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Disabled people can be successfully employed in most production processes, provided that one knows how to exploit their abilities and take into account their limitations in order to give them an appropriate job. However, because the level and type of production must be constantly adapted to the needs of the market, the involvement of disabled people in the production process may also change. Additionally, people with disabilities have limitations as well as additional rights that must be considered. As a result, the organisation and planning of their work, side by side with other employees, becomes more complex. Computer simulations can be a support for organising and planning the involvement of employees with disabilities in production processes. The aim of the article is to show how simulations can facilitate the organisation of work of employees with disabilities, with the changing demand for manufactured products. The paper identifies the factors that should be considered, and then presents how the employment of disabled people can affect the operation of the production line and the commercial image of the company. The study uses a combination of System Dynamics and Discrete Event Simulations. The relevant data for the simulation were derived from a production company. [ABSTRACT FROM AUTHOR]

In this paper, we established a polynomial scaling method to investigate the numerical solution of Rosenau–Korteweg De Vries‐regularized long wave (Rosenau‐KdV‐RLW) equation. We start with discretization of the time variable of the equation using a finite difference approach equipped with a linearization. After the time discretization, we have used polynomial scaling functions for the discretization of the spatial variable. These two discretizations give us the desired discrete system of equations to obtain numerical solutions. We further derive an error estimate for the proposed method. We have applied the proposed method to Rosenau‐KdV, Rosenau‐RLW, and Rosenau‐KdV‐RLW equations and used error norms to examine the accuracy and reliability of the presented method. Also, to enhance accuracy of the results, we utilize Richardson extrapolation. The comparisons with the analytical solution and earlier studies that use different methods indicate that the proposed method is accurate and reliable. [ABSTRACT FROM AUTHOR]

With the advancement of information and communication technology, the integration of smart systems into discrete sequential processes has been realized in manufacturing systems. Specifically, to optimize the efficiency of operations and production, accurate and rapid detection of faults is crucial. Numerous studies have attempted to identify faults in various electromechanical systems; however, the performance and effectiveness often depend on the quality of the collected signals and the system operation methodology. For instance, the measurements of various types of analog sensor signals—such as voltage, current, 3-axis acceleration, and temperature—vary according to the installation locations and positions within a system. Moreover, although an automated manufacturing system typically operates under predefined control sequences, identifying common signal patterns for every healthy or faulty state is challenging. Consequently, we focused on detecting faults using only image data captured from on-site camera in automated sequential manufacturing processes, without relying on additional manufacturing information. We proposed a method based on convolutional long short-term memory (LSTM) networks for the next visual status prediction and an unsupervised statistical process control chart to classify the current status as normal or faulty. Following the detection of a fault, we conducted unsupervised fault type clustering to provide valuable insights for maintenance efforts. The validation and verification demonstrated accurate fault detection (94.2%) and effective fault type clustering in two distinct manufacturing processes of a USB packaging system. Since no information other than the original process images captured by the on-site camera were used for fault detection and fault type classification, it can be assumed that the proposed methodology can be easily applied to other or more complex manufacturing processes. [ABSTRACT FROM AUTHOR]

We consider discrete dynamical systems obtained as deformations of mutations in cluster algebras associated with finite-dimensional simple Lie algebras. The original (undeformed) dynamical systems provide the simplest examples of Zamolodchikov periodicity: they are affine birational maps for which every orbit is periodic with the same period. Following on from preliminary work by one of us with Kouloukas, here we present integrable maps obtained from deformations of cluster mutations related to the simple root systems A 3 , C 2 , B 3 and D 4 . We further show how new cluster algebras arise, by considering Laurentification, that is, a lifting to a higher-dimensional map expressed in a set of new variables (tau functions), for which the dynamics exhibits the Laurent property. For the integrable map obtained by deformation of type A 3 , which already appeared in our previous work, we show that there is a commuting map of Quispel–Roberts–Thompson (QRT) type which is built from a composition of mutations and a permutation applied to the same cluster algebra of rank 6, with an additional 2 frozen variables. Furthermore, both the deformed A 3 map and the QRT map correspond to translation by a generator in the Mordell-Weil group of a rational elliptic surface of rank two, and the underlying cluster algebra comes from a quiver that is mutation equivalent to the q -Painlevé III quiver found by Okubo. The deformed integrable maps of types C 2 , B 3 and D 4 are also related to elliptic surfaces. From a dynamical systems viewpoint, the message of the paper is that special families of birational maps with completely periodic dynamics under iteration admit natural deformations that are aperiodic yet completely integrable. [ABSTRACT FROM AUTHOR]

Recently, the research on the modified Leslie–Gower model has become an appealing topic. Due to economic efficiency and the complexity of discrete models, we investigate a discrete modified Leslie–Gower predator–prey model with prey harvesting in this paper. The stability of fixed points and bifurcations of the interior fixed points are studied. According to bifurcation theory and normal forms, we derived the conditions of codimension 2 bifurcations occurred, including 1:1 strong resonance bifurcation and fold-flip bifurcation. These two bifurcations are unusual in bifurcation analysis on discrete systems. In addition, the continuation curves, bifurcation diagrams, and phase diagrams are used to demonstrate theoretical results. Our study shows the interesting dynamics of this model that are very different from the continuous one. [ABSTRACT FROM AUTHOR]

