Abstract: This study proposes a neural-augmented Libor Market Model (LMM) for swaption-surface calibration that enhances expressive power while maintaining the interpretability, arbitrage-free structure, and numerical stability of the classical framework. Classical LMM parametrizations, based on exponential-decay volatility functions and static correlation kernels, are known to perform poorly in sparsely quoted and long-tenor regions of swaption volatility cubes. Machine-learning–based diffusion models offer flexibility but often lack transparency, stability, and measure-consistent dynamics. To reconcile these requirements, the present approach embeds a compact neural network within the volatility and correlation layers of the LMM, constrained by structural diagnostics, low-rank correlation construction, and HJM-consistent drift. Empirical tests across major currencies (EUR, GBP, USD) and multiple quarterly datasets from 2024–2025 show that the neural-augmented LMM consistently outperforms the classical model. Improvements of approximately 9–15% in implied-volatility RMSE and 11–17% in PV RMSE are observed across all datasets, with no deterioration in any region of the surface. These results reflect the model’s ability to represent cross-tenor dependencies and surface curvature beyond the reach of classical parametrizations, while remaining economically interpretable and numerically tractable. The findings support hybrid model designs in quantitative finance, where small neural components complement robust analytical structures. The approach aligns with ongoing industry efforts to integrate machine learning into regulatory-compliant pricing models and provides a pathway for future generative LMM variants that retain arbitrage-free diffusion structure while learning data-driven volatility geometry.

Abstract: This paper investigates a delayed reaction-diffusion-advection population model that incorporates delay and strong Allee effect. Firstly, the effect of the advection rate on the stability of constant steady state within the model is examined. Analysis indicates that under the given conditions, larger advection rate can stabilize the constant steady state. Then, the existence of Hopf bifurcations is studied by adopting delay as the varying parameter. Besides, the normal form in the vicinity of the Hopf singularity on the center manifold is calculated by adopting a weighted inner product. Simulations are conducted to validate the theoretical findings. Research shows that under certain conditions, there exists a sequence of bifurcation singularities in the system.

Abstract: This study investigates how U.S. Federal Reserve interest rate cuts during the 2019–2020 easing cycle influenced the performance of equity mutual funds, with a focus on con-trasting growth and value strategies. Using an event study framework, we examine abnormal returns (AR), cumulative abnormal returns (CAR), and risk-adjusted perfor-mance measured by both static and rolling (30-day) Jensen’s alpha () and Sharpe ratios (SR) across short-term (30-day) and long-term (6-month and 1-year) windows surrounding three major rate cut events. Further statistical tests reveal that growth funds significantly outperform value funds following rate reductions, especially over longer horizons. This performance premium is more pronounced in risk-adjusted returns and becomes stronger when accounting for rolling dynamics, indicating that growth funds are more responsive and sensitive to monetary easing. These findings underscore a persistent and asymmetric sensitivity of different fund styles to interest rate changes, shaped by differences in duration exposure and investor sentiment. This study offers novel insights into how monetary policy influences fund-level dynamics beyond broad market movements and deepens the understanding of monetary trans-mission in asset management by incorporating time-varying performance metrics.

Abstract: Based on the Muskat-Leverett two-phase filtration equations, a model problem of water and air movement in melting snow is considered, taking into account the external heat flow. The maximum principle and the finite-velocity lemma for perturbations are proven for water saturation. An algorithm for numerically studying the self-similar problem is presented. Calculations of the temperature and water saturation distributions by depth are presented. The significant influence of the specified flux at the boundary and the thermal conductivity coefficient on the temperature field in the snow layer is demonstrated, which is important for predicting melting and hydrothermal processes in snow and ice covers. A theorem on the existence of a weak solution to this problem is formulated. A literature review is provided on mathematical models of multiphase filtration in porous media, taking into account phase transitions (melting, sublimation) and external heat fluxes.

