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Hesitant linguistic preference relations (HLPRs) are useful tools for decision makers (DMs) to express their qualitative judgements. However, the traditional HLPRs have one prominent drawback, which is to sort the linguistic values in a hesitant linguistic set. This will distort the DMs' initial judgements. In the present paper, a revised definition of HLPR, called general HLPR (GHLPR), was proposed. A characterization was explored for LPRs. Then, the characterization was extended to GHLPRs. Based on the characterization, the estimation of unknown entries in incomplete GHLPRs were carried out by two algorithms. The group decision-making problems with incomplete GHLPRs were settled by another algorithm. Finally, a case study was illustrated, and comparisons showed that our methods were more reasonable than the existent methods.

This paper aims to study the existence of solutions for Hadamard fractional nonlocal boundary value problems with mean curvature operator at resonance. Based on the coincidence degree theory, some new results are established. Moreover, an example is given to verify our main results.

In this paper, we have discussed a class of second-order neutral stochastic differential evolution systems, based on the Wiener process, with random impulses and state-dependent delay. The system is an extension of impulsive stochastic differential equations, since its random effect is not only from stochastic disturbances but also from the random sequence of the impulse occurrence time. By using the cosine operator semigroup theory, stochastic analysis theorem, and the measure of noncompactness, the existence of solutions was obtained. Then, giving appropriate assumptions, the approximate controllability of the considered system was inferred. Finally, two examples were given to illustrate the effectiveness of our work.

Inequalities are essential in solving mathematical problems in many different areas of mathematics. Among these, problems involving coefficient combinations that occurred in the Taylor–Maclaurin series of the inverse of complex-valued analytic functions are the challenging ones to solve. In the current article, our aim is to study certain coefficient-related problems that construct from coefficients of the inverse of specific analytic functions. These problems include the Zalcman and Fekete–Szegö inequalities, as well as sharp estimates of the second and third-order Hankel determinants with inverse function coefficients. Also, one of the obtained results gives an improvement of the problem that has been recently published in the journal "AIMS Mathematics".

In his lost notebook, Ramanujan presented unique categories of remarkable infinite series, known as the Ramanujan-type Eisenstein series. The objective of this paper is to generate various differential identities related to classical $ \eta $-functions and $ h $-functions with the help of the Ramanujan-type Eisenstein series. Moreover, we present particular identities that incorporate Eisenstein series of different levels and $ h $-functions, thereby establishing links between class one infinite series and $ h $-functions.

We investigated a novel stochastic fractional partial differential equation (FPDE) characterized by a mixed operator that integrated the standard Laplacian, the fractional Laplacian, and the gradient operator. The equation was driven by a random noise, which admitted a covariance measure structure with respect to the time variable and behaved as a Wiener process in space. Our analysis included establishing the existence of a solution in the general case and deriving an explicit form for its covariance function. Additionally, we delved into a specific case where the noise was modeled as a generalized fractional Brownian motion (gfBm) in time, with a particular emphasis on examining the regularity of the solution's sample paths.

Total variation (TV) regularization is a powerful tool in image denoising, but it often exhibits limited performance in preserving edges. In contrast, non-convex TV regularization can more effectively preserve edges and contours, albeit posing challenges when solving. Recently, the convex non-convex (CNC) strategy has emerged as a potent approach that allows incorporating non-convex TV regularization terms while maintaining the overall convexity of the objective function. Its superior performance has been validated through various numerical experiments; however, theoretical analysis remains lacking. In this paper, we provided theoretical analysis of the performance of the CNC-TV denoising model. By utilizing the oracle inequality, we derived an improved upper bound on its performance compared to TV regularization. In addition, we devised an alternating direction method of multipliers (ADMM) algorithm to address the proposed model and verified its convergence properties. Our proposed model has been validated through numerical experiments in 1D and 2D denoising, demonstrating its exceptional performance.

In this paper, we are concerned with the study of the existence and uniqueness of fixed points for the class of functions $ f: C\to C $ satisfying the inequality$ \ell\left(\alpha f(t)+(1-\alpha)f(s)\right)\leq \sigma \ell(\alpha t+(1-\alpha)s) $for every $ t, s\in C $ with $ f(t)\neq f(s) $, where $ C $ is a closed subset of $ [0, \infty) $, $ \alpha, \sigma\in (0, 1) $ are constants, and $ \ell: [0, \infty)\to [0, \infty) $ is a function satisfying the condition $ \inf_{t > 0} \frac{\ell(t)}{t^\rho} > 0 $ for some constant $ \rho > 0 $. Namely, under a weak continuity condition imposed on $ f $, we show that $ f $ possesses a unique fixed point, and for every $ t_0\in C $, the Picard sequence defined by $ t_{n+1} = f(t_n) $, $ n\geq 0 $, converges to this fixed point. Next, we study the special cases when $ C $ is a closed interval and $ \ell $ is a convex or concave function. Namely, making use of the Hermite-Hadamard inequalities, we obtain several new fixed point theorems. To the best of our knowledge, the considered class of functions was never previously investigated in the literature.

