potential of physics-informed neural network theory in characterizing the complex mechanical behaviors of VE damper. [ABSTRACT FROM AUTHOR]

Every fluid problem is greatly affected by its boundary conditions, especially the near-shore seabed could produce an irrevocable harm when a tsunami wave is approaching, and a real-life mathematical model could stave off the worst effect. This paper assumes that the unsmooth seabed is a fractal surface, and fractal-fractional governing equations are established according to physical laws in the fractal space. The geometrical potential theory is used to explain the force produced by the wave surface, and Kong-He friction law is applied to further figuring out the local and memory properties of the friction along the fractal boundary. This paper aims at studying tsunami waves in a fractal space, rendering a reliable mathematical model for both prediction of the tsunami motion and the coastal protection. [ABSTRACT FROM AUTHOR]

The mathematical skeleton of a complex form has been essential for a variety of scientific fields and of great interest to many researchers for decades. It is based on several concepts such as the reconstruction of forms and image processing. This paper aims to develop a novel mathematical algorithm to approximate the skeleton of a non-polygonal shape and to compare it to the most used methods. The mathematical technique of skeletonization is used as a reference to validate and compare the proposed method to the most used ones. The crux of the proposed technique is to Cartesianize the shape (polygonize in 2D), then skeletonize it. Moreover, this novel method is grounded upon the construction of bisectors on the simplex of the corresponding Cartesianized shape. Python is used to implement the algorithm proposed and test it on multiple shapes. The comparison of the results generated by the proposed algorithm and the Python predefined function skeletonize() shows that the proposed method is more effective and could be adjusted through the rate of Cartesianization of the target shape. The major contributions of this novel technique include the mitigation of some issues of existing methods, simplification, and optimization of the processing performance mainly in terms of algorithm complexity. [ABSTRACT FROM AUTHOR]

This paper systematically constructs a multi-project and a multi-objective human resource scheduling mathematical model in construction projects and puts forward an improved genetic algorithm to solve it by aiming at the problems existing in the process of human resource scheduling and optimization. Specifically, first, the basic mathematical models of GPRs and resource-constrained construction project human resource scheduling problem (RCWSP/GPRs) are established, and the multi-project equilibrium problem is extended. Then, an improved inter-cluster separation (ICS) algorithm is proposed and used to solve the RCWSP/GPRs problem. Finally, on this basis, the mathematical model of multi-project and multi-objective human resource scheduling problem and the solution method based on multi-objective-integrated circuit are proposed. At the same time, the resource-constrained multi-project and multi-skill human resource scheduling problem and the integer programming mathematical model under the generalized priority relationship are proposed. Also, the simulation results verify the accuracy of the proposed algorithm and model. [ABSTRACT FROM AUTHOR]

This paper studies the well-known mathematical model's analytical wave solutions (modified Benjamin–Bona–Mahony (BBM) equation), which demonstrates the propagation of long waves in the nonlinear dispersive media in a visual illusion. Six recent analytical and semi-analytical schemes (extended simplest equation (ESE) method, modified Kudryashov (MKud) method, sech–tanh expansion method, Adomian decomposition (ADD) method, El Kalla (EK) expansion method, variational iteration (VI) method) are applied to the considered model for constructing abundant analytical and semi-analytical novel solutions. This variety of solutions aims to investigate the analytical techniques' accuracy by calculating the absolute error between analytical and semi-analytical solutions that shows the matching between them. The analytical results are sketched through two-dimensional (2D), three-dimensional (3D), contour plot, spherical plot and polar plot. The stability characterization of the analytical solutions is investigated through the Hamiltonian system's features. The originality and novelty of this paper are discussed, along with previously published papers. [ABSTRACT FROM AUTHOR]

A broad nontechnical coverage of many of the developments in game theory since the 1950s is given, together with some comments on important open problems and where some of the developments may take place. The reference section given serves only as a minimal guide to the many thousands of books and articles that have been written on this topic. The purpose here is to present a broadbrush picture of the many areas of study and application that have come into being. The use of deep techniques flourishes best when it stays in touch with application. There is a vital symbiotic relationship between good theory and practice. The breakneck speed of development of game theory calls for an appreciation of both the many realities of conflict, coordination and cooperation and their abstract investigation. [ABSTRACT FROM AUTHOR]

In this paper, we study a novel model of the dynamics of alcohol consumption under induced complications. The mentioned model is considered under some advanced concept of fractional derivative called piecewise fractional-order derivative. Currently, most real-world problems are considered under fractional derivatives because of their stable and global behavior. To deal with and detect the crossover behavior in the dynamics of the proposed model, the piecewise derivative containing the Mittag-Leffler-type kernel combined with classical integer order derivatives in piecewise form is used. First, we will investigate the model for qualitative theory in detail. For qualitative theory, we will use fixed point theory. Additionally, we establish sufficient conditions for Ulam–Hyers (UH) stability. To simulate the model, we develop a numerical algorithm based on the Euler technique. The numerical method is applied to present graphically the approximate solutions of the model. In the final part of the paper, we give a detailed discussion of our numerical results. [ABSTRACT FROM AUTHOR]

This paper describes the novel mathematical modeling of the 3-phase induction motor, various operations and study of its dynamic behavior and regenerative braking based on the model. This model uses v/f scheme to apply braking operation with the energy flow to the supply system instead of wasting the energy in braking resistor. It discusses the theory of induction motors, which is explored through both equations and computer simulation model using SIMULINK. The model also helps to study the behavior of the motor during its starting and load variation. The results from the analysis prove the demonstration of regenerative braking and the dynamic behavior and can give an opportunity to learn the different characteristics during these conditions. [ABSTRACT FROM AUTHOR]

In this paper, we study a nonlinear mathematical model which addresses the transmission dynamics of COVID-19. The considered model consists of susceptible (S), exposed (E), infected (I), and recovered (R) individuals. For simplicity, the model is abbreviated as S E I R. Immigration rates of two kinds are involved in susceptible and infected individuals. First of all, the model is formulated. Then via classical analysis, we investigate its local and global stability by using the Jacobian matrix and Lyapunov function method. Further, the fundamental reproduction number ℛ 0 is computed for the said model. Then, we simulate the model through the Runge–Kutta method of order two abbreviated as RK2. Finally, we switch over to the fractional order model and investigate its numerical simulations corresponding to different fractional orders by using the fractional order version of the aforementioned numerical method. Finally, graphical presentations are given for the approximate solution of various compartments of the proposed model. Also, a comparison with real data has been shown. [ABSTRACT FROM AUTHOR]

The original minimum exposure path (MEP) problem in WSNs (wireless sensor networks) requires the starting point and ending point of a moving target to be fixed, thus limiting the evaluation of coverage quality relative to the locations of these points. To resolve this issue, a minimum exposure path problem with various boundaries (VB-MEP) is proposed in this paper. Because the corresponding graph model cannot be established, the original classical methods (grid method and Voronoi diagram method) used to solve the minimum exposure path problem are no longer effective for the VB-MEP problem. This paper first transforms the problem into a hybrid optimization problem with constraint conditions and then considers the characteristics of the transformed mathematical optimization model with high dimensionality, unfixed dimensionality and high nonlinearity so that the deterministic optimization methods are no longer applicable. A hybrid artificial colony solution algorithm that incorporates the actual characteristics of the problem is designed, and a convergence analysis and a proof of the designed algorithm are given. Through simulation experiments based on large-scale node distribution scenarios, it is found that the designed hybrid optimization model with constraints and hybrid artificial bee colony solution algorithm can effectively solve the proposed VB-MEP problem. [ABSTRACT FROM AUTHOR]

This paper reviews the literature on the impact of marijuana decriminalization policy on marijuana smoking prevalence. Due to mixed findings in the existing studies, we attempt to find a common basis to explain the different results across papers. The main purpose is to provide a coherent background as to what outcomes may be expected from certain type of data, econometric models, and explanatory variables. If possible, we also try to provide the explanation as to why certain results are found. [ABSTRACT FROM AUTHOR]

This paper first provides an introduction to the mathematical approach to the modeling, qualitative analysis, and simulation of large systems of living entities, specifically self-propelled particles. Subsequently, a presentation of the papers published in this special issue follows. Finally, a critical analysis of the overall contents of the issue is proposed, thus leading to define some challenging research perspectives. [ABSTRACT FROM AUTHOR]

In this paper, we consider a degenerate hyperbolic inequality in an exterior domain under three types of boundary conditions: Dirichlet-type, Neumann-type, and Robin-type boundary conditions. Using a unified approach, we show that all the considered problems have the same Fujita critical exponent. Moreover, we answer some open questions from the literature regarding the critical case. [ABSTRACT FROM AUTHOR]

Perfect C∗-algebras were introduced by Akeman and Shultz in [Perfect C*-algebras, Mem. Amer. Math. Soc. 55(326) (1985)] and they form a certain subclass of C*-algebras determined by their pure states, and for which the general Stone–Weierstrass conjecture is true. In this paper, we introduce the notion of perfect JC-algebras, and we use the strong relationship between a JC-algebra A and its universal enveloping C∗-algebra C ∗ (A) , to establish that if C ∗ (A) is perfect and A is of complex type, then A is perfect. It is also shown that every scattered JC-algebra of complex type is perfect, and the same conclusion holds for every JC-algebra of complex type whose primitive spectrum is Hausdorff. [ABSTRACT FROM AUTHOR]

This paper has been motivated by the following ecological question: how influential is the water stress on plants production? The aim of this paper is to investigate the impact of water stress and irrigation on plants production. We propose a mathematical model for the dynamics growth of plants that takes into account the concentration of available water in the soil, the absorption of water by plants, water stress, the plants production and the plants compensation. We present the theoretical analysis of the model. More precisely, we show that the model is well-posed. We also compute trivial equilibria and derive a threshold parameter that determines the outcome of water stress within a plantation. Further, we perform a numerical simulation in the case of banana-plantain plant to support and valid theoretical results. We found that the Hopf bifurcation occurs for a specific value of the water absorption rate of unstressed plants. The impact of the water stress on the banana-plantain production is also numerically investigated. We found that the water stress can cause about 62.57% tons of loss of banana-plantain production within a plantation with 1600 rejects initially planted. We also consider the irrigation as a control parameter of water stress. We found that the irrigation increases the stressed plant production to more than 60% for 1600 rejects initially planted. This suggests that climate change may play a detrimental role on banana-plantains production. We also investigate the role of the type of soil in banana-plantain production. Our finding suggests that the Fine Sandy Loam soil is more resilient to water stress than Silty Clay and Loamy soils. [ABSTRACT FROM AUTHOR]

Micro-Electro-Mechanical System (MEMS)-based pressure sensors operating on the principle of piezoresistivity have found profound application in various fields like automobile, aerospace, aviation, biomedical and consumer electronics. Various research studies have been conducted to optimize the design of MEMS-based pressure sensors to meet specific requirements of different fields. Modification in the structure of the piezoresistors placed on these sensors has shown great effect in this regard. However, most of these improvements have been validated through fabrication and measurement, but there has been a lack of significant studies developing analytical models to explain these improvements. This paper studies the performance of a single-turn piezoresistor design on a square silicon diaphragm. The analytical model relates the dimensions of the single-turn piezoresistor on a square diaphragm to the output voltage, and hence, sensor sensitivity is laid out. The correctness of the relation is also validated through Finite Element Analysis (FEA) performed using COMSOL Multiphysics software. Hence, an optimized single-turn design is presented which achieves a sensitivity of 203.57 mV/V/MPa over a pressure range of 0–1 MPa. These results are then compared to work from existing literature. The comparison shows an improved performance which was achieved by optimizing the design through its derived analytical model. The proposed sensor can be utilized in disposable blood pressure measurement system where high sensor sensitivity is required. [ABSTRACT FROM AUTHOR]

With the aim of solving the detection problems for current complex event detection models in detecting a related event for a complex event from the high proportion disordered RFID event stream due to its big uncertainty arrival, an efficient complex event detection model based on Extended Nondeterministic Finite Automaton (ENFA) is proposed in this paper. The achievement of the paper rests on the fact that an efficient complex event detection model based on ENFA is presented to successfully realize the detection of a related event for a complex event from the high proportion disordered RFID event stream. Specially, in our model, we successfully use a new ENFA-based complex event detection model instead of an NFA-based complex event detection model to realize the detection of the related events for a complex event from the high proportion disordered RFID event stream by expanding the traditional NFA-based detection model, which can effectively address the problems above. The experimental results show that the proposed model in this paper outperforms some general models in saving detection time, memory consumption, detection latency and improving detection throughput for detecting a related event of a complex event from the high proportion out-of-order RFID event stream. [ABSTRACT FROM AUTHOR]

In this paper, a mathematical model of the eye corneal shape is introduced which is a nonlinear boundary value problem. This boundary value problem is converted to a nonlinear integral equation and by means of the collocation method, the problem is reduced into a system of the nonlinear algebraic equations. The approximate solutions are obtained by solving this nonlinear system and numerical results are provided to show that introduced method is efficient. Also, comparisons with other works are made to confirm the reliability of the method. [ABSTRACT FROM AUTHOR]

Context: Model comparison plays a central role in many software engineering activities. However, a comprehensive understanding about the state-of-the-art is still required. Goal: This paper aims at classifying and performing a thematic analysis of the current literature. Method: For this, we have followed well-established empirical guidelines to define and perform a systematic mapping study. Results: Some studies (14 out of 40) provide generic model comparison techniques, rather than specific ones for UML diagrams. Conclusion: Fine-grained techniques are still required to support ever-present and complex model comparison tasks during the evolution of design models. [ABSTRACT FROM AUTHOR]

In this paper, we use a previously developed measles model to forecast measles in Turkey for the period 1970–2021. We study the structural identifiability of the model both by hand and using software. By hand, we assume the prevalence and the total population size are given. Using software, we assume the incidence and the total population size are given. The model is structurally identifiable if one of the three parameters is fixed. We notice that Turkey has a significant change in time of the immigration rate and vaccination proportions, so we assume these two quantities are time-dependent. We fit the nonautonomous model to the measles incidences in Turkey for 1970–2021. We perform practical identifiability of the fitted model, and find that all parameters but one are practically identifiable. When fixing the unidentifiable parameter to a value derived from additional data, we obtain that all parameters are practically identifiable. [ABSTRACT FROM AUTHOR]

Game theory is of substantial significance in diverse domains, acting as a potent instrument to comprehend and assess strategic engagements among rational decision-makers. It formulates mathematical models to represent strategic interactions among rational decision-makers in the competitive world. Due to ambiguity in the real-world problems, acquiring the precise payoff values of a matrix game proves challenging. However, in numerous scenarios, these payoffs fluctuate within specific ranges, making them suitable for consideration as interval numbers. This leads to the formulation of a special form of game problem known as the interval valued game problem (IVGP). Some methodologies exist in the literature to find the optimal strategies as well as the value of game for IVGP, but most of them possess some limitations, resulting in the need for proposing a new methodology to find the optimal strategies and value of game. Thus, in this paper, a new solution method for game problems with payoffs represented as interval numbers is presented, utilizing the fuzzy concept. The process begins by transforming the interval payoffs into fuzzy numbers using a ranking function. Subsequently, these fuzzy payoffs are converted into crisp values, leading to the formulation of the crisp matrix game. The resulting crisp matrix game is then solved using linear programming approach. Additionally, MATLAB code for the proposed method is developed and proposed to streamline the computation process, enhancing comparison and decision-making efficiency, particularly when dealing with large payoff matrices. Furthermore, three numerical examples are provided to illustrate the validity of the proposed approach as well as its MATLAB code. A real-life example of IVGP in the realm of tourism industry is also provided. Finally, a comparative analysis is conducted, comparing the proposed method with some existing methods. [ABSTRACT FROM AUTHOR]

The problem of the Chinese postman is one of the types of the problem of the Chinese postman, which includes 4 models in this paper. In the first case, the postman moves from the origin, he must go through each edge at least once and then move to the destination, which in the first case, the destination is the same as the original origin. That is, the postman returns to the original origin. In the second case, the postman moves from the origin. We determine the destination so that the postman does not have to go back to the original source to incur a fee. In the third case, the postman moves from the origin to the destination that the computer program determines for him, in this way, he incurs a lower cost than in the second case because the GAMS programming determines a destination for us that costs less than all destinations. In the fourth case, both the origin and the destination are determined by programming so that all the edges are covered, which is less expensive than all the origins and destinations. The weight of edges is not constant due to different factors. Triangular fuzzy numbers are used in this study, which is included in the coefficients of the objective function of these fuzzy numbers. Two different ranking methods are used for fuzzification and the obtained results are compared with each other. The solution is done using GAMS software. Mathematical models cannot find solutions in large sizes and for this reason, the Lagrangian algorithm is used to solve these problems. After the problems are solved using the Lagrangian algorithm, the results of different fuzzy ranking methods are compared [ABSTRACT FROM AUTHOR]

The nonlinear Fitzhugh–Nagumo (FN) model is a well-known nonlinear reaction-diffusion model, which is a simplified form of the Hodgkin–Huxley (HH) model. Several important phenomena are analyzed via the FN model, such as nerve impulse transmission through the neurons, biological population genetics, noise formations in circuit theory, intercellular trigger wave propagation, and others. The FN model is definitely an important mathematical model in the domain of neurobiological sciences and engineering applications. In this paper, we study the nonlinear fractional FN model, computationally and numerically using the auxiliary equation (AE) method through the conformable derivative. We have established numerous fresh, useful, efficient and wide-ranging closed-form traveling wave solutions of the model. Additionally, we examine the influence of fractional parameter on the signal transmission through the nerve system and other related wave propagation by sketching the three-dimensional graphs of the solutions with the aid of the Mathematica program. The established results authenticate the efficiency and reliability of the considered method. [ABSTRACT FROM AUTHOR]

Difficulty in maintaining tuning due to water depth fluctuation makes overhead water tanks (OWTs) ineffective as tuned liquid or mass dampers. Recently, a semi-active damper involving OWT, that varies the stiffness of the tank-supporting columns with liquid depth variation to maintain the impulsive frequency of the tank constant at a value required for tuning, has been proposed. In this paper, the concept is extended to develop a passive tuned damper involving the OWT (PTD-OWT), which is more reliable, cost-effective, and has a simpler configuration than its semi-active counterpart but achieves the same objective as the latter. For the PTD-OWT, a novel mechanism involving a spring-supported platform, a rigid frame, and tank-supporting columns is developed. The working principle and mathematical model of the PTD-OWT are presented followed by an illustrative design example considering the host building undergoing base excitation. The results revealed that the PTD-OWT remains tuned and thereby performs consistently despite wide variations in water depth in the tank. Significant reductions have been achieved by the PTD-OWT in peak and root-mean-square displacement and acceleration responses of the structure for a variation in liquid depth between 100% full tank to empty tank condition, with the maximum fall in control achieved as only 6.8%. A comparison of PTD-OWT is made with the case when the tank is designed as a conventional passive tuned mass damper (TMD) without the provision for maintaining tuning. The conventional mass damper suffers significant performance degradation as liquid depth fluctuates in the tank. [ABSTRACT FROM AUTHOR]

In this paper, the new modification of the Sardar sub-equation method is used to generate a wide variety of exact solutions for the (2+1)-dimensional Konopelchenko–Dubrovsky system. We focus on investigating the Konopelchenko–Dubrovsky equation, which serves as a mathematical model for studying nonlinear waves in the field of mathematical physics. This equation specifically captures the behavior of waves with weak dispersion, allowing us to explore the intricate dynamics and characteristics associated with such wave phenomena. By delving into the properties and solutions of this system, we aim to deepen our understanding of nonlinear wave propagation and its implications in the broader field of mathematical physics. The exact solutions generated through this modified method provide valuable insights into the propagation and interaction of waves with weak dispersion in the system. The obtained novel solutions are expressed as hyperbolic, and trigonometric functions. The proposed model successfully constructs various types of solutions, including singular, dark, bright, trigonometric, periodic, dark–bright, exponential, and hyperbolic. These solutions are presented with appropriate parameter values in both 3D and 2D graphics. [ABSTRACT FROM AUTHOR]

In this paper, to investigate the dynamic responses of underground circular shells subjected to subsurface denotations and provide a feasible engineering design method, a simplified mathematical modelling was proposed. The dynamic medium–structure interaction (MSI) was introduced into the equations of motions through an interfacial damping between the structure element and the surrounding geomaterial, in which the effects of the shear and the rotary inertia were neglected. By means of modal superposition, the analytical solutions of the dynamic responses were deduced. The effects of geometric parameters and acoustic impedances on the dynamic responses were discussed. It is suggested that protective structures are better to be constructed in geomaterial with small impedance to attenuate the intense shock wave effects. [ABSTRACT FROM AUTHOR]

A large number of herbivorous mammals and reptiles in many terrestrial ecosystems across the globe are presently in the receiving end of extinction. Over-exploitation by its immediate predator and anthropogenic actions is one of the main reasons. Reintroduction of apex predator or top predator at some instances has proven to be a successful strategy in restoring ecological balance. In this paper, we conceptualize the role of top predator in enriching the density of vulnerable species of lower trophic level, with the help of mathematical modeling. First, the dynamical behavior of two species system (prey and mesopredator) is studied, where growth of prey is subject to strong Allee effect. Also, the cost of predation induced fear is incorporated in the growth term. Parametric regions, for which the species perceive extinction risk are analyzed and depicted numerically. We consider that whenever density of the vulnerable species reach a certain threshold, minimum viable population, top predator is introduced in the habitat. Our obtained results show that a species population can be restored from the verge of extinction to a stable state with much higher population density with the introduction of top predator and even it stabilizes an oscillatory system. [ABSTRACT FROM AUTHOR]

Many of the computational models in science, engineering, and social studies are agent-based models. However, despite their growing importance and potential attractiveness to students, agent-based models are not taught in elementary, middle or high school. In this paper, the author explores the feasibility of teaching agent-based models to elementary and middle school students, and the extent students can learn modeling using agent-based mathematical and computational models. [ABSTRACT FROM AUTHOR]

The contents of this editorial is proposed in three parts devoted to the modeling and simulation of mutating virus pandemics in a globally connected world. The presentation is as follows: first, a general framework is presented according to the idea that mathematical models should go beyond deterministic population dynamics by considering the multiscale, heterogeneous features of the complex system under consideration; second, the contents of the papers in this issue are presented; finally, there is a critical analysis looking ahead to research perspectives. [ABSTRACT FROM AUTHOR]

In this paper, we revisit the classical SIR epidemic model by replacing the simple bilinear transmission rate by a nonlinear one. Our results show that in the presence of environmental fluctuations represented by Brownian motion and that mainly act on the transmission rate, the generalized non-concave force of infection adopted here, greatly affects the long-time behavior of the epidemic. Employing the Markov semigroup theory, we prove that the model solutions do not admit a unique stationary distribution but converge to 0 in p th moment for any p > 0. Furthermore, we prove that the disease extinguishes asymptotically exponentially with probability 1 without any restriction on the model parameters and we also determine the rate of convergence. This is an unexpected qualitative behavior in comparison with the existing literature where the studied epidemic models have a threshold dynamics behavior. It is also a very surprising behavior regarding the deterministic counterpart that can exhibit a rich qualitative dynamical behaviors such as backward bifurcation and Hopf bifurcation. On the other hand, we show by several numerical simulations that as the intensity of environmental noises becomes sufficiently small, the epidemic tends to persist for a very long time before dying out from the host population. To solve this problem and to be able to manage the pre-extinction period, we construct a new process in terms of the number of infected and recovered individuals which admits a unique invariant stationary distribution. Finally, we discuss the obtained analytical results through a series of numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, two different approaches for tumor growth modeling are presented and implemented. In the first part of the paper, a macroscopic approach using a PDE model, where the tumor is viewed as a cell mass, is implemented using the level-set method to track the tumor moving boundary in one hand by using Darcy's law to compute the normal velocity of the free boundary and on the other hand using the shape optimization to draw the normal velocity. In the second part of the paper, a microscopic approach, which focuses on the cellular scale, is presented. A hybrid model using agent-based modeling for the cell behavior and a PDE for the description of the tumor environment is presented. A sensitivity analysis is performed on the hybrid model for a better understanding of its impact on the tumor growth. Numerical experiments are provided for the proposed approaches. [ABSTRACT FROM AUTHOR]

Existing results on H ∞ stability analysis problems for 2D digital filters are limited to external interference and saturation arithmetic. Unfortunately, developed results so far are not sufficient to tackle Markovian jumping parameters (MJPs) and state-delay. Such stability problem for 2D digital filters under MJPs, saturation arithmetic, state-delay and external interference has not been considered in the existing literature. In this paper, novel H ∞ performance analysis criterion is first proposed for 2D interfered digital filters in which state-delay, saturation nonlinearities and MJPs are considered. The mathematical model of the underlying 2D system is described by the Roesser model. Furthermore, improved H ∞ performance analysis criterion over the existing result is also obtained for 2D interfered digital filters with saturation nonlinearities only. At the end, two examples are employed to illustrate the effectiveness of the devised stability results. [ABSTRACT FROM AUTHOR]

In this paper, a method is presented for the mathematical modeling and analysis of the DC–DC Buck Converter output voltage. This paper consists of the demonstration of a mathematical model for the converter transient response submitted to a pulse width modulated (PWM) input voltage, resulting in accurate symbolic expressions for the output voltage. The novelty of the method is the capability of the expressions derived to describe correctly the behavior of the converter submitted to time-varying control reference input signals modulating the switch pulse width. The mathematical model was then validated by comparing it with the responses obtained using the Runge–Kutta numerical method. By using different circuit parameters and PWM input signals with constant and time-varying duty cycles, it was possible to validate the model for different cases, showing the effectiveness of the approach. [ABSTRACT FROM AUTHOR]

The SARS-CoV-2 leads to a worldwide COVID-19 pandemic, which has caused tremendous damage to the world. In this paper, we develop a dynamic model in vivo, fitting and estimating parameters for T lymphocytes and pro-inflammatory cytokines IL-6 in patients with mild and severe COVID-19 at Yale New Haven Hospital through the GWMCMC algorithm. Meanwhile, we also analyze the structural identifiability and practical identifiability of the model. Further, we add time-varying parameters to the model, using the least squares method to perform data fitting and parameter estimation on survivors and non-survivors of the Italian infectious disease hospital. Then analyze the similarities and differences in immune response mechanisms between the two countries. Finally, we demonstrate the existence and stability of the equilibrium state of the model and analyze the Hopf bifurcation at the positive equilibrium state by using the central manifold theory and normal form theory. This result may explain the recurrence of infection in some COVID-19 patients. [ABSTRACT FROM AUTHOR]

The heart is an organ with a limited capacity for regeneration and repair. In this paper, a new mathematical model is presented to study the left ventricular remodeling after myocardial infarction (MI) and followed stem cell therapeutic effort. The model represents the post-MI regeneration process of cardiomyocytes under stem cell therapy with oxygen restoration. The resulting system of nonlinear ordinary differential equations (ODE) is studied numerically in order to demonstrate the functionality and performance of the new model. The optimal time of stem cell injection for various oxygen restorations is determined. Moreover, the regeneration of cardiomyocytes is successfully correlated with improved left ventricle function observed in experiments. The proposed nonlinear ODE model is able to capture the complicated biological interactions in post-MI remodeling and can serve as a platform for in silico simulation and perturbation to optimize MI stem cell therapy. [ABSTRACT FROM AUTHOR]

In December 2019, human cases of novel coronavirus infection were detected in Wuhan, China which have been named as COVID-19 by the World Health Organization (WHO). Since COVID-19 was first detected in China, the virus has reached more than 120 countries and was declared a global pandemic on March 11, 2020 by the WHO. In this paper, we have highlighted the influence of temperature on the spread of COVID-19. For this, the dynamic transmission of COVID-19 is modeled taking into account the influence of the temperature on the persistence of coronavirus in the environment. We also took into account the impact of proportion of people who respect the barrier measures published by the WHO on the scale of the COVID-19 pandemic. Taking into account the influence of the temperature on the persistence of the virus in the environment, the dynamic transmission has been described by a system of ordinary differential equations (ODEs). First, we analyzed the solutions of system in the case where the impact of the temperature on the virus is neglected. Second, we carried out the mathematical analysis of the solutions of the system in the non-autonomous case. Mathematical analyzes have enabled us to establish that the temperature and proportion of persons who respect the barrier rules can affect the spread of COVID-19. Some numerical simulations have been proposed to illustrate the behavior of the pandemic in some countries. [ABSTRACT FROM AUTHOR]

The influence line of bridge can reflect the performance of the bridge under the moving vehicle load. It has a wide range of applications in structural damage detection, performance evaluation, model correction and bridge weigh-in-motion. Fast moving vehicles will cause the dynamic effect of the bridge, resulting in the change of the bridge response curve and the difficulty of identifying the influence line. In this paper, an influence line identification method based on variational mode decomposition (VMD) combined with improved wavelet threshold denoising is proposed. Firstly, the mathematical model of influence line identification is established based on vehicle load matrix and bridge response. Then, VMD combined with improved wavelet threshold denoising method is used to eliminate dynamic fluctuation effect and noise. Finally, the elastic net penalty term is introduced in the influence line identification problem, and the B-spline basis function is used to reconstruct the influence line. In order to verify the effectiveness of the proposed method, a vehicle-bridge coupling model is established for numerical calculation, and the identification of bridge displacement influence lines under different conditions such as vehicle speed, noise level, road roughness and vehicle weight is investigated. The results show that the proposed method can effectively eliminate the dynamic fluctuation components and noise of the bridge response. In the case of good road roughness, the influence line can still be accurately identified when the vehicle speed reaches 15 m/s. [ABSTRACT FROM AUTHOR]