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A set of jobs has to be processed on identical machines. Every job may be processed on any available machine without preemptions. The criterion is to minimise the makespan (i.e. the completion time of the last job in a schedule). During the realisation of a schedule, durations of some jobs may deviate from the initial values estimated before scheduling. Other jobs have fixed durations that are known before scheduling. We conduct a stability analysis of the optimal semi-active schedule. First, we derive necessary and sufficient conditions for an optimal schedule to be unstable with respect to infinitely small variations of the non-fixed durations (the stability radius of an unstable schedule is equal to zero). Second, we show that the stability radius of an optimal schedule could be infinitely large. Furthermore, several lower and upper bounds on the stability radius have been established. Third, we derive a formula and develop an algorithm for calculating stability radii. [ABSTRACT FROM AUTHOR]

BACKGROUND RESULTS CONCLUSION Whey, a nutrient‐rich byproduct of the dairy sector, possesses high potential for creating novel nutraceutical products. The present study investigates a potential new functional food by incorporating polyphenolic extracts from Myrtus communis and Arbutus unedo fruits into whey in both liquid (LA) and powder (PA) addition forms. Chemical, microbiological, physical stability and antioxidant activity were monitored for 60 days (from T0 to T60).Both LA and PA of fruit extracts remained chemically stable for the whole period, except for A. unedo PA, which showed a decline in polyphenols after T45. Enriched whey samples showed higher antioxidant activity than pure whey. Microbiological analysis revealed the presence of lactic acid bacteria, indicating potential prebiotic effects. However, the high tannin concentration of A. unedo extracts partially modified the casein micelle structure.Whey enriched with Mediterranean fruit extracts shows great potential as a functional food, combining the benefits of plant antioxidants, probiotic bacteria and good stability. © 2024 The Author(s). Journal of the Science of Food and Agriculture published by John Wiley & Sons Ltd on behalf of Society of Chemical Industry. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and study an age‐structured epidemiological compartment model and its respective problem, applied but not limited to the COVID‐19 pandemic, in order to investigate the role of the age of the individuals in the evolution of epidemiological phenomena. We investigate the well‐posedness of the model, as well as the global dynamics of it in the sense of basic reproduction number, via constructing Lyapunov functions. [ABSTRACT FROM AUTHOR]

In order to comprehend the dynamics of disease propagation within a society, mathematical formulations are essential. Examining how hand contamination might induce pink eye infection (conjunctivitis virus) and treating it early with immunizations is the goal of this research. An immune system-boosting mathematical model is established, and it is converted to a fractional order model by using the Caputo fractional operator. To find the steady position of a recently constructed system SEVIR, a qualitative and quantitative analysis is conducted. Reliable bounded findings are ensured by assessing the generated system's boundedness, positivity, and uniqueness all crucial characteristics of epidemic models. The proposed non-linear system is verified to be present, and a unique solution is shown using fixed-point theorems to validate reliable solutions. Reproductive number with sensitivity analysis of parameters are also determined to verify the rate of spread and see how rate of change of each parameter is most sensitive. Using Lyapunov first derivative functions, the system is examined for local and global stability in order to evaluate the overall effect of early detection strategies and vaccination programs for people with weakened immune systems. Caputo operator is utilized for reliable solution using power law kernel with different fractional values for continuous monitoring of spread of pink eyes infection. Simulations have been made to see the real behavior and effects of pink eyes (conjunctivitis virus) infection to verify that the low immune individuals become strengthen due to early detection and vaccination combine measures. Also identify the true behavior for the control of pink eyes (conjunctivitis virus) infection after early detection and treatment as well as vaccination due to strong immune system of the patients. Investigating the transmission and management of diseases, as well as creating novel control techniques based on our validated findings to stop the conjunctivitis virus from spreading, would be aided by this kind of research. [ABSTRACT FROM AUTHOR]

This paper examines the stability analysis and exact solitary wave solutions of the nonlinear partial differential equation known as the Heimburg model. The several types of solitary wave solutions, soliton solutions and Jacobi elliptic doubly periodic function solutions are explored by using the extended Sinh-Gordon equation expansion approach. These investigations exhibit the system's astounding diversity of waveforms, highlighting its potential applications in nerves and biomembranes. By selecting some appropriate values for the parameters, 3D, 2D, and its corresponding contour graph are plotted to represent the physical relevance of some of the solutions. Additionally, the linearized stability of this system is analyzed. The suggested approach is the finest resource for the analytical investigation of any nonlinear issue that occurs in various scientific fields. [ABSTRACT FROM AUTHOR]

Cholera is a disease of poverty affecting people with inadequate access to safe water and basic sanitation. Conflict, unplanned urbanization and climate change all increase the risk of cholera. In this article, an optimal control deterministic mathematical model of cholera disease with cost-effectiveness analysis is developed and analyzed considering both direct and indirect contact transmission pathways. The model qualitative behaviors, such as the invariant region, the existence of a positive invariant solution, the two equilibrium points (disease-free and endemic equilibrium), and their stabilities (local as well as global stability) of the model are studied. Moreover, the basic reproduction number of the model is obtained. We also performed sensitivity analysis of the basic parameters of the model. Then an optimal control problem is designed with a control functional having five controls: vaccination, treatment, environment sanitation and personal hygiene, and water quality improvement program. We examined the existence and uniqueness of the optimal controls of the system. Through the implementation of Pontryagin's maximum principle, the characterization of the optimal controls optimality system is established. The numerical simulation results the integrated control strategies demonstrated that strategy 2, 7, and 12 are effective programs to combat cholera disease from the community. Based on the local circumstances, available funds, and resources, it is recommended to the government stakeholders and policymakers to execute any one of the three integrated intervention programs. [ABSTRACT FROM AUTHOR]