We demonstrate the power of Experimental Mathematics and Symbolic Computation to study intriguing problems on rational difference equations, studied extensively by Difference Equations giants, Saber Elaydi and Gerry Ladas (and their students and collaborators). In particular we rigorously prove some fascinating conjectures made by Amal Amleh and Gerry Ladas back in 2000. For other conjectures we are content with semi-rigorous proofs. We also extend the work of Emilie Purvine (formerly Hogan) and Doron Zeilberger for rigorously and semi-rigorously proving global asymptotic stability of arbitrary rational difference equations (with positive coefficients), and more generally rational transformations of the positive orthant of $ R^k $ R k into itself. [ABSTRACT FROM AUTHOR]

The FCDET is considered as a promising and advanced agricultural machinery due to its convenience and controllability. To enhance the control performance of the FCDET unit dynamic system, understanding the accurate position of the center of gravity (CoG) of the tractor unit in longitudinal motion and the operating environment is essential. In this paper, we proposed a real-time estimation method of CoG position of longitudinal motion for FCDET plowing and transportation conditions. CoG height and longitudinal axis distance distribution coefficients are used as state estimation variables, and the data obtained from displacement and velocity sensors are used as state observation variables, establishing a discrete system state space model and proving the observability. The proposed Derived UKF algorithm introduces the Sage-Husa adaptive noise equation within the Square-Root UKF framework to address the non-positive definite matrix problem. The research shows that the precise CoG longitudinal position effectively reflects changes in operational pavement load. The Derived UKF algorithm exhibits high state estimation accuracy in plowing and transportation conditions, with mean absolute errors of 14.2% and 5.0% of the state amplitude, respectively. This study supports the practical application of real-time state parameter estimation algorithms in controlling advanced agricultural machinery distributed drive systems. [ABSTRACT FROM AUTHOR]

This paper deals with the numerical threshold stability of a nonlinear age-space structured heroin transmission model. A semi-discrete system is established by spatially domain discretization of the original nonlinear age-space structured model. A threshold value is proposed in stability analysis of the semi-discrete system and named as a numerical basic reproduction number. Besides the role it plays in numerical threshold stability analysis, the numerical basic reproduction number can preserve qualitative properties of the exact basic reproduction number and converge to the latter while stepsizes vanish. A fully discrete system is established via a time discretization of the semi-discrete system, in which an implicit-explicit technique is implemented to ensure the preservation of the biological meanings (such as positivity) without CFL restriction. Some numerical experiments are exhibited in the end to confirm the conclusions and explore the final state. • A numerical scheme is constructed for nonlinear age-structured reaction-diffusion models. • A numerical stability threshold is proposed in numerical stability analysis. • The numerical stability threshold we proposed can preserve qualitative properties of the exact stability threshold. [ABSTRACT FROM AUTHOR]

This paper deals with the limiting behavior of invariant measures of the stochastic delay lattice systems with fractional discrete Laplacian driven by nonlinear noise. Under certain conditions, we first show the existence of invariant measures of the systems. We then prove that any limit point of a tight sequence of invariant measures of the stochastic delay lattice systems with fractional discrete Laplacian must be an invariant measure of the corresponding limiting system as the intensity of noise converges or the time-delay approaches zero. [ABSTRACT FROM AUTHOR]

In this paper, we propose and study a discretized one‐predator two‐prey system along with prey refuge and Michaelis–Menten‐type prey harvesting. The interaction among the species is considered as Holling type III functional response. Firstly, existence and local stability of all the fixed points are derived under certain parametric conditions. Furthermore, a special consideration is made to global asymptotic stability of the interior fixed point. Then, we have shown that the system undergoes different types of bifurcations including transcritical bifurcation, flip bifurcation, and Neimark–Sacker bifurcation by using center manifold theorem, bifurcation theory, and normal form method. Also, Feigenbaum's constant of the system is calculated. It is observed that both harvesting and refuge have a stabilizing effect on the system, and the stabilizing effect of harvesting dominates the stabilizing effect of refuge. Of most interest is the finding of coexisting attractors and multistability. In particular, optimal harvesting policy has been obtained by extension of Pontryagin's maximum principle to discrete system. Finally, some intriguing numerical simulations are provided to verify our analytic findings and rich dynamics of the three species system. [ABSTRACT FROM AUTHOR]

Structural lattices with quasi-periodic patterns possess interesting dynamic features that can be exploited to control, localize and redirect propagating waves. In this work, we show that the properties of a large class of quasi-periodic locally resonant systems (approximated as periodic, with arbitrarily large period) can be performed by defining an equivalent discrete system. Several properties of wave propagation can a priori be demonstrated with reference to this system. Results in terms of bulk spectrum, showing the Hofstadter butterfly pattern, and of topological modes are then discussed in detail with reference to a simple example of quasi-periodic lattice. This article is part of the theme issue 'Current developments in elastic and acoustic metamaterials science (Part 2)'. [ABSTRACT FROM AUTHOR]