Abstract: This paper introduces a similarity index aimed at modeling psychological well-being through a set-theoretic formalization of self-ideal alignment. Inspired by Tversky’s feature-based model of similarity, the proposed index quantifies the degree of overlap and divergence between the current self-perception and the ideal self, each represented as a vector of signed attributes. The formulation extends traditional approaches in Personal Construct Psychology by incorporating directional and magnitude-based comparisons across constructs, and its mathematical properties can be expressed within a fuzzy similarity space that ensures boundedness and internal coherence. Unlike standard correlational methods commonly used in psychological assessment, this model provides an alternative framework that allows for asymmetric weighting of discrepancies and non-linear representations of similarity. Developed within the WimpGrid formalism—a graph-theoretical extension of constructivist assessment—the index offers potential applications in clinical modeling, idiographic measurement, and the mathematical analysis of dynamic self-concept systems. We discuss its relevance as a generalizable tool for quantitative psychology, and its potential for integration into computational models of personality and self-organization.

Abstract: This study develops a fractional-order three-species predator–prey model incorporating the effects of prey refuge and predator competition. The prey population grows logistically, with a fraction protected by refuge, while intermediate and top predators interact through linear functional responses with intraspecific competition.Fractional derivatives introduce memory effects, providing a more realistic description of population dynamics. We analyze the equilibria, perform stability analysis using the fractional Routh-Hurwitz criteria, and conduct numerical simulations to illustrate the impact of prey refuge, predator competition, and fractional order on population persistence and oscillations. The results provide insights for ecological management and understanding of memory effects in predator–prey systems.

Abstract: This paper presents a unified framework for constructing partially unstructured B-spline transfinite finite elements with arbitrary nodal distributions. Three novel distinct classes of elements are investigated and compared with older single Coons-patch elements. The first consists of classical transfinite elements reformulated using B-spline basis functions. The second includes elements defined by arbitrary control point networks arranged in parallel layers along one direction. The third features arbitrarily placed boundary nodes combined with a tensor-product structure in the interior. For all three classes, novel macro-element formulations are introduced, enabling flexible and customizable nodal configurations while preserving the partition of unity property. The key innovation lies in reinterpreting the generalized coefficients as discrete samples of an underlying continuous univariate function, which is independently approximated at each station in the transfinite element. This perspective generalizes the classical transfinite interpolation by allowing both the blending functions and the univariate trial functions to be defined using non-cardinal bases such as Bernstein polynomials or B-splines, offering enhanced adaptability for complex geometries and nonuniform node layouts.

Abstract: The aim of this paper is to give necessary and sufficient optimality conditions for nonconvex optimization problems such that the constraint inequalities are both nonnegative and nonpositive, where the objective function and the constraint functions are tangentially convex, but are not necessarily convex. We do this first by introducing a novel constraint qualification, call “tangential nearly convexity” ((TNC), in short). Next, by using the cone of tangential subdifferentials together with the novel constraint qualification, we show that Karush-Kuhn-Tucker (KKT) conditions are necessary and sufficient for the optimality. Several examples are presented to clarify and compare the novel constraint qualification with the other well known constraint qualifications.

Abstract: This paper develops a comprehensive theory of fractional Landau inequalities with mixed Sobolev norms, extending classical gradient bounds to anisotropic function spaces. Building upon the foundational work of Landau (1925) and recent advances in fractional calculus by Anastassiou (2025), we address the critical limitation of existing theories that operate primarily within isotropic settings. Our framework introduces mixed fractional Sobolev spaces $W^{\nu,p}_\alpha(\mathbb{R}^k)$ that capture directional scaling behavior through parameters $\alpha = (\alpha_1,\dots,\alpha_k)$, enabling precise characterization of functions with heterogeneous regularity across different coordinates. We establish sharp fractional Landau inequalities with constants that explicitly track dependence on both fractional order $\nu$ and anisotropic scaling $\alpha$, proving these bounds through innovative harmonic analysis techniques including directional Littlewood-Paley theory and anisotropic maximal function estimates. The theoretical framework finds compelling applications in neural operator theory, where we prove stability bounds under input perturbations and derive optimal approximation rates for deep networks processing multiscale data. Our results demonstrate that neural operators achieve approximation rates of order $N^{-\nu/d_\alpha}$, where $d_\alpha$ is the anisotropic dimension, substantially improving upon classical isotropic rates when scaling parameters are heterogeneous. This work bridges fractional calculus, harmonic analysis, and deep learning, providing new mathematical foundations for understanding and designing algorithms for high-dimensional, multiscale problems.