In this paper, we introduce an innovative hybrid discrete‐continuum model that provides a comprehensive framework for understanding the intricate interactions between tumor cells, immune cells, and the effects of immunotherapy. This study distinguishes itself by addressing the limitations of traditional diffusion models, which often fail to capture the irregular and nonlocal movements of cells within the complex tumor microenvironment. To overcome these challenges, we employ fractional time derivatives and the fractional Laplacian operator, offering a more accurate representation of anomalous diffusion processes that are critical in cancer dynamics. Our research begins with a rigorous mathematical analysis, where we establish the global existence of a unique mild solution, laying a solid theoretical foundation for the model. A key innovation of our study is the introduction of the “invasion threshold,” a critical parameter inspired by the next‐generation operator used in epidemiological modeling. This threshold provides a powerful tool for determining the existence and stability of equilibrium points, offering deep insights into the conditions that either promote or inhibit tumor growth under immunotherapeutic interventions. By integrating a hybrid discrete‐continuum approach, we capture the individual behavior of each cell, allowing for a more detailed exploration of the dynamic interplay within the tumor microenvironment. This model not only advances our understanding of tumor‐immune interactions but also holds potential for informing more effective therapeutic strategies, making a significant contribution to the field of mathematical oncology. [ABSTRACT FROM AUTHOR]

The modular multilevel converter (MMC) plays an important role in large-scale renewable energy integration and transmission, and it can also operate in standalone mode, powering AC passive loads. This paper focuses on the impact of load variation on the stability of the MMC. First, the impact of load variation on the MMC transfer function is analyzed in detail using the harmonic state-space (HSS) modeling method. Then, by means of the impedance-based stability analysis method, it is found that the MMC tends to become unstable with the increase in inductive loads. If the controller is not well-designed, the system may fail when loads change. Therefore, the worst-case design is used to guarantee the overall system's stability under all load conditions. The impact of traditional proportional resonant (PR) controller parameters on the system's stability is analyzed, revealing that the stability margin and control performance of the controller are limited. Thus, an improved controller structure with an additional series of compensators is proposed. Extensive simulation results in MATLAB/Simulink R2024a verify the analysis of this work and the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This study explores the dynamics of crime and substance abuse within a population by developing a novel mathematical model that integrates social interactions, rehabilitation efforts, and relapse probabilities. The model introduces a critical metric, the control reproduction number , to quantify the invasion threshold for these behaviors. The findings reveal that the crime/substance-free equilibrium is globally asymptotically stable when . At the same time, entrenched equilibria become stable where . Additionally, the model predicts the potential for a co-existent equilibrium where crime/substance abuse and a free state can coexist if all reproduction numbers exceed unity. Sensitivity analysis identifies key factors influencing , including behavioral transmission, internal progression rates, intervention efficacy, and recovery/relapse probabilities. Numerical simulations validate theoretical predictions regarding the stability of different equilibria, highlighting the critical importance of interventions targeting transmission reduction and rehabilitation efficiency. The research underscores the significance of understanding invasion dynamics for the coexistence of behaviors. It demonstrates the utility of mathematical modeling in elucidating the spread of social phenomena and informing effective control strategies. [ABSTRACT FROM AUTHOR]

This study analyzes the steady-state dynamics and stability of a structure with a particle damper considering the friction effect between the particle and container, with a focus on whether the system can maintain stable-state motion for an extended period. The determination of friction's contribution and the maximum allowable gap clearance for steady-state motion is demonstrated through the solution of motion of the primary structure with a particle damper subjected to low-frequency vibration conditions. Additionally, stability analysis is conducted to assess if initial disturbances cause deviations from the original stable state and identify necessary parameters for stability when the system parameters are uncertain. Analytical descriptions for the stability of the system are derived. The effects of friction on the dynamics and stability regions of the particle dampers are systematically revealed, where the theoretical and numerical models are mutually verified and supported by the cases of previous studies. Results show that the inclusion of the rolling friction effect will disrupt the steady-state motion as gap clearance approaches the optimal value. As the coefficient of rolling friction increases, the stability region's area gradually decreases with a notable leftward shift of its right boundary. This shift ultimately leads to a leftward shift in the optimal vibration reduction curve. In the range of gap clearance variation allowing for steady-state motion with two symmetrical impacts per cycle, the relative velocity of the particle is more effective and intuitive to reveal the vibration reduction mechanism of particle dampers than other perspectives such as momentum, energy, and phase. [ABSTRACT FROM AUTHOR]

This paper is devoted to analyzing a new model of a coupled Langevin system with fractional operators under nonlocal antiperiodic integral boundary conditions. This model involves nonlinear Langevin fractional equations with Caputo–Hadamard and Caputo fractional operators. Also, the existence and uniqueness of solutions to the suggested model have been investigated by the fixed-point technique. Moreover, the Hyers–Ulam stability of the solutions has been discussed. Finally, we provide an illustrative example to support the theoretical results. [ABSTRACT FROM AUTHOR]

In this article, we propose two procedures focusing on the computation of the time‐dependent convected wave equation in a free field with a uniform background flow. Both procedures are based on a framework, expended from Du et al. (SIAM J. Sci. Comput. 40 (2018), A1430–A1445.), of constructing the Dirichlet‐to‐Dirichlet (DtD)‐type discrete absorbing boundary conditions (ABCs). The first procedure is dedicated to reducing the infinite problem into a finite problem by a direct application of the framework on the finite difference discretization of the convected wave equation. However, the presence of convection terms makes the stability analysis hard to implement, which motivates us to develop the second procedure. First, the convected wave equation is transformed into a standard wave equation by using the Prandtl‐Glauert‐Lorentz transformation. After that, we obtain the DtD‐type ABC by using the above framework, and on this basis, derive an equivalent Dirichlet‐to‐Neumann‐type ABCs, which makes stability and convergence analysis easy to be obtained by the classical energy method. The effectiveness and comparison of these two procedures are investigated through numerical experiments. [ABSTRACT FROM AUTHOR]