The present study investigates non-fragile H∞ state estimation based on a dynamic event-triggered mechanism for a class of discrete time-varying nonlinear systems subject to dynamical bias and fading measurements. The dynamic deviation caused by unknown inputs is represented by a dynamic equation with bounded noise. Subsequently, the augmentation technique is employed and the dynamic event-triggered mechanism is introduced in the sensor-to-estimator channel to determine whether data should be transmitted or not, thereby conserving resources. Furthermore, an augmented state-dependent non-fragile state estimator is constructed considering gain perturbation of the estimator and fading measurements during network transmission. Sufficient conditions are provided based on Lyapunov stability and matrix analysis techniques to ensure exponential mean-square stability of the estimation error system while satisfying the H∞ disturbance fading level. The desired estimator gain matrix can be obtained by solving the linear matrix inequality (LMI). Finally, an example is presented to illustrate the effectiveness of the proposed method for designing estimators. [ABSTRACT FROM AUTHOR]

This paper delves into the dynamics of a discrete-time predator–prey system. Initially, it presents the existence and stability conditions of the fixed points. Subsequently, by employing the center manifold theorem and bifurcation theory, the conditions for the occurrence of four types of codimension 1 bifurcations (transcritical bifurcation, fold bifurcation, flip bifurcation, and Neimark–Sacker bifurcation) are examined. Then, through several variable substitutions and the introduction of new parameters, the conditions for the existence of codimension 2 bifurcations (fold–flip bifurcation, 1:2 and 1:4 strong resonances) are derived. Finally, some numerical analyses of two-parameter planes are provided. The two-parameter plane plots showcase interesting dynamical behaviors of the discrete system as the integral step size and other parameters vary. These results unveil much richer dynamics of the discrete-time model in comparison to the continuous model. [ABSTRACT FROM AUTHOR]

This article presents a study of interval estimation approach based on functional interval observers for mecanum‐wheels omnidirectional automated guided vehicle (MOAGV). In the context of MOAGV, the nonlinear system in discrete time incorporates model uncertainty and unknown bounded disturbances. A functional observer is developed by integrating terminal sliding mode and H∞$$ {H}_{\infty } $$ techniques, aiming to reduce the impact of lumped disturbances/uncertainties. Additionally, a novel observer structure is introduced to increase the degrees of freedom in the design process. Subsequently, the linear function bounds are obtained using the reachability analysis of the estimation error. Finally, the performance of the improved functional interval observer is demonstrated by numerical simulations. [ABSTRACT FROM AUTHOR]

In this research paper, we delve into the analysis of a generalized discrete reaction-diffusion system. Our study begins with the discretization of a generalized reaction-diffusion model, achieved through second-order and L 1-difference approximations. We explore the local stability of its unique solution, both in the absence and presence of the diffusion term. To determine the conditions for global asymptotic stability of the steady-state solution, we employ suitable techniques including the direct Lyapunov method. To illustrate the practical application of this theoretical framework, we provide several numerical simulations that examine both the Lengyel-Epstein reaction-diffusion model and the discrete Degn-Harrison reaction-diffusion model. These simulations serve to validate the predictions of asymptotic stability. [ABSTRACT FROM AUTHOR]

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The uniform exponential stabilities (UESs) of two hybrid control systems comprised of a wave equation and a second‐order ordinary differential equation are investigated in this study. Linear feedback law and local viscosity are considered, as are nonlinear feedback law and internal anti‐damping. The hybrid system is first reduced to a first‐order port‐Hamiltonian system with dynamical boundary conditions, and the resulting system is discretized using the average central‐difference scheme. Second, the UES of the discrete system is obtained without prior knowledge of the exponential stability of the continuous system. The frequency domain characterization of UES for a family of contractive semigroups and the discrete multiplier approach are used to validate the main conclusions. Finally, the Trotter–Kato theorem is used to perform a convergence study on the numerical approximation approach. Most notably, the exponential stability of the continuous system is derived by the convergence of energy and UES, which is a novel approach to studying the exponential stability of some complex systems. Numerical simulation is used to validate the effectiveness of the numerical approximating strategy. [ABSTRACT FROM AUTHOR]

In a multi-level quantum system Fano coherences stand for the formation of quantum coherences due to the interaction with the continuum of modes characterizing an incoherent process. In this paper we propose a V-type three-level quantum system on which we certify the presence of genuinely quantum traits underlying the generation of Fano coherences. We do this by determining work conditions that allows for the loss of positivity of the Kirkwood-Dirac quasiprobability distribution of the stochastic energy changes within the discrete system. We also show the existence of nonequilibrium regimes where the generation of Fano coherences leads to a non-negligible excess energy given by the amount of energy that is left over with respect to the energy of the system at the beginning of the transformation. Excess energy is attained provided the initial state of the discrete system is in a superposition of the energy eigenbasis. We conclude the paper by studying the thermodynamic efficiency of the whole process. [ABSTRACT FROM AUTHOR]

Large scale geospatial simulation projects require multidisciplinary efforts by actors with highly variable skills and domains of expertise. Subject matter experts, modelers, developers, analysts, and decision makers must collaborate closely to model a real‐world system, simulate it, analyze its results and disseminate them. Simulation environments, tailored to business scenarios, can provide the necessary support to facilitate their collaboration throughout the simulation lifecycle. Commercial modeling and simulation software can provide an environment to facilitate simulation studies for users but, they tend to be narrowly scoped. This research focuses on the different categories of users and introduces four business processes that carry those users across the simulation lifecycle. These concepts are translated into an architecture that facilitates the operationalization of geospatial simulation environments using modeling and simulation as a service and Discrete Event Systems Specification. [ABSTRACT FROM AUTHOR]