In this paper, we first introduced the notion of $ \theta $-hyperbolic sine distance functions on a metric space and studied their properties. We investigated the existence and uniqueness of fixed points for some classes of single-valued mappings defined on a complete metric space and satisfying contractions involving the $ \theta $-hyperbolic sine distance function.

We first utilized the Bayes positive diagonal BEKK generalized autoregressive conditional heteroskedasticity (Bayes-pdBEKK-GARCH) model to evaluate the risk spillovers between the e-commerce and logistics, then applied the adaptive Fourier decomposition method to measure the extent of these spillovers and detect structural changes. The results showed that there were structural breaks in both markets, which may lead to extreme risks. At last, we applied the GARCH-copula quantile regression model to analyze the extreme risks. We found that: (1) there were asymmetric volatility spillovers and positive correlations between them. (2) The dynamic risk spillovers exhibited heterogeneity over time. The logistics market had a smaller downside risk spillover, while the e-commerce market had a stronger upside risk spillover. (3) The study indicated that important events, such as the Chinese stock market crash, the Sino-U.S. trade friction, the COVID-19 epidemic, and the "either-or choice" monopoly policy of e-commerce platforms, had a significant influence on them, resulting in dramatic risk spillovers.

Ecological aquaculture represents an important approach for maintaining sustainable economic income. Unreasonable aquaculture may result in resource wastage and population extinction. Human activities and behaviors such as predation among populations make the ecosystem very complex. Thus, seeking an appropriate intervention strategy is a favorable measure to overcome this situation. In this paper, we present a novel ecological aquaculture management model with stage-structure and impulsive nonlinear releasing larval predators. The sufficient conditions for the prey and the predators coexistence as well as global stability of a prey-vanishing periodic solution were obtained using the Floquet theorem and other analytic tactics. Subsequently, we verified our findings using mathematical software. We also found a system with a nonlinear impulse exhibiting rich dynamical properties by drawing bifurcation parameter graphs. These findings provide a firm theoretical basis for managing ecological aquaculture.

Deepfake images are combined media constructed from deep learning (DL) methods, usually Generative Adversarial Networks (GANs), to manipulate visual content, often giving rise to convincing and fabricating descriptions of scenes or people. The Bayesian machine learning (ML) model has made crucial strides over the past two decades, illustrating promise in diverse applications. In deepfake images, detection utilizes computer vision (CV) and ML to spot manipulated content by analyzing unique artefacts and patterns. Recent techniques utilize DL to train neural networks to discriminate between real and fake images, improving the fight against digital manipulation and preserving media integrity. These systems can efficiently detect subtle inconsistencies or anomalies specific to deepfake creations by learning from large datasets of both real and deepfake images. This enables the mitigation of fraudulent content and reliable detection in digital media. We introduce a new Coronavirus Herd Immunity Optimizer with a Deep Learning-based Deepfake Image Detection and Classification (CHIODL-DIDC) technique. The CHIODL-DIDC technique aimed to detect and classify the existence of fake images. To accomplish this, the CHIODL-DIDC technique initially used a median filtering (MF) based image filtering approach. Besides, the CHIODL-DIDC technique utilized the MobileNetv2 model for extracting feature vectors. Moreover, the hyperparameter tuning of the MobileNetv2 model was accomplished using the CHIO method. For deepfake image detection, the CHIODL-DIDC technique implements the deep belief network (DBN) model. Finally, the Bayesian optimization algorithm (BOA) was utilized to select the effectual hyperparameter of the DBN model. The CHIODL-DIDC method's empirical analysis was examined using a benchmark fake image dataset. The performance validation of the CHIODL-DIDC technique illustrated a superior accuracy value of 98.16% over other models under $ Acc{u}_{y} $ , $ Pre{c}_{n} $ , $ Rec{a}_{l} $ , $ {F}_{Score} $ , and MCC metrics.

This study explored and examined soliton solutions for the Quintic Benney-Lin equation (QBLE), which describes the dynamic of liquid films, using the Riccati modified extended simple equation method (RMESEM). The proposed approach, which is designed for nonlinear partial differential equations (NPDEs), effectively generates a large number of soliton solutions for the given QBLE, which basically captures the fundamental dynamics of the system. The rational, hyperbolic, rational-hyperbolic, trigonometric, and exponential forms of the scientifically specified soliton solutions are the main determinants of the hump solitons. We used 2D, 3D, and contour visualizations to offer accurate representations of the researched soliton phenomena associated with these solutions. These representations revealed the existence of dark and bright hump solitons in the framework of the QBLE and offer a thorough way to examine the model's behavioral characteristics in the liquid film by analyzing the QBLE model's soliton dynamics. Moreover, applying the suggested approach advances our knowledge of the unique features of the other similar NPDEs and the underlying dynamics.

