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In our present paper, we have employed the Atangana–Baleanu derivative in the multi-layered Navier–Stokes condition to analyse the nature of the flow. Actually, the stream, the impacts and modifications caused by the operator and the mathematical technique approach are the main subjects of our attention. In this exploratory work, the Laplace transform strategy and the Atangana–Baleanu fractional operator were combined. Due to the Atangana–Baleanu operator's convergence in many engineering and technological issues, it is employed. We have also carefully evaluated the presence and uniqueness of the outcome. To visualize the variations in the flow, we have presented the graphs of the stream's velocity components in each direction during the study.

The outbreak of COVID-19 causes a serious threat to human health and life around the world and puts enormous pressure on the healthcare system. The lockdown policy has effectively reduced the number of cases and suppressed the spread of the COVID-19 epidemic, but it also requires high social and economic costs. In this paper, we aim to use feedback control to help decision-makers establish lockdown policies, which can effectively constrain the spread of the COVID-19 pandemic with minimal financial loss. The time-dependent susceptible-infected-removed (SIR) model is used for the dynamics of the COVID-19 pandemic. The feedback control is based on a modified nonlinear active disturbance rejection controller (ADRC) that includes modified nonlinear extended state and nonlinear state error feedback with parameters tuned by particle swarm optimization, and the performances are compared with a well-known proportional-–integral–-derivative (PID) controller. The final simulation results show that the modified nonlinear ADRC has better performances and is more robust against uncertainties in the parameters of the epidemiological model.

ABSTRACTRecently, degenerate harmonic numbers and degenerate hyperharmonic numbers are introduced by Kim-Kim. In this paper, we study the series involving the degenerate harmonic numbers and degenerate Stirling numbers and investigate those properties.

This paper develops a mathematical framework that aims to control the temperature and rotational speed in the activation process of a gas turbine in an optimal way. These controls influence the deformation and the stress in the component due to centripetal loads and transient thermal stress. An optimal control problem is formulated as the minimization of maximal von Mises stress over a given time and over the whole component. To find a solution for this, we need to solve the linear thermoelasticity and the heat equations using the finite element method. The results for the optimal control as functions of the rotation speed and external gas temperature over time are computed by sequential quadratic programming, where gradients are computed using finite differences. The overall outcome reveals a significant reduction of approximately 10%, from [Formula: see text] to [Formula: see text], in von Mises stress by controlling two parameters, along with the temporal separation of physical control phenomena.

In this paper, a modified method is used to approximate the solution to the time-fractional n-dimensional Navier–Stokes equation. The modified method is the Variational Iteration Transform Method, which is implemented in the equation whose fractional order derivative is described in the Caputo sense. The proposed method's findings are presented and examined using figures. It is demonstrated that the proposed method is efficient, dependable, and simple to apply to various science and engineering applications.

The fuzzy stochastic differential equations with Markovian switching are considered. First, under the [Formula: see text] assumptions, the existence and uniqueness theorem for the aforementioned equations is given by means of stopping time techniques, discretization method, and the Gronwall-Bellman inequality. Then the boundedness of the second moment of the solutions for such equations is established. Furthermore, by using the averaging method and stochastic analysis, as well as the Bihari's inequality, this paper mainly demonstrates the asymptotic relationship between the solutions of the original equations and the corresponding averaged equations in terms of mean square and probability. Finally, the theoretical result of the averaging method is illustrated by an example.

In this paper, the existing Susceptible-Infected-Recovered-Deceased (SIRD) compartmental epidemiologic process model is modified for forecasting the coronavirus effect in India. The data from India was studied for weekly fatalities, weekly infected, weekly recovered, new cases, infected and recovered individuals, Reproductive Number [Formula: see text], recovery rate, death rate, and coefficient of transmission from 30 January 2020 to 31 July 2021. SARS Coronavirus 2 (SARS-CoV-2) is the Covid strain that causes Covid sickness (COVID-19), a respiratory ailment that triggered the outbreak of COVID-19 at the beginning of December 2019. We aim to provide a hybrid SIRD model for predicting the COVID-19 outbreak. In the proposed method, to improve the exploration ability of the Grey Wolf Optimizer (GWO) or to avoid stagnation in the swarm, a modified Grey Wolf Optimization Algorithm is used to optimize the initial value of Infected individuals. The modified SIRD model is further applied to get the predicted values. The data is examined on weekly basis to prevent noise. Depending on the fact, that the precise mode of transmission is highly dependent on how and when different precautions such as isolation, confinement, and other preventative measures were implemented, we put together our projections concerning satisfactory speculations based on genuine realities. The experimental results show the various trends observed in the pandemic in terms of number of peaks, increasing trend, decreasing trend, and continuous trend for infected individuals, weekly change in number of cases, weekly deaths, weekly infected, and weekly recoeverd cases of Covid-19. The proposed modified SIRD model could be a valuable tool for assessing the impact of government measures on COVID-19 outbreak.