Abstract: In Banach space optimization, solving inclusion and convex-composite problems through iterative methods depends on various convergence conditions. In this work, we develop an extended semi-local convergence analysis for two algorithms used to generate sequences converging to solutions of inclusion and convex-composite optimization problems for Banach space-valued operators. The applicability of these algorithms is extended with benefits: weaker sufficient convergence criteria and tighter error estimates on the distances involved. These advantages are obtained at the same computational cost since the Lipschitz constants used are special cases of the Lipschitz constant used in earlier studies. The implementation issues for these algorithms are also addressed by introducing hybrid algorithms.

Abstract: This short communication develops a formal proof of Castilgiano Theorem in a elasticity context. The results are base on standard tools of applied functional analysis and calculus of variations. It is worth mentioning such results here presented may be easily extended to a non-linear elasticity context. Finally, in the last section we present a numerical example in order to illustrate the results applicability.

Abstract: Analysis of a Crowdsourcing Markovian Queue with Phase-type Service is considered in this paper. In this model, a customer not only receives service but assists in delivery. In other words, in a retail environment, while some customers shop in-store, others place orders online or by phone and require home delivery. Store management can utilize online customers as couriers to complete these deliveries. However, because not every customer may agree to take part, a probabilistic element is included to capture the chances of their participation. The model also incorporates imperfect service, reflecting cases where deliveries may fail or require rework, and working breakdowns, representing partial disruptions in service capacity rather than complete stoppages. To analyse the system under steady-state conditions, matrix-analytic methods are applied. Numerical examples illustrate the significant benefits of incorporating these dynamics into traditional queueing models.

Abstract: The Logistics Performance Index (LPI), developed by the World Bank, is a global benchmark for assessing national logistics efficiency. However, most studies have treated the LPI as a dependent or descriptive variable, overlooking its potential as a predictive indicator of sustainable development. This study reformulates the LPI as a multivariable explanatory construct to evaluate the predictive capacity of its six dimensions—customs, infrastructure, international shipments, logistics competence, tracking and tracing, and timeliness—on three key sustainability indicators: GDP per capita, the Human Develop- ment Index (HDI), and CO₂ emissions. Using 2023 data for approximately 120 countries from the World Bank database, thirteen statistical and machine learning models were applied, including linear regression, penalized regressions, support vector regression (SVR), k-nearest neighbors (KNN), and ensemble methods such as ExtraTrees, Random Forest, Gradient Boosting, CatBoost, and XGBoost. Model performance was evaluated using Spearman’s correlation, mean absolute error (MAE), root mean squared error (RMSE), and SHAP interpretability analysis. Among all models, ensemble algorithms—particularly ExtraTrees—achieved the highest predictive accuracy (ρ ≥ 0.79), identifying infrastructure and tracking as the most influential predictors. K-means clustering revealed three distinct logistic–environmental profiles (low, medium, and high emissions), reflecting structural heterogeneity among countries. The findings demonstrate that the LPI can function as a robust and explainable predictive tool for anticipating economic, social, and environmental outcomes, offering a data-driven framework for designing sustainability-oriented logistics policies.