Aluminum parts are used in the aviation industry because of the need for light. However, in addition to lightness, critical parts that must have high strength properties have also been developed. The corrosion resistance, resistance to high temperatures, and workability were investigated in this case. It becomes difficult to choose among many aluminum materials that can be alternatives to each other when these features are included. The developed approach, which considers many of the features listed above and ultimately recommends to the user the most suitable aluminum material for the relevant critical part, will be used in overcoming the difficulties in this process. A material selection model is proposed in this paper for this purpose, and the decision-making model is demonstrated with examples from the aviation industry. Therefore, the developed model, which will enable the selection of the most suitable materials among alternative materials, especially for critical parts in the aviation industry, will guide professionals working in this field. For this purpose, the fuzzy TOPSIS method is used in the study, and suitable alternatives are determined. Finally, a robustness analysis is proposed to determine the most suitable aluminum material for highly uncertain situations. We apply a stability evaluation study based on process control theory in the robustness analysis. [ABSTRACT FROM AUTHOR]

Failure in cancer treatment often stems from drug resistance, which can manifest as either intrinsic (pre-existing) or acquired (induced by drugs). Despite extensive efforts, overcoming this resistance remains a challenging task due to the intricate and highly individualized biological mechanisms involved. This paper introduces an innovative extension of an already well-established mathematical model to account for tumour resistance development against chemotherapy. This study examines the existence and local stability of model solutions, as well as exploring the model asymptotic dynamics. Additionally, a numerical analysis of the optimal control problem is conducted using an objective functional. The numerical simulations demonstrate that a constant anti-angiogenic treatment leads to a concatenation of bang-bang and singular intervals in chemotherapy control, resembling a combined protocol comprising maximal tolerated dose and metronomic protocols. This observation lends support to the hypothesis that mean-dose chemotherapy protocols may help circumvent acquired drug resistance. Lastly, a sensitivity analysis is undertaken to scrutinize the dependence of model parameters on the outcomes of the previously examined therapeutic protocols. • We consider a heterogeneous tumour consisting of two cellular subpopulations: sensitive and resistant to chemotherapy. • We change the therapy paradigm from total tumour eradication to controlling tumour growth and preventing drug resistance. • An optimal chemotherapy scheduling directly penalizes the subpopulation of resistant cells. • Penalizing chemoresistance gives rise to singular controls, supporting the metronomic chemotherapy administration scheme. • Sensitivity analysis shows how the optimal control structure depends on model parameters and initial conditions. [ABSTRACT FROM AUTHOR]

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Mass movements can be caused by factors from different categories, such as geological factors and climate change. From a geological point of view, the soil profile and the geotechnical properties of the materials are crucial in influencing slope instability. From a climate change perspective, rainfall intensity is one of the main triggers of mass movements. Studies related to rainfall infiltration focus on saturated slope zones; therefore, areas of slope stability with infiltration in the unsaturated zone present large gaps. The Brazilian government environmental diagnostics company, the Mineral Resources Research Company (CPRM), identified the municipality of Areia/PB as a danger zone. The region has landslides that occur mostly during the rainy season. Such events lead to the presumption that rainwater infiltration is responsible for the failure of the municipality's slopes. Thus, the studies proposed in this research aim to determine the influence of precipitation on the stability of the slopes present in the region. The results show that antecedent precipitation has a greater influence on stability, indicating that daily precipitation alone cannot be used as a determinant for landslides. It was concluded that the role of precipitation in slope stability will vary for different locations, with varying surface conditions, variable tropical rainfall, or different microclimatic conditions. [ABSTRACT FROM AUTHOR]

Mining causes damage to the soil and rock mass, while rainfall has a pivotal impact on the mining slope stability, even leading to geological hazards such as landslides. Therefore, the study evaluated the mine landslide stability and determined the effectiveness of the treatment measures under the impact of pore water pressure changes caused by rainfall, taking the Kong Mountain landslide in Nanjing, Jiangsu Province, China, as the research object. The geological conditions and deformation characteristics were clarified, and the failure mechanism and influencing factors were analyzed. Also, the landslide stability was comprehensively evaluated and calculated utilizing the finite element-improved limit equilibrium method and FLAC 3D 6.0, which simulated the distribution of pore water pressure, displacement, etc., to analyze the influence of rainfall conditions and reinforcement effects. The results indicated the following: (1) Rainfall is the key influencing factor of the landslide stability, which caused the pore water pressure changes and the loosening of the soil due to the strong permeability; (2) The distribution of the pore water pressure and plastic zone showed that, during the rainfall process, a large area of transient saturation zone appeared at the leading edge, affecting the stability of the whole landslide and led to the further deformation; (3) After the application of treatment measures (anti-sliding piles and anchor cables), the landslide stability increased under both natural and rainfall conditions (from 1.02 and 0.94 to 1.38 and 1.31, respectively), along with a reduction in displacement, plastic zones, etc. The Kong Mountain landslide, with the implemented treatment measures, is in good stability, which is in line with the evaluation and calculation results. The study provides certain contributions to the stability evaluation and treatment selection of similar engineering under rainfall infiltration. [ABSTRACT FROM AUTHOR]

Accurate soil stratification is crucial for levee safety evaluation, yet limited field sampling often hinders comprehensive analysis. This study applies the Partitioning Around Medoids (PAM, also known as K-Medoids) clustering approach for levee soil stratification using data from multiple probe drilling sites. Focusing on a Yellow River levee section in China as a study case, the PAM clustering approach effectively identifies its distinct soil types and reconstructs its soil stratification by analyzing key soil properties relevant to levee seepage and stability characteristics, including coefficient of permeability, angle of internal friction, and cohesion. The resulting soil stratification, when applied to seepage and stability analyses of the levee section, yields relatively high safety factors, indicating low failure risks under design flood conditions. These analytical results align with recent monitoring records, validating the effectiveness of the approach. A sensitivity analysis on the number of clusters, the key parameter in the PAM clustering approach, demonstrates the typical existence of an optimal value balancing computational accuracy and practical interpretability. A comparison with a hierarchical clustering approach further confirms the robustness of the PAM clustering approach. This study contributes to improving levee soil stratification methodology and enhancing levee safety evaluation, particularly when dealing with limited and spatially distributed sampling data. [ABSTRACT FROM AUTHOR]