This study addresses the state feedback control associated with D-admissible assurance for discrete singular systems subjected to parameter uncertainties in both the difference term and system matrices. Firstly, a refined analysis criterion of D-admissible assurance is presented, where the distinct form embraces multiple slack matrices and has lessened linear matrix inequalities (LMIs) constraints, which may be beneficial for reducing the conservatism of admissibility analysis. In consequence, by hiring the state feedback control, controller design issues with pole locations, which directly dominate the system performance, are mainly treated. For all the presented criteria can be formulated by the strict LMIs, they are thus suitably solved via current LMI solvers to conduct a state feedback controller with specific poles' locations of system's performance requirements. Finally, two numerical examples illustrate that the presented results are efficient and practicable. [ABSTRACT FROM AUTHOR]

Mathematical models such as Fitzhugh–Nagoma and Hodgkin–Huxley models have been used to understand complex nervous systems. Still, due to their complexity, these models have made it challenging to analyze neural function. The discrete Rulkov model allows the analysis of neural function to facilitate the investigation of neuronal dynamics or others. This paper introduces a fractional memristor Rulkov neuron model and analyzes its dynamic effects, investigating how to improve neuron models by combining discrete memristors and fractional derivatives. These improvements include the more accurate generation of heritable properties compared to full-order models, the treatment of dynamic firing activity at multiple time scales for a single neuron, and the better performance of firing frequency responses in fractional designs compared to integer models. Initially, we combined a Rulkov neuron model with a memristor and evaluated all system parameters using bifurcation diagrams and the 0–1 chaos test. Subsequently, we applied a discrete fractional-order approach to the Rulkov memristor map. We investigated the impact of all parameters and the fractional order on the model and observed that the system exhibited various behaviors, including tonic firing, periodic firing, and chaotic firing. We also found that the more I tend towards the correct order, the more chaotic modes in the range of parameters. Following this, we coupled the proposed model with a similar one and assessed how the fractional order influences synchronization. Our results demonstrated that the fractional order significantly improves synchronization. The results of this research emphasize that the combination of memristor and discrete neurons provides an effective tool for modeling and estimating biophysical effects in neurons and artificial neural networks. [ABSTRACT FROM AUTHOR]

In this paper, we study the local, global, and bifurcation properties of a planar nonlinear asymmetric discrete model of Ricker type that is derived from a Darwinian evolution strategy based on evolutionary game theory. We make a change of variables to both reduce the number of parameters as well as bring symmetry to the isoclines of the mapping. With this new model, we demonstrate the existence of a forward invariant and globally attracting set where all the dynamics occur. In this set, the model possesses two symmetric fixed points: the origin, which is always a saddle fixed point, and an interior fixed point that may be globally asymptotically stable. Moreover, we observe the presence of a supercritical Neimark–Sacker bifurcation, a phenomenon that is not present in the original non-evolutionary model. [ABSTRACT FROM AUTHOR]

This paper addresses the problem of cyber-attack detection in a discrete event system by proposing a novel model. The model utilizes graph convolutional networks to extract spatial features from event sequences. Subsequently, it employs gated recurrent units to re-extract spatio-temporal features from these spatial features. The obtained spatio-temporal features are then fed into an attention model. This approach enables the model to learn the importance of different event sequences, ensuring that it is sufficiently general for identifying cyber-attacks, obviating the need to specify attack types. Compared with traditional methods that rely on synchronous product computations to synthesize diagnosers, our deep learning-based model circumvents state explosion problems. Our method facilitates real-time and efficient cyber-attack detection, eliminating the necessity to specifically identify system states or distinguish attack types, thereby significantly simplifying the diagnostic process. Additionally, we set an adjustable probability threshold to determine whether an event sequence has been compromised, allowing for customization to meet diverse requirements. Experimental results demonstrate that the proposed method performs well in cyber-attack detection, achieving over 99.9 % accuracy at a 1 % threshold and a weighted F1-score of 0.8126, validating its superior performance. [ABSTRACT FROM AUTHOR]

In this paper, we combine simultaneous transmitting and reflecting reconfigurable intelligent surface (STAR-RIS) with rate-splitting multiple access (RSMA) technology and investigate the ergodic rate performance of an STAR-assisted RSMA system. Considering the discrete phase shifts of the STAR-RIS in practice, the downlink performance of STAR-RIS-assisted RSMA with discrete phase shifts is compared to that with continuous phase shifts. Firstly, the cumulative distribution function of signal-to-interference-plus-noise ratio (SINR) of users is analyzed. Then, the total ergodic rate of the system and its approximate closed-form solution are, respectively, derived based on the cumulative distribution function of users. The simulation results validate the effectiveness of the theoretical analysis, showing good agreement between the derived theoretical ergodic rate and the corresponding simulations. Although the system performance with discrete phase shifts is inferior to that with continuous phase shifts due to quantization errors, the performance of the continuous phase shift system is well approximated when the quantization bit of the phase shift system reaches 3 in the simulations. Additionally, the impact of the number of STAR-RIS elements on the system's performance is analyzed. [ABSTRACT FROM AUTHOR]