Abstract: Integral calculus is a fundamental component of mathematics with extensive applications, particularly in computing the volumes of solids of revolution—three-dimensional objects generated by rotating a plane curve around a given axis. This study aims to explore the application of integral calculus in determining the volumes of solids formed by rotating simple curves, supported by GeoGebra as a dynamic visualization tool. A descriptive-exploratory approach was employed, consisting of four main steps: (1) selecting relevant functions and intervals, (2) analytically calculating volume using the disk or shell method, (3) modeling the curve and its rotation in GeoGebra 3D, and (4) verifying and comparing analytical results with the software’s visual estimations. The functions analyzed include y = x2, y = 2x + 1, and y = sin 2 (x) , rotated about both the x-axis and y-axis. Findings indicate that volume values generated by GeoGebra closely align with analytical calculations, with a relative error of less than 1%. Moreover, the interactive three-dimensional visualizations significantly enhance students’ conceptual understanding of integrals by allowing them to observe the geometric formation of solids of revolution and validate their computational results. The integration of analytical methods with digital tools like GeoGebra not only improves computational accuracy but also enriches calculus instruction through intuitive, engaging visual representations that bridge abstract concepts and concrete understanding.

Abstract: Mathematical communication ability refers to the capacity to express mathematical ideas or concepts using mathematical language, either orally or in writing. However, students’ mathematical communication skills remain generally low. One instructional approach that may enhance this ability is Problem-Based Learning (PBL). To increase student engagement in PBL, innovative teaching media such as GeoGebra can be integrated into instruction. This study aimed to examine the effectiveness of using the GeoGebra application within a PBL framework on students’ mathematical communication ability. A quantitative research design was employed, specifically a pretest–posttest control group design. The population comprised all eighth-grade students at SMP Negeri 1 Padangsidimpuan, North Sumatra, Indonesia. Two classes—VIII-F (experimental) and VIII-G (control)—were selected through purposive sampling. Data were collected using a mathematical communication ability test and a GeoGebra usage questionnaire. The Mann–Whitney U test was applied for statistical analysis. Findings indicated that students taught with GeoGebra-assisted PBL demonstrated significantly greater improvement in mathematical communication ability compared to those taught with conventional direct learning (DL). However, none of the students in either group achieved the minimum passing criterion (KKM). Furthermore, student responses to the GeoGebra questionnaire fell into the high category, suggesting a positive perception and favorable impact on the learning process. These results support the integration of dynamic digital tools like GeoGebra within student-centered pedagogies to foster mathematical communication.

Abstract: The shift toward digital learning has become an essential direction in higher education, necessitating the development of relevant and effective instructional materials. This study focuses on the development of online-based Calculus learning materials assisted by GeoGebra, designed to support effective and engaging mathematics instruction in digital environments. The research employed a Research and Development (R&D) approach, evaluating both the practicality and effectiveness of the materials. Data were collected through questionnaires and basic Calculus tests administered to 20 students from the Mathematics Education Study Program at Universitas Islam Negeri Syekh Ali Hasan Ahmad Addary Padangsidimpuan, North Sumatra, Indonesia, who had completed the Basic Calculus course. Practicality was assessed based on user responses, while effectiveness was measured through student performance. The results indicated that the developed materials fall into the “good” category, with a practicality score of 3.36 and an effectiveness score of 72.75. These findings suggest that the GeoGebra-assisted, online-based Calculus materials are suitable for implementation as an alternative resource in digital Calculus instruction. However, further refinement is recommended—particularly in enriching content that fosters learner creativity and integrates realistic mathematics education approaches. Enhancing these aspects could strengthen the material’s capacity to support deeper conceptual understanding and active engagement in online learning settings.

