Search Results (363)

Academic performance has become a consolidated indicator of a nation’s educational and social equity. Consequently, increasing attention has been paid to determining the factors associated with school performance, particularly in the case of students with extreme academic outcomes. The aim of this study is to identify and compare the factors related to the level of mathematical competence of Spanish students with low and high levels of achievement, based on data from the Spanish sample of PISA 2022 (n = 30,800). The results of the multilevel quantile regression analysis reveal that the social, economic, and cultural status of the students have a significant and positive effect on both groups. Other variables, such as gender, grade repetition, and length of pre-primary education, show differentiated effects depending on the level of competence. Moreover, school-related factors, such as school location and competition among centres, exhibit opposite effects. Finally, aspects such as school ownership, average class size, and the degree of curricular autonomy only have a significant impact on the mathematical competence of low-achieving students. These findings highlight the need for differentiated educational policies that address the specific needs of each group of students. Full article

The current work establishes the geometrical bearing for hypersurfaces in a Golden Riemannian manifold with constant golden sectional curvature with respect to k-almost Newton-conformal Ricci solitons. Moreover, we extensively explore the immersed r-almost Newton-conformal Ricci soliton and determine the sufficient conditions for total geodesicity with adequate restrictions on some smooth functions using mathematical operators. Furthermore, we go over some natural conclusions in which the gradient k-almost Newton-conformal Ricci soliton on the hypersurface of the Golden Riemannian manifold becomes compact. Finally, we establish a Schur’s type inequality in terms of k-almost Newton-conformal Ricci solitons immersed in Golden Riemannian manifolds with constant golden sectional curvature. Full article

This article explores the role of the European Union (EU) as a normative gender actor promoting women’s participation in STEM (Science, Technology, Engineering, and Mathematics) within the Eastern Partnership (EaP) region. In a context marked by global inequality and overlapping international efforts, this paper assesses the extent to which EU-driven Europeanisation influences national gender policies in non-EU states. Using a postfunctionalist lens, this research draws on a qualitative analysis of EU-funded programmes, strategic documents, and a detailed case study encompassing Armenia, Georgia, Moldova, Ukraine, Belarus, and Azerbaijan. This study highlights both the opportunities created by EU initiatives such as Horizon Europe, Erasmus+, and regional programmes like EU4Digital and the challenges presented by political resistance, institutional inertia, and socio-cultural norms. The findings reveal that although EU interventions have fostered significant progress, structural barriers and limited national commitment hinder the long-term sustainability of gender equality in STEM. Moreover, the withdrawal of other global actors increases pressure on the EU to maintain leadership in this area. This paper concludes that without stronger national alignment and global cooperation, EU gender policies risk becoming symbolic rather than transformative. Full article

In this paper, a hybrid flying robot that utilizes water thrust and aerial propeller actuation is proposed and analyzed, with the aim of applications in hazardous tasks in the marine field, such as firefighting, ship inspections, and search and rescue missions. For such tasks, existing solutions like drones and water-powered robots inherited fundamental limitations, making their use ineffective. For instance, drones are constrained by limited flight endurance, while water-powered robots struggle with horizontal motion due to the couplings between translational motions. The proposed hydro-aerodynamic hybrid actuation in this study addresses these significant drawbacks by utilizing water thrust for sustainable vertical propulsion and propeller-based actuation for more controllable horizontal motion. The characteristics and mathematical models of the proposed flying robots are presented in detail. A state feedback controller and a proportional–integral–derivative (PID) controller are designed and implemented in order to govern the proposed robot’s motion. In particular, a linear matrix inequality approach is also proposed for the former design so that a robust performance is ensured. Simulation studies are conducted where a purely water-powered flying robot using a nozzle rotation mechanism is deployed for comparison, to evaluate and validate the feasibility of the flying robot. Results demonstrate that the proposed system exhibits superior performance in terms of stability and tracking, even in the presence of external disturbances. Full article