Accurate and efficient modeling and simulation of spacecraft electrical systems are crucial because of their complexity. However, existing models often struggle to balance simulation efficiency and accuracy. This paper introduces a model reduction method based on singular perturbation theory to simplify the full-order model of spacecraft electrical systems. The experimental results show that the reduced-order simplified model saves 50% of the simulation time with almost no degradation in the simulation accuracy and can be applied to real-world scenarios, such as digital twins. This method offers a new approach for rapid simulation of spacecraft electrical systems and has broad application prospects. [ABSTRACT FROM AUTHOR]

Numerous studies have investigated the stability of highly nonlinear stochastic systems (HNSSs). However, previous works have primarily focused on either deterministic or random switchings. In this paper, we examine HNSSs with delays and two switching modes. First, we introduce a hybrid switching rule and construct a stopping time in segments, dividing the switching interval of the entire system into a deterministic switching interval and a stochastic switching interval. Second, we establish the existence and boundedness of the global solution of the system by using the Lyapunov function and the average dwell time method. Additionally, we prove the asymptotic stability and exponential stability of the system without relying on the linear growth condition (LGC). Finally, we provide an illustrative example to demonstrate the validity of the obtained results. [ABSTRACT FROM AUTHOR]

This study aims to explore the complexity of a discrete-time predator–prey system with a weak Allee effect. The existence and stability of fixed points, as well as period-doubling and Neimark–Sacker bifurcations, are all investigated. The system’s bifurcating and fluctuating behavior is controlled using feedback and hybrid control techniques. Additionally, numerical simulations are performed as evidence to support theoretical results. From an ecological perspective, these findings suggest that the Allee effect plays a pivotal role in shaping predator–prey dynamics. The moderate Allee effect fosters stability in both predator and prey populations, promoting coexistence and persistence within ecosystems. However, the disproportionate impact on predator populations underscores predators’ vulnerability to changes in prey behavior and availability, highlighting the importance of considering indirect effects in ecological modeling and conservation efforts. [ABSTRACT FROM AUTHOR]

In this paper, the distributed moving horizon fusion estimation of uncertain systems with constraints of system noise and state variables is studied. Firstly, relying on the basic idea of consensus algorithm, the cost function in the performance index is reconstructed by weighted fusion of the state prediction values. Secondly, considering the performance index with uncertain parameters, the min‐max optimization problem of the algorithm is transformed into the least squares optimization problem based on 2‐norm regularization method. Thirdly, the scalar‐weighted linear minimum variance fusion estimation strategy is used to realize the weighted fusion of local state estimation values. Then, on the premise of minimum network connectivity and collective observability, the stability of the proposed algorithm is studied, and the sufficient conditions for the expected convergence of the fused estimation error norm square are given. Finally, the effectiveness of the algorithm is verified by numerical simulation. [ABSTRACT FROM AUTHOR]

In this paper, an observer‐based nonlinear controller is proposed to regulate blood glucose concentration (BGC) in type 1 diabetes mellitus (T1DM). The considered virtual patient model is the extended Bergmann minimal model, which is augmented by a meal disturbance and adapted to represent the insulin–glucose homeostasis of T1DM. The backstepping (BS) technique is used to design a closed‐loop feedback controller. The proposed controller does not need to measure insulin, plasma concentrations, and external disturbances while improving control performance and robustness against uncertainty. Insulin concentrations and plasma levels are estimated using state observers and disturbance using a disturbance estimator. These estimations are used as feedback to the controller. The asymptotic stability of the observer‐based controller is proved using the Lyapunov theorem. Furthermore, it is proven that the system is bounded input–bounded output (BIBO) stable in the presence of uncertainties caused by uncertain parameters and external disturbances. For real situations, we consider only the BGC available for measurement, and in addition, inter‐ and intra‐patient variability of system parameters is considered. The results confirm that the proposed controller can asymptotically regulate BGC through appropriate injection of insulin under meal disturbance and ±25% of variations in system parameters. [ABSTRACT FROM AUTHOR]

A mathematical model is designed to investigate Tuberculosis (TB) disease under the vaccination, treatment, and environmental impact with real cases. First, we introduce the model formulation in non-integer order derivative and then, extend the model into fractional order derivative. The fractional system's existence, uniqueness, and other relevant properties are shown. Then, we study the stability analysis of the equilibrium points. The disease-free equilibrium (DFE) 0 is locally asymptotically stable (LAS) when ℛ v < 1. Further, we show the global asymptotical stability (GAS) of the endemic equilibrium (EE) ∗ for ℛ v > 1 and 0 for ℛ v ≤ 1. The existence of bifurcation analysis in the model is investigated, and it is shown the system possesses the forward bifurcation phenomenon. Sensitivity analysis has been performed to determine the sensitive parameters that impact ℛ v. We consider the real TB statistics from Khyber Pakhtunkhwa in Pakistan and parameterized the model. The computed basic reproduction number obtained using the real cases is ℛ 0 ≈ 3.6615. Various numerical results regarding disease elimination of the sensitive parameters are shown graphically. [ABSTRACT FROM AUTHOR]

False data injection (FDI) attacks have significantly threatened the security of the cyberphysical system (CPS). To ensure the stability of the CPS under FDI attacks, resilient model predictive control (MPC) has been extensively researched. However, most of the existing resilient MPC methods fail to consider the network resource limitation of the CPS, which may not be applicable in some real systems. Therefore, in this article, a resilient self-triggered (ST) MPC strategy is developed for a discrete-time nonlinear CPS under FDI attacks, which can not only ensure the system’s stability but also reduce resource consumption via decreasing the update frequency of MPC and economizing the utilization of the protection resource. First, an input signal reconstruction mechanism is designed based on key control data selection, which could reconstruct a feasible control sequence for the CPS even if the original ST control sequence is tampered with by FDI attacks. Then, a resilient ST-MPC algorithm based on the input signal reconstruction mechanism is proposed to weaken the adverse effects of FDI attacks and reduce resource consumption simultaneously. Moreover, the recursive feasibility of the resilient ST-MPC mechanism and input-to-state stability of the controlled system are respectively proved. Finally, the performance of the resilient ST-MPC mechanism is shown through a cart–damper–string system and an intelligent vehicle system. [ABSTRACT FROM AUTHOR]