Chen (1993) developed the theory of $ \delta $-invariants to establish novel necessary conditions for a Riemannian manifold to allow a minimal isometric immersion into Euclidean space. Later, Siddiqui et al. (2024) derived optimal inequalities involving the CR $ \delta $-invariant for a generic statistical submanifold in a holomorphic statistical manifold of constant holomorphic sectional curvature. In this work, we extend the study of such optimal inequality to the contact CR $ \delta $-invariant on contact CR-submanifolds in Sasakian statistical manifolds of constant $ \phi $-sectional curvature. This paper concludes with a summary and final remarks.

Let $ \tau(n) $ be the Dirichlet divisor function and $ k\geqslant2 $ be a fixed integer. We give an asymptotic formula of the mean square of$ \begin{equation*} \Delta_k(x) = \sum\limits_{n_1, \cdots, n_k\leqslant x}\tau(n_1 \cdots n_k)-x^kP_k(\log x). \end{equation*} $

Regularity for elliptic equations with oscillatory coefficients was concerned. Problem domains were periodic and consisted of a connected region with normal permeability and a disconnected matrix block subset with high permeability. Coefficients of the elliptic equations depending on the permeability of the domains were highly oscillatory. Let $ {\epsilon}\in(0, 1) $ be the periodic size of domain, $ {\epsilon}\mu\in(0, 1) $ the size ratio of a matrix block to the whole domain, and $ \omega^2\in(1, \infty) $ the permeability ratio of the disconnected matrix block subset to the connected sub-region of the domains. This work presented Lipschitz estimate uniformly in $ {\epsilon}, \mu, \omega $ for the Green's functions and the solutions of the elliptic equations.

In recent years, conventional Ricker maps have enjoyed widespread applications across crucial domains such as modeling and security. However, their limitation to a single changeable parameter poses constraints on their adaptability. This paper introduces a generalized form of the Ricker map, incorporating arbitrary powers, thus offering enhanced versatility compared to the traditional Ricker map. By introducing an additional parameter (arbitrary power), the map gains increased degrees of freedom, thereby accommodating a broader spectrum of applications. Consequently, the conventional Ricker map emerges as merely a special case within each proposed framework. This newfound parameter enhances system flexibility and elucidates the conventional system's performance across diverse contexts. Through numerous illustrations, we meticulously investigate the impact of the arbitrary power and equation parameters on equilibrium points, their positions, basin of attraction, stability conditions, and bifurcation diagrams, including the emergence of chaotic behavior.

To improve the performance of genetic algorithms (GAs) in complex optimization settings, this work offered two novel real-coded crossover operators: one based on the Gumbel distribution (GX) and the other on the Rayleigh distribution (RX). These innovative operators, when combined with three different mutation techniques, created a significant improvement in GA methodology. Our meticulous simulations showed that the GX operator significantly outperformed RX and other traditional operators, demonstrating its superior capacity to address complex optimization problems. The GX operator's unusual robustness was further validated through detailed performance analysis utilizing the VlseKriterijuska Optimizacija I Komoromisno Resenje (VIKOR) multi-criteria decision-making technique, setting a new standard in crossover operator design and significantly improving the state of the art in GAs.

During the engineering structure's operation, the mechanical structure's performance and loading will change with time, so the parameter uncertainty and structural reliability will also have dynamic characteristics. The time-varying reliability analysis method can more accurately evaluate structural reliability by fully using this dynamic uncertainty. However, the time-varying reliability analysis was mainly based on the spanning rate method, which was complex and difficult to obtain the final result. Therefore, this study proposed an enhanced dung beetle optimization (EDBO) assisted time-varying reliability analysis method based on the adaptive Kriging model. With the help of the adaptive Kriging model and the EDBO optimization algorithm, the efficiency of the time-varying reliability analysis method was improved. At the same time, to prevent prematurely falling into the local search trap, the method improved the uniformity of the sample by initializing the sample through improved tent chaotic mapping (ITCM). Next, the Gaussian random walk strategy was used to search the updated position, which further improved the accuracy of the reliability analysis results. Finally, the accuracy and effectiveness of the proposed time-varying reliability analysis method were verified by four mechanical structure model examples. From the calculation results, it can be seen that with the help of the new DBO optimization algorithm, the relative error of the proposed reliability analysis results was about 20%~30% lower than that of the traditional reliability analysis method. What's more, the calculation efficiency was higher than that of other reliability analysis methods.

This paper investigated the application of analytical methods, specifically the Mohand transform iterative method (MTIM) and the Mohand residual power series method (MRPSM), to solve the fractional Boussinesq equation. Utilizing the Caputo operator to manage fractional derivatives, these semi-analytical approaches provide accurate solutions to complex fractional differential equations. Through convergence analysis and error estimation, the study validated the efficacy of these methods by comparing numerical solutions to known exact solutions. Graphical and tabular representations illustrated the accuracy of the proposed methods, highlighting their performance for varying fractional orders. The findings demonstrated that both MTIM and MRPSM offer reliable, efficient solutions, making them valuable tools for addressing fractional differential systems in fields such as applied mathematics, engineering, and physics.