This paper presents an edge‐based event‐triggered delay distributed algorithm for solving the economic dispatch problem (EDP) in smart grids. The objective of the EDP is to minimize the total generation cost by allocating power to individual generators, each with its local generation constraint. To save the overhead of communication resources between agents, an edge‐based event‐triggered mechanism is suggested. By setting distinct triggering thresholds for each communication edge, the agent may efficiently regulate the communication frequency among all neighbors. However, in practice, owing to the instability of the network, the agent may receive information regarding its neighbors, leading to communication lags for every communication link. The virtual agent technique and double‐stochastic matrix augmentation technique provide an equivalent delay‐free EDP. It is demonstrated that the proposed algorithm can asymptotically converge to the global optimal solution as long as the communication delay is arbitrary, time‐varying, and random, but bounded. Objective and clear evidence is provided through a case study in smart grids to verify the algorithm's feasibility. [ABSTRACT FROM AUTHOR]

This paper considers the equilibrium‐free stability and performance analysis of discrete‐time nonlinear systems. Two types of equilibrium‐free notions are considered. Namely, the universal shifted concept, which considers stability and performance w.r.t. all equilibrium points of the system, and the incremental concept, which considers stability and performance between trajectories of the system. This paper shows how universal shifted stability and performance of discrete‐time systems can be analysed by making use of the time‐difference dynamics. Moreover, the existing results are extended for incremental dissipativity for discrete‐time systems based on dissipativity analysis of the differential dynamics to more general state‐dependent storage functions for less conservative results. Finally, it is shown how both these equilibrium‐free notions can be cast as a convex analysis problem by making use of the linear parameter‐varying framework, which is also demonstrated by means of an example. [ABSTRACT FROM AUTHOR]

A modified wavelet interpolation Galerkin method (WIGM) with improved flexibility of nodal distribution is formulated and utilized to solve the Bratu's problem. Such a method treats the nonlinear term as an independent function and directly approximates it through the proposed wavelet interpolation, resulting in a low-cost discretization of the Bratu's equation with exponential nonlinearity. An efficient implementation of Newton's method to find the lower and upper branches of solution as well as the turning point is then presented. Numerical results demonstrate that the present WIGM can accurately estimate both two solution branches and turning point for the Bratu's problem. Compared with many other existing methods, the proposed WIGM also offers marked superiority in terms of accuracy when using the same node distribution. Moreover, a convergent solution to the resulting nonlinear discrete system obtained by the WIGM can be observed in a few iterations even when the initial guess significantly deviates from the exact solution. Finally, a highly accurate approximation of both two-branched solutions and the turning point for the two-dimensional Bratu's problem is obtained by the proposed WIGM. [ABSTRACT FROM AUTHOR]

Starting from a characterization of polynomial dichotomy by means of admissibility, recently proved in [Dragicevic, D.; Sasu, A. L.; Sasu, B. Admissibility and polynomial dichotomy of discrete nonautonomous systems. Carpath. J. Math. 38 (2022), 737-762.], the aim of this paper is to explore the roughness of polynomial dichotomy in the presence of perturbations and to obtain a new robustness criterion. We show that the polynomial dichotomy is robust when subjected to linear additive perturbations which are bounded by a well-chosen sequence. We emphasize that the new bounds imposed to the perturbation family improve and extend the previous approaches. Furthermore, we mention that the main result applies to discrete nonautonomous systems in Banach spaces with the only requirement that their propagators exhibit a polynomial growth. [ABSTRACT FROM AUTHOR]

In this work we provide detailed estimates of maximal principal angles between subspaces and we analyse their smoothness for smoothly varying subspaces. This leads to a new definition of angular values for linear dynamical systems in continuous time. We derive some of their properties complementary to the theory of angular values developed in Beyn, et al. [Angular values of nonautonomous and random linear dynamical systems: Part I – fundamentals, SIAM J. Appl. Dyn. Syst. 21(2) (2022), pp. 1245–1286; Angular values of nonautonomous linear dynamical systems: Part II – reduction theory and algorithm, SIAM J. Appl. Dyn. Syst. 22(1) (2023), pp. 162–198] for discrete time systems. The estimates are further employed to establish upper semicontinuity of angular values for some parametric model examples of discrete and continuous type. [ABSTRACT FROM AUTHOR]

Emergency Medical Services play a fundamental societal role since they provide pre-hospital care to patients in critical and time-constrained conditions. In this context, the hospital selection decision is vital to respond in a timely, effective and efficient way. By means of simulation experiments, the present study compares the effects of different assignment logics against a set of performance dimensions. To this end, we develop a Discrete Event Simulation model that covers the entire Emergency Medical Service process, from the ambulance transportation to final departure of the patient from the Emergency Department. Results demonstrate that the use of effectiveness-related criteria (e.g. expected waiting time, resource saturation) significantly enhances the overall performance and, at the same time, guarantees higher quality of care. Thus, the study contributes in enhancing hospital selection decisions by supporting decision-makers through a comprehensive decisional model, distancing from prior researches that predominantly considered efficiency-driven criteria (i.e. proximity). [ABSTRACT FROM AUTHOR]

In manufacturing and service systems, the negative effects of variability propagation are usually addressed through approximation models and other tools, such as simulation and optimization algorithms. This paper investigates the conditions in which these approaches are ineffective, and considering only the mean and variance of the processing time distribution is misleading. A scenario analysis deepens the impacts of considering the entire processing time distribution (beyond its mean and variance) on the inter-departure times in balanced and unpaced lines modeled through Discrete Event Simulation. The results correlate the impacts on variability propagation of approximating the processing time distribution with system characteristics such as utilization levels, line sizes, and inter-arrival and processing time variability. Production planning approaches can benefit from these results to reduce variability propagation, particularly in flexible and reconfigurable manufacturing systems, largely adopted in Industry 4.0, that can highly influence processing time distributions by varying product mix and line configuration. A balanced and unpaced line, with a single inter-arrival time distribution, and two processing time distributions, alpha and beta, rispectively, which have the same Squared Coefficient of Variation and different shape that lead to different variability propagation in the inter-departure time distribution at the end of the line. [ABSTRACT FROM AUTHOR]