Regenerative chatter is a prominent form of vibration in any machining process caused by the waviness of the workpiece surface. During internal turning processes, regenerative chatter constitutes a significant concern due to the highly flexible nature of boring bars and workpieces. As a result, the surface finish is poor, tool wear is accelerated, and machining at a high depth of cut is challenging. Typically, stability lobe diagrams (SLDs), plots of spindle speeds versus depth of cuts, are employed to select stable machining parameters. In the present work, a numerical linear stability analysis of a two-degree-of-freedom finite element model of a boring tool–workpiece system is carried out in the frequency domain to construct SLDs that are utilized to investigate how changing dynamics of the workpiece affect machining stability. The numerical model is validated using an analytical model, and the results of both models are found to be in agreement. Moreover, the results show that the depth of cut of a tool–workpiece system with moderately low and high workpiece stiffness is 11.8% and 16.2% lower than that of a single degree-of-freedom (DOF) system that does not take the workpiece into account. The SLDs of two DOF systems with workpieces of high and very high stiffness are observed to overlap with that of a single DOF system. It is also inferred that the damping ratio of the workpiece has no significant effect on the stability lobes. The machining experiments are conducted on a boring tool–workpiece system, and it is found that the experimental results align with the analytical and numerical findings. Additionally, a digital twin framework based on the computational model is suggested to facilitate the real-time monitoring and optimization of boring processes. [ABSTRACT FROM AUTHOR]

This paper aims to investigate some new dynamics of a new model describing the rabies virus dynamics, taking into account the effect of proper vaccination. The model's population is divided into three main compartments, namely, susceptible S(t), infected I(t), and recovered R(t) individuals. The model is formulated and then the equilibrium points of the model are found. The local and global stabilities of equilibrium points of the proposed model are investigated where conditions of stability are attained in terms of key parameters in the model. Bifurcation analysis is performed for the possible occurrence of codimension‐one bifurcations in the model. In addition, bifurcation surfaces are plotted in the space of parameters in the model. For the numerical verification, a nonstandard finite difference method is adapted for solving the model and the accurate results of numerical simulations are depicted to reveal the dynamics of the model. The method provides realistic data for the model and these data can be used to predict the spread of the virus and to provide insight into proper procedures and control measures that can be taken. [ABSTRACT FROM AUTHOR]

Malaria remains a substantial public health challenge and economic burden globally. Currently, malaria has been declared as endemic in 85 countries. In this study, we developed and analyzed a fractional-order mathematical model for malaria transmission dynamics that incorporates variability of temperature and rainfall using Caputo-type AB operators. The existence and uniqueness of the model's solutions were established using the Banach fixed-point theorem. The model system's equilibria (both disease-free and endemic) were identified, and lemmas and theorems were developed to prove their stability. Furthermore, we used different temperature ranges and rainfall data, validating them against existing literature. Numerical simulations using the Toufik-Atangana schemes with various fractional-order alpha values revealed that as the value of alpha approaches 1, the behavior of the fractional-order model converges to that of the classical model. The numerical results are promising and are expected to be valuable for future research related to fractional-order models. [ABSTRACT FROM AUTHOR]

The purpose of this work was to assess the capability of radiomic features in distinguishing PET image regions with different uptake patterns. Furthermore, we assessed the stability of PET radiomic features with varying image reconstruction settings. An in-house phantom was designed and constructed, consisting of homogenous and heterogenous artificial phantom inserts. Four artificially constructed inserts were placed into a water filled phantom and filled with varying levels of radioactivity to simulate homogeneous and heterogeneous uptake patterns. The phantom was imaged for 80 min. PET images were reconstructed whilst varying reconstruction parameters. The parameters adjusted included, number of ordered subsets, number of iterations, use of time-of-flight and filter cut off. Regions of interest (ROI) were established by segmentation of the phantom inserts from the reconstructed images. In total seventy eight 3D radiomic features for each ROI with unique reconstructed parameters were extracted. The Friedman test was used to determine the statistical power of each radiomic feature in differentiating phantom inserts with different hetero/homogeneous configurations. The Coefficient of Variation (COV) of each feature, with respect to the reconstruction setting was used to determine feature stability. Forty three out of seventy eight radiomic features were found to be stable (COV ≤5%) against all reconstruction settings. To provide any utility, stable features are required to differentiate between regions with different hetro/homogeneity. Of the forty three stable features, fifteen (35%) features showed a statistically significant difference between the artificially constructed inserts. Such features included GLCM (Difference average, Difference entropy, Dissimilarity and Inverse difference), GLRL (Long run emphasis, Grey level non uniformity and Run percentage) and NGTDM (Complexity and Strength). The finding of this work suggests that radiomic features are capable of distinguishing between radioactive distribution patterns that demonstrate different levels of heterogeneity. Therefore, radiomic features could serve as an adjuvant diagnostic tool along with traditional imaging. However, the choice of the radiomic features needs to account for variability introduced when different reconstruction settings are used. Standardization of PET image reconstruction settings across sites performing radiomic analysis in multi-centre trials should be considered. [ABSTRACT FROM AUTHOR]

This paper presents a comprehensive study on the dynamic modeling of distribution power systems with a focus on the integration of renewable energy sources (RESs) for stability analysis. Our research delves into the static and dynamic behavior of distribution systems, emphasizing the need for enhanced load modeling to mitigate planning and operational uncertainties. Using MATLAB/Simulink®, we simulate four distinct study cases characterized by varying load types and levels of distributed generation (DG), particularly solar PV, under both balanced and unbalanced conditions. Our findings highlight the critical role of DG in influencing voltage stability, revealing that deviations in voltage and current during grid imbalances remain within acceptable limits. The study underscores the importance of DG-based inverters in maintaining grid stability through reactive power support and sets the stage for future research on microgrid simulations and battery storage integration to further enhance system stability and performance. [ABSTRACT FROM AUTHOR]

