World Academy of Science, Engineering and Technology

Authors: Shai Sarussi, Chai Sarussi, Pavel Satianov

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This paper proposes a structured approach to introducing foundational geometric concepts within the framework of STEM education. The primary objective is to cultivate in students the capacity to articulate precise and coherent definitions, with particular emphasis on concepts derived from Euclidean and analytic geometry. It is well-documented in the mathematics education literature that developing a rigorous understanding of definitions and their logical implications presents a significant challenge for learners.To address this issue, the paper presents multiple representational strategies for describing elementary geometric figures in one- and two-dimensional spaces. These include line segments, rays, half-planes, and strips, which are expressed through both verbal and mathematical formulations. The methodologies employed draw upon the principles of Euclidean and analytic geometry, the application of inequalities, the use of complex numbers, and the analysis of function domains. Each geometric object is ultimately encapsulated in a single, formal equation that synthesizes its defining characteristics.The overarching aim is to engage mathematics educators—and, by extension, their students—in recognizing the intellectual value and pedagogical potential of logical reasoning within the study of analytic geometry. This work consciously departs from an overreliance on procedural techniques, advocating instead for a focus on conceptual depth and theoretical understanding.In light of the increasing automation of routine mathematical procedures, the necessity for technical proficiency in solving standard problems has diminished. Nonetheless, many higher education programs in STEM fields continue to prioritize the development of these procedural skills. In response, this paper calls for a paradigm shift toward instructional practices that emphasize conceptual insight, encourage independent thought, and foster mathematical creativity—competencies that are increasingly recognized as essential in contemporary scientific and technological contexts.

Keywords: verbal definition, analytical description, logical thinking, euclidean geometry

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Authors: Muhammad Ahmed

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The purpose of this research is to understand the dynamical characteristics of the universe and to exhibit the robust behavior of charged-anisotropic fluid in different epochs. For this, we study charged-anisotropic fluid and spherically-asymmetric space-time in f(R) theory, where R represents the Ricci scalar. We will explore new charged-f(R) models on spherically symmetric stars. The behavior of structural factors is evaluated using diagrams, and the feasibility of compact objects is investigated. Precise solutions to the field equations are found for different cosmic models. All the parameters for an anisotropic fluid are investigated using the equation of state constant and the Tolman-Oppenheimer-Volkoff (TOV) equations. Observed stars such as 4U 1820-30, V ela−X-12 and PSR − J1614-2230 are used to verify their existence and stability within the regions. The anisotropy parameter and causality constraints are also taken into account. The implications of the solutions are then inferred geometrically and mathematically from the data.

Keywords: general relativity, cosmology, compact stars, black holes, energy conditions

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Authors: Deborah Arangno

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Albert Einstein eloquently observed that “the most incomprehensible thing about the universe is that it is comprehensible.”This paper will argue that the universe is comprehensible, that the universe was conceived in such a way as to be intelligible to human reason, and that we are capable through our rational capacity to grow in an understanding of truth which redounds to a discovery of the Creator. Indeed, it is the scientist who attests to this transcendental reality beyond the physical world – by relying on the assumption that there is in fact an order in the universe. Logically speaking, if there were no order, science itself would be rendered moot.

Keywords: philosophy of mathematics, naturalized epistemology, mathematical realism, trnasendence

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Authors: Shyan-Shou Chen, Tzu-Hsuan Chan

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This study develops a fractional-order three-compartment model to investigate the within-host dynamics of Human Immunodeficiency Virus (HIV-1), incorporating uninfected cells, infected cells, and free virus particles. By employing the Caputo fractional derivative, the model captures memory effects inherent in viral transmission processes. it analytically derive conditions for the existence and stability of both disease-free and endemic equilibria and identify a threshold governed by the basic reproduction number R0. Furthermore, we explore the influence of the fractional order q on system dynamics and demonstrate, through both theoretical analysis and numerical simulations, the occurrence of a Hopf bifurcation that induces sustained oscillations in viral load. These results highlight how memory-dependent dynamics fundamentally alter stability landscapes and viral persistence patterns within the host.

Keywords: HIV dynamics, hopf bifurcation, stability analysis, fractional differential equations

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Authors: Priyanka, Shelly Arora, Saroj Sahani

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Fractional-order dynamical problems play an important role in the mathematical modelling of real-life phenomena in various sciences and engineering disciplines. In this study, the fractional-order advection-diffusion problems are considered with the Caputo derivative. Discretization of the Caputo derivative is conducted using the familiar L1 scheme. The semi-discretized problem is fully discretized using the orthogonal collocation method with splines as the basis functions. The unconditional stability analysis and the convergence analysis of the proposed scheme are elaborated using appropriate norm inequalities. Numerical illustrations validate the technique. Comparisons with other methods check the efficiency and accuracy of the technique.