Repulsion systems under the discrete dynamical systems perspective are considered. The goal is to study the nonlinear dynamics of an arrangement of individual or cells under various types of repulsion laws. Repulsion is a natural mechanism, so we consider the following laws: global, open, cyclic and bounded repulsion. A first scenario under consideration is when particles are freely located on an Euclidean space and the second scenario where they are restricted to remain in a bounded set. We consider those two scenarios under the previous types of repulsion. The analysis culminates in a unification of two mechanisms: attraction and repulsion via a specific social behaviour problem. [ABSTRACT FROM AUTHOR]

In this section of Resonance, we invite readers to pose questions likely to be raised in a classroom situation. We may suggest strategies for dealing with them, or invite responses, or both. "Classroom" is equally a forum for raising broader issues and sharing personal experiences and viewpoints on matters related to teaching and learning science. Beyond the maximum power transfer theorem, we suggest a class of linear two-terminal circuits where impedance matching is the condition for maximum power transfer to a fixed load resistor. As such a discrete case, for a given total number of identical cells, impedance matching has been used to find the maximum load current (MLC) (hence, maximum load power) when all possible series-parallel combinations (SPCs) of cells are connected to a load resistor. When the impedance matching solution is located between two adjacent SPCs in the ordered list of SPCs, a simple selection rule for determining which of the two combinations gives the MLC without directly calculating and comparing their load currents is presented in this article. As a by-product, the spectrum of SPCs producing the MLC for a given total number of cells can be obtained as a function of the resistance ratio (internal resistance of the cell/load resistance). [ABSTRACT FROM AUTHOR]

Petri nets are a graphical notation for describing a class of discrete event dynamic systems whose behaviours are characterised by concurrency, synchronisation, mutual exclusion and conflict. They have been used over the years for the modelling of various distributed systems applications. With the advent of pervasive systems and the Internet of Things, the Calculus of Context-aware Ambients (CCA) has emerged as a suitable formal notation for analysing the behaviours of these systems. In this paper, we are interested in comparing the expressive power of Petri nets to that of CCA. That is, can the class of systems represented by Petri nets be modelled in CCA? To answer this question, an algorithm is proposed that maps any Petri net onto a CCA process. We prove that a Petri net and its corresponding CCA process are behavioural equivalent. It follows that CCA is at least as expressive as Petri nets, i.e., any system that can be specified in Petri nets can also be specified in CCA. Moreover, tools developed for CCA can also be used to analyse the behaviours of Petri nets. [ABSTRACT FROM AUTHOR]

Hydraulic fracture, natural fracture and fracture networks play a vital role for heat mining of Enhanced Geothermal System (EGS). In this work, a two-dimensional thermo-hydro-mechanical (THM) EGS model was proposed to investigate the effect of natural fracture on heat extraction performance. Based on the local thermal non-equilibrium theory and discrete natural fracture network, the spatial and temporal distribution of temperature, pore pressure, effective stress, rock matrix porosity and permeability are investigated. The results show that the natural fracture has a significant negative effect on the production temperature. After the 40-year prediction, the production temperature of the base model is 45.5°C lower than that of the without natural fracture model. In the initial operation stage, the low-temperature region is mainly distributed in the region of artificial fracture and injection well, then it expands significantly to the natural fracture due to the stress redistribution. The key parameters of quantity and orientation of natural fracture can lead to a decline in production temperature and earlier thermal breakthroughs within the thermal reservoir. [ABSTRACT FROM AUTHOR]

Flat-band periodic materials are characterized by a linear spectrum containing at least one band where the propagation constant remains nearly constant irrespective of the Bloch momentum across the Brillouin zone. These materials provide a unique platform for investigating phenomena related to light localization. Meantime, the interaction between flat-band physics and nonlinearity in continuous systems remains largely unexplored, particularly in continuous systems where the band flatness deviates slightly from zero, in contrast to simplified discrete systems with exactly flat bands. Here, we use a continuous superhoneycomb lattice featuring a flat band in its spectrum to theoretically and numerically introduce a range of stable flat-band solitons. These solutions encompass fundamental, dipole, multi-peak, and even vortex solitons. Numerical analysis demonstrates that these solitons are stable in a broad range of powers. They do not bifurcate from the flat band and can be analyzed using Wannier function expansion leading to their designation as Wannier solitons. These solitons showcase novel possibilities for light localization and transmission within nonlinear flat-band systems. [ABSTRACT FROM AUTHOR]

Let (X, d) be a metric space and H(X) represent all non-empty, compact subsets of X. The expansivity of the multivalued map sequence  f̄1,∞ : H(X) → H(X), including expansivity, positive ℵ0-expansivity, were investigated. Also, stronger forms of sensitivities, such as multi-sensitivity and syndetical sensitivity, were explored. This research demonstrated that some chaotic properties can be mutually derived between (f1,∞, X) and (  f̄1,∞, H(X)), showing fundamental similarities between these systems. Conversely, the inability to derive other properties underlined essential differences between them. These insights are crucial for simplifying theoretical models and enhancing independent research. Lastly, the relationship between expansivity and sensitivity was discussed and the concept of topological conjugacy to the system (  f̄1,∞, H(X)) was extended. [ABSTRACT FROM AUTHOR]