Abstract Introduction It is well known that social contact patterns differ from country to country. This variation coincides with significant socioeconomic heterogeneity that complicates the design of effective nonpharmaceutical interventions. This study examined how socioeconomic heterogeneity in selected African countries might be factored in to explain better patterns of social contact mix between countries. Methods We used a standardized contact matrix for 32 African countries, estimated in (Prem et al. in PLoS Comput Biol 17(7):e1009098, 2021). We scaled the matrices using an epidemic model from (Röst et al. in Viruses 12(7):708, 2020). We also analyzed aggregated data from the World Bank country website. The data includes 28 variables; social, economic, environmental, institutional, governance, health and well-being, education, gender inequality, and other development-related indicators that describe countries. Principal component analysis was used to visualize socioeconomic similarities between countries and identify the indicators for maximum variation. The ( 2 D ) 2 P C A $(2D)^{2} PCA$ approach was used to reduce the dimension of synthetic contact matrices for each country to avoid the dimensionality curse. Then, hierarchical aggregate clustering was used to identify groups of countries with similar social patterns, taking into account the country’s socioeconomic performance. Results Our model yielded four meaningful clusters, each with a few distinguishing features. Social contacts varied between groups, but were generally similar within each set. The socioeconomic performance of the country influenced the clusters. Conclusions Our results suggest that integrating socioeconomic factors into social contacts can better explain infectious disease transmission dynamics and that similar interventions can be implemented in countries within the cluster

Abstract This study investigates machine learning (ML) techniques for optimizing Network-on-Chip (NoC) application mapping, focusing on supervised learning, unsupervised learning, reinforcement learning, and neural networks. Through a comparative analysis of recent research, the study reveals that supervised learning methods, like artificial neural networks (ANNs), enhance core vulnerability prediction and runtime mapping. Unsupervised learning techniques improve NoC mapping via multi-label models, while reinforcement learning approaches, including actor-critic frameworks, reduce communication costs and power consumption. Scenario-aware strategies adapt mapping processes to varying operational contexts. Despite these advancements, challenges such as computational overhead, data quality, and model interpretability persist. Future research should focus on scalable ML algorithms, improving data quality, and enhancing model transparency. This study underscores the significant potential of ML to advance NoC application mapping and highlights the need for ongoing innovation to address existing challenges.

Abstract In this paper, we attempt to use the Dunkl analog to study the convergence properties of q-Phillips operators by using the q-Appell polynomials. By applying the new sequences of continuous functions ν s , q ( z ) = ( z − 1 2 [ s ] q ) ϱ $\nu _{s,q}(z)=\Bigl(z- \frac{1}{2[s]_{q}}\Bigr)_{\varrho}$ on [ 0 , ∞ ) $[0, \infty )$ , we construct an improved version of the q-Phillips operators. We calculate the qualitative outcomes in weighted Korovkin spaces to better understand the Phillips operators’ uniform convergence results. We obtain the approximation properties by use of the modulus of continuity and functions belonging to the Lipschitz class. Moreover, we give some direct theorems for the function belonging to Peetre’s K-functional.

In most lifetime models, the bivariate -quantile inactivity time is a vector of increasing functions. A novel estimator of this vector was created and investigated under this assumption. It was expected that the application of this knowledge would improve the efficiency of the estimator. It was proven that the proposed estimator is consistent and converges weakly to a bivariate Gaussian process under a suitable transformation. A simulation study was conducted to compare the performance of the proposed estimator with that of the usual estimator. Finally, the application of the proposed estimator is illustrated by analyzing a dataset comprising the time to blindness in patients with diabetic retinopathy.

This paper studies the finite-time stabilization (FTS) and finite-time contraction stabilization (FTCS) of parameter-uncertain systems subjected to impulsive disturbances by using an event-triggered aperiodic intermittent control (EAPIC) method, which combines aperiodic intermittent control with event-triggered control. By employing the Lyapunov method and linear matrix inequality techniques, sufficient conditions for FTS and FTCS are derived. Additionally, within the finite-time control framework, relationships among impulsive disturbance, intermittent control parameters, and event-triggered mechanism (ETM) thresholds are established under EAPIC to ensure FTS and FTCS. The sequence of impulsive moments is determined by a predetermined ETM, and Zeno phenomena are also excluded. Finally, the effectiveness of the EAPIC approach is demonstrated through two numerical examples.

The application of a doubly Type-Ⅱ censoring scheme, where observations are censored at both the left and right ends, is often used in various fields including social science, psychology, and economics. However, the observed sample size under this censoring scheme may not be large enough to apply a likelihood-based approach due to the occurrence of censoring at both ends. To effectively respond to this difficulty, we propose a pivotal-based approach within a doubly Type-Ⅱ censoring framework, focusing on two key aspects: Estimation for parameters of interest and prediction for missing or censored samples. The proposed approach offers two prominent advantages, compared to the likelihood-based approach. First, this approach leads to exact confidence intervals for unknown parameters. Second, it addresses prediction problems in a closed-form manner, ensuring computational efficiency. Moreover, novel algorithms using a pseudorandom sequence, which are introduced to implement the proposed approach, have remarkable scalability. The superiority and applicability of the proposed approach are substantiated in Monte Carlo simulations and real-world case analysis through a comparison with the likelihood-based approach.