Keywords: caputo derivative, L1-scheme, orthogonal collocation, advection-diffusion problems

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Authors: Costa Karavas

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The rise of Generative Artificial Intelligence (GenAI) is reshaping instructional methods and learning experiences across STEM disciplines in higher education. This research explores the evolution of mathematics instruction at the tertiary level, highlighting how GenAI technologies can be strategically integrated to enhance pedagogical practices and assessment methodologies in mathematics.GenAI-powered methodologiessuch as adaptive learning platforms, intelligent tutoring systems, and automated feedback tools, can enhance student engagement, personalize learning pathways, and support formative assessment practices.These capabilities can advance instructional quality, improve student learning, and address longstanding barriers in mathematics pedagogy.While GenAI offers numerous pedagogical benefits, its adoption in higher math education also presents notable limitations and risks, such as algorithmic opacity, overdependence on technology, undermining critical thinking and problem-solving skillsand ethical challenges around data use. A key concern is the increasing ease with which students can engage in academic dishonesty through AI-generated responses.To mitigate these risks, strategies are proposed for integrating GenAI in a manner that upholds academic integrity and promotes deep learning. These include redesigning math assessments to emphasize process and originality, incorporation of process-oriented evaluation,embedding digital ethics into curricula, and fostering faculty development in AI literacy.When strategically and ethicallyimplemented, GenAI has the potential to enrich mathematics education in higher education, enhancing both teaching effectiveness and student learning outcomes. It can serve as a complement to human instruction rather than replacing it.This study establishes a foundational framework that guides the integration of Generative AI into mathematics instruction and assessment and supports continued research into its in its efficacy, pedagogical implications, and role in reshaping mathematics education.

Keywords: artificial intelligence, math education, curriculum development, STEM, educational innovation, higher education, teaching and learning

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Authors: Hanzheliuk Taras

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In recent years, the integration of digital tools into the mathematics classroom has transformed traditional teaching methods and enhanced student engagement. This paper presents a practical case study of using free and accessible digital resources?primarily GeoGebra and Desmos to teach geometry in a rural Ukrainian school. The study highlights how these platforms help visualize complex geometric concepts, support individualized learning, and develop students' spatial thinking skills. The author, a mathematics and computer science teacher, implemented digital tools across multiple grade levels and documented improvements in student motivation, participation, and problem-solving capabilities. The use of interactive applets allowed students to explore geometric relationships dynamically rather than through static images or rote memorization. In addition, digital learning tools enabled greater inclusion of students with diverse learning styles and abilities. This research contributes to the growing body of literature on digital pedagogy in underserved educational contexts. It offers evidence that, even with limited technological infrastructure, meaningful innovation in math instruction is possible. The findings support calls for broader integration of educational technology into rural curricula and provide a model that can be adapted by educators in similar contexts across the globe

Keywords: geometry, digital tools, GeoGebra, rural education, educational technology, mathematics teaching

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Authors: Samuel Hwere Tsok, Rwat Isa Solomon, Niri Martha Choji

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This paper seeks to unveil the primitivity and regularity of Dihedral group of degrees 2p, where p is prime, focusing on cases where these groups are not p-groups. By utilizing numerical approaches, the properties of these groups are examined to shed light on their structure, behavior, and underlying algebraic characteristics. Key numerical methods are employed to calculate invariants and test conditions for primitivity and regularity in these groups

Keywords: dihedral group, primitivity, regularity, numerical approach, GAP

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Authors: Fairuz M. N., Nur Riza Mohd Suradi

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This paper aims to examine the influence of talent management as predictor of organizational commitment in Malaysian public sector. The study used a quantitative approach, with an initial sample of 397 federal government officials from M9 to M15 level. The theoretical framework was based on previous studies of talent management and organizational commitment. The questionnaire consists of multiple-items type, designed to measure factors based on 5-point Likert Scale. For the statistical analysis of the collected data, three-step procedure of exploratory factor analysis (EFA), confirmatory factor analysis (CFA) and Partial least squares-structural equation modelling (PLS-SEM) was used. The results of the study supported the hypothesis that there is a positive significant effect of talent management on organizational commitment. This paper provides theoretical contributions by broadening the knowledge of talent management and organizational commitment in the Malaysian public sector, a relevant but underexplored issue, and offering several avenues for future research. In addition, it contributes to the body of knowledge by filling a gap in the literature on talent management, as it provides valid empirical evidence to justify the relationship between talent management and organizational commitment. The findings have beneficial practical implications for both policy makers and managers which reflect the performance of organization in the context of public sector in Malaysia.