In this paper, we study the degenerate unipoly-Dedekind sums rising from the type 2 degenerate unipoly Bernoulli functions and degenerate unipoly-Bernoulli functions of arbitrary indices, respectively.

ABSTRACTThe aim of this paper is to further study probabilistic versions of the degenerate Stirling polynomials of the second kind, namely the probabilistic degenerate Stirling polynomials of the second kind associated with [Formula: see text], which are also degenerate versions of the probabilistic Stirling polynomials of the second kind investigated earlier. Here [Formula: see text] is a random variable whose moment generating function exists in some neighbourhood of the origin. We derive some properties, explicit expressions and certain identities for those polynomials. In addition, we apply our results to the Bernoulli random variable with probability of success [Formula: see text], the normal random variable with parameters [Formula: see text], and to the uniform random variable on [Formula: see text].

ABSTRACTIn this paper, a discrete predator-prey model incorporating herd behaviour and square root response function is deduced from its continuous version by the semi-discretization method. Firstly, the existence and local stability of fixed points of the system are studied by applying a key lemma. Secondly, by employing the centre manifold theorem and bifurcation theory, the conditions for the occurrences of the transcritical bifurcation and Neimark-Sacker bifurcation are obtained. Not only that but the direction and stability conditions of the bifurcated closed orbits are also clearly shown. Finally, numerical simulations are also given to confirm the existence of Neimark-Sacker bifurcation.

ABSTRACTThe structural stability of the hepatitis C model with the proliferation of infected and uninfected hepatocytes is investigated in this paper. The model is clinically verified to accurately reflect the viral dynamics of hepatitis C. It is demonstrated that the limit transition from the hepatitis C model to the Riccati system coupled with the diffusive terms leads to the elimination of the quadratic terms. Such a novel effect leads to the introduction of the concept of the deformed order-1 solitary solutions. The generalized operator of differentiation is used to construct the deformed order-1 solitary solutions to the Riccati system coupled with the diffusive terms. Finally, it is demonstrated that the Riccati system coupled with the diffusive terms admits non-deformed order-1 solitary solutions, which proves the structural instability of the hepatitis C model with the proliferation of infected and uninfected hepatocytes.

ABSTRACTThis paper introduces a method for deriving an accurate regression equation based on a set of any paired data, and a technique for solving the equation. For a practical example, we used five hundred seventy-one pairs of sediment concentration and river flow data to derive an accurate sediment rating equation. The graphs of the measured and predicted sediment concentrations matched each other, and data correlation showed Nash–Sutcliffe efficiency (NSE) of 0.9999860, coefficient of determination ([Formula: see text]) of 0.99998679, root mean square error (RMSE) of 0.0345, mean average error (MAE) of 0.0067, volume error (VE) of 1, and sum of square error (SSE) of 0.678631. To explain the technique of deriving and solving the accurate regression equation, separate files of video presentation and excel spreadsheet are provided as supplementary materials. In general, the method can be used to model any processes, and any calibration and validation processes can be addressed.

ABSTRACTIn this paper, we investigate a novel class of Hermite-Hadamard inequalities applicable to functions with h-convex absolute derivatives. Graphical representations are provided to bolster the validity of our key findings. Some limiting results of our main findings are discussed as corollaries. Furthermore, we establish error estimates in terms of trapezoid formulae for differences between generalized means.

In this paper, we address the weighted multi-objective re-entrant owshop scheduling problem considering release dates in order to minimize makespan, total completion time, total tardiness, maximum idle time, and number of tardy jobs. Each job is taken into account with deterministic processing times, and release dates. The flow-shop comprised of two workshops in whose jobs are entered to the main workshop and after the first part of the processing, they are transferred to the second workshop and after this stage, the jobs are returned to the main workshop for the last part of the processing. We model the problem by a new mixed integer programming based on formulating sum of idle time as a new concept. Moreover, a hybrid evolutionary algorithm is proposed based on some dispatching rules, ant colony optimization, and genetic algorithm. The performance of the proposed algorithm on some test instances is compared to the mixed integer linear programming model as well as the state-of-the-art algorithms called genetic algorithm, tabu search, bio-geography based optimization, and artificial bee colony. The computational experiments show that our proposed approach outperforms other algorithms and the results indicate efficiency and capability of the proposed algorithm in comparison with the traditional algorithms. [ABSTRACT FROM AUTHOR]

