Search Results (12,633)

Stability analysis of switched nonlinear fractional differential equations is considered in this paper. The main characteristic of our problem is random switching times when the switching rule is activated. Here, the switching rule is independent of the state of the system, but it depends on the random activation points. The dynamics between two consecutive switching times are described by nonlinear fractional differential equations with the Caputo fractional derivative with respect to another function. The lower limit of the fractional derivative changes at each switching time, and the waiting time between consecutive switching times is an Erlang-distributed random variable. We define p-moment stability, and we obtain some sufficient conditions; the study is based on an application of a Lyapunov function method. We consider both the case of Lyapunov functions with a negative fractional derivative and the case with a positive fractional derivative. It is of interest to note that the applied function in the Caputo-type fractional derivative has a huge influence on the stability behavior of the system. Full article

This study provides a systematic review of mathematical programming models applied to agricultural water management, with a focus on their relevance for policy design addressing water scarcity and agricultural pollution. Following the PRISMA (Preferred Reporting Items for Systematic Reviews and Meta-Analyses) methodology, 42 peer-reviewed studies were selected from an initial sample of 438 records and analysed using a multi-dimensional framework covering research context, economic objectives and policy orientation, and model features. The analysis reveals a pronounced geographical and thematic segmentation: water scarcity studies are concentrated in Asia, while water quality studies are predominantly European and regulatory-driven, with limited mutual influence. While deterministic optimisation approaches remain prevalent, models increasingly integrate biophysical processes through coupling with agro-hydrological components. However, policy applicability is often constrained by the limited representation of farmers’ behavioural responses, trade-offs between model complexity and usability, and difficulties in transferring results across institutional contexts. Emerging policy instruments remain limited in the sample. Progress in this field depends less on technical elaboration within existing frameworks and more on integration across disciplinary approaches. A suitable pathway would be the development of models that treat water availability and quality as jointly determined outcomes and embed institutional design within the optimisation framework. Full article

This paper investigates the projective synchronization problem for a class of non-autonomous neural networks with Caputo fractional derivatives and mixed delays. First, by simultaneously introducing discrete and distributed delays into the model, the drive and response systems and the corresponding error system are constructed, and a synchronization controller is designed. Second, by constructing an appropriate quadratic Lyapunov function and estimating the nonlinear and mixed-delay terms in a unified manner, a fractional Halanay-type delay inequality is derived. Based on this inequality, sufficient conditions are obtained to guarantee global asymptotic projective synchronization for this class of neural networks. Finally, numerical simulations are presented to verify the theoretical results and the numerical consistency of the adopted discretization scheme. Full article

Power skiving has become an increasingly adopted process for manufacturing spur face gears. However, achieving satisfactory meshing performance remains challenging, mainly because the tooth surface produced by skiving does not fully coincide with the ideal conjugate surface, while direct modification of the face gear is relatively difficult in practice. To overcome this limitation, a meshing performance regulation strategy is developed by applying topological modification to the mating cylindrical gear. First, the geometry of the skived spur face gear is mathematically formulated. Subsequently, the modified tooth flank of the cylindrical gear is generated using a rack surface described by a bivariate quadratic function. The deviations of the two mating tooth surfaces were mapped to construct an ease-off difference surface, from which the contact ellipse, contact path, and geometric transmission error were evaluated. For modification coefficients of a1 = −9.03 × 10⁻⁵ mm⁻¹, a2 = −5.0 × 10⁻⁴ mm⁻¹, and a3 = −1.0 × 10⁻³ mm⁻¹, the calculated transmission error amplitude was 6.362 μrad. The predicted contact ellipse had an inclination angle of 14.13°, while rolling tests gave approximately 14.6°. The experimental to numerical deviations in inclination angle, tooth length ratio, and tooth depth ratio were 0.5°, 7.1%, and 8.0%, respectively. These results demonstrate that modifying the mating cylindrical gear provides a practical means of controlling the meshing performance of skived spur face gear pairs. Full article

Audio–visual depression recognition in real-world scenarios is often challenged by temporal sparsity and cross-modal asynchrony, where depression-related cues may appear only in short segments and may not align precisely across modalities. Under such conditions, global pooling or dense attention tends to dilute sparse discriminative evidence with redundant context, leading to unstable utterance-level representations. To address this issue, we propose an audio–visual depression recognition framework that integrates modality feature adaptation, bidirectional cross-modal interaction, and graph-based prototype abstraction. Specifically, heterogeneous audio and visual streams are first transformed into compatible representations, after which bidirectional cross-attention models content-dependent dependencies across modalities without requiring index-wise correspondence. The fused tokens are then interpreted as graph nodes and aggregated into a compact set of semantic prototypes through graph convolution and differentiable soft clustering. In addition, audio perturbation is introduced during training as a task-oriented regularisation strategy for partial acoustic evidence loss and temporal misalignment. Experiments on the LMVD dataset demonstrate clear improvements on the primary depression-recognition task, while auxiliary evaluations on MIntRec and CMU-MOSI suggest that the structured prototype representation is beneficial for other temporally sparse audio–visual recognition tasks. These results indicate that structured prototype learning is effective for preserving sparse depression-related cues, while training-time perturbation provides a complementary regularisation effect under asynchronous multimodal conditions. Full article