Keywords: confirmatory factor analysis (CFA), exploratory factor analysis (EFA), organizational commitment (OC), talent partial least squares structural equation modelling (PLS-SEM), talent management (TM)

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Authors: Anton Alexa

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We construct a scalar geometric flow based on the function C(v), which encodes conformal deformations of geometry as a scalar evolution. The flow is defined as a gradient descent of an energy functional, ensuring global monotonicity and smooth convergence. Within this model, we prove that the geometry evolves toward the 3-sphere S³ in the conformal class, without requiring surgery or encountering singularities, unlike in classical Ricci flow approaches. This provides a restricted but rigorous resolution of the Poincaré conjecture in the scalar framework. The model is purely geometric and variational, based on a well-defined energy landscape and scalar flow equations. Potential extensions include spectral decomposition and quantum generalizations.

Keywords: scalar flow, conformal geometry, Poincaré conjecture, energy functional, geometric evolution, Ricci flow

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Authors: Tara Kaboodvand

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This article presents a comparative case study of two schools employing distinct instructional approaches to mathematics education, with particular attention to time management and school ICT leadership. The analysis indicates markedly enhanced student outcomes and increased levels of engagement in the school that implemented a concentrated daily schedule with a strong emphasis on mathematics instruction. Key contributing factors to these outcomes include increased opportunities for in-class practice, a reduced dependence on homework, and sustained institutional support. The study suggests that heightened focus on the two independent variables—time management and ICT leadership—may play a critical role in reducing disparities in mathematics achievement. Central to the research is an examination of the schools' scheduling structure, whereby students engage with only two subjects per day—for example, mathematics in the morning and English in the afternoon. These findings align with existing literature emphasizing the benefits of focused instructional time and active learning environments in enhancing mathematics education.

Keywords: schedual, ICT leadership, time magement, and school environments

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Authors: Abu Salek, Jannatun Nayeem, M. Humayun Kabir

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In this article, we develop and analyse a deterministic mathematical model to understand the transmission dynamics of tuberculosis (TB). The model incorporates asymptomatic and symptomatic contamination levels of people and also considers treatments for these classes. We determine R_0, which is known as the number of reproductions that help us to understand whether tuberculosis persists within the human population. Our study shows that the tuberculosis-free equilibrium is locally and globally asymptotically stable, while the basic quantityR_0<1, whereas the model's endemic equilibrium points are also locally and globally asymptotically stable under a Lyapunov function whenever R_0>1. Sensitivity analysis indicates that certain parameters play an important role in eradicating tuberculosis infectious among the population. To obtain analytical outcomes, a 4th-order Runge-Kutta numerical technique is used, and numerical experiments demonstrate that the implementation of monitored treatment can effectively reduce the disease burden within the community.

Keywords: tuberculosis (TB), reproduction number, sensitivity analysis, Lyapunov function, local and global stability

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Authors: Sachin Somra, Deepa Sinha

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A subset C of the vertex set of a graph Gamma is called a perfect code of Gamma if every vertex of Gamma is at a distance of no more than one vertex in C. The biclique partition number of a graph Gamma is the minimum number of complete bipartite subgraphs (bicliques) required to partition the edge set of Gamma. The decision form of the minimum biclique cover problem is classified as NP-Complete. Let G be a finite abelian group and S be any subset of G. The Cayley sum graph Gamma(G, S) is a simple graph with G as its vertex set, and two vertices u and v$are adjacent if u+v in S. In this paper, we give some conditions on a subset S of G for finding the perfect code set and inequality of biclique partition number of Cayley sum graph Gamma(G, S) and Cayley sum signed graph.

Keywords: cayley sum graphs, perfect codes, biclique partition number, signedgraphs

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Authors: Logan Miller, Wisam Bukaita

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The research focuses on the design and construction of an image-based disease classification model based on deep learning techniques. The model aims to classify plants' leaves and stems into one of the five categories: black spots, downy mildew, powdery mildew, healthy, and other diseases. A dataset downloaded from a public sourced datasets and preprocessing techniques involving resizing, color normalization, and augmentation techniques, like rotation and flip, are used to enhance the model's efficiency. The deep model, built from the use of TensorFlow and the Keras API, performs image-based extraction of the images through the use of the convolution layer, enhancing the model's ability to distinguish between different health states in plants. Evaluation results show the model achieves around 40% confidence when identifying one of the three diseases, indicating reasonable performance with room for future improvement. The model's efficiency in terms of classification measurement confirms the model's reliability in disease prediction. The current research identifies the use of deep models in the future in the field of agriculture to offer scalable and automatable means to disease prediction and monitoring in plants.