Society is in an incessant process of reflection, but the educational system is not following the same path, creating an urgent need for a quality educational renovation in which new methodologies, approaches and educational resources are developed based on creation, collaboration and learning by doing. In this sense, the integrated education of science, technology, engineering, art, and mathematics (STEAM) is postulated as an educational approach through which to transform the teaching-learning processes into processes that contribute to the development of critical, creative, and scientific thinking. Proof of this is the continuous increase in publications in this line of research. This article presents a systematic review with a total of 19 studies published in high-impact journals with the aim of making a critical reflection and evaluating the real scope of incorporating STEAM projects in education to improve the students' mathematical skills. In particular, five areas of interest have been evaluated: active learning in the teaching of STEAM subjects, the development of technological resources, the design and implementation of educational proposals, the evaluation of STEAM education and teacher training in STEAM education. Considering the results, we emphasize the need to continue working on the theoretical foundation and educational practice of this approach to allow teachers to implement it effectively. [ABSTRACT FROM AUTHOR]

For any Q\in \{\frac {3}{2},2,\frac {5}{2},3,\dotsc \}, we establish a structure theory for the class \mathcal {S}_Q of stable codimension 1 stationary integral varifolds admitting no classical singularities of density

We prove that the Cohn–Elkies linear programming bound for sphere packing is not sharp in dimension 6. The proof uses duality and optimization over a space of modular forms, generalizing a construction of Cohn–Triantafillou [Math. Comp. 91 (2021), pp. 491–508] to the case of odd weight and non-trivial character. [ABSTRACT FROM AUTHOR]

Telescopers for a function are linear differential (resp. difference) operators annihilating the definite integral (resp. definite sum) of this function. They play a key role in Wilf–Zeilberger theory and algorithms for computing them have been extensively studied in the past 30 years. In this paper, we introduce the notion of telescopers for differential forms with D-finite function coefficients. These telescopers appear in several areas of mathematics, for instance parametrized differential Galois theory and mirror symmetry. We give a sufficient and necessary condition for the existence of telescopers for a differential form and describe a method to compute them if they exist. Algorithms for verifying this condition are also given. [ABSTRACT FROM AUTHOR]

Recently, graph-based deep learning models have exhibited remarkable performance in generating solution expressions for the math word problem (MWP). However, most of these models have not taken into account the limitations and errors in constructing prior knowledge graphs, which may affect their accuracy and reliability in practical applications. In addition, during graph learning, they focus on extracting information from each given graph, while neglecting the adaptability and unification of graph representation learning. In this paper, we propose a novel multi-view graph learning-to-tree model with dual-strategy (MVG-DS-T), in which it performs adaptive and consistent multi-view representation learning through two benchmark graphs. Specifically, we construct benchmark graphs via semantic dependency parsing of MWP text, considering both semantic and quantitative aspects, i.e., semantic graph and quantitative graph. Then, the reconstruction strategy is employed to reconstruct the structure of the benchmark graphs to capture the adaptive representation information suitable for downstream tasks, while the alignment strategy is utilized to overcome the limitation of independent view representations by unifying the semantic and quantity embedding information through graph structure. Also, an adaptive length normalized loss balancing term for the tree-based decoder is introduced to control the model focus on label length during training, resulting in better equation generation. Extensive experiments demonstrate the effectiveness of the proposed approach on the MWP task. The empirical results show that MVG-DS-T achieves performance comparable to that of the state-of-the-art graph-based models in the existing literature. [ABSTRACT FROM AUTHOR]