We construct a class of Gorenstein-projective modules over Milnor squares of rings. As an application, we obtain Gorenstein-projective modules over Morita context rings with two bimodule homomorphisms zero in the general setting instead of Artin algebras or Noetherian rings.

In this paper, polynomial equations with real coefficients and in one variable were considered which contained a small, positive but specified and fixed parameter $ \varepsilon_0 \neq 0 $. By using the classical asymptotic method, roots of the polynomial equations have been constructed in the literature, which were proved to be valid for sufficiently small $ \varepsilon $-values (or equivalently for $ \varepsilon \to 0 $). In this paper, it was assumed that for some or all roots of a polynomial equation, the first few terms in a Taylor or Laurent series in a small parameter depending on $ \varepsilon $ exist and can be constructed. We also assumed that at least two approximations $ x_1(\varepsilon) $ and $ x_2(\varepsilon) $ for the real roots exist and can be constructed. For a complex root, we assumed that at least two real approximations $ a_1(\varepsilon) $ and $ a_2(\varepsilon) $ for the real part of this root, and that at least two real approximations $ b_1(\varepsilon) $ and $ b_2(\varepsilon) $ for the imaginary part of this root, exist and can be constructed. Usually it was not clear whether for $ \varepsilon = \varepsilon_0 $ the approximations were valid or not. It was shown in this paper how the classical asymptotic method in combination with the bisection method could be used to prove how accurate the constructed approximations of the roots were for a given interval in $ \varepsilon $ (usually including the specified and fixed value $ \varepsilon_0 \neq 0 $). The method was illustrated by studying a polynomial equation of degree five with a small but fixed parameter $ \varepsilon_0 = 0.1 $. It was shown how (absolute and relative) error estimates for the real and imaginary parts of the roots could be obtained for all values of the small parameter in the interval $ (0, \varepsilon_0] $.

In this study, changes in westerly waves and their connections to increased global warming under the influence of greenhouse gases were investigated via a Caputo fractional four-dimensional atmospheric system. The idea of the existence of chaotic behavior in the westerly wind's motion was depicted. It has been noted that westerlies are becoming stronger due to rising air temperatures. An analysis of the existence, uniqueness, boundedness, stability of equilibrium points, and conservative behavior of the solutions was conducted. To prove the existence of chaos in the modified model, the Lyapunov exponents, Poincaré map, and bifurcation were computed. A sliding mode controller to control the chaos in this novel fractional-order system was designed, and conditions for the global stability of the controlled system with and without external disturbances and uncertainties were derived. The finite-time interval for the system to reach the sliding surface was computed. The developed controller's performance was evaluated with respect to both commensurate and non-commensurate fractional derivatives. In each scenario, the impact of fractional orders was investigated. Numerical simulations were used to support theoretical statements about how the controller affects the system.

We continue the study of the properties of the $ V $-Moreau envelope and generalized $ (f, \lambda) $-projection that we started in [5]. In this paper, we study the differentiability and the regularity of the $ V $-Moreau envelope and the Hölder continuity of the generalized $ (f, \lambda) $-projection. Our results extend many existing results from the convex case to the nonconvex case and from Hilbert spaces to Banach spaces. Even on Hilbert spaces and for convex functions and sets, we derived new results.

This study investigated the point-wise superconvergence of block finite elements for the variable coefficient elliptic equation in a regular family of rectangular partitions of the domain in three-dimensional space. Initially, the estimates for the three-dimensional discrete Greens function and discrete derivative Greens function were presented. Subsequently, employing an interpolation operator of projection type, two essential weak estimates were derived, which were crucial for superconvergence analysis. Ultimately, by combining the aforementioned estimates, we achieved superconvergence estimates for the derivatives and function values of the finite element approximation in the point-wise sense of the $ L^\infty $-norm. A numerical example illustrated the theoretical results.

In this paper, based on the Ulm-Chebyshev iterative procedure, we present a multi-step Ulm-Chebyshev-like method to solve systems of nonlinear equations $ F(x) = 0 $,$ \begin{equation*} \left\{\begin{array}{l} \quad {\bf{y}}_{n} = {\bf{x}}_{n}-B_{n}F( {\bf{x}}_{n}),\\ \quad {\bf z}_{n} = {\bf{y}}_{n}-B_{n}F( {\bf{y}}_{n}),\\ {\bf{x}}_{n+1} = {\bf z}_{n}-B_{n}F( {\bf z}_{n}),\\ \quad \bar{B}_{n} = 2B_{n}-B_{n}A_{n+1}B_{n},\\ B_{n+1} = \bar{B}_{n}+\bar{B}_{n}(2I-A_{n+1}\bar{B}_{n})(I-A_{n+1}\bar{B}_{n}),\quad n = 0,1,2,\ldots, \end{array}\right. \end{equation*} $where $ A_{n+1} $ is an approximation of the derivative $ F'({\bf{x}}_{n+1}) $. This method does not contain inverse operators in its expression, and does not require computing Jacobian matrices for solving Jacobian equations. We have proved that the multi-step Ulm-Chebyshev-like method converges locally to the solution with $ R $-convergence rate 4 under appropriate conditions. Some applications are given, compared with other existing methods, where the most important features of the method are shown.