Keywords: black spots, computer vision, downy mildew, feature extraction, keras, plant disease, powdery mildew

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Authors: Renad Taha Shahbhai, Jehan Alawi Al-Bar, Hanaa Salem Al-Ashwali

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Just as the study of the finite symmetric plays a fundamental role in group theory, the analysis of various finite semigroups of transformations significantly contributes to the development of semigroup theory. For a semigroup S and a subset A of S, the relative rank of S modulo A is defined as the minimal cardinality of a set B⊆S such that A ∪ B generates S. This concept provides a measure of the efficiency or sufficiency of generating sets relative to a given subset, leading to a deeper understanding of the internal structure and generating requirements of semigroups. The symmetric inverse semigroup on a finite set Xₙ consists of all partial one-to-one transformations and is denoted by Iₙ. To study the relative rank of the symmetric inverse semigroup Iₙ modulo some subsets (subsemigroups) of it, we used a proposition that compute the relative rank of Tₙ modulo some subsets of it. Also, we study the J classes to find the relative rank. Finally, we used the GAP program to study the structure and the elements in each subsemigroup of Iₙ. In our study, we have proven that the formula provided in the proposition that compute the relative rank of Tₙ modulo some subsets of it is also valid for computing the relative rank of Iₙ modulo some subsets (subsemigroups). Also, we computed the relative rank of Iₙ modulo OIₙ, the semigroup of order-preserving partial one-to-one transformations on Xₙ; PORIₙ, the semigroup of all orientation preserving or reversing partial one-to-one transformations on Xₙ; CIₙ, the semigroup of all contraction partial one-to-one transformations. Finally, we characterized subsets (subsemigroups) of Iₙ, of relative rank t for each t∈{1,2,3}, since we observed that the relative rank of A (⊆I_n) is at most 3.

Keywords: relative rank, contraction, inverse semigroup, orientation preserving or reversing

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Authors: Hanadi Taysir Allayli, Jehan Alawi Al-Bar

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The study of semigroups of full transformations on finite chains is an important area within algebra, particularly in semigroup theory. A finite chain is a totally ordered finite set, and transformations on these chains are essentially functions from the set to itself. The full transformation semigroup consists of all possible functions on a finite chain, forming a structure under composition of functions.For a semigroup S and a set A ⊆S, the relative rank of S modulo A is the minimal cardinality of a set B such that A ∪ B generates S. Relative rank provides a measure of how efficiently a semigroup can be generated relative to a given subset, offering deeper insight into its internal structure and generating properties. To study the relative rank of the full transformationssemigroup T_nmodulo some subsets (subsemigroups) of it, the used a proposition that compute the relative rank of T_nmodulo some subsets of it. Also, we study the J classes to find the relative rank. Finally, it used the GAP program to study the structure and the elements in each subsemigroup of T_n. it found the relative ranks of O_n, the semigroup of order-preserving full transformations on X_n={1,2,…,n};D_n, the semigroup of order-decreasing full transformations on X_n; O_n∩ D_n=C_n,, the semigroup of order-preserving and order-decreasing full transformations on X_n (also known as the Catalan monoid); 〖OP〗_n, the semigroup of orientation-preserving full transformations on X_n; 〖OR〗_n, the semigroup of orientation-preserving/reversing full transformations onX_n;〖CT〗_n, the semigroup of full contraction transformations on X_n; 〖CT〗_n∩O_n=〖OCT〗_n, the semigroup of order-preserving full contraction mappings on X_n;〖CT〗_n∩〖OR〗_n=〖ORCT〗_n, the semigroup of order-preserving/reversing full contraction mappings on X_n;〖OCT〗_n∩D_n=〖ODCT〗_n,the semigroup of order-preserving and order-decreasing full contraction mappings on X_n. Finaly, it characterized subsets(subsemigroups) of T_n, the full transformation semigroup, of relative rank t for each t ∈{ 1,2,3}, in observed that the relative rank of A (〖⊆T〗_n,) is at most 3. In conclusion, it determined the relative ranks of various subsemigroups of T_n,, showing that many can be generated with small sets, often of size at most 3. The study of semigroups of full transformations on finite chains is an important area within algebra, particularly in semigroup theory. A finite chain is a totally ordered finite set, and transformations on these chains are essentially functions from the set to itself. The full transformation semigroup consists of all possible functions on a finite chain, forming a structure under composition of functions.For a semigroup S and a set A ⊆S, the relative rank of S modulo A is the minimal cardinality of a set B such that A ∪ B generates S. Relative rank provides a measure of how efficiently a semigroup can be generated relative to a given subset, offering deeper insight into its internal structure and generating properties. To study the relative rank of the full transformationssemigroup T_nmodulo some subsets (subsemigroups) of it, the used a proposition that compute the relative rank of T_nmodulo some subsets of it. Also, we study the J classes to find the relative rank. Finally, it used the GAP program to study the structure and the elements in each subsemigroup of T_n. it found the relative ranks of O_n, the semigroup of order-preserving full transformations on X_n={1,2,…,n};D_n, the semigroup of order-decreasing full transformations on X_n; O_n∩ D_n=C_n,, the semigroup of order-preserving and order-decreasing full transformations on X_n (also known as the Catalan monoid); 〖OP〗_n, the semigroup of orientation-preserving full transformations on X_n; 〖OR〗_n, the semigroup of orientation-preserving/reversing full transformations onX_n;〖CT〗_n, the semigroup of full contraction transformations on X_n; 〖CT〗_n∩O_n=〖OCT〗_n, the semigroup of order-preserving full contraction mappings on X_n;〖CT〗_n∩〖OR〗_n=〖ORCT〗_n, the semigroup of order-preserving/reversing full contraction mappings on X_n;〖OCT〗_n∩D_n=〖ODCT〗_n,the semigroup of order-preserving and order-decreasing full contraction mappings on X_n. Finaly, it characterized subsets(subsemigroups) of T_n, the full transformation semigroup, of relative rank t for each t ∈{ 1,2,3}, in observed that the relative rank of A (〖⊆T〗_n,) is at most 3. In conclusion, it determined the relative ranks of various subsemigroups of T_n,, showing that many can be generated with small sets, often of size at most 3.