Rapid urbanization, increasing demand variability, and digitalisation of urban infrastructure require intelligent decision-support systems that can improve sustainability, resilience, and operational efficiency in smart city operations. Artificial intelligence (AI) and data-driven optimization offer strong potential for adaptive urban services, including dynamic pricing, demand response, resource allocation, and energy-aware management. However, many reinforcement learning applications still focus mainly on short-term performance while giving limited attention to transparency, fairness, stability, and accountability. This study proposes a trustworthy reinforcement learning framework for AI-driven urban decision-making, using sustainable dynamic pricing and resource optimization as mechanisms for adaptive and responsible decision-making. A custom reinforcement learning environment was developed using historical e-commerce transactional data as a methodological proxy to simulate interactions among demand, resource or inventory availability, service categories, price elasticity, and changing market conditions. Three reinforcement learning algorithms, namely Deep Q-Network, Proximal Policy Optimization, and Advantage Actor–Critic, were evaluated under comparable experimental conditions. Performance was assessed using profitability, decision stability, fairness-oriented pricing behavior, decision consistency, and interpretability. To improve transparency, trajectory-based policy audits and SHapley Additive exPlanations were applied to identify the main factors influencing pricing decisions. The results show that the Deep Q-Network agent achieved the most balanced performance, increasing total profit by 12.58% while recording no unethical price increases under low-demand conditions. Explainability analysis showed that stock or resource levels, demand shifts, and price elasticity were the strongest positive drivers of pricing actions, whereas inventory hoarding and unfavorable price increases reduced decision quality. The findings indicate that reinforcement learning can support sustainable and resilient urban decision-making when optimization objectives are combined with trustworthy AI principles. The proposed framework provides a practical basis for accountable AI-based decision-support systems in smart city operations, including demand-responsive services, resource optimization, sustainable dynamic pricing, and energy-aware management. Full article

Rapid technological innovation and digitalization have intensified the demand for STEM-related skills, yet many educational systems face stagnant or declining student engagement in STEM, particularly in the later years of secondary education. This study examined how gender, study track (STEM versus non-STEM) and grade level are related to secondary school students’ STEM motivation, interest and identity. The study also examined the role of perceived autonomy, relatedness and competence support from mathematics teachers in these associations. Using a comparative cross-sectional survey design, data were collected from 317 students in two secondary schools in the Kempenrand region of Antwerp, Flanders (Belgium). Linear regression models and school-specific simple-effects analyses were used to examine school and subgroup differences. Concurrent indirect-association and moderation analyses were performed to examine the role of perceived need support with Benjamini–Hochberg corrections applied for multiple testing. The results revealed variation between school contexts. The association between gender and STEM identity differed between schools, while study-track differences in STEM interest, identity and intrinsic motivation were greater in one school than in the other. The clearest contextual variation concerned grade level. In one school, 5th-year students reported higher STEM identity and identified regulation, whereas 6th-year students reported higher levels of these outcomes in the other; 6th-year students in the latter school also reported higher STEM interest and intrinsic motivation. No total concurrent indirect associations through perceived need support remained statistically significant after correction. However, the association between study track and STEM identity varied significantly as a function of perceived autonomy and relatedness support, with both forms of support positively associated with STEM identity among STEM track students but not among non-STEM students. These findings indicate that subgroup differences in STEM-related outcomes are not uniform across school contexts and that pooled estimates may obscure meaningful contextual heterogeneity. Context-sensitive analyses are therefore important when identifying groups with lower STEM motivation, interest or identity. Full article

Most multimodal transit studies use pairwise or multilayer graphs that discard route membership. We construct route-preserving bus–metro hypergraphs for 45 Chinese cities. A route-support rule makes node viability depend on the fraction of incident routes that remain viable. Transfer-first attack is the most damaging static strategy in 33 cities. PPCR is associated with greater connectivity retention under random disruption ($r=0.807$), but with deeper route-support pruning under targeted triggering. Connectivity retention, route-support outcomes, and recovery are only moderately aligned (mean $\left|\rho \right|=0.52$). Three principal components are needed to explain 90% of their variance. Multimodal resilience, therefore, cannot be summarized by one ranking. The hypergraph preserves route-dependent failure as a native model property. Full article