Mathematical models play a crucial role in understanding the dynamics of epidemic diseases by providing insights into how they spread and be controlled. In biomathematics, mathematical modeling is a powerful tool for interpreting the experimental results of biological phenomena related to disease transmission, offering precise and quantitative insights into the processes involved. This paper focused on a discrete mathematical model of the Hepatitis C virus (HCV) to analyze its dynamical behavior. Initially, we examined the local dynamics at steady states, providing a foundation for understanding the system's stability under various conditions. We then conducted a detailed bifurcation analysis, revealing that the discrete HCV model undergoes a Neimark-Sacker bifurcation at the uninfected steady state. Notably, our analysis showed that no period-doubling or fold bifurcations occur at this state. Further investigation at the infected steady state demonstrated the presence of both period-doubling and Neimark-Sacker bifurcations, which are characterized using explicit criteria. By employing a feedback control strategy, we explored chaotic behavior within the HCV model, highlighting the complex dynamics that can arise under certain conditions. Numerical simulations were conducted to verify the theoretical results, illustrating the model's validity and applicability. From a biological perspective, the insights gained from this analysis enhance our understanding of HCV transmission dynamics and potential intervention strategies. The presence of Neimark-Sacker bifurcation at the uninfected steady state implies that small perturbations could lead to oscillatory behavior, which may correspond to fluctuations in the number of infections over time. This finding suggests that maintaining stability at this steady state is critical for preventing outbreaks. The period-doubling and Neimark-Sacker bifurcations at the infected steady state indicate the potential for more complex oscillatory patterns, which could represent persistent cycles of infection and remission in a population. Finally, exploration of chaotic dynamics through feedback control highlights the challenges in predicting disease spread and the need for careful management strategies to avoid chaotic outbreaks.

Improving the mathematics performance of school children is an objective for many policy-makers around the world. Student-centered interactive pedagogies like classroom discussions and other dialogic interaction practices have been considered the best practice to engage learners effectively in the learning process. However, dialogic teaching practices are least used in most Asian countries that on average achieve the highest mathematics scores in international assessments. Based on this conundrum, this paper utilized a large-scale education dataset for five Asian countries, namely the Trends in International Mathematics and Science Study (TIMSS) dataset for learner data from Chinese Taipei, Hong Kong, Korea, Malaysia, and Singapore to examine the relationship between dialogic classroom interaction teaching practices and the mathematics performance of 8th-grade learners. Using a within-learner-between-subject estimation strategy to account for endogeneity, we established that learners who are taught more frequently through dialogic interactive teaching practices in mathematics classes achieve higher mathematics scores. Our results confirm that interactive pedagogies do provide learning benefits, even in countries that use them sparingly. Thus, our findings challenge the held assumption that the efficacy of dialogic classroom interaction practices is context and learning culture specific. Nevertheless, our study also shows that the highly endogenous nature of the teaching and learning environment and learner performance limits the ability of any study that uses observational data to establish the true impact of dialogic practices on learner mathematics performance.

In this paper, we enhanced change point detection in skew normal distribution models by integrating the EM algorithm's Q-function with the modified information criterion (MIC). The new QMIC framework improves sensitivity and accuracy in detecting changes, outperforming the modified information criterion (MIC) and the traditional Bayesian information criterion (BIC). Due to the complexity of deriving analytic asymptotic distributions, bootstrap simulations were used to determine critical values at various significance levels. Extensive simulations demonstrate that QMIC offers superior detection capabilities. We applied the QMIC method to two stock market datasets, successfully identifying multiple change points, and highlighting its effectiveness for real-world financial data analysis.