Keywords: relative rank, semigroup theory, full transformation, contraction

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Authors: Fatima Dib

Abstract:

Partial differential equations and functional differential equations, delay ones in particular, are the most mathematical tools used in the study of infinite dimensional phenomena. Variational methods provide a solid basis for the existence theory of partial differential equations. However, it is not the case in delay differential equations. As it is known, variational methods consist in transforming a differential equation into an integral problem, where the differential operator can be formulated as the first variation derivative of an appropriate functional energy, on a suitable Banach space. This technic identifies an important class of problems which can be solved using relatively simple techniques from nonlinear functional analysis. This paper is devoted to the study of the existence of nonconstant periodic solutions for a class of nonautonomous second-order delay differential equations. Our study consists in the application of a variational approach based on a direct minimization with constraints. Simple sufficient conditions are provided that enable us to obtain nonconstant periodic weak solutions. Some recent results in the literature are extended.

Keywords: direct minimization, periodic solution, second order delay differential equation, variational method

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Authors: Attajer Ali, Mecheri Boubakeur, Bouchnita Anass, Amoo Solomon

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Modular‑Integrated‑Construction (MiC) accelerates building projects by fabricating volumetric modules off‑site and assembling them on‑site. While the schedule and quality advantages of MiC are well documented, the carbon consequences of the long, multi‑modal supply chains that link global factories to local construction sites remain poorly quantified. This study develops a hybrid decision‑support framework that combines multi‑agent simulation (MAS) with deep learning to provide rapid, scenario‑based estimates of CO₂ emissions, costs, and schedule performance for MiC logistics. First, we build a MAS model of the MiC supply chain in AnyLogic, representing suppliers, the prefabrication plant, road-haul fleets, and the destination site as autonomous agents. Each agent incorporates activity data and emission factors specific to the process, enabling each movement - raw material deliveries, module transfers, round trips, module assembly - to be translated into kilograms of CO₂ equivalent in real time. A design of experiments generates more than 23 000 simulation scenarios. The simulation records three key performance indicators (KPIs): cumulative carbon footprint, logistics cost, and project completion time. Second, the resulting data set trains a feed‑forward neural network that captures the non‑linear interactions between fleet decisions and project outcomes. Hyper‑parameters (e.g., layers, neurons, dropout rates) are tuned to maximize predictive accuracy while avoiding over‑fitting. Once trained, the model predicts KPI values for unseen fleet compositions within milliseconds, enabling interactive ‘what‑if’ analyses during project planning or real‑time rescheduling when disruptions occur.