Background: Real-world problems are important in math instruction, but they do not necessarily trigger students' task motivation. Personalizing real-world problems by (1) matching problems to students' shared living environment (context personalization) and (2) asking students to pose their own problems (active personalization) might be two interventions to increase students' task motivation., Aim: In the current study, we investigated the effects of context personalization and active personalization on students' self-efficacy expectations, intrinsic value, attainment value, utility value, and cost., Sample: The participants were 28 fifth- and sixth-grade students who voluntarily took part in a six-month afterschool program in which they posed problems with the aim of creating a math walk in their hometown., Method: Using a within-subjects design, at the end of the afterschool program, the students rated their self-efficacy expectations and task values for four self-developed problems associated with their hometown, four peer-developed problems associated with their hometown, and four instructor-provided problems associated with unfamiliar locations., Results: Students reported higher self-efficacy expectations, intrinsic value, attainment value, and utility value for active-personalized than non-personalized problems. To a lesser extent, context personalization promoted intrinsic value and attainment value. No effect was found for cost., Conclusions: Active personalization (i.e. asking students to pose their own real-world problems) is suited to enhance students' task motivation, specifically their self-efficacy expectations, intrinsic value, attainment value, and utility value. Context personalization still boosts students' intrinsic value and attainment value. Implementation in classroom instruction is discussed., (© 2024 The Authors. British Journal of Educational Psychology published by John Wiley & Sons Ltd on behalf of British Psychological Society.)

Background: Math anxiety (MA) is a worldwide appearing academic anxiety that can affect student mental health and deter students from math and science-related career choices., Method: Using the Arabic version of the Modified-Abbreviated Math Anxiety Scale (m-AMAS), the prevalence of MA was investigated in a very large sample of students (N = 10093) from grades 7 to 12 in Qatar., Results: The results showed a better fit to the original two-factor model of the m-AMAS (learning MA and Evaluation MA) than to a single-factor solution. This two-factor model was also confirmed in each grade. Notably, the distribution of MA scores was right-skewed, especially for learning MA. Using the inter-quartiles ranges, norms for MA were provided: A score of ≤16 indicates low MA whereas a score of ≥30 identifies high MA. Previous studies conducted in Western countries defined high math-anxious students as those who score above the 90th percentile corresponding to a score of 30 on the m-AMAS. Using this cut-off criterion, the current study found that one-fifth of students in Qatar were highly math-anxious, with a higher proportion of females than males. We also calculated the percentage of participants selecting each response category for each questionnaire item. Results showed that attending a long math class was the context that elicited the highest levels of learning MA. In contrast, having an unexpected math test was the situation that triggered the highest levels of evaluation MA., Conclusion: The prevalence of MA might vary across different cultures., (© 2024 British Psychological Society.)

The task of math word problem (MWP) generation, which generates an MWP given an equation and relevant topic words, has increasingly attracted researchers' attention. In this work, we introduce a simple memory retrieval module to search related training MWPs, which are used to augment the generation. To retrieve more relevant training data, we also propose a disentangled memory retrieval module based on the simple memory retrieval module. To this end, we first disentangle the training MWPs into logical description and scenario description and then record them in respective memory modules. Later, we use the given equation and topic words as queries to retrieve relevant logical descriptions and scenario descriptions from the corresponding memory modules, respectively. The retrieved results are then used to complement the process of the MWP generation. Extensive experiments and ablation studies verify the superior performance of our method and the effectiveness of each proposed module. The code is available at https://github.com/mwp-g/MWPG-DMR. [ABSTRACT FROM AUTHOR]

Plutella xylostella, commonly called Diamondback moth (DBM), a highly destructive and rapidly spreading agricultural pest originally from Europe. This pest poses a significant threat to global food security, with estimates suggesting that periodic outbreaks of Diamondback moth lead to annual crop losses of up to $US 4−5 billion worldwide. Given the potential for such substantial losses, it is crucial to employ various methods and techniques to understand the factors affecting the interaction between Diamondback moths and cabbage plants, which, in turn, impact cabbage biomass. In this paper, we propose a deterministic ecological model to capture the dynamics of Plutella xylostella infestations in cabbage biomass. The model is designed based on the life cycle stages of the pest, aiming at targeting the specific stage effectively. The synthetic data is generated using Least Square Algorithm through addition of Gaussian noise into numerically obtained values from existing literature to simulate real-world data. Global sensitivity analysis was done through Latin Hypercube sampling, highlights the significance of parameters such as ψ,αE and δ positively influence the growth of the diamondback moth in a cabbage biomass. In light of these findings, the study proposes that control strategies should be specifically directed towards these sensitive parameters. By doing so, we mitigate the pest population and enhance cabbage production.

In this paper, we investigate the stability analysis of the equilibrium points and the influence of the orientation on the suppression of chaotic behavior of the generalized Lorenz system proposed. A three-dimensional system model is obtained using the spectral method. We proved that the first equilibrium point is globally asymptotically stable and the other two equilibria are asymptotically stable under certain conditions on the control parameters σ, P, r, b1 and b2. These theoretical results are supported by numerical simulations. Also, we showed that chaos can be suppressed by a boundary crisis or period-doubling by choosing an appropriate tilt angle. Bifurcation diagrams are drawn to confirm these results.