Given a conformal vector field $ X $ defined on an $ n $-dimensional Riemannian manifold $ \left(N^{n}, g\right) $, naturally associated to $ X $ are the conformal factor $ \sigma $, a smooth function defined on $ N^{n} $, and a skew symmetric $ (1, 1) $ tensor field $ \Omega $, called the associated tensor, that is defined using the $ 1 $-form dual to $ X $. In this article, we prove two results. In the first result, we show that if an $ n $-dimensional compact and connected Riemannian manifold $ \left(N^{n}, g\right) $, $ n > 1 $, of positive Ricci curvature admits a nontrivial (non-Killing) conformal vector field $ X $ with conformal factor $ \sigma $ such that its Ricci operator $ Rc $ and scalar curvature $ \tau $ satisfy $ Rc\left( X\right) = -(n-1)\nabla \sigma \; \; \text{ and }\; \; X(\tau ) = 2\sigma \left( n(n-1)c-\tau \right) $ for a constant $ c $, necessarily $ c > 0 $ and $ \left(N^{n}, g\right) $ is isometric to the sphere $ S_{c}^{n} $ of constant curvature $ c $. The converse is also shown to be true. In the second result, it is shown that an $ n $-dimensional complete and connected Riemannian manifold $ \left(N^{n}, g\right) $, $ n > 1 $, admits a nontrivial conformal vector field $ X $ with conformal factor $ \sigma $ and associated tensor $ \Omega $ satisfying$ Rc\left( X\right) = -div\Omega \; \; \text{ and }\; \; \Omega \left( X\right) = 0, $if and only if $ \left(N^{n}, g\right) $ is isometric to the Euclidean space $ \left(E^{n}, \langle, \rangle \right) $.

This study investigated the effects of fluctuating boundary water levels and surface recharge on groundwater flow within unconfined aquifers. We aimed to understand how changes in recharge patterns and variable boundary water levels, such as those from rivers or canals, affect groundwater levels over time and space. To achieve this, we solved the linearized Boussinesq equation using the time-marching method alongside the generalized integral transformation method. Our analysis focused on how different types of recharge affect groundwater level variations and flow dynamics. We found that boundary effects on groundwater level change propagate from the edges toward the aquifer's center, becoming more pronounced with increased boundary water levels. Over time, the system stabilizes, leading to a steady water table height and flow rate, which depend on the disparity between the boundary water levels. Our analytical model demonstrated flexibility and practical applicability by allowing for the consideration or omission of various influencing factors, thus facilitating complete knowledge about groundwater variations and offering future strategic insights for sustainable groundwater resource management.

This paper explores a fractional integro-differential equation with boundary conditions that incorporate the Hilfer-Hadamard fractional derivative. We model the RLC circuit using fractional calculus and define weighted spaces of continuous functions. The existence and uniqueness of solutions are established, along with their Ulam-Hyers and Ulam-Hyers-Rassias stability. Our analysis employs Schaefer's fixed-point theorem and Banach's contraction principle. An illustrative example is presented to validate our findings.

The concept of being uniform strong interval-valued intuitionistic fuzzy (also termed as USIVIF) is an integration of two ideologies, which are called "uniformity" and "strong interval-valued intuitionistic fuzzy sets". Inspired by the study on uniform fuzzy topological indices, it is natural to introduce uniform IVIFTIs. Originally, topological indices were generalized for the fuzzy sets However, the utilization of the interval-valued intuitionistic fuzzy topological indices provides a finer approach, especially if there are multiple uncertainties based on intervals. Consequently, both theories imply that topological indices are not fixed and depend on certain situations or problems in the question. In this article, the generalized results for the uniform degree of the fuzzy sets associated with individual vertices/edges of strong interval-valued intuitionistic fuzzy graphs were presented and results for the total uniform degree of such graphs were also included. In addition, the nature of the implemented methods and models was discussed based on the cellular neural interval-valued intuitionistic fuzzy graphs of sets of membership and non-membership values.

As a pivotal branch within the realm of differential equations, the theory of oscillation holds a crucial position in the exploration of natural sciences and the construction of modern control theory frameworks. Despite the extensive research conducted globally, focusing on individual or combined analyses of key elements such as explicit damping terms, positive and negative coefficients, time-varying delays, and nonlinear neutral terms, systematic investigations into the oscillatory behavior of even-order differential equations that concurrently embody these four complex characteristics remain scarce. This paper, by establishing reasonable assumptions, innovatively presents two crucial criteria, aiming to preliminary delve into the oscillation patterns of even-order differential equations under specific complex settings. In the course of the study, a variety of mathematical techniques, such as Riccati transformation, calculus scaling methods, and partial integration, have been utilized by the researchers to perform the necessary derivations and confirmations.

In the present work, we have established some new fractional integral inequalities for functions whose $ k $th-derivatives are generalized modified $ h $-convex and symmetric about the midpoint involving the Caputo fractional derivatives. Many particular cases are obtained by using the findings.

This paper is concerned with almost sure exponential synchronization of multilayer complex networks with Markovian switching via aperiodically intermittent discrete observation noise. First, Markovian switching and multilayer interaction factors are taken into account simultaneously, which make our system more general compared with the existing literature. Meanwhile, the network architecture may be undirected or directed, and consequently, the adjacency matrix is symmetrical and asymmetrical. Second, the control strategy is based on aperiodically intermittent discrete observation noise, where the average control rate is integrated to depict the distributions of work/rest intervals of the control strategy from an overall perspective. Third, different from the work about th moment exponential synchronization of network systems, by utilizing M-matrix theory and various stochastic analysis techniques including the Itô formula, the Gronwall inequality, and the Borel-Cantelli lemma, some criteria on almost sure exponential synchronization of multilayer complex networks with Markovian switching have been constructed and the upper bound of the duration time has been also estimated. Finally, several numerical simulations are exhibited to validate the effectiveness and feasibility of our analytical findings.