Keywords: modular integrated construction (MiC), carbon footprint, multi-agent simulation, logistics optimisation, neural networks

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Authors: Lung-Hui Chen

Abstract:

In this paper, we explore the inverse spectral problem of Sturm-Liouville operator on a star-like graph. To this fixed star-like graph centered at the origin as its vertex, we attach $m$ edges. On each edge, we impose the Sturm-Liouville operator with certain non-local potential functions with some suitable non-local boundary value conditions. At the vertex, we consider a frozen argument type of condition at zero to model a network that fixed on the end of each edge on the graph. The vibration and flow changes are monitored at that vertex which serves as certain control center. There is an inverse uniqueness subject to the suitable non-local boundary condition. We show that the system is solvable. Additionally, we give a Weyl's type of spectral asymptotics.

Keywords: sturm-Liouville operator, star graph, inverse spectral problem, network theory, non-local regulator, interpolation theory, traffic control

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Authors: Ehit Tesfu Damtie

Abstract:

The purpose of this study was to assess the job satisfaction of administrative employees in the placement of Jobs Evaluation grading (JEG) among Dilla, Wachamo, Wolyita Sodo, and Aribaminch Universities. The primary data was collected for this study from four universities in SNNPR, Ethiopia, with 380 administrative staff, and a stratified random sampling technique was used as the sampling method. Qualitative (frequency distribution table) and quantitative (ordinal logistic regression) analysis were used to predict the outcome variable. Among the five ordinal logistic regression models, adjacent logistic was the best model for the data based on the results of AIC and BIC. Willingness to extra effort, experience, and education, payment fair for work, intention to stay for extra years, and adequate training were significant variables on the satisfaction of administrative staff in the placement of JEG. The other factors that affect the satisfaction of administrative staff in the placement of a new job evaluation grade at a 5% level of significance are organization provides training. The odds of the Disagree (OR=6.17445; CI=0.1886307, 1.799774) that staff who disagree with the training that the organization provides as much training as they need are 6.17 times more likely to be dissatisfied compared to those who strongly disagree. And the odds for strongly agree (OR=3.25258, CI: (.005534, 2.358572) on dissatisfied of staff in the new placement of JEG. The administrative staff who strongly agree with the statement that the organization provides as much training as they need are 3.25 times more likely to be dissatisfied compared to those who strongly disagree. The analysis indicates that administrative staff who disagree and strongly agree with the adequacy of training provided by the organization are significantly more likely to experience higher levels of dissatisfaction in their new placement. We can recommend that organizations should focus on ensuring that staff feel supported through sufficient training opportunities to improve overall job satisfaction and reduce dissatisfaction.

Keywords: job satisfaction, ordinal logistic, SPSS, STATA 18

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Authors: Osawaru E. K., Olaleru J. O.

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We introduce in this paper the generalized α-admissible map defined on a Cone Banach algebra and the generalized α − ψ−contractive map of integral type defined on cone b-metric spaces over Banach algebras. We prove some fixed point theorems of the generalized α − ψ−contractive map of integral type defined on a complete cone b-metric spaces over Banach algebras. Specifically, the Banach- and Kannan-type theorems are formulated with proofs of conditions for the existence of fixed points. The results are shown to be significant generalizations of several known related results in the literature.

Keywords: fixed point, cone b-metric space, Banach algebra, α-admissible maps, α − ψ-$contractive, integral type

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Authors: Hycienth Ortser Orapine, Nyiutya Cephas Ine

Abstract:

Diphtheria is a highly infectious respiratory disease posing a significant threat to global public health. In Nigeria, children and low-immunity adults have been at continual high risk due to consistent, yearly recurring outbreaks of diphtheria over the last decade, with a fatality rate as high as 68.8%. This paper presents a mechanistic mathematical model to evaluate the effectiveness of various interventions implemented by the Nigerian government to manage these outbreaks and control the disease. The model flow diagram and system of seven nonlinear ordinary differential equations are presented. We rigorously investigate the model analytically and numerically. The non-negativity and boundedness of the solution are verified, establishing the model’s mathematical and epidemiological validity. The basic reproduction number,〖 R〗_(0,) A key threshold parameter for disease spread is derived using the next-generation matrix. The local stability of the endemic equilibrium point near the equilibrium point is investigated using bifurcation analysis. Global stability is analyzed using the Castillo-Chavez-Song approach. We establish that the model is locally and globally asymptotically stable if 〖 R〗_0< 1 and unstable whenever〖 R〗_0> 1. A sensitivity study of the model’s parameters is conducted to determine their contribution to〖 R〗_0. Plots of the most sensitive parameters are obtained to study the role of the various interventions deployed to curb transmission. The analysis results show that quarantine intervention alone cannot sufficiently curb the spread of the infection but it can only slow it down. Eventually, cases will surge as health facilities become overburdened. However, when combined with strict enforcement of social distancing measures, it can significantly reduce infections to zero in less than 20 days during diphtheria outbreaks. This underscores the effectiveness of non-pharmaceutical interventions in controlling disease transmission during the outbreak period. Further, numerical experiments confirm that social distancing measures are important in managing diphtheria outbreaks. Increased vaccination coverage will drastically reduce transmission and break the burden of recurrent diphtheria outbreaks in the susceptible population.