A Hadamard fractional boundary value problem with semi-positone nonlinearity is studied in this paper, and the local existence and uniqueness of solutions are derived by a recent fixed point theorem involving with increasing φ−(h,r)-concave operators defined on ordered spaces. This is an unprecedented approach to solve the semi-positone problems. In practice, this method has a wider range of applicability since it can obtain the local uniqueness of the solutions. Furthermore, we can approximate the unique solution by constructing convergent iterative sequences. In the end, a persuasive example is provided to illustrate that the theoretical results we obtained are applicable and valid.

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We consider a convex combination of two classes of Lotka–Volterra operators defined on 2-dimensional simplex. Earlier, the dynamics of a particular case of the considered operators has been investigated. However, its bijective property was not studied. In this paper, we are able to establish that such maps are homeomorphism of the simplex.

In this paper, we give a main example indicating the ineffectiveness of the local fractional derivatives on the Riemann curvature tensor that is a common tool in calculating curvature of a Riemannian manifold. For this, first we introduce a general local fractional derivative operator that involves the mostly used ones in the literature as conformable, alternative, truncated M− and V−fractional derivatives. Then, according to this general operator, a particular Riemannian metric on the real affine space Rn that is different from the Euclidean one is defined. In conclusion, our main example states that the Riemann curvature tensor of Rn endowed with this particular metric is identically 0, that is, one is locally isometric to Euclidean space.

For many years, finite differences in hexagonal grids have been developed to solve elliptic problems such as the Poisson and Helmholtz equations. However, these schemes are limited to constant coefficients, which reduces their usefulness in many applications. The main challenge is accurately approximating the diffusive term. This paper presents examples of both successful and unsuccessful attempts to obtain accurate finite differences based on a hexagonal stencil with equilateral triangles to approximate two-dimensional Poisson equations. Local truncation error analysis reveals that a second-order scheme can be achieved if the derivative of the diffusive coefficient is included. Finally, we provide numerical examples to verify the accuracy of the proposed methods.

It was conjectured by Asmiati (2018) that the generalized Petersen graph Pn,k has a locating chromatic number 4 if and only if (noddandk=1) or (n=4andk=2). In this paper, we give a negative answer to the conjecture posed by Asmiati. As a consequence, we are able to exhibit many counterexamples to the recent conjecture proposed, by proving that if (5≤n≤12) and (2≤k≤⌊n−12⌋) and (n,k)≠(12,5), then χLP(n,k)=4.

In a recent paper (Araya and Harada, 2023), Araya and Harada gave examples of self-dual near-extremal ternary codes of length 48 for 145 distinct values of the number A12 of codewords of minimum weight 12, and raised the question about the existence of codes for other values of A12. In this note, we use symmetric 2-(47,23,11) designs with an automorphism group of order 6 to construct self-dual near-extremal ternary codes of length 48 for 150 new values of A12.

In this paper, we determine some degree-based topological indices, such as the Sombor index, the first and second Zagreb indices, the forgotten topological index, the Narumi–Katayama index, the first and second multiplicative Zagreb indices, the atom-bond connectivity index, and eccentricity-based topological indices such as total eccentricity, the first and second Zagreb eccentricity indices, and the eccentricity connectivity index of the zero divisor graph with vertex set non-zero zero divisors of the reduced ring of the direct product of three finite fields.

In this paper we give an algebraic characterization of assemblies in terms of bands of groups. We also consider substructures and homomorphisms of assemblies. We give many examples and counterexamples.

This paper considers two classical age-based replacement models within a discrete-time framework: a standard age replacement model and an opportunistic age replacement model. Specifically, our analysis incorporates the concept of replacement priority in situations where failure replacement and preventive replacement occur at a given age or opportunity. We explore two priority cases within each replacement model. First, we formulate optimal preventive replacement policies aimed at minimizing the associated expected cost rate in the age replacement model and the opportunistic age replacement model by the familiar renewal reward argument. Next, we extend the findings presented earlier to scenarios involving discounting. We develop formulations for the expected total discounted costs over an infinite time horizon and obtain optimal preventive replacement policies minimizing these total expected costs. Additionally, we explore unified models incorporating probabilistic priority. To provide practical insights, we present numerical illustrations using real failure data from pole air switches, comparing the performance of these optimal preventive policies.