Large Language Models (LLMs) are increasingly incorporated into software systems. Their non-deterministic behavior, external hosting, response latency, and operational cost create challenges for established design approaches such as Clean Architecture. This paper examines the integration of an LLM component into a layered software system and compares three possible placements within Clean Architecture: Domain, Application, and Infrastructure. The evaluation considers dependency management, testability, separation of concerns, and implementation complexity. The study proposes an approach in which the LLM is implemented in the Infrastructure layer and accessed through an interface defined in the Application layer. This approach is combined with the Command and Query Responsibility Segregation pattern to isolate LLM interaction within dedicated query handlers. The proposed pattern is demonstrated through the implementation of Budget, a personal finance tracking system that uses GPT-4.1 to convert free-form natural language input into structured transaction records. The results show that placement in the infrastructure layer provides the clearest separation between business logic and external AI services and avoids the introduction of non-deterministic behavior into the core application logic. Full article

We construct and analyze optimal quadrature formulas for the right-sided Riemann–Liouville fractional integral in the Sobolev space $L_2^{(m)}(t,1)$, using $\phi ,{\phi }^{\prime },\dots ,{\phi }^{(m-1)}$ at $N+1$ equally spaced nodes. The analysis is carried out through the Peano kernel of the error functional, for which we give an exact closed form; this yields the norm of the error functional, existence and uniqueness of the optimal coefficients by an orthogonal-projection argument, and computable error bounds. Our main result is structural: the functions attached to the coefficients form a basis of the space of discontinuous piecewise polynomials of degree $m-1$ on the mesh, so that the optimality problem is an $L_2$ projection that decouples panel by panel. Consequently, the globally optimal (Sard) coefficients—not only the sequentially optimal ones—are available in closed form for every m, at a cost of $O(m^{3}N)$ operations with no global linear system and with a condition number independent of N, h, $\alpha$ and t. The globally optimal rule is exact on polynomials of degree $2m-1$ and converges as $O(h^{2m})$ for smooth integrands, whereas the sequential rule is exact on degree m; we quantify the gap between them. We also prove sharp asymptotics for the error norm, ${\parallel R\parallel }^2\sim {\kappa }_m{(1-t)}^{2\alpha -1}{(2\alpha -1)}^{-1}{h}^{2m}$ for $\alpha >\frac{1}{2}$ with ${\kappa }_m={(-1)}^{m-1}{B}_{2m}/(2m)!$, with a $\ln (1/h)$ factor exactly at $\alpha =\frac{1}{2}$ and a loss of half an order for $\alpha <\frac{1}{2}$. An extensive numerical study over five fractional orders, three evaluation points and eight integrands of prescribed Sobolev regularity confirms every theoretical statement, and the formulas are compared with product, spline and Gauss–Jacobi quadratures and applied to an Abel integral equation. Full article

Motivated by the interplay between discrete orthogonal polynomials and geometric function theory, we introduce and investigate some new Ma-Minda-type subclasses of bi-univalent functions generated by the Poisson-Charlier polynomials through their following analytic generating function: ${\mathcal{E}}_a(x,z)={(1+z)}^x{e}^{-az}\left(\right|z|<1).$ Within the classical class $\Sigma$ of analytic and bi-univalent functions, we first define the Poisson-Charlier-generated bi-starlike and bi-convex families via the subordination relations involving ${\mathcal{E}}_a(x,·)$ for both a function f and its inverse $f^{-1}$. By combining the Carathéodory representation with the series expansion of ${\mathcal{E}}_a(x,z)$ and the Lagrange inversion formula for $f^{-1}$, we derive coefficient estimates for the initial Taylor-Maclaurin coefficients $a_2$ and $a_3$ of functions in the starlike class ${\Sigma }_{{𝒮}^{*}}\left(\mathcal{E}(a,x)\right)$ and in the convex class ${\Sigma }_{𝒦}\left(\mathcal{E}(a,x)\right)$. In addition, we obtain corresponding Fekete-Szegö type inequalities of the form $\left|a_3-\mu a_2^2\right|$ for a real parameter $\mu$ in both settings, which are expressed explicitly in terms of the parameters a and x of the Poisson-Charlier framework. To the best of our knowledge, these Poisson-Charlier-generated bi-starlike and bi-convex classes have not previously been investigated, so the resulting coefficient and Fekete-Szegö estimates constitute a distinct contribution rather than direct special cases of previously studied Ma-Minda families. Full article