The mathematical modeling of infectious diseases plays a vital role in understanding and predicting disease transmission, as underscored by recent global outbreaks; to delve deep into the dynamic of infectious disease considering latent period presciently is inevitable as it bridges the gap between realistic nature and mathematical modeling. This study extended the classical Susceptible–Infected–Recovered (SIR) model by incorporating vaccination strategies during incubation. We introduced multiple time delays to an account incubation period to capture realistic disease dynamics better. The model is formulated as a system of delay differential equations that describe the transmission dynamics of diseases such as polio or COVID-19, or diseases for which vaccination exists. Critical aspects of the study include proving the positivity of the model's solutions, calculating the basic reproduction number ( R 0 ) using next-generation matrix theory, and identifying disease-free and endemic equilibrium points. The local stability of these equilibria is then analyzed using the Routh–Hurwitz criterion. Due to the complexity introduced by the delay components, we examine the stability by studying the roots of a fourth-degree exponential polynomial. The effects of educational campaigns and vaccination efficacy are also investigated as control measures. Furthermore, an optimization problem is formulated, based on Pontryagin's maximum principle, to minimize the number of infections and associated intervention costs. Numerical simulations of the delay differential equations are conducted, and a modified Runge–Kutta method with delays is used to solve the optimal control problem. Finally, we present a few simulation results to illustrate the analytical findings. [ABSTRACT FROM AUTHOR]

ABSTRACT Safety analysis of power systems is concerned with the system's ability to maintain critical variables within specified limits following a disturbance. Frequency control adequacy has become increasingly important as the system inertia decreases due to the increase in renewable energy penetration. Various controllers for inverters have been proposed to improve the system frequency response and few are capable to ensure the safety of the response. In this article, a diesel‐wind energy system is considered and modeled as a switching system between normal, faulted, and post‐fault modes. A safety feedback controller is designed as a supplementary signal for a wind turbine generator such that the speed of the diesel generator stays within a permissible range in the presence of a finite energy disturbance. Numerical results on the modified 33‐bus microgrid system obtained of the proposed novel approach indicate that the suggested control configuration can guarantee adequate frequency response without excessive conservativeness. [ABSTRACT FROM AUTHOR]

In this study, nonlinear vibrations and stability of multilayer functionally graded (FG) pipes conveying fluid laying on nonlinear elastic foundation and reinforced by graphene nanoplatelets (GPLs) are investigated with an emphasis on optimized analytical method. Various types of GPL distribution patterns are considered and to estimate the mechanical characteristics of the reinforced pipe the Halpin–Tsai micromechanics theory is applied. The nonlinear differential equation of motion is obtained by using Von–Kármán strain relations in conjunction with the Euler–Bernoulli beam theory and applying Hamilton's principle. The Galerkin technique has been used for discretizing the partial differential equation. The optimized homotopy analysis method (HAM), as a strong analytical method, is utilized to solve the nonlinear differential equation by considering different initial excitations. The convergence-control parameter is taken into account to guarantee the convergence of the analytical solution. In this study, an exact solution based on HAM for the critical flow velocity and n th nonlinear frequency is presented. Additionally, series solutions for the nonlinear time responses of the transverse and longitudinal vibrations of fluid-conveying pipe based on optimized HAM are obtained for the first time. In the numerical results, the effects of arbitrary initial conditions and different physical characteristics on the nonlinear frequencies and time responses are extensively examined. It is shown that the nonlinear frequencies and critical flow velocity of the pipe depend not only on the initial excitation amplitude, but also on the entire initial excitation function applied on the pipe. [ABSTRACT FROM AUTHOR]

This study presents, a numerical method for the solutions of the generalized nonlinear Benjamin-Bona-Mahony-Burgers' equation, with variable order local time fractional derivative. This derivative is expressed as a product of two functions, the usual integer order time derivative, and a function of time having a fractional exponent. Then, forward difference approximation is used for time derivative. The unknown solution of the differential problem and corresponding derivatives are estimated using Haar wavelet approximations (HWA). The collocation procedure is then implemented in HWA, to transform the given model to the system of linear algebraic equations for the determination of unknown constant coefficient of the Haar wavelet series, which update the derivatives and the numerical solutions. The sufficient condition is established for the stability of the proposed technique, and then verified computationally. To check the performance of the scheme, few illustrative examples in one and two dimensions along with l ∞ and l 2 error norms are also given. Besides this, the computational convergence rate is calculated for both type equations. Additionally, computed solutions are compared with available results in literature. Simulations and graphical data discloses, that suggested scheme works well for such complex problems. [ABSTRACT FROM AUTHOR]

Quinoa (Chenopodium quinoa Willd.) can offer an alternative for staple food considering its tolerance to abiotic stresses and high seed quality. However, its cultivation in temperate regions has not been successful due to its photoperiod sensitivity and low seed yield. This study investigated the agronomical performance and quality traits of 48 accessions for cultivation in northern Europe. We conducted two-year field trials and phenotyped traits related to phenological development, plant architecture, yield components, seed quality, and disease resistance. The major determinants of seed yield in this study were days to flowering, days to maturity, thousand-kernel weight, and panicle density, while downy mildew susceptibility and stem lodging showed a negative correlation with seed yield. We developed a selection index to enable simultaneous selection based on different important agronomical traits. We evaluated the stability of different accessions over the two years of the experiment. Finally, we provided a list of 10 selected accessions that can be directly integrated and serve as new crossing parents in quinoa breeding programs for temperate regions. [ABSTRACT FROM AUTHOR]