In this paper, we introduced a new contraction principle via altering distance and $ C $-class functions with rational forms which extends and generalizes the existing version provided by Hasan Ranjbar et al. [H. Ranjbar, A. Niknam, A fixed point theorem in Hilbert $ C^\ast $-modules, Korean J. Math., 30 (2022), 297–304]. Specifically, the rational forms involved in the contraction condition we presented involve the $ p $-th power of the displacements which can exceed the second power mentioned in Hasan Ranjbar et al.'s paper. Moreover, we also proved a fixed point theorem for this type of contraction in the Hilbert $ C^\ast $-module. Some adequate examples were provided to support our results. As an application, we applied our result to prove the existence of a unique solution to an integral equation and a second-order $ (p, q) $-difference equation with integral boundary value conditions.

In this paper, an analytical and numerical technique are examined in order to analyse the Stokes flow determination problem due to a viscous sphere droplet moving at a concentric instantaneous position inside a spherical interface separating finite and semi-infinite immiscible fluid phases. Here, when only one of the three phases of the fluid (micropolar fluid) has a microstructure, attention is focused on this case. The motion is considered when Reynolds- and capillary-numbers are low, and the droplet surface and the fluid-fluid interface have insignificant deformation. A general solution is obtained in a spherical coordinate system based on a concentric position to analyse the slow axisymmetric movement of the micropolar fluid, considering microrotation and velocity components. Boundary conditions are initially fulfilled at the fluid-fluid interface and subsequently at the droplet surface. The normalised hydrodynamic drag force applying to a moving viscous droplet appears to be a function of the droplet-to-interface radius ratio, which increases monotonically and becomes unbounded when the droplet surface touches the fluid-fluid interface. The numerical outcomes of the normalised drag force acting on the viscous droplet are derived for different values of the parameters, and are presented in a tabular and graphical framework. A comparison was made between our numerical outcomes for the drag force and the pertinent data for the special cases found in the literature.

This paper employs differential subordination and quantum calculus to investigate a new class of $ q $-starlike functions associated with an eight-like image domain. Our study laid a foundational understanding of the behavior of these $ q $-starlike functions. We derived the results in first-order differential subordination. We established sharp inequalities for the initial Taylor coefficients and provided optimal estimates for solving the Fekete-Szegö problem and a second-order Hankel determinant applicable to all $ q $-starlike functions in this class. Furthermore, we presented a series of corollaries that demonstrate the broader implications of our findings in geometric function theory.

In this paper, the control problem of prescribed-time adaptive neural stabilization for a class of non-strict feedback stochastic high-order nonlinear systems with dynamic uncertainty and unknown time-varying powers is discussed. The parameter separation technique, dynamic surface control technique, and dynamic signals were used to eradicate the influences of unknown time-varying powers together with state and input unmodeled dynamics, and to mitigate the computational intricacy of the backstepping. In a non-strict feedback framework, the radial basis function neural networks (RBFNNs) and Young's inequality were deployed to reconstruct the continuous unknown nonlinear functions. Finally, by establishing a new criterion of stochastic prescribed-time stability and introducing a proper bounded control gain function, an adaptive neural prescribed-time state-feedback controller was designed, ensuring that all signals of the closed-loop system were semi-global practical prescribed-time stable in probability. A numerical example and a practical example successfully validated the productivity and superiority of the control scheme.

A generalization of the Lebesgue number lemma is obtained. For a metric space X in the class of strongly metrizable spaces, sufficient conditions for each open cover of X with a Lebesgue number has a finite subcover are obtained. It is proved that, if each countably infinite locally finite open cover of a chainable metric space X has a Lebesgue number, then X is totally bounded. A property for metric spaces which is a generalization of connectedness and Menger convexity is introduced. It is observed that Atsujiness and compactness are equivalent for a metric space with this introduced property as well as for a chainable metric space.

Fractal interpolation has been conventionally treated as a method to construct a univariate continuous function interpolating a given finite data set with the distinguishing property that the graph of the interpolating function is the attractor of a suitable iterated function system. On the one hand, attempts have been made to extend the univariate fractal interpolation from a finite data set to a countably infinite set. On the other hand, fractal interpolation in higher dimensions, particularly the theory of fractal interpolation surfaces (FISs), has received increasing attention for more than a quarter century. This article targets a two-fold extension of the notion of fractal interpolation by providing a general framework to construct FISs for a prescribed set consisting of countably infinite data on a rectangular grid. By using this as a crucial tool, we obtain a parameterized family of bivariate fractal functions simultaneously interpolating and approximating a prescribed bivariate continuous function. Some elementary properties of the associated nonlinear (not necessarily linear) fractal operators are established, thereby allowing the interaction of the notion of fractal interpolation with the theory of nonlinear operators.