Abstract: This study aims to analyze the partial and simultaneous influence of learning interest and learning creativity on students’ academic achievement in Calculus courses. Employing an ex post facto design with a correlational approach, the research was conducted at UIN Syekh Ali Hasan Ahmad Addary Padangsidimpuan, North Sumatra, Indonesia. A total of 30 students were selected as participants through simple random sampling. Data were collected using three instruments: a Calculus achievement test, a learning interest questionnaire, and a learning creativity questionnaire. Data analysis was carried out using both descriptive and inferential statistics, specifically multiple linear regression. The findings reveal three key results: (1) learning interest significantly affects Calculus achievement (t_calculated = 4.392 > t_table = 1.669); (2) learning creativity also significantly influences Calculus achievement (t_calculated = 3.102 > t_table = 1.669); and (3) learning interest and creativity together have a positive and statistically significant combined effect on Calculus achievement (p < 0.05). The regression model obtained is Y = 22.044 + 0.502X₁ + 0.120X₂, indicating that an increase in either learning interest or learning creativity is associated with higher Calculus performance. The standardized coefficients further suggest that learning interest has a stronger predictive power than learning creativity in this context. These results underscore the critical role of affective and cognitive engagement in mathematics education, particularly in challenging courses like Calculus. Therefore, educators are encouraged to design instructional strategies that foster students’ intrinsic motivation and creative thinking to enhance academic outcomes. Integrating active learning methods, open-ended problem-solving tasks, and student-centered approaches may effectively cultivate both interest and creativity, thereby improving Calculus achievement among undergraduate students.

Abstract: This study is a development research aimed at producing a GeoGebra-based mathematics learning media grounded in the Van Hiele theory to support the teaching and learning of maximum and minimum values. The 4-D development model (define, design, develop, disseminate) was employed, though the study was implemented only up to the third phase (develop). Data were collected through expert validation instruments, practicality questionnaires administered to both teachers and students, and an effectiveness test. Both qualitative and quantitative descriptive analyses were applied to interpret the data. The research was conducted at SMA Negeri 2 Padangsidimpuan with a small-scale trial involving nine participants. The developed media was evaluated based on three key criteria: validity, practicality, and effectiveness. Results indicated high validity, with average scores of 4.67 (on a 5-point scale) from media experts and 4.30 from subject-matter teachers—both categorized as “very high.” Practicality was also rated highly: teachers reported a practicality percentage of 97.75%, while students reported 90%, both falling into the “very high” category. Furthermore, the effectiveness test revealed a student mastery rate of 88.89%, demonstrating the media’s capacity to facilitate meaningful learning outcomes. These findings confirm that the GeoGebra-based learning media, integrated with the Van Hiele theoretical framework, satisfies the standards of validity, practicality, and effectiveness for teaching maximum and minimum values in secondary mathematics. The dynamic visualization and structured cognitive progression aligned with Van Hiele’s levels of geometric thought enhance students’ conceptual understanding, offering a promising digital tool for mathematics instruction in technology-enhanced classrooms.

Abstract: A Multi-Structure replaces classical operations with mappings from tuples to finite multisets, allowing multiple outputs for a single input tuple simultaneously and flexibly. An Iterative Multi-Structure extends these multiset operations across hierarchical levels, combining multisets of multisets through k iterative stages of layered aggregation. In this paper, we define the MultiRough, MultiGrey, MultiGranular, MultiInterval, and MultiFunctorial Numbers by extending the Rough, Grey, Granular, Interval, and Functorial Numbers using the frameworks of Multi-Structure and Iterative Multi-Structure. Furthermore, we introduce their corresponding Iterative versions—Iterative MultiRough, Iterative Multi-Grey, Iterative MultiGranular, Iterative MultiInterval, and Iterative MultiFunctorial Numbers—and briefly discuss their fundamental properties.

Abstract: This paper develops a unified framework for project scheduling under uncertainty using Iterative MultiStructures. We introduce Fuzzy, Neutrosophic, and Plithogenic Project Iterative MultiScheduling, where schedules are composed across hierarchical levels as finite multisets and evaluated after canonical flattening and selection. Using componentwise extensions of sum and max, we propagate uncertain activity times and derive fuzzy expectations and credibility constraints (and their neutrosophic/plithogenic counterparts). We prove that the schedule space forms an Iterative MultiStructure and that our models strictly generalize classical fuzzy project scheduling, neutrosophic project scheduling, and plithogenic project scheduling, as well as their non-iterative multischeduling variants. The framework supports precedence networks, multi-criteria costs, and admits exact reductions under natural embeddings.