The Green–Ampt (GA) model is a widely used analytical method to calculate the depth of the wetting front during intense rainfall. However, it neglects the existence of the transition layer and the seepage parallel to the slope surface. Therefore, a modified stratified Green–Ampt (MSGA) model is proposed. A process to assess the stability of the finite slope during a rainfall event is demonstrated by combining the MSGA model and the limit equilibrium method. In the case of the Liangshuijing landslide, the factor of safety presents a negative correlation with the depth of the wetting front. The factor of safety obtained by the stratified Green–Ampt (SGA) model is smaller than that calculated by the MSGA model, and the gap between the factor of safety based on the two methods widens with time. The moving speed of the wetting front accelerates with the increase in the length of the slope surface, and the size effect becomes apparent when the length is short. In the initial stage of infiltration, the effect of the seepage parallel to the slope surface is small. The effect of the seepage cannot be neglected at the latter stage. The result calculated by the MSGA model agrees well with the measured result in the test. [ABSTRACT FROM AUTHOR]

Information deviations are inevitable under the influence of multifarious factors in real-world traffic, leading to discrepancies between the information obtained by automated vehicles (AVs) and the true information. However, due to the lack of an appropriate analytical model that incorporates various information with deviations, we have limited knowledge of the relationships between different types of information deviations and anomalous dynamics of AVs and traffic flow. This study aims to fill this gap. Specifically, we first expound the possible information deviations in AVs, upon which we categorize them into three types: velocity, gap, and driving decision deviations. Subsequently, we modify the input parameters in the adaptive cruise control (ACC) model that calibrated using real experimental data to capture the car-following dynamics of AVs with information deviations. By using H ∞ control theory and characteristic equation-based method, we derive the local and string stability criteria of traffic flow with AVs, so as to discern the effects of various system factors on traffic flow stability. Experimental results show that information deviations could provoke abrupt acceleration or deceleration of AVs, leading to instability in automated traffic flow, oscillation, and even collision accidents. Overall, this paper unveils the influence mechanisms of diverse information deviations on AVs and traffic flow, providing valuable suggestions and theoretical guidance for the future development of AVs. [ABSTRACT FROM AUTHOR]

Studying slope stability under different water contents and stress conditions is very important for the early warning and prevention of slope disasters. In this study, the stability of a side slope in Xingwen County was studied via field investigations, laboratory tests, and numerical simulations. The results show that a dry sample has a greater rockburst proneness than a water‐rich sample. Compared with that of the dry sample, the strength of the sample representing the water‐rich area of the slope decreased significantly, the peak strength decreases by 28.5% on average under the different confining pressure conditions tested, and the stress–strain curve has more jitter after the peak and shows more obvious plastic characteristics. The peak shear strain in the XZ direction on the lower slope under water‐rich conditions is 48.5% greater than that under dry conditions, and the range of the slope plastic zone is also significantly greater than that under dry conditions. This indicates that the stability of the slope under water‐rich conditions is much lower than that under dry conditions. The safety factors of the three types of slopes are calculated. The slope safety factors under the "water‐rich and deadweight" and "water‐rich and earthquake" conditions are 3.1% and 5.4% lower, respectively, than that under the "dry and deadweight" conditions. Therefore, it is necessary to strengthen the protection of water‐rich areas on slopes with frequent microearthquakes. [ABSTRACT FROM AUTHOR]

Nonlinear problems, which often arise in various scientific and engineering disciplines, typically involve nonlinear equations or functions with multiple solutions. Analytical solutions to these problems are often impossible to obtain, necessitating the use of numerical techniques. This research proposes an efficient and stable Caputo-type inverse numerical fractional scheme for simultaneously approximating all roots of nonlinear equations, with a convergence order of 2 ψ + 2 . The scheme is applied to various nonlinear problems, utilizing dynamical analysis to determine efficient initial values for a single root-finding Caputo-type fractional scheme, which is further employed in inverse fractional parallel schemes to accelerate convergence rates. Several sets of random initial vectors demonstrate the global convergence behavior of the proposed method. The newly developed scheme outperforms existing methods in terms of accuracy, consistency, validation, computational CPU time, residual error, and stability. [ABSTRACT FROM AUTHOR]

We study the loss landscape of training problems for deep artificial neural networks with a one-dimensional real output whose activation functions contain an affine segment and whose hidden layers have width at least two. It is shown that such problems possess a continuum of spurious (i.e., not globally optimal) local minima for all target functions that are not affine. In contrast to previous works, our analysis covers all sampling and parameterization regimes, general differentiable loss functions, arbitrary continuous nonpolynomial activation functions, and both the finite- and infinite-dimensional setting. It is further shown that the appearance of the spurious local minima in the considered training problems is a direct consequence of the universal approximation theorem and that the underlying mechanisms also cause, e.g., L p -best approximation problems to be ill-posed in the sense of Hadamard for all networks that do not have a dense image. The latter result also holds without the assumption of local affine linearity and without any conditions on the hidden layers. [ABSTRACT FROM AUTHOR]

This article introduces a unified criterion for input‐to‐state stability (ISS), integral input‐to‐state stability (iISS) and eσt$$ {e}^{\sigma t} $$‐input‐to‐state stability (eσt$$ {e}^{\sigma t} $$‐ISS) of impulsive stochastic system with switching. The criterion demonstrates that the premise of a switching‐impulse system to achieve three types of ISS is that a mutually constraining relationship between switching, impulse and continuous dynamics needs to be satisfied. Furthermore, using it we know that switching can stabilize a system containing stabilizing factors by affecting both continuous dynamics and impulses, that switching itself is one of the factors in system instability, and that impulses have a dual effect on the stability of the system. The coefficients of the upper bound of Lyapunov functional differential operators are time‐varying functions and the impulses contain stable and unstable impulses, including the case of constants, which advances and improves the existing results. Finally, an example and its simulation results are given to verify the validity of theoretical analysis. [ABSTRACT FROM AUTHOR]