YouTube, one of the prominent online video-sharing platforms, plays a pivotal role in modern media consumption, making it crucial to understand and predict the view-count dynamics of its videos. The viewership of YouTube videos can be influenced by three distinct sources: subscribers, word-of-mouth, and recommendation systems. This paper presents a comprehensive modelling framework that takes into account the view-count obtained through these three sources, assuming that a single view-count can only be attributed to one of these sources at any given time. We investigate the interplay among these sources in shaping YouTube video view-count dynamics, proposing a novel approach to model and analyse their impact on video popularity. Additionally, the VIKOR multi-criteria decision-making method is employed to validate and rank our proposed models. This study's findings deepen our understanding of the intricate mechanisms within the YouTube ecosystem, offering insights for predicting and managing video viewership.

Carbon emissions can be decreased by adopting the carbon cap-and-alternate policy. The current study suggests a carbon buying and selling mechanism for things that are deteriorating or of poor quality while taking into account chilled logistics services in a fresh food supply chain. In addition to deliveries of perishables, suppliers also provide retailers with chilled logistics services and carbon emission certificates for excess inventory. The retail price, the cost of chilled strategies, and the contributions to various carbon trading options—such as internal carbon trade, external carbon exchange, and carbon exchange both internally and externally for the destruction of low-quality goods have all been evaluated in this paper. The store network members give estimating systems to new food, emanation permits and refrigerated planned operations administrations. We likewise uncover the connection between carbon purchasing and advancing and refrigerated strategies administrations and test out their joint effect on the provider retailer's helpful dating. Store network donors are also encouraged to participate in the carbon exchanging mechanism, which benefits from more sophisticated asset utilisation and more ruthless stockpile chains. The numerical examples have helped to validate the results. In the end, a thorough sensitivity analysis has been provided.

Based on the unmanned ship swarm system, a resilience model for unmanned ship swarms is proposed by comprehensively considering the preventive indicators, robustness indicators, recoverability indicators, and reconfigurability indicators of the swarm system. Firstly, preventive and robust indicators are proposed based on the characteristics of the unmanned ship swarm system, and the improvement of system performance efficiency by redundant unmanned ships is established as a recoverability indicator. Then, reconfigurable indicators are proposed based on importance, and the resilience indicator of the unmanned ship swarm is determined. Finally, a numerical example is used to model and simulate the performance change and capricious process of the unmanned ship swarm. Most of the research on the resilience assessment model of unmanned ship swarms considered too single indicators. The model of the unmanned ship swarm under attack is constructed, and the superiority of the resilience optimization strategy proposed in this paper is verified.

This paper introduces a novel computational approach utilizing the quartic B-spline method on a uniform mesh for the numerical solution of non-linear singularly perturbed delay differential equations (NSP-DDE) of second-order with a small negative shift. These types of equations are encountered in various scientific and engineering disciplines, including biology, physics, and control theory. We are using quartic B-spline methods to solve NSP-DDE without linearizing the equation. Thus, the set of equations generated by the quartic B-spline technique is non-linear and the obtained equations are solved by Newton-Raphson method. The success of the approach is assessed by applying it to a numerical example for different values of perturbation and delay parameter parameters, the maximum absolute error (MAE) is obtained via the double mesh principle. The convergence rate of the proposed method is four. Obtained numerical results are compared with existing numerical techniques in literature and observe that the proposed method is superior with other numerical techniques. The quartic B-spline method provides the numerical solution at any point of the given interval. It is easy to implement on a computer and more efficient for handling second-order NSP-DDE.

There are several classical characterisations of the valuative dimension of a commutative ring. Constructive versions of this dimension have been given and proven to be equivalent to the classical notion within classical mathematics, and they can be used for the usual examples of commutative rings. To the contrary of the classical versions, the constructive versions have a clear computational content. This paper investigates the computational relationship between three possible constructive definitions of the valuative dimension of a commutative ring. In doing so, it proves these constructive versions to be equivalent within constructive mathematics. [ABSTRACT FROM AUTHOR]

In view of a better understanding of the geometry of scalar flat Kähler metrics, this paper studies two families of scalar flat Kähler metrics constructed by Hwang and Singer (Trans Am Math Soc 354(6):2285–2325, 2002) on C n + 1 and on O (- k) . For the metrics in both the families, we prove the existence of an asymptotic expansion for their ϵ -functions and we show that they can be approximated by a sequence of projectively induced Kähler metrics. Further, we show that the metrics on C n + 1 are not projectively induced, and that the Burns–Simanca metric is characterized among the scalar flat metrics on O (- k) to be the only projectively induced one as well as the only one whose second coefficient in the asymptotic expansion of the ϵ -function vanishes. [ABSTRACT FROM AUTHOR]