Keywords: bifurcation, diphtheria outbreaks, mathematical models, sensitivity index, social distancing measures

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Authors: Hossein Bisheh, Pranish Rai

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Beams are one of the common elements used in engineering applications such as aerospace, marine, civil, and automotive structures. They resist applied transverse loads and bending moments. Beams are usually characterised based on their profile (shape of cross-section), length, equilibrium conditions, manner of support, and material. Loads from the external sources, such as wind and earthquake, may cause the vibration of beam structures, which should be controlled to prevent catastrophic failures of the structures. Hence, determining vibration characteristics of beam structures and knowing their natural frequencies can be helpful to prevent structural failures when the resonance phenomenon occurs. One method to control vibration and prevent failure of beam structures under external excitations is to use elastic foundations. To understand the vibration behaviour of beam structures, a finite element (FE) model of the beam is developed to simulate the beam geometry with assigned material properties, a generated FE mesh, elastic foundations, and applied loading and boundary conditions. Vibration modal analysis of the FE beam model is done to determine natural frequencies, and then harmonic responses are obtained to calculate the vibration displacement and phase angle for different natural frequencies. The effects of boundary conditions, beam material, elastic foundations, and excitation forces on the natural frequencies and harmonic responses are investigated.

Keywords: beams, elastic foundations, finite element analysis, structural dynamics, vibration

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Authors: Mohamed Kouadria, Halim Zeghdoudi

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This paper presents and investigates the properties of truncated variants of the New-XLindley distribution. We focus on the monotonic behavior of the density and hazard functions. It also discusses the quantile function, order statistics, moments, and other statistical features. Additionally, the paper develops maximum likelihood estimators for the unknown parameters of the upper, lower, and double truncated New-XLindley distributions. To demonstrate the practicality of the proposed distribution, we apply it to analyze three different data sets related to medical data.

Keywords: truncated distribution, New-XLindley distribution, moments, maximum likelihood estimation

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Authors: Nacéra Maachou, Mustapha Moulai, Fatima Fali

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This paper introduces an exact method for solving integer indefinite quadratic bilevel problems with multiple upper-level objectives (IIQMOBP). The problem consists of linear constraints, while the objective functions at both levels are formulated as products of two linear functions. The proposed algorithm employs a branch-and-cut approach, transforming the indefinite quadratic objective at the upper level into an equivalent multi-objective integer linear problem. The process begins by solving the continuous upper-level linear problem, after which the obtained integer solution is evaluated for efficiency by solving the lower-level indefinite quadratic problem. Initially, the integer optimal solution is found for a bilevel problem where each level has a single objective linear at the upper level and indefinite quadratic at the lower level. Once this solution is identified, an efficient cut is introduced to refine the search space, leading to the generation of new integer solutions. Each time a non-dominated bilevel solution is obtained, the efficient set is updated. The algorithm terminates once all possible regions of the original domain have been explored. A numerical example and computational experiments are presented to demonstrate the effectiveness of the approach.

Keywords: multi-objective programming, bilevel programming, integer programming, indefinite quadratic programming, linear programming, branch-and-cuts

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Authors: Chai Sarussi, Shai Sarussi, Pavel Satianov

Abstract:

Combinatorial reasoning is crucial in both mathematical theory and real-world problem-solving. However, many students find it challenging to develop strong combinatorial skills, leading to difficulties in tackling such problems effectively. This study examines the pedagogical benefits of employing diverse problem-solving methods, using the attendance problem as a case study. By exploring multiple ways to approach and represent this problem, we aim to boost student engagement and enhance their problem-solving capabilities. This paper advocates for a teaching methodology that introduces combinatorial concepts through varied perspectives to improve comprehension and motivation across different educational levels.