Modern manufacturing enterprises are increasingly transitioning to multi-variety, small-batch production. This shift introduces significant scheduling challenges, particularly due to the job hierarchy constraints inherent in assembling multi-level intermediate parts. Furthermore, non-machining preparation times—such as tool switching, material handling, and equipment standby—significantly impact production efficiency. To address these challenges, this paper investigates the flexible job shop batch scheduling problem by integrating order and operation consolidation under strict job hierarchy constraints. To mathematically formulate the scheduling problem with non-serial operation precedence networks and dynamic batching, we develop a mixed-integer programming model. The primary objective is to simultaneously minimize the maximum completion time (makespan) and total tardiness. To solve this efficiently, an Improved Grey Wolf Optimization (IGWO) algorithm is proposed. The algorithm features a novel two-tier coding scheme tailored for consolidation logic and employs a hybrid population initialization strategy to enhance initial solution quality. Moreover, it improves the standard hunting mechanism, utilizes Variable Neighborhood Search (VNS) for local exploitation, and independently applies a Simulated Annealing (SA) dynamic acceptance mechanism to balance global exploration and local exploitation. Extensive experiments using small-, medium-, and large-scale industrial data from a power station valve manufacturer validate the effectiveness of the proposed model and algorithm in optimizing complex batch scheduling schemes. Full article

Objectives: Despite the central role of metabolic–immune crosstalk in pulmonary arterial hypertension (PAH), integrative quantitative tools remain lacking. We aimed to construct and validate a metabolic–immune molecular classification score (MIRS) as a quantitative metric to capture the inflammation–metabolism balance and to assess its discriminatory performance for molecular subtyping, cross-cohort applicability, and biological implications. Methods: We integrated five PAH lung tissue transcriptomic datasets from the Gene Expression Omnibus (GEO). A training set was used to identify differentially expressed genes and to derive MIRS as the first principal component of 20 core genes. MIRS was projected onto independent validation cohorts. Immune microenvironment, pathway activities, protein–protein interaction, and drug repositioning analyses were performed. Results: MIRS significantly distinguished Non-IPAH from IPAH in GSE117261 (AUC = 0.718, p = 0.010) and revealed internal heterogeneity in SSc-PAH. MIRS-related gene expression patterns showed significant differences across COPD and ILD lung tissues in independent datasets. A unified fixed PCA projection pipeline with mean imputation for missing core genes was applied to all pulmonary disease datasets, enabling consistent numerical quantification of MIRS across cohorts under the same mathematical framework. MIRS failed to discriminate PAH from controls in PBMCs, indicating that this tissue-derived signature is not readily detectable in peripheral blood—a limitation that restricts its applicability to lung tissue specimens and highlights challenges for blood-based biomarker development in PAH. Higher MIRS correlated with increased immune scores and myeloid cell infiltration in Non-IPAH. Drug prediction identified sirolimus and tocilizumab as top candidates, with MIRS-stratified sensitivity patterns aligning with pathway loading directions. Conclusions: MIRS is a quantitative, tissue-restricted metric that captures metabolic–immune activation in PAH, with exploratory observations in other pulmonary diseases that warrant further validation. It provides a molecular stratification basis for subtype discrimination and a hypothesis-generating framework for future therapeutic investigations. Full article

Hepatitis C virus (HCV) infection remains highly prevalent among people who inject drugs (PWID), where treatment effectiveness is strongly influenced by adherence and behavioral relapse. In this study, we develop and analyze a deterministic compartmental model to examine the impact of treatment adherence, relapse, and risk-reduction behaviors on HCV transmission dynamics. The model incorporates key behavioral pathways, including treatment initiation, partial adherence, and relapse to high-risk behavior. Analytical results establish positivity and boundedness of solutions, and the basic reproduction number is derived using the next-generation matrix approach. We show that the disease-free equilibrium is globally asymptotically stable when the reproduction number is below unity, while uniform persistence and a globally stable endemic equilibrium occur when transmission exceeds this threshold. Numerical simulations and sensitivity analyses indicate that the probability of transmission per needle-sharing event and the number of sharing partners are dominant drivers of epidemic persistence. In contrast, treatment uptake and sustained adherence significantly reduce transmission. Relapse to drug misuse undermines treatment benefits by expanding the infectious pool. These findings underscore the importance of integrating antiviral therapy with behavioral support to achieve long-term HCV control among PWID. Full article

In this work, we prove the strong convergence of an inertial iterative scheme to approximate solutions of the equilibrium fixed point problem associated with nonexpansive mappings in Hilbert spaces. Numerical simulations are carried out to examine the performance of the proposed approach. The results indicate that the proposed inertial approach achieves faster convergence when compared with existing comparable iterative schemes. We also investigate how different choices of initial values influence the convergence behavior of our algorithms and we compare these effects with those observed in classical iterative schemes through graphical illustrations. In applications, we used our approach to solve the signal processing problem. We also apply it to a mathematical model describing the spread of an infectious disease, which illustrates its relevance to real-world dynamical systems. Finally, we show that the proposed method can be applied in solving constrained optimization, variational inequality and split feasibility problems which highlight its flexibility and wide applicability. Full article