This editorial paper reviews the articles published in a special issue devoted to the application of active particle methods applied to the study of the collective dynamics of large systems of interacting entities in science and society. The applications presented in this special issue focus on the study of financial markets, cell dynamics in the context of cancer modeling, vehicle and crowd vehicle and crowd dynamics, and classical problems in the kinetic theory of active particles and swarm theory. A critical analysis is proposed to look forward to research. Perspectives with emphasis on the interaction of multiple social dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we study a discrete momentum consensus-based optimization (Momentum-CBO) algorithm which corresponds to a second-order generalization of the discrete first-order CBO [S.-Y. Ha, S. Jin and D. Kim, Convergence of a first-order consensus-based global optimization algorithm, Math. Models Methods Appl. Sci. 30 (2020) 2417–2444]. The proposed algorithm can be understood as the modification of ADAM-CBO, replacing the normalization term by unity. For the proposed Momentum-CBO, we provide a sufficient framework which guarantees the convergence of algorithm toward a global minimum of the objective function. Moreover, we present several experimental results showing that Momentum-CBO has an improved success rate of finding the global minimum compared to vanilla-CBO and show the stability of Momentum-CBO under different initialization schemes. We also show that Momentum-CBO can be used as the alternative of ADAM-CBO which does not have a proper convergence analysis. Finally, we give an application of Momentum-CBO for Lyapunov function approximation using symbolic regression techniques. [ABSTRACT FROM AUTHOR]

This paper presents a bi-level approach to support retailers in making investment decisions in renewable-based systems to provide clean electricity. The proposed model captures the strategic nature of the problem and combines capacity sizing decisions for installed technologies with pricing decisions regarding the electricity tariffs to offer to a reference end-user, representative of a class of residential prosumers. The interaction between retailer and end-user is modeled using the Stackelberg game framework, with the former acting as a leader and the latter as follower. The reaction of the follower to the electricity tariff affects the retailer’s profit, which is calculated as the difference between the revenue generated from selling electricity and the total investment, operation and management costs. To account for uncertainty in wholesale electricity prices, renewable resource availability and electricity request, the upper-level problem is formulated as a two-stage stochastic programming model. First-stage decisions refer to the sizing of installed technologies and electricity tariffs, whereas second-stage decisions refer to the operation and management of the designed system. The model also incorporates a safety measure to control the average profit that can be achieved in a given percentage of worst-case situations, thus providing a contingency against unforeseen changes. At the lower level, the follower reacts to the offered tariffs by defining the procurement plan in terms of energy to purchase from the retailer or potential competitors, with the final aim of minimizing the expected value of the electricity bill. A tailored approach that exploits the specific problem structure is designed to solve the proposed formulation and extensively tested on a realistic case study. The numerical results demonstrate the efficiency of the proposed approach and validate the significance of explicitly dealing with the uncertainty and the importance of incorporating a safety measure.

Home Health Care (HHC) services are essential for delivering healthcare programs to patients in their homes, with the goal of reducing hospitalization rates and improving patients’ quality of life. However, HHC organizations face significant challenges in scheduling and routing caregivers for home care visits due to complex criteria and constraints. This paper addresses these challenges by considering both caregiver assignments and transportation logistics. The objective is to minimize the total travel distance and CO2 emissions while ensuring a balanced workload for caregivers, meeting patients’ preferences, synchronization, precedence, and availability constraints. To tackle this problem, we propose a multiperiodic Green Home Health Care (GHHC) framework. In the first stage, we utilize multiobjective programming and the NSGA-II algorithm to generate Pareto front solutions that consider travel distance and CO2 emissions. In the second stage, a Mixed-Integer Linear Programming (MILP) model is proposed to balance caregivers’ workload by assigning them to the patient routes generated in the first stage. The results highlight the trade-off between shorter routes and lower emissions. Furthermore, we examine the impact of prioritizing continuity of care and patient satisfaction. This research provides valuable insights into addressing the scheduling and routing challenges in HHC services, contributing to a more efficient and environmentally friendly healthcare delivery.