This paper presents some of the most significant findings in the design of a hydraulic servomechanism for flight controls, which were primarily achieved by the first author during his activity in an aviation institute. These results are grouped into four main topics. The first one outlines a classical theory, from the 1950s–1970s, of the analysis of nonlinear automatic systems and namely the issue of absolute stability. The uninformed public may be misled by the adjective “absolute”. This is not a “maximalist” solution of stability but rather highlights in the system of equations a nonlinear function that describes, for the case of hydraulic servomechanisms, the flow-control dependence in the distributor spool. This function is odd, and it is therefore located in quadrants 1 and 3. The decision regarding stability is made within the so-called Lurie problem and is materialized by a matrix inequality, called the Lefschetz condition, which must be satisfied by the parameters of the electrohydraulic servomechanism and also by the components of the control feedback vector. Another approach starts from a classical theorem of V. M. Popov, extended in a stochastic framework by T. Morozan and I. Ursu, which ends with the description of the local and global spool valve flow-control characteristics that ensure stability in the large with respect to bounded perturbations for the mechano-hydraulic servomechanism. We add that a conjecture regarding the more pronounced flexibility of mathematical models in relation to mathematical instruments (theories) was used. Furthermore, the second topic concerns, the importance of the impedance characteristic of the mechano-hydraulic servomechanism in preventing flutter of the flight controls is emphasized. Impedance, also called dynamic stiffness, is defined as the ratio, in a dynamic regime, between the output exerted force (at the actuator rod of the servomechanism) and the displacement induced by this force under the assumption of a blocked input. It is demonstrated in the paper that there are two forms of the impedance function: one that favors the appearance of flutter and another that allows for flutter damping. It is interesting to note that these theoretical considerations were established in the institute’s reports some time before their introduction in the Aviation Regulation AvP.970. However, it was precisely the absence of the impedance criterion in the regulation at the appropriate time that ultimately led, by chance or not, to a disaster: the crash of a prototype due to tailplane flutter. A third topic shows how an important problem in the theory of automatic systems of the 1970s–1980s, namely the robust synthesis of the servomechanism, is formulated, applied and solved in the case of an electrohydraulic servomechanism. In general, the solution of a robust servomechanism problem consists of two distinct components: a servo-compensator, in fact an internal model of the exogenous dynamics, and a stabilizing compensator. These components are adapted in the case of an electrohydraulic servomechanism. In addition to the classical case mentioned above, a synthesis problem of an anti-windup (anti-saturation) compensator is formulated and solved. The fourth topic, and the last one presented in detail, is the synthesis of a fuzzy supervised neurocontrol (FSNC) for the position tracking of an electrohydraulic servomechanism, with experimental validation, in the laboratory, of this control law. The neurocontrol module is designed using a single-layered perceptron architecture. Neurocontrol is in principle optimal, but it is not free from saturation. To this end, in order to counteract saturation, a Mamdani-type fuzzy logic was developed, which takes control when neurocontrol has saturated. It returns to neurocontrol when it returns to normal, respectively, when saturation is eliminated. What distinguishes this FSNC law is its simplicity and efficiency and especially the fact that against quite a few opponents in the field, it still works very well on quite complicated physical systems. Finally, a brief section reviews some recent works by the authors, in which current approaches to hydraulic servomechanisms are presented: the backstepping control synthesis technique, input delay treated with Lyapunov–Krasovskii functionals, and critical stability treated with Lyapunov–Malkin theory. Full article

A partially ordered set (or a poset, for short) is a set endowed with a partial order relation, i.e., with a reflexive, anti-symmetric, and transitive binary relation. As mathematical objects, posets have been intensively studied in the last century, coming to play essential roles in pure mathematics, logic, and theoretical computer science. More recently, they have been increasingly employed in data analysis, multi-criteria decision-making, and social sciences, particularly for building synthetic indicators and extracting rankings from multidimensional systems of ordinal data. Posets naturally represent systems and phenomena where some elements can be compared and ordered, while others cannot be and are then incomparable. This makes them a powerful data structure to describe collections of units assessed against multidimensional variable systems, preserving the nuanced and multi-faceted nature of the underlying domains. Moreover, poset theory collects the proper mathematical tools to treat ordinal data, fully respecting their non-numerical nature, and to extract information out of order relations, providing the proper setting for the statistical analysis of multidimensional ordinal data. Currently, their use is expanding both to solve open methodological issues in ordinal data analysis and to address evaluation problems in socio-economic sciences, from multidimensional poverty, well-being, or quality-of-life assessment to the measurement of financial literacy, from the construction of knowledge spaces in mathematical psychology and education theory to the measurement of multidimensional ordinal inequality/polarization. Full article

Non-unique fixed-point theorems play a pivotal role in the mathematical modeling to solve certain typical equations, which admit more than one solution. In such situations, traditional outcomes fail due to uniqueness of fixed points. The primary aim of the present article is to investigate a non-unique fixed-point theorem in the framework of a metric space endowed with a local class of transitive binary relations. To obtain our main objective, we introduce a new nonlinear contraction-inequality that subsumes the ideas involved in four noted contraction conditions, namely: almost contraction, Boyd–Wong contraction, Pant contraction and relational contraction. We also establish the corresponding uniqueness theorem for the proposed contraction under some additional hypotheses. Several examples are furnished to illustrate the legitimacy of our newly proved results. In particular, we deduce a fixed-point theorem for almost Boyd–Wong contractions in the setting of abstract metric space. Our results generalize, enhance, expand, consolidate and develop a number of known results existing in the literature. The practical relevance of the theoretical findings is demonstrated by applying to study the existence and uniqueness of solution of a specific periodic boundary value problem. Full article

In response to systemic inequities in mathematics education, we developed and evaluated a five-year, multi-phase curriculum model to cultivate effective secondary mathematics teacher leaders. Supported by NSF Noyce Master Teacher Fellowships, the APLUS in MATH (APLUS in Math: Alabama Practitioner Leaders for Underserved Schools in Mathematics) program engaged 22 inservice teachers through graduate coursework, National Board Certification preparation, and leadership project development. Using a mixed-methods design, we analyzed data from classroom observations (MCOP²), National Board Certification assessments, course performance ratings, and teacher leadership project proposals. Results indicate significant improvements in instructional practices, content knowledge, and leadership readiness. Findings underscore the importance for sustained, structured professional development to prepare teachers as instructional experts and change agents in high-need educational contexts. Full article