In this paper a framework for engineering supervisory controllers for product lines with dynamic feature configuration is proposed. The variability in valid configurations is described by a feature model. Behavior of system components is achieved using (extended) finite automata and both behavioral and dynamic configuration constraints are expressed by means of requirements as is common in supervisory control theory. Supervisory controller synthesis is applied to compute a behavioral model in which the requirements are adhered to. For the challenges that arise in this setting, multiple solutions are discussed. The solutions are exemplified in the CIF toolset using a model of a coffee machine. A use case of the much larger Body Comfort System product line is performed to showcase feasibility for industrial-sized systems. [ABSTRACT FROM AUTHOR]

This paper addresses a class of uncertain nonlinear systems with disturbances that are challenging to model by proposing a novel model-free adaptive sliding mode control (MFASMC) scheme based on a discrete-time extended state observer (DESO). Initially, leveraging the pseudo partial derivative (PPD) concept in the model-free adaptive control (MFAC) framework, the discrete-time nonlinear model is converted into a full-form dynamic linearization (FFDL) model. Secondly, using the FFDL data model, a discrete sliding mode controller is designed. A discrete integral sliding mode surface is chosen to mitigate chattering during the reaching phase, and a hyperbolic tangent function with minimal slope variation is selected for smoother switching control. Furthermore, a DESO is designed to estimate uncertainties in the discrete system, enabling real-time compensation for the controller. Finally, a genetic optimization algorithm is employed for parameter tuning to minimize the time cost associated with selecting control parameters. The design process of this scheme relies solely on the data of the controlled system, without depending on a mathematical model. The proposed DESO-MFASMC scheme is tested through simulations using a typical numerical equation and the existing EFG-BC/320 electric heavy-duty forklift from the Quzhou Special Equipment Inspection Center. Simulation results show that the proposed method is significantly superior to the traditional MFAC and PID control methods in tracking accuracy and robustness when dealing with nonlinear disturbance of the system. The DESO-MFASMC scheme proposed in this paper not only shows its advantages in theory but also verifies its effectiveness and practicability in engineering through practical application. [ABSTRACT FROM AUTHOR]

The integration of polymers, supramolecular macrocycles and aggregation‐induced emission (AIE) molecules provides numerous possibilities for constructing various functional supramolecular systems. Herein, we constructed supramolecular assembled systems based on discrete macrocyclic polymer hosts via the cooperation of hydra‐headed macrocycles containing two or three pillar[5]arene units (defined as P2, P3), the block polymer F127 and AIE molecules (alkyl‐cyano modified tetraphenylethene, alkyl‐triazole‐cyano modified 9,10‐distyrylanthracene, defined as TPE‐(CN)4 and DSA‐(TACN)2). Compared with the binary assembly between hydra‐headed hosts or F127 and AIE molecules, cascaded supramolecular assembly‐induced emission enhancement (SAIEE) in aqueous solution was achieved in discrete macrocyclic polymer‐based supramolecular assembled systems. Considering the cascaded SAIEE performance, we have successfully applied discrete macrocyclic polymer‐based supramolecular assembled systems to bioimaging and constructed an artificial light‐harvesting system (LHs) to explore more potential applications. The supramolecular assembly form of discrete macrocyclic polymers hosts and AIE molecules proposed in this work provides new inspiration for the construction and application of high‐performance supramolecular luminescent systems. [ABSTRACT FROM AUTHOR]

In this study, the energy control and asymptotic stability of the 1D sine-Gordon equation were investigated from the viewpoint of numerical approximation. An order reduction method was employed to transform the closed-loop system into an equivalent system, and an average-central finite difference scheme was constructed. This scheme is not only energy-preserving but also possesses uniform stability. The discrete multiplier method was utilized to obtain the uniformly asymptotic stability of the discrete systems. Moreover, to cope with the nonlinear term of the model, a discrete Wirtinger inequality suitable for our approximating scheme was established. Finally, several numerical experiments based on the eigenvalue distribution of the linearized approximation systems were conducted to demonstrate the effectiveness of the numerical approximating algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we consider a discrete dynamic control system with noise. It is required that at the terminal moment of process, the phase point is contained in a given ring-shaped set. We find the operator of program absorption, which allows one to formulate conditions for the set of initial positions that guarantee the fulfillment of the required inclusion at a given moment of time. [ABSTRACT FROM AUTHOR]

The meshing and limit equations of worm drive usually have strong nonlinearities such as multiple solutions, solution nonexistence and equation singularity. Meanwhile, the tooth surfaces of worm drive are in nonconforming line contact, which often requires mesh refinement of contact region for the loaded contact analysis. These two challenges cause that the modeling of worm drive heavily relies on manual adjustment and the loaded contact analysis of worm drive is still rare especially when edge contact and assembly error are concerned. Focusing on the double enveloping hourglass worm (DEHW) drive with planar generatrix, this work presents procedures to solve meshing and limit equations with global convergence. The instantaneous contact line, meshing limit line, curvature interference limit line and tooth surface grid discretization are adaptively generated, without manual trial or adjustment. On the basis of adaptive mesh refinement of tooth surface, the mortar virtual element method is adopted for loaded contact analysis of DEHW drive with edge contact and center distance error. Under sliding friction, the discrete system of governing equalities and inequalities is solved by semi-smooth Newton algorithm after constraint condensation. Numerical results for meshing theory and loaded contact analysis of DEHW drive with planar generatrix are discussed. [ABSTRACT FROM AUTHOR]