The presence of congestion is a common scenario in tertiary-level hospitals worldwide. Current research suggests that an increase in hospital bed capacity is not a long-term solution given that patient demand adapts to added capacity. Recent literature suggests the need for the implementation of a policy of inter-hospital transfers to divert patients to outpatient priority services or home care. This policy has proven to be effective in reducing ED boarding without compromising patient safety. However, determining the required number of patients to be admitted is key. The dynamic nature of hospital bed availability and discharges requires an admission process able to be in synchrony with those variations. A mismatch between patient demand and hospital admissions will result in either ED boarding or idle capacity. The purpose of this paper is to introduce a methodology to support the process of hospital admissions by providing as an input a threshold for the number of patients to be admitted. The methodology is tested using a system dynamics model that replicates one year of operations of a tertiary-level hospital. The simulations reveal the potential of the methodology to decrease the ED inpatient boarding rate as well as ED and hospital length of stay.

This paper proposes a novel method of Pareto front generation from a set of piecewise linear trade-off curves typically encountered in bi-objective just-in-time (JIT) scheduling problems. We have considered the simultaneous minimization of total weighted earliness and tardiness (TWET) and total flowtime (TFT) objectives in a single-machine scheduling problem (SMSP) with distinct job due dates allowing inserted idle times in the schedules. An optimal timing algorithm (OTA) is presented to generate the trade-off curve between TWET and TFT for a given sequence of jobs. The proposed method of Pareto front generation generates a Pareto-optimal front constituted of both line segments and points. Further, we employ a simple local search method to generate sequences of jobs and their respective trade-off curves, which are trimmed and merged to generate the Pareto-optimal front using the proposed method. Computational results obtained using problem instances of different sizes reveal the efficiency of the proposed OTA and the Pareto front generation method over the state-of-the-art methodologies adopted from the literature.

Study on fragmentation and defragmentation of reflective thinking structures has never been conducted. Therefore, the purpose of this study was threefold: (1) to identify the types and forms of fragmentation of students' reflective thinking structures in solving mathematical problems, (2) to describe attempts to defragment students' reflective thinking structures in each type and form of fragmentation, and (3) to find out if such defragmentation attempts can work for reflective thinkers who experience fragmentation. This research was qualitative, exploratory, and descriptive. The subjects included in this study were students who thought reflectively and experienced fragmentation at each level of reflective thinking when solving mathematical problems. Data collection was conducted using tests, interviews, think-aloud protocols, and observation. Data analysis was conducted using constant comparative method. Data validity was established using method and source triangulation. The results showed: (1) Scanning Defragmentation work for Less-Strict Fragmentation, (2) Schema Emergence Defragmentation work for Pseudo-True Fragmentation, (3) Schema Activation work for Pseudo-False Fragmentation, (4) Connection Emergence Defragmentation work for Nonexistent-Connection Fragmentation, (5) Compare-Reflect Defragmentation work for Confidence-False Fragmentation. The results of this study can be reference for mathematics researchers and educators to develop learning models that can prevent the occurrence of fragmentation of reflective thinking structures. [ABSTRACT FROM AUTHOR]

Parity is an important and easy to recognise property for meromorphic functions. On the parity of meromorphic functions, Liu, Liu and Korhonen [J Math Anal Appl 512(2022):126129] obtained some meaningful results. In this paper, we investigate the parity of a meromorphic function y(z) under the hypothesis that y(z)2n-2y(z)n is even. In addition, we discuss the relationship on the parity of a meromorphic function with its q-difference polynomials and differential expressions. For instance, we consider the parity of a meromorphic function y(z) under the assumption that y'(z)/ y(z)n and y(qz)/y(z)n are odd or even functions, where n is a positive integer. [ABSTRACT FROM AUTHOR]

The purpose of this study was to investigate the self-perception, difficulties, and mathematical performance of junior high school students at Datu Mitmug Memorial High School in Mapantao Lumba-Bayabao, Lanao del Sur, during the academic year 2022-2023. To investigate the association between these characteristics and junior high school students' mathematics performance, the study used a descriptive survey correlational methodology. Two hundred twenty-five learners in grades 7 through 10 made up the sample. The results showed that the students' overall proficiency in mathematics was satisfactory. Additionally, the students exhibited a positive self-concept in learning mathematics, particularly in the dimensions of learned, organized, and dynamic. Notably, the organized self-concept significantly influenced their performance in mathematics. Moreover, the study identified anxiety and lack of confidence as the main challenges faced by the learners, which significantly impacted their academic performance. As a recommendation, teachers were encouraged to implement positive reinforcement techniques in the classroom to address the mathematics learning gap and enhance students' self-concept. These interventions had the potential to improve students' performance and contribute to their overall mathematical achievement. [ABSTRACT FROM AUTHOR]