The Road-STEAMer Horizon Europe Program examines STEAM (Science, Technology, Engineering, Arts, and Mathematics) education policies across Europe, with a specific focus on integrating the arts into traditional STEM disciplines. Through the analysis of open-access repositories, official documents, and stakeholder interviews, this study conducts both a macroanalysis of European policies and a detailed analysis of national initiatives. The research categorizes EU member states into three groups: high-priority countries (Belgium, France, Bulgaria, Finland, and Germany), countries acknowledging the importance of STEAM with partial initiatives, and those in early development stages. Special attention is given to grassroots initiatives. The findings reveal significant variation among member states and affiliated countries, driven by unique national challenges. In many cases, STEM/STEAM programs are closely linked to broader societal issues, such as financial development, digital transition, and social inequalities. Full article

Over the past century, nonlinear analysis has been widely and significantly applied in many areas of mathematics, including nonlinear ordinary and partial differential equations, functional analysis, fixed point theory, nonlinear optimization, variational analysis, convex analysis, dynamical system theory, mathematical economics, signal processing, control theory, data mining, and more [...] Full article

This study explored innovative methods for teaching mathematics to seventh-grade students with persistently low performance by using an AI-driven neural network approach, specifically focusing on solving first-degree inequalities. Guided by the Response to Intervention (RTI) framework, the intervention aimed to reduce math anxiety and build academic resilience through the development of cognitive and metacognitive strategies. A rigorous pre- and post-test design was employed to evaluate changes in performance, anxiety levels, and resilience. Fifty-six students participated in the 12-week program, receiving personalized instruction tailored to their individual needs. The AI tool provided real-time feedback and adaptive problem-solving tasks, ensuring students worked at an appropriate level of challenge. Results indicated a marked decrease in math anxiety alongside significant gains in cognitive skills such as problem-solving and numerical reasoning. Students also demonstrated enhanced metacognitive abilities, including self-monitoring and goal setting. These improvements translated into higher academic performance, particularly in the area of inequalities, and greater resilience, highlighting the effectiveness of AI-based strategies in supporting learners who struggle persistently in mathematics. Overall, the findings underscore how AI-driven teaching approaches can address both the cognitive and emotional dimensions of mathematics learning. By offering targeted, adaptive support, educators can foster a learning environment that reduces stress, promotes engagement, and facilitates long-term academic success for students with persistently low performance in mathematics. Full article

In this paper, we are studying a class of nonlinear fractional difference equations with time-varying delays in Banach space. By means of mathematical induction and the Picard iteration method, we first obtain the existence result of this fractional difference system. Under some new criteria along with the Schauder’s fixed point theorem, we then derive the attractivity conclusions. Subsequently, with the aid of Grönwall’s inequality, we prove that the system is globally attractive. Finally, we give two examples to prove the validity of our theorems. Full article

Harmonic functions are renowned for their application in the analysis of minimal surfaces. These functions are also very important in applied mathematics. Any harmonic function in the open unit disk $\mathbb{U}=\left\{z\in \mathbb{C}:\left|z\right|<1\right\}$ can be written as a sum $f=h+\overline{g}$, where h and g are analytic functions in $\mathbb{U}$ and are called the analytic part and the co-analytic part of f, respectively. In this paper, the harmonic shear $f=h+\overline{g}\in S_{\mathcal{H}}$ and its rotation $f^{\mu }$ by $\mu \left(\mu \in \mathbb{C},\left|\mu \right|=1\right)$ are considered. Bounds are established for this rotation $f^{\mu }$, specific inequalities that define the Jacobian of $f^{\mu }$ are obtained, and the integral representation is determined. Full article

In the author’s previous studies, new infinite numbers, their properties, and calculations were introduced. These infinite numbers quantify infinity and offer new possibilities for solving complicated problems in mathematics and applied sciences in which infinity appears. The current study presents additional properties and topics regarding infinite numbers, as well as a comparison between infinite numbers. In this way, complex problems with inequalities involving series of numbers, in addition to limits of functions of x $\in$ ℝ and improper integrals, can be addressed and solved easily. Furthermore, this study introduces rotational infinite numbers. These are not single numbers but sets of infinite numbers produced as the vectors of ordinary infinite numbers are rotated in the complex plane. Some properties of rotational infinite numbers and their calculations are presented. The rotational infinity unit, its inverse, and its opposite number, as well as the angular velocity of rotational infinite numbers, are defined and illustrated. Based on the above, the Riemann zeta function is equivalently written as the sum of three rotational infinite numbers, and it is further investigated and analyzed from another point of view. Furthermore, this study reveals and proves interesting formulas relating to the Riemann zeta function that can elegantly and simply calculate complicated ratios of infinite series of numbers. Finally, the above theoretical results were verified by a computational numerical simulation, which confirms the correctness of the analytical results. In summary, rotational infinite numbers can be used to easily analyze and solve problems that are difficult or impossible to solve using other methods. Full article