The critical global buckling load is a fundamental parameter governing the performance of tall buildings, however, the existing literature lacks an efficient solution that comprehensively captures the behavior of tall structures with uniform or variable properties. In response to this gap, this study introduces a novel and generalized solution, employing the coupled shear-flexural model. This solution is designed for determining the critical global buckling load in tall buildings subjected to vertical loads with diverse profiles, while also incorporating soil flexibility. The analytical solution, designed for the uniform continuous model, offers a breakthrough by providing graphical representations facilitating the direct determination of eigenvalues based on a single dimensionless parameter. Addressing the unique challenge posed by tall buildings with variable properties, a numerical transfer matrix method based on a Laplacian approach is proposed. This method enables the direct calculation of the transfer matrix for each level, displaying exceptional convergence in just three iterations. The study sheds light on a crucial finding that emphasizes the adverse impact of rotational flexibility on soil, leading to a decrease in eigenvalues as soil flexibility increases. Importantly, the proposed solution methods not only show excellent accuracy but also serve as invaluable tools for performing parametric analyses. Furthermore, they present cost-effective alternatives to exact methods, providing a solid foundation for studying the overall stability of tall buildings. This research contributes significantly to the existing literature by introducing efficient methodologies that improve our understanding and analysis of the behavior of tall buildings under vertical loads. [ABSTRACT FROM AUTHOR]

The purpose of this article is to propose a novel framework employing a looped‐functional approach for the stability analysis of continuous‐time linear systems with asynchronous sampling. In this approach, a negative forward‐difference of a Lyapunov functional consisting of a Lyapunov function and a looped‐functional sufficiently guarantees asymptotic stability of the sampled‐data systems. To reduce the conservatism of the stability criteria, we develop a consecutive time‐intervals‐dependent looped‐functional approach that satisfies a convex looping inequality with respect to each sampling interval. Compared to the existing looped‐functional approaches, the proposed method provides a more general looped‐functional and in turn a more relaxed stability conditions. The existing looped functionals and their associated looping conditions can be considered as special cases of the proposed ones. This relationship can easily be verified by excluding time‐intervals‐dependent terms in the general looped functional. Four numerical examples that consider both periodic and asynchronous sampling cases demonstrate that the proposed looped‐functional approach shows better performance in terms of allowable maximum sampling intervals at a cost of a small additional number of decision variables. [ABSTRACT FROM AUTHOR]

The Nelson–Siegel and the Svensson models are two widely used models for the term structure of interest rates. These models are quite simple and intuitive, but fitting them to market data is numerically challenging and various difficulties have been reported. In this paper, we provide a novel mathematical analysis of the fitting problem based on parametric optimization. We formulate the fitting problem as a separable nonlinear least-squares problem, in which the linear parameters can be eliminated. We provide a thorough discussion on the conditioning of the inner part of the reformulated problem and show that many of the reported difficulties encountered when solving it are inherent to the problem formulation itself and cannot be tackled by choosing a particular optimization algorithm. Our stability analysis provides novel insights that we use to show that some of the ill-conditioning can be avoided, and that a suitably chosen penalty approach can be used to address the remaining ill-conditioning. Numerical results indicate that this approach has the expected impact while being independent of any choice of a particular optimization algorithm. We further establish smoothness properties of the reduced objective function, putting global optimization methods for the reduced problem on a sound mathematical basis. [ABSTRACT FROM AUTHOR]

Stability assessment based on failure mechanisms is extremely crucial for slope quantitative evaluation. In this study, a vector sum particle flow method is proposed based on the mechanism of stepped tensile failure. This mechanism involves the mechanical behavior, lithology, and fracture properties. Furthermore, the proposed fracture criteria are reflected in the particle contact model of the 2D Particle Flow Code using a predefined strength envelope. Mesoscopic parameters are calibrated according to a certain strength parameter relationship, thereby realizing the construction of a vector sum numerical model. The failure evolution process of four slopes with different stepped crack arrangements is analyzed. Based on the analysis results, the stability analysis process of the slope is elaborated. This research analyzes the stability of the above four slopes and examines the stability of different failure stages during the formation of the sliding plane. The proposed method provides more accurate calculation results compared to the limit equilibrium method and gravity increase method. It accurately reflects the actual stress state of the sliding plane and indirectly considers the impact of the crack arrangement. The findings of this study are highly valuable for evaluating the stability of slopes experiencing stepped failure. [ABSTRACT FROM AUTHOR]

The development and stability of acoustic thin-shell wormholes (WHs) within the context of acoustic black holes are examined in this paper. Utilizing linearized radial perturbations, the stability of these WHs is examined. In this study, a variety of equations of state are taken into account, including barotropic, variable Chaplygin, and phantom-like equations of state. According to the findings, the acoustic black hole structure has an unstable configuration for barotropic fluid. However, as the parameter ℰ gets closer to zero, it does not show any stable or unstable configurations at the event horizon position. For higher values of n and ξ , the resulting structure for the phantom-like variable equation of state (EoS) displays stable behavior away from the horizon while presenting unstable configurations close to the event horizon. The possibility of a stable structure rises as n is increased. Additionally, the constructed structure exhibits stable behavior for n = 1 under extreme acoustic black holes, whereas thin-shell topologies demonstrate unstable behavior outside the event horizon for the generalized Chaplygin variable EoS. However, the structure stabilizes for n = 1 at higher values of ξ. The stability of acoustic thin-shell WHs is higher than that of Schwarzschild thin-shell WHs for smaller values of n , indicating that the acoustic black hole parameter greatly influences the stable configurations of thin-shell WHs. [ABSTRACT FROM AUTHOR]

This paper proposes a new pair of block techniques (NPBT) for the direct solution of third-order singular initial-value problems (IVPs). The proposed method uses a polynomial and two intermediate points to approximate the theoretical solution of third-order singular IVPs, resulting in a reasonable approximation within the integration interval. The method's essential features, including stability and convergence order, are analyzed. The proposed NPBT method is improved by using an embedding-like strategy that allows it to be executed in a variable step size mode in order to gain better efficiency. The effectiveness of the proposed method is assessed using various model problems. The approximate solution provided by the proposed NPBT method is more accurate than that of the existing methods utilized for comparison. This efficient solution positions NPBT as a good numerical method for integrating third-order singular IVP models in the fields of applied sciences and engineering. [ABSTRACT FROM AUTHOR]