Keywords: combinatorial reasoning, pedagogical strategies, multiple representations, the attendance problem

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Authors: Rasoul Samei

Abstract:

The research focuses on identifying unusual adviser behaviors through unsupervised methods while minimizing false positives. Regulatory compliance and financial risk management are critical challenges in financial advisory services, particularly in monitoring the behavior of Mortgage Conduct of Business (MCOB) advisers. This research addresses the pressing need for ethical compliance in financial advisory services by developing an advanced anomaly detection system tailored for MCOB advisers in the UK. The study initiates with data acquisition and preprocessing, incorporating extensive feature engineering to capture financial metrics, client demographics, and product-specific risk factors. Due to the absence of labeled data, various unsupervised anomaly detection models were evaluated, including Isolation Forest, Histogram-Based Outlier Score (HBOS), and Density-Based Spatial Clustering of Applications with Noise (DBSCAN). HBOS and DBSCAN were deemed unsuitable due to their limitations in handling feature dependencies and high-dimensional data, leading to the selection of Isolation Forest as the optimal solution. This model demonstrated superior performance in detecting both global and contextual anomalies while maintaining interpretability. A key aspect of the study is the integration of SHAP (Shapley Additive Explanations) values, which enhance model explainability by providing transparency into the decision-making process. The system is deployed on Microsoft Azure as a fully automated pipeline, encompassing data ingestion, anomaly scoring, and model retraining. Additionally, a Power BI dashboard was developed to present real-time insights, facilitating compliance monitoring and risk assessment for business stakeholders. Key findings reveal that the Isolation Forest model outperformed others in accurately detecting anomalies, while SHAP integration fostered transparency and trust. Ultimately, this research work contributes to the field of regulatory compliance, consumer protection, and maintaining market integrity within the mortgage advisory sector. The proposed methodology can be extended to other advisory sectors, improving risk detection and regulatory compliance in financial institutions.

Keywords: anomaly detection, financial advisory compliance, machine learning, isolation forest, SHAP, Azure deployment, regulatory risk management

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Authors: Abootaleb Shirvani

Abstract:

Risk measurement is essential in financial markets, particularly for assessing systemic risk and financial contagion. Traditional risk measures like Value at Risk (VaR) and Expected Shortfall (ES) focus on first and second moments, failing to capture asymmetric risk transmission and extreme tail dependencies. Higher-order moment measures such as co-skewness and co-kurtosis address these limitations but lack coherence properties, reducing their reliability. This research compares higher-order moment risk measures with Co-Expected Shortfall (Co-ES) and Co-Value at Risk (Co-VaR), analyzing their mathematical properties, coherence, and effectiveness in systemic risk assessment. While Co-ES satisfies coherence axioms and provides robust tail risk estimation, Co-VaR captures conditional risk spillovers but lacks full coherence. The study integrates higher-order moments with Co-ES to enhance systemic risk modeling. Through theoretical analysis and empirical validation, this paper provides insights into risk transmission mechanisms and proposes an improved framework for financial risk management. The findings offer valuable implications for policymakers and financial institutions in designing effective risk mitigation strategies.

Keywords: systemic risk, coherent risk measures, higher-order moments, tail risk

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Authors: Ramazan Kadiev, Arkadi Ponossov

Abstract:

Stability properties of linear stochastic difference equations with delays are of great importance in many real-world applications, including those in economic, biological, physical modeling, control theory and computational mathematics. The specific methodology considered in the talk combines the theory of inverse-positive matrices with the asymptotic methods developed by N.V. Azbelev and his students for deterministic functional differential equations. The major findings of the study can be summarized as follows: several efficient conditions for p-stability and exponential p-stability of systems of linear Ito-type difference equations with delays are obtained; the stability criteria are conveniently formulated in terms of the coefficients of the equations; carefully chosen illustrative examples show the feasibility of the analysis. The results can be used to study theoretical and computational models based on stochastic difference equations, especially in cases where the method of Lyapunov functionals may be difficult to apply.

Keywords: Brownian motion, delay equations, inverse-positive matrices, stochastic difference equations

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Authors: Najmeddine Attia, Hajer Jebali

Abstract:

Fractal interpolation function (FIF) f that interpolates a given data set ∆ is defined as a fixed point of the Read–Bajraktarevic operator and is constructed via an iterated function system (IFS). In this work, we investigate the smoothness of a class of generalized affine FIF, proving that under specific conditions, it is a Holder function. Moreover, we examine the impact of a perturbation on ∆, denoted by ω(∆), where ω is an affine transformation. We establish a sufficient condition ensuring that ω(G∆) = Gω(∆). where G∆ is the graph of the FIF interpolates ∆. This study is illustrated with examples and some applications highlighting the effectiveness of the given results. We will also provide a construction of some general class of FIF on the Koch Curve.

Keywords: k-Fibonacci sequence, Lagrange interpolation, Banach contraction principle, Markov chain

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