Energy-preserving algorithms, as one of the core research areas in numerical ordinary differential equations, have achieved great success by many methods such as symplectic methods and discrete gradient methods. This paper considers the numerical integration of quasi-bi-Hamiltonian systems, which, as a generalization of bi-Hamiltonian systems, can be expressed in two distinct ways: y ˙ = P 1 (y) ∇ H 2 (y) = 1 ρ (y) P 2 (y) ∇ H 1 (y) . The quasi-bi-Hamiltonian systems have two Hamiltonians H 1 (y) and H 2 (y) . Conventional discrete gradient methods can only preserve one Hamiltonian at a time. In this paper, based on discrete gradient and projection, new energy-preserving integrators that can preserve the two Hamiltonians simultaneously are proposed. They show better qualitative behaviours than traditional discrete gradient methods do. Numerical integrations of Hénon-Heiles type systems and the Korteweg-de Vries (KdV) equation are conducted to show the effectiveness of the new integrators in comparison with traditional discrete gradient methods. [ABSTRACT FROM AUTHOR]

In this paper, we consider solutions for discrete systems arising from multi-term time-fractional diffusion equations. Using discrete sine transform techniques, we find that all-at-once systems of such equations have a structure similar to that of diagonal-plus-Toeplitz matrices. We establish a generalized circulant approximate inverse preconditioner for the all-at-once systems. Through a detailed analysis of the preconditioned matrices, we show that the spectrum of the obtained preconditioned matrices is clustered around one. We give some numerical examples to demonstrate the effectiveness of the proposed preconditioner. [ABSTRACT FROM AUTHOR]

We study multiple orthogonal polynomials exploiting their explicit determinantal representation in terms of moments. Our reasoning follows that applied to solve the Hermite–Padé approximation and interpolation problems. We also study families of multiple orthogonal polynomials obtained by variation of the measures known from the theory of discrete‐time Toda lattice equations. We present determinantal proofs of certain fundamental results of the theory, obtained earlier by other authors in a different setting. We also derive quadratic identities satisfied by the polynomials, which are new elements of the theory. Resulting equations allow to present multiple orthogonal polynomials within the theory of integrable systems. [ABSTRACT FROM AUTHOR]

In this study, to approximate nabla sequential differential equations of fractional order, a class of discrete Liouville–Caputo fractional operators is discussed. First, some special functions are re-called that will be useful to make a connection with the proposed discrete nabla operators. These operators exhibit inherent symmetrical properties which play a crucial role in ensuring the consistency and stability of the method. Next, a formula is adopted for the solution of the discrete system via binomial coefficients and analyzing the Riemann–Liouville fractional sum operator. The symmetry in the binomial coefficients contributes to the precise approximation of the solutions. Based on this analysis, the solution of its corresponding continuous case is obtained when the step size p 0 tends to 0. The transition from discrete to continuous domains highlights the symmetrical nature of the fractional operators. Finally, an example is shown to testify the correctness of the presented theoretical results. We discuss the comparison of the solutions of the operators along with the numerical example, emphasizing the role of symmetry in the accuracy and reliability of the numerical method. [ABSTRACT FROM AUTHOR]

In this paper, we consider the problem of finding the order 0<α<1$$ 0<\alpha <1 $$ in the fractional discrete system: C∇αun=Aun,n≥1,u0=x0,$$ \left\{\begin{array}{cll}{\kern0.1em }_C{\nabla}^{\alpha }{u}^n& =& A{u}^n,\kern0.30em n\ge 1,\\ {}{u}^0& =& {x}_0,\end{array}\right. $$where A$$ A $$ is a closed linear operator defined in a Banach space X,x0∈X$$ X,{x}_0\in X $$, and C∇αun$$ {\kern0.1em }_C{\nabla}^{\alpha }{u}^n $$ is the discrete Caputo fractional derivative of a given vector‐valued sequence (un)n∈ℕ0$$ {\left({u}^n\right)}_{n\in {\mathrm{\mathbb{N}}}_0} $$. [ABSTRACT FROM AUTHOR]

The objective of this work is to investigate the complex dynamics of a discrete predator–prey system using the method of piecewise constant argument for discretization. An analysis is conducted to examine the presence and stability of fixed points. Furthermore, the system is shown to undergo period-doubling (PD) and Neimark–Sacker (NS) bifurcations by the use of center manifold and bifurcation theories. The feedback and hybrid control strategies are used to regulate the system's bifurcating and chaotic behaviors. Both strategies seem to be effective in managing bifurcation and chaos inside the system. Finally, the main results are validated by numerical evidence. Parameters of the system are varied to produce time graphs, phase portraits, bifurcation diagrams, and maximum Lyapunov exponent (MLE) graphs. The discrete model displays rich dynamics, as seen in the numerical simulations and graphs, indicating a complex and chaotic system. [ABSTRACT FROM